Tag Archives: Classical Physics

Timescales of Chaos in the Inner Solar System: Lyapunov Spectrum and Quasi-integrals of Motion [EPA]

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http://arxiv.org/abs/2305.01683


Numerical integrations of the Solar System reveal a remarkable stability of the orbits of the inner planets over billions of years, in spite of their chaotic variations characterized by a Lyapunov time of only 5 million years and the lack of integrals of motion able to constrain their dynamics. To open a window on such long-term behavior, we compute the entire Lyapunov spectrum of a forced secular model of the inner planets. We uncover a hierarchy of characteristic exponents that spans two orders of magnitude, manifesting a slow-fast dynamics with a broad separation of timescales. A systematic analysis of the Fourier harmonics of the Hamiltonian, based on computer algebra, reveals three symmetries that characterize the strongest resonances responsible for the orbital chaos. These symmetries are broken only by weak resonances, leading to the existence of quasi-integrals of motion that are shown to relate to the smallest Lyapunov exponents. A principal component analysis of the orbital solutions independently confirms that the quasi-integrals are among the slowest degrees of freedom of the dynamics. Strong evidence emerges that they effectively constrain the chaotic diffusion of the orbits, playing a crucial role in the statistical stability over the Solar System lifetime.

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F. Mogavero, N. Hoang and J. Laskar
Thu, 4 May 23
34/60

Comments: 24 pages, 11 figures. Published in Physical Review X

Internal kinematics of {\it GAIA} DR3 wide binaries: anomalous behaviour in the low acceleration regime [GA]

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http://arxiv.org/abs/2304.07322


The {\it Gaia} eDR3 catalogue has recently been used to construct samples of nearby wide binaries to study the internal kinematics of these objects using relative velocities of the two component stars, $\Delta V$, total binary masses, $m_{B}$, and separations, $s$. For $s \gtrsim 0.035$ pc, these binaries probe the low acceleration $a<a_{0}$ regime over which the gravitational anomalies usually attributed to dark matter are observed in the flat rotation curves of spiral galaxies, where $a_{0}\approx 1.2\times 10^{10}$ is the acceleration scale of MOND. Such experiments test the degree of generality of these anomalies, by exploring the same acceleration regime using independent astronomical systems of vastly smaller mass and size. A signal above Newtonian expectations has been observed when $a<a_{0}$, alternatively interpreted as evidence of a modification in the relevant fundamental physics, or as being due to kinematic contaminants affecting the experiment; the presence of undetected stellar components, unbound encounters and spurious projection effects. Here I take advantage of the enhanced DR3 {\it Gaia} catalogue to perform a more rigorous and detailed study of the internal kinematics of wide binaries than what has previously been possible. Having internally determined accurate {\it Gaia} stellar masses and estimates of binary probabilities for each star using spectroscopic information, together with a larger sample of radial velocities, allows for a significant improvement in the analysis of wide binaries and careful exclusion of possible kinematic contaminants. Resulting $\Delta V$ vs. $s$ and $\Delta V$ vs. $m_{B}$ scalings accurately tracing Newtonian expectations for the high acceleration regime, but consistent with the distance and mass velocity scalings observed in spiral galaxies in the low acceleration one, are obtained.

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X. Hernandez
Tue, 18 Apr 23
59/80

Comments: 10 pages, 6 figures, 2 tables

Mutual gravitational energy of homogeneous prolate spheroids. Collinear case [EPA]

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http://arxiv.org/abs/2303.13892


The problem of mutual gravitational energy $W_{mut}$ for a system of two homogeneous prolate spheroids, whose symmetry axes are on the same line, is set and solved. The method of equigravitating elements is applied, where the external potentials of three-dimensional spheroids are represented by the potentials of one-dimensional inhomogeneous focal rods. The solution of the problem is reduced to the integration of the potential of one rod over the segment of the second rod. As a result, the expression $W_{mut}$ for two prolate spheroids can be obtained in a finite analytic form through elementary functions. The force of attraction between the spheroids is found. The function $W_{mut}$ is also represented by a power series in eccentricity of the spheroids. Possible applications of the obtained results are discussed.

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B. Kondratyev, V. Kornoukhov and E. Kireeva
Mon, 27 Mar 23
25/59

Comments: 8 pages, 4 figures

A Simple Derivation of the Gertsenshtein Effect [CL]

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http://arxiv.org/abs/2301.02072


As shown by Gertsenshtein in 1961, an external magnetic field can catalyze the mixing of graviton and photon states in a manner analogous to neutrino-flavor oscillations. We first present a straightforward derivation of the mechanism by a method based on unpublished notes of Freeman Dyson. We next extend his method to include boundary conditions and retrieve the results of Boccaletti et al. from 1970. We point out that, although the coupling between the graviton and photons states is extremely weak, the large magnetic fields around neutron stars $\sim 10^{14}$ G make the Gertsenshtein effect a plausible source of gravitons. Indeed, an “in principle” observable consequence would be the change of optical brightness of a neutron star between directions parallel and perpendicular to the field. We also point out that axion-photon mixing, a subject of active current research, is essentially the same process as the Gertsenshtein effect, and so the general mechanism may be of broad astrophysical and cosmological interest.

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A. Palessandro and T. Rothman
Fri, 6 Jan 23
9/55

Comments: 15 pages, no figures

Milankovitch equations with spinors [CL]

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http://arxiv.org/abs/2212.05929


We investigate the use of spinors to describe the secular evolution of quasi-Keplerian systems. Evaluating their Poisson brackets, we show that the components of a properly-chosen spinor are canonical variables. We illustrate this formalism with a satellite’s motion around an oblate body.

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B. Deme and J. Fouvry
Tue, 13 Dec 22
26/105

Comments: 12 pages, no figures

Dynamics of ultrarelativistic charged particles with strong radiation reaction. I. Aristotelian equilibrium state [CL]

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http://arxiv.org/abs/2209.07469


Previous studies from the astrophysics and laser physics communities have identified an interesting phenomenon wherein ultrarelativistic charged particles experiencing strong radiation reaction tend to move along special directions fixed by the local electromagnetic field. In the relativity literature these are known as the “principal null directions” (PNDs) of the Maxwell field. A particle in this regime has “Aristotelian” dynamics in the sense that its velocity (rather than acceleration) is determined by the local field. We study this Aristotelian equilibrium in detail, starting from the Landau-Lifshitz equation describing charged particle motion including radiation reaction. Using a Frenet-Serret frame adapted to the PNDs, we derive the Lorentz factor describing motion along the local PND, together with drift velocities reflecting slower passage from one PND to another. We derive conditions on the field configuration that are necessary for such an equilibrium to occur. We demonstrate agreement of our analytic formulas with full numerical solutions of the Landau-Lifshitz equation in the appropriate regime.

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Y. Cai, S. Gralla and V. Paschalidis
Fri, 16 Sep 22
62/84

Comments: N/A

Statistical Mechanics of Collisionless Orbits. V. The approach to equilibrium for idealized self-gravitating systems [GA]

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http://arxiv.org/abs/2208.11709


Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exist. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, $n(E) \propto \exp (-\beta(E-\Phi_0))-1$, known as DARKexp. This differential energy distribution, and the resulting density structures, closely approximate those of dark-matter halos with central cusps, $\rho \sim r^{-1}$, and outer parts, $\rho \sim r^{-4}$. Here we define a non-equilibrium functional, $S_D$, which is maximized for DARKexp and increases monotonically during the evolution towards equilibrium of idealized collisionless systems of the Extended Spherical Infall Model. Systems that undergo more mixing more closely approach DARKexp.

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L. Williams and J. Hjorth
Fri, 26 Aug 22
9/49

Comments: 12 pages, 6 figures, 1 appendix, accepted to ApJ

A Comprehensive Perturbative Formalism for Phase-Mixing in Perturbed Disks. I. Phase spirals in an Infinite, Isothermal Slab [GA]

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http://arxiv.org/abs/2208.05038


Galactic disks are highly responsive systems that often undergo external perturbations and subsequent collisionless equilibration, predominantly via phase-mixing. We use linear perturbation theory to study the response of infinite isothermal slab analogues of disks to perturbations with diverse spatio-temporal characteristics. Without self-gravity of the response, the dominant Fourier modes that get excited in a disk are the bending and breathing modes, which, due to vertical phase-mixing, trigger local phase-space spirals that are one- and two-armed, respectively. We demonstrate how the lateral streaming motion of slab stars causes phase spirals to damp out over time. The ratio of the perturbation timescale ($\tau_{\mathrm{P}}$) to the local, vertical oscillation time ($\tau_z$) ultimately decides which of the two modes is excited. Faster, more impulsive ($\tau_{\mathrm{P}} < \tau_z$) and slower, more adiabatic ($\tau_{\mathrm{P}} > \tau_z$) perturbations excite stronger breathing and bending modes, respectively, although the response to very slow perturbations is exponentially suppressed. For encounters with satellite galaxies, this translates to more distant and more perpendicular encounters triggering stronger bending modes. We compute the direct response of the Milky Way disk to several of its satellite galaxies, and find that recent encounters with all of them excite bending modes in the Solar neighborhood. The encounter with Sagittarius triggers a response that is at least $1-2$ orders of magnitude larger than that due to any other satellite, including the Large Magellanic Cloud. We briefly discuss how ignoring the presence of a dark matter halo and the self-gravity of the response might impact our conclusions.

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U. Banik, M. Weinberg and F. Bosch
Thu, 11 Aug 22
49/68

Comments: Accepted for publication in ApJ; 7 figures, 1 table

Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence [CL]

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http://arxiv.org/abs/2205.11516


We report on three-dimensional direct numerical simulation of wave turbulence on the free surface of a magnetic fluid subjected to an external horizontal magnetic field. A transition from capillarywave turbulence to anisotropic magneto-capillary wave turbulence is observed for an increasing field. At high enough field, wave turbulence becomes highly anisotropic, cascading mainly perpendicularly to the field direction, in good agreement with the prediction of a phenomenological model, and with anisotropic Alfv{\’e}n wave turbulence. Although surface waves on a magnetic fluid are different from Alfv{\’e}n waves in plasma, a strong analogy is found with similar wave spectrum scalings and similar magnetic-field dependent dispersionless wave velocities.

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E. Kochurin, G. Ricard, N. Zubarev, et. al.
Wed, 25 May 22
32/56

Comments: in press in Phys. Rev E (Letter). For Supplemental Material, see this http URL

Prograde spin-up during gravitational collapse [EPA]

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http://arxiv.org/abs/2205.09748


Asteroids, planets, stars in some open clusters, as well as molecular clouds appear to possess a preferential spin-orbit alignment, pointing to shared processes that tie their rotation at birth to larger parent structures. We present a new mechanism that describes how collections of particles or ‘clouds’ gain a prograde rotational component when they collapse or contract while subject to an external, central force. The effect is geometric in origin, as relative shear on curved orbits moves their shared center-of-mass slightly inward and toward the external potential during a collapse, exchanging orbital angular momentum into aligned (prograde) rotation. We perform illustrative analytical and N-body calculations to show that this process of prograde spin-up proceeds quadratically in time ($\delta L_\mathrm{rot} \propto t^2$) until the collapse nears completion. The total rotational gain increases with the size of the cloud prior to its collapse: $\delta L_\mathrm{rot}/L_\mathrm{H} \propto (R_\mathrm{cl}/R_\mathrm{H})^5$, and typically with distance to the source of the potential ($L_\mathrm{H}\propto r_0)$. For clouds that form at the interface of shear and self-gravity ($R_\mathrm{cl} \sim R_\mathrm{H}$), prograde spin-up means that even setups with large initial retrograde rotation collapse to form prograde-spinning objects. Being a geometric effect, prograde spin-up persists around any central potential that triggers shear, even those where the shear is strongly retrograde. We highlight an application to the Solar System, where prograde spin-up can explain the frequency of binary objects in the Kuiper belt with prograde rotation.

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R. Visser and M. Brouwers
Fri, 20 May 22
38/65

Comments: Accepted for publication in A&A. Co-first authors. Comments and questions welcome

The specific heat of astro-materials: Review of theoretical concepts, materials and techniques [EPA]

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http://arxiv.org/abs/2205.08212


We provide detailed background, theoretical and practical, on the specific heat cp of minerals and mixtures thereof, ‘astro-materials’, as well as background information on common minerals and other relevant solid substances found on the surfaces of solar system bodies. Furthermore, we demonstrate how to use specific heat and composition data for lunar samples and meteorites as well as a new database of endmember mineral heat capacities (the result of an extensive literature review) to construct reference models for the isobaric specific heat cP as a function of temperature for common solar system materials. Using a (generally linear) mixing model for the specific heat of minerals allows extrapolation of the available data to very low and very high temperatures, such that models cover the temperature range between 10 and 1000 K at least (and pressures from zero up to several kbars). We describe a procedure to estimate cp(T) for virtually any solid solar system material with a known mineral composition, e.g., model specific heat as a function of temperature for a number of typical meteorite classes with known mineralogical compositions. We present, as examples, the cp(T) curves of a number of well-described laboratory regolith analogues, as well as for planetary ices and ‘tholins’ in the outer solar system. Part II will review and present the heat capacity database for minerals and compounds and part III is going to cover applications, standard reference compositions, cp(T) curves and a comparison with new and literature experimental data.

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J. Biele, M. Grott, M. Zolensky, et. al.
Wed, 18 May 22
65/66

Comments: submitted to Special Issue for International Journal of Thermophysics ‘Thermophysics of Advanced Spacecraft Materials and Extraterrestrial Samples’ Part II to be submitted still in 2022

Long-term instability of the inner Solar System: numerical experiments [EPA]

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http://arxiv.org/abs/2205.04170


Apart from being chaotic, the inner planets in the Solar System constitute an open system, as they are forced by the regular long-term motion of the outer ones. No integrals of motion can bound a priori the stochastic wanderings in their high-dimensional phase space. Still, the probability of a dynamical instability is remarkably low over the next 5 billion years, a timescale thousand times longer than the Lyapunov time. The dynamical half-life of Mercury has indeed been estimated recently at 40 billion years. By means of the computer algebra system TRIP, we consider a set of dynamical models resulting from truncation of the forced secular dynamics recently proposed for the inner planets at different degrees in eccentricities and inclinations. Through ensembles of $10^3$ to $10^5$ numerical integrations spanning 5 to 100 Gyr, we find that the Hamiltonian truncated at degree 4 practically does not allow any instability over 5 Gyr. The destabilisation is mainly due to terms of degree 6. This surprising result suggests an analogy to the Fermi-Pasta-Ulam-Tsingou problem, in which tangency to Toda Hamiltonian explains the very long timescale of thermalisation, which Fermi unsuccessfully looked for.

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N. Hoang, F. Mogavero and J. Laskar
Tue, 10 May 22
30/70

Comments: Accepted for publication in MNRAS. 9 pages, 7 figures

The origin of chaos in the Solar System through computer algebra [EPA]

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http://arxiv.org/abs/2205.03298


The discovery of the chaotic motion of the planets in the Solar System dates back more than 30 years. Still, no analytical theory has satisfactorily addressed the origin of chaos so far. Implementing canonical perturbation theory in the computer algebra system TRIP, we systematically retrieve the secular resonances at work along the orbital solution of a forced long-term dynamics of the inner planets. We compare the time statistic of their half-widths to the ensemble distribution of the maximum Lyapunov exponent and establish dynamical sources of chaos in an unbiased way. New resonances are predicted by the theory and checked against direct integrations of the Solar System. The image of an entangled dynamics of the inner planets emerges.

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F. Mogavero and J. Laskar
Mon, 9 May 22
20/63

Comments: 16 pages, 8 figures. Astronomy & Astrophysics Letters

Quasi-spherical hydrodynamic adiabatic accretion in a Keplerian potential [HEAP]

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http://arxiv.org/abs/2204.08448


We present an exact $\gamma=5/3$ spherical accretion model which modifies the Bondi boundary condition of $\rho \to const.$ as $r\to \infty$ to one where $\rho \to 0$ as $r \to \infty$. This change allows for simple power law solutions on the density and infall velocity fields, ranging from a cold empty free-fall condition where pressure tends to zero, to a hot hydrostatic equilibrium limit with no infall velocity. As in the case of the Bondi solution, a maximum accretion rate appears. As in the $\gamma=5/3$ case of the Bondi solution, no sonic radius appears, this time however, because the flow is always characterised by a constant Mach number. This number equals 1 for the case of the maximum accretion rate, diverges towards the cold empty state, and becomes subsonic towards the hydrostatic equilibrium limit. Deviations from sphericity are then explored through an analytic perturbative analysis. The perturbed solution yields a rich phenomenology through density and radial velocity fields in terms of Legendre polynomials, which we begin to explore for simple angular velocity boundary conditions having zeros on the plane and pole. Infall/outflow solutions appear for the sub-sonic parameter region, closely resembling the outputs of recent numerical experiments. The strong density gradients in these cases result in significant pressure gradients which accelerate the polar outflows to many times the local escape velocity, well within the validity range of the perturbative analysis. Our results could complement our understanding of the origin of outflows in a variety of astrophysical settings surrounding infall situations, through purely hydrodynamical physics.

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X. Hernandez and L. Nasser
Tue, 19 Apr 22
14/52

Comments: 7 pages, 4 figures

The cosmological constant vs adiabatic invariance [CL]

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http://arxiv.org/abs/2204.06048


The property of adiabatic invariance is studied for the generalized potential satisfying the condition of identity of sphere’s and point mass’s gravity. That function contains a second term corresponding to the cosmological constant as weak-field General Relativity and enables to describe the dynamics of groups and clusters of galaxies and the Hubble tension as a result of two flows, local and global ones. Using the adiabatic invariance approach we derive the orbital parameters via Weierstrass functions, including the formula for the eccentricity which explicitly reveals the differences from the Kepler problem.

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S. Sh.Khlghatyan, A. A.A.Kocharyan, A. A.Stepanian, et. al.
Mon, 18 Apr 22
6/34

Comments: 6 pages, 2 figures; Eur. Phys. J. Plus (in press)

On the derivations of the Equation of Hydrostatic Equilibrium [SSA]

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http://arxiv.org/abs/2204.03999


We develop and present a geometrical and an analytical derivation of the equation of hydrostatic equilibrium in spherically symmetric stars with a generalized stress tensor. The analytical derivation is based on the Navier-Cauchy equation. We also critically examine the derivation of this equation found in textbooks on stellar astrophysics and show that there are errors in many of the derivations presented in textbooks.

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K. Dev
Mon, 11 Apr 22
14/61

Comments: N/A

Unit Vectors for Similar Oblate Spheroidal Coordinates and Vector Transformation [CL]

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http://arxiv.org/abs/2204.01474


The unit vectors transformation between the Cartesian and the novel Similar Oblate Spheroidal coordinates, and vice versa, is derived. It can help to transform vector fields between these two types of orthogonal coordinates which can advantageously simplify solutions of problems exhibiting oblate spheroidal geometry. Several examples demonstrate the use of the derived relations. Generalized sine and cosine applicable in Similar Oblate Spheroidal coordinate system are introduced.

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P. Strunz
Tue, 5 Apr 22
41/83

Comments: 33 pages, 1 figure

AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations [CL]

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http://arxiv.org/abs/2203.12610


We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schr\”odinger equation.

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Z. Liu, V. Madhavan and M. Tegmark
Thu, 24 Mar 22
21/56

Comments: 17 pages, 10 figures

Nested spheroidal figures of equilibrium I. Approximate solutions for rigid rotations [SSA]

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http://arxiv.org/abs/2202.11044


We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient pressure), approximations can be obtained for configurations involving a small confocal parameter. The problem then admits two families of solutions, depending on the pressure along the common interface (constant or quadratic with the cylindrical radius). We give in both cases the pressure and the rotation rates as a function of the fractional radius, ellipticities and mass-density jump. Various degrees of flattening are allowed but there are severe limitations for global rotation, as already known from classical theory (e.g. impossibility of confocal and coelliptical solutions, gradient of ellipticity outward). States of relative rotation are much less constrained, but these require a mass-density jump. This analytical approach compares successfully with the numerical solutions obtained from the Self-Consistent-Field method. Practical formula are derived in the limit of small ellipticities appropriate for slowly-rotating star/planet interiors.

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J. Huré
Wed, 23 Feb 22
50/50

Comments: Accepted for publication in MNRAS

Representation of the gravitational potential of a level ellipsoid by a simple layer [CL]

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http://arxiv.org/abs/2202.05934


A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting force on its surface can be represented in this way. A family of density functions defined on the whole volume of a level ellipsoid of revolution is found. Several density examples are considered.

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D. Milanov
Tue, 15 Feb 22
49/75

Comments: 12 pages, 4 figures

An algorithm for coalescence of classical objects and formation of planetary systems [EPA]

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http://arxiv.org/abs/2201.02195


Isaac Newton formulated the central difference algorithm (Eur. Phys. J. Plus (2020) 135:267) when he derived his second law. The algorithm is under various names (“Verlet, leap-frog,…”) the most used algorithm in simulations of complex systems in Physics and Chemistry, and it is also applied in Astrophysics. His discrete dynamics has the same qualities as his exact analytic dynamics for contineus space and time with time reversibility, symplecticity and conservation of momentum, angular momentum and energy. Here the algorithm is extended to include the fusion of objects at collisions. The extended algorithm is used to obtain the self-assembly of celestial objects at the emergence of planetary systems. The emergence of twelve planetary systems is obtained. The systems are stable over very long times, even when two “planets” collide or if a planet is engulfed by its sun.

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S. Toxvaerd
Fri, 7 Jan 22
34/34

Comments: 6 figures

The toroidal field surfaces in the standard poloidal-toroidal representation of magnetic field [CL]

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http://arxiv.org/abs/2112.13665


The representation of magnetic field as a sum of a toroidal field and a poloidal field has not rarely been used in astrophysics, particularly in relation to stellar and planetary magnetism. In this representation, each toroidal field line lies entirely in a surface, which is named a toroidal field surface. The poloidal field is represented by the curl of another toroidal field and it threads a stack of toroidal field surfaces. If the toroidal field surfaces are either spheres or planes, the poloidal-toroidal (PT) representation is known to have a special property that the curl of a poloidal field is again a toroidal field . We name a PT representation with this property a standard PT representation while one without the property is called a generalized PT representation. In this paper, we have addressed the question whether there are other toroidal field surfaces allowing a standard PT representation than spheres and planes. We have proved that in a three dimensional Euclidean space, there can be no standard toroidal field surfaces other than spheres and planes, which render the curl of a poloidal field to be a toroidal field.

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S. Yi and G. Choe
Tue, 28 Dec 21
12/55

Comments: N/A

The toroidal field surfaces in the standard poloidal-toroidal representation of magnetic field [CL]

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http://arxiv.org/abs/2112.13665


The representation of magnetic field as a sum of a toroidal field and a poloidal field has not rarely been used in astrophysics, particularly in relation to stellar and planetary magnetism. In this representation, each toroidal field line lies entirely in a surface, which is named a toroidal field surface. The poloidal field is represented by the curl of another toroidal field and it threads a stack of toroidal field surfaces. If the toroidal field surfaces are either spheres or planes, the poloidal-toroidal (PT) representation is known to have a special property that the curl of a poloidal field is again a toroidal field . We name a PT representation with this property a standard PT representation while one without the property is called a generalized PT representation. In this paper, we have addressed the question whether there are other toroidal field surfaces allowing a standard PT representation than spheres and planes. We have proved that in a three dimensional Euclidean space, there can be no standard toroidal field surfaces other than spheres and planes, which render the curl of a poloidal field to be a toroidal field.

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S. Yi and G. Choe
Tue, 28 Dec 21
47/55

Comments: N/A

Celestial Mechanics Solutions where the Future is a Perfect Reflection of the Past [CL]

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http://arxiv.org/abs/2112.11922


Newton’s equations of celestial mechanics are shown to possess a continuum of solutions in which the future trajectories of the N bodies are a perfect reflection of their past. These solutions evolve from zero initial velocities of the N bodies. Consequently, the future gravitational forces acting on the N bodies are also a perfect reflection of their past. The proof is carried out via Taylor series expansions. A perturbed system of equations of the N body problem is also considered. All real valued solutions of this perturbed system have no singularities on the real line. The perturbed system is shown to have a continuum of solutions that possess symmetry where the future velocities of the N bodies are a perfect reflection of their past. The positions and accelerations of the N bodies are then odd functions of the time. All N bodies then evolve from one location in space.

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A. Abdulhussein and H. Gingold
Thu, 23 Dec 21
13/63

Comments: N/A

Dynamical Friction, Buoyancy and Core-Stalling — I. A Non-perturbative Orbit-based Analysis [GA]

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http://arxiv.org/abs/2112.06944


We examine the origin of dynamical friction using a non-perturbative, orbit-based approach. Unlike the standard perturbative approach, in which dynamical friction arises from the LBK torque due to pure resonances, this alternative, complementary view nicely illustrates how a massive perturber significantly changes the energies and angular momenta of field particles on near-resonant orbits, with friction arising from an imbalance between particles that gain energy and those that lose energy. We treat dynamical friction in a spherical host system as a restricted three-body problem. This treatment is applicable in the `slow’ regime, in which the perturber sinks slowly and the standard perturbative framework fails due to the onset of non-linearities. Hence it is especially suited to investigate the origin of core-stalling: the cessation of dynamical friction in central constant-density cores. We identify three different families of near-co-rotation-resonant orbits that dominate the contribution to dynamical friction. Their relative contribution is governed by the Lagrange points (fixed points in the co-rotating frame). In particular, one of the three families, which we call Pac-Man orbits because of their appearance in the co-rotating frame, is unique to cored density distributions. When the perturber reaches a central core, a bifurcation of the Lagrange points drastically changes the orbital make-up, with Pac-Man orbits becoming dominant. In addition, due to relatively small gradients in the distribution function inside a core, the net torque from these Pac-Man orbits becomes positive (enhancing), thereby effectuating a dynamical buoyancy. We argue that core stalling occurs where this buoyancy is balanced by friction.

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U. Banik and F. Bosch
Wed, 15 Dec 21
81/85

Comments: Accepted for publication in ApJ; 12 figures, 1 table

Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks [EPA]

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http://arxiv.org/abs/2112.01129


Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural networks can assist us in exploring the fundamental laws of classical mechanics from data of planetary motion. Firstly, we predict the orbits of planets in the geocentric system using the gate recurrent unit, one of the common neural networks. We find that the precision of the prediction is obviously improved when the information of the Sun is included in the training set. This result implies that the Sun is particularly important in the geocentric system without any prior knowledge, which inspires us to gain Copernicus’ heliocentric theory. Secondly, we turn to the heliocentric system and make successfully mutual predictions between the position and velocity of planets. We hold that the successful prediction is due to the existence of enough conserved quantities (such as conservations of mechanical energy and angular momentum) in the system. Our research provides a new way to explore the existence of conserved quantities in mechanics system based on neural networks.

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J. Zhang, Y. Liu and Z. Tu
Fri, 3 Dec 21
27/81

Comments: 6 pages, 5 figures

Invariants in Polarimetric Interferometry: a non-Abelian Gauge Theory [CL]

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http://arxiv.org/abs/2108.11400


The discovery of magnetic fields close to the M87 black hole using Very Long Baseline Interferometry by the Event Horizon Telescope collaboration utilized the novel concept of “closure traces”, that are immune to antenna-based corruptions. We take a fundamentally new approach to this promising tool of polarimetric interferometry. The corruption of measurements of polarized signals at the individual antennas are represented by general $2\times 2$ complex matrices, which are identified with gauge transformations belonging to the group $\textrm{GL}(2,\mathbb{C})$, so the closure traces now appear as gauge-invariant quantities. We apply this formalism to polarimetric interferometry and generalize it to any number of interferometer elements. Our approach goes beyond existing studies in the following respects: (1) we do not need auto-correlations, which are susceptible to large systematic biases, and therefore unreliable (2) we use triangular combinations of correlations as basic building blocks (analogous to the “elementary plaquettes” of lattice gauge theory), and (3) we use the Lorentz group and its properties to transparently identify a complete and independent set of invariants. This set contains all the information immune to corruption available in the interferometer measurements, thus providing robust constraints which would be important in future interferometric studies.

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J. Samuel, R. Nityananda and N. Thyagarajan
Fri, 27 Aug 21
35/67

Comments: 9 pages (including references), 0 figures, submitted to Physical Review Letters. Contains appendices not included in the journal version

Invariants in Co-polar Interferometry: an Abelian Gauge Theory [IMA]

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http://arxiv.org/abs/2108.11399


An $N$-element interferometer measures correlations between pairs of array elements. Closure invariants associated with closed loops among array elements are immune to multiplicative, local, element-based corruptions that occur in these measurements. Till now, it has been unclear how a complete set of independent invariants can be analytically determined. We view the local, element-based corruptions in co-polar correlations as gauge tranformations belonging to the gauge group $\textrm{GL}(1,\mathbb{C})$. Closure quantities are then naturally gauge invariant. Using an Abelian $\textrm{GL}(1,\mathbb{C})$ gauge theory, we provide a simple and effective formalism to isolate the complete set of independent closure invariants from co-polar interferometric correlations only using quantities defined on the $(N-1)(N-2)/2$ elementary and independent triangular loops. The $(N-1)(N-2)/2$ closure phases and $N(N-3)/2$ closure amplitudes (totaling $N^2-3N+1$ real invariants), familiar in astronomical interferometry, naturally emerge from this formalism, which unifies what has required separate treatments until now. Our formalism does not require auto-correlations, but can easily include them if reliably measured, including potentially from cross-correlation between two short-spaced elements. The gauge theory framework presented here extends to $\textrm{GL}(2,\mathbb{C}$) for full polarimetric interferometry presented in a companion paper, which generalizes and clarifies earlier work. Our findings can be relevant to cutting-edge co-polar and full polarimetric very long baseline interferometry measurements to determine features very near the event horizons of blackholes at the centers of M87, Centaurus~A, and the Milky Way.

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N. Thyagarajan, R. Nityananda and J. Samuel
Fri, 27 Aug 21
66/67

Comments: 10 pages (including references), 0 figures, submitted to Physical Review D

Approximating Orbits in a Rotating Gravity Field with Oblateness and Ellipticity Perturbations [EPA]

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http://arxiv.org/abs/2108.09607


This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for the orbit radius and other elements. The conservation of the Jacobi integral is used to make the problem solvable to first-order in the perturbations. The solutions are characterized as small deviations from an unperturbed circular orbit. The approximations are developed for near-circular orbits with initial mean motion $n_{0}$ around a body with rotation rate $c$. The approximations are shown to be valid for values of angular rate ratio $\Gamma = c/n_{0} > 1$, with accuracy decreasing as $\Gamma \rightarrow 1$, and singularities at and near $\Gamma = 1$. Extensions of the methodology to eccentric orbits are discussed, with commentary on the challenges of obtaining generally valid solutions for both near-circular and eccentric orbits.

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E. Burnett and H. Schaub
Tue, 24 Aug 21
24/76

Comments: N/A

Natural dynamical reduction of the three-body problem [EPA]

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http://arxiv.org/abs/2107.12372


The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation of a mechanical problem to fewer degrees of freedom, a process known as dynamical reduction. However, extant reductions are either non-general, or hide the problem’s symmetry or include unexplained definitions. This paper presents a dynamical reduction that avoids these issues, and hence is general and natural. Any three-body configuration defines a triangle, and its orientation in space. Accordingly, we decompose the dynamical variables into the geometry (shape + size) and orientation of the triangle. The geometry variables are shown to describe the motion of an abstract point in a curved 3d space, subject to a potential-derived force and a magnetic-like force with a monopole charge. The orientation variables are shown to obey a dynamics analogous to the Euler equations for a rotating rigid body, only here the moments of inertia depend on the geometry variables, rather than being constant. The reduction rests on a novel symmetric solution to the center of mass constraint inspired by Lagrange’s solution to the cubic. The formulation of the orientation variables is novel and rests on a little known generalization of the Euler-Lagrange equations to non-coordinate velocities. Applications to special exact solutions and to the statistical solution are described or discussed. Moreover, a generalization to the four-body problem is presented.

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B. Kol
Wed, 28 Jul 21
60/68

Comments: 27 pages, 2 figures

Deriving Kepler's Laws Using Quaternions [EPA]

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http://arxiv.org/abs/2107.02678


In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily describe rotations in three dimensional space. In this article, we will harness this system to provide a new and intuitive way to derive Kepler’s laws. This will include using a quaternionic version of the spatial Kepler problem differential equation, and using the general solution to describe the motion of planets orbiting a central body. We use the standard method for regularizing celestial mechanics, but this article will be solely focused on showing the validity of Kepler’s laws.

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C. Abel
Wed, 7 Jul 21
49/58

Comments: 4 pages, 1 figure

Optimization of Magnetic Flux Ropes Modeled with the RBSL method [SSA]

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http://arxiv.org/abs/2106.02789


The so-called regularized Biot-Savart laws (RBSLs) provide an efficient and flexible method for modeling pre-eruptive magnetic configurations of coronal mass ejections (CMEs) whose characteristics are constrained by observational images and magnetic-field data. This method allows one to calculate the field of magnetic flux ropes (MFRs) with small circular cross-sections and an arbitrary axis shape. The field of the whole configuration is constructed as a superposition of (1) such a flux-rope field and (2) an ambient potential field derived, for example, from an observed magnetogram. The RBSL kernels are determined from the requirement that the MFR field for a straight cylinder must be exactly force-free. For a curved MFR, however, the magnetic forces are generally unbalanced over the whole path of the MFR. To minimize these forces, we apply a modified Gauss-Newton method to find optimal MFR parameters. This is done by iteratively adjusting the MFR axis path and axial current. We then try to relax the resulting optimized configuration in a subsequent line-tied zero-beta magnetohydrodynamic simulation toward a force-free equilibrium. By considering two models of the sigmoidal pre-eruption configuration for the 2009 February 13 CME, we demonstrate how this approach works and what it is capable of. We show, in particular, that the building blocks of the core magnetic structure described by these models match to morphological features typically observed in such type of configurations. Our method will be useful for both the modeling of particular eruptive events and theoretical studies of idealized pre-eruptive MFR configurations.

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V. Titov, C. Downs, T. Török, et. al.
Tue, 8 Jun 21
86/86

Comments: 21 pages, 11 figures, accepted to ApJS

Analytic inversion of closed form solutions of the satellite's $J_2$ problem [EPA]

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http://arxiv.org/abs/2105.11960


This report provides some closed form solutions — and their inversion — to a satellite’s bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the $J_{2}$ spherical zonal harmonic. The equatorial track of satellite motion — assuming the co-latitude $\varphi$ fixed at $\pi/2$ — is investigated: the relevant time laws and trajectories are evaluated as combinations of elliptic integrals of first, second, third kind and Jacobi elliptic functions. The new feature of this report is: from the inverse $t = t(c)$ to get the period $T$ of some functions $c(t)$ of mechanical interest and then to construct the relevant $c(t)$ expansion in Fourier series, in such a way performing the inversion. Such approach — which led to new formulations for time laws of a $J_{2}$ problem — is benchmarked by applying it to the basic case of keplerian motion, finding again the classic results through our different analytic path.
Keywords: $J_2$ problem, bounded satellite motion, Fourier series, elliptic integrals, Jacobi elliptic functions.

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A. Bocci and G. Scarpello
Wed, 26 May 21
41/66

Comments: N/A

Bivariate Infinite Series Solution of Kepler's Equations [IMA]

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http://arxiv.org/abs/2101.00925


A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on the exact analytical computation of the partial derivatives of the eccentric anomaly with respect to the eccentricity $e$ and mean anomaly $M$ in a given base point $(e_c,M_c)$ of the $(e,M)$ plane. Explicit examples of such bivariate infinite series are provided, corresponding to different choices of $(e_c,M_c)$, and their convergence is studied. In particular, the polynomials that are obtained by truncating the infinite series up to the fifth degree reach high levels of accuracy in significantly large regions of the parameter space $(e,M)$.

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D. Tommasini
Tue, 5 Jan 21
42/82

Comments: N/A

Application of Regge-theory to astronomical objects [CL]

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http://arxiv.org/abs/2012.14276


Using the model based on the Regge-like laws, new analytical formulas are obtained for the moment of inertia and the radius of astronomical non-exotic objects (planets, stars, galaxies, and clusters of galaxies). For main sequence stars, the estimate of the moment of inertia is compared with the corresponding rigid-body moment of inertia. The Darwin instability effect in the binary systems (di-planets, di-stars, and di-galaxies) is also analyzed. The rotation frequency and moment of inertia of neutron star and the observable Universe are estimated.

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G. Adamian, N. Antonenko, H. Lenske, et. al.
Tue, 29 Dec 20
12/66

Comments: 11 pages

Application of Regge-theory to astronomical objects [CL]

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http://arxiv.org/abs/2012.14276


Using the model based on the Regge-like laws, new analytical formulas are obtained for the moment of inertia and the radius of astronomical non-exotic objects (planets, stars, galaxies, and clusters of galaxies). For main sequence stars, the estimate of the moment of inertia is compared with the corresponding rigid-body moment of inertia. The Darwin instability effect in the binary systems (di-planets, di-stars, and di-galaxies) is also analyzed. The rotation frequency and moment of inertia of neutron star and the observable Universe are estimated.

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G. Adamian, N. Antonenko, H. Lenske, et. al.
Tue, 29 Dec 20
41/66

Comments: 11 pages

Application of Regge-theory to astronomical objects [CL]

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http://arxiv.org/abs/2012.14276


Using the model based on the Regge-like laws, new analytical formulas are obtained for the moment of inertia and the radius of astronomical non-exotic objects (planets, stars, galaxies, and clusters of galaxies). For main sequence stars, the estimate of the moment of inertia is compared with the corresponding rigid-body moment of inertia. The Darwin instability effect in the binary systems (di-planets, di-stars, and di-galaxies) is also analyzed. The rotation frequency and moment of inertia of neutron star and the observable Universe are estimated.

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G. Adamian, N. Antonenko, H. Lenske, et. al.
Tue, 29 Dec 20
63/66

Comments: 11 pages

Invariants in Interferometry: Geometric Insight into Closure Phases [IMA]

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http://arxiv.org/abs/2012.05254


Closure phase is the phase of a closed-loop product of spatial coherences formed by a $\ge 3$-element interferometer array. Its invariance to element-based phase corruption acquired during propagation and measurement processes, and phase calibration and errors therein, makes it invaluable for interferometric applications that otherwise require high-accuracy phase calibration. However, its understanding has remained mainly mathematical and limited to the aperture plane (Fourier dual of image plane). Here, we lay the foundations for a geometrical insight. We develop and demonstrate a shape-orientation-size (SOS) conservation theorem for images made from a closed triad of elements, in which the relative location of the Null Phase Curves (NPCs) of the three interferometer responses (“fringes”) are preserved, even in the presence of large element-based phase errors, besides overall translation of the fringe pattern. We present two geometric methods to measure the closure phase directly in the image plane (without an aperture-plane view) with a 3-element array and its interference pattern: (i) the closure phase is directly measurable from the positional offset of the NPC of one fringe from the intersection of the other two fringe NPCs, and (ii) the squared closure phase is proportional to the product of the areas enclosed by the triad of array elements and the three fringe NPCs in the aperture and image planes, respectively. We validate this geometric understanding using data observed with the Jansky Very large Array radio telescope. This geometric insight can be potentially valuable to other interferometric applications including optical interferometry. Close parallels exist between interferometric closure phases, structure invariants in crystallography, and phases of Bargmann invariants in quantum mechanics. We generalize these geometric relationships to an N-element interferometer.

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N. Thyagarajan and C. Carilli
Fri, 11 Dec 20
12/75

Comments: 22 pages, 10 captioned figures (12 including sufigures), submitted to Physical Review X. Abstract may be slightly abridged compared to the actual manuscript due to length limitations on arXiv. Comments are welcome!

Tidal locking and the gravitational fold catastrophe [EPA]

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http://arxiv.org/abs/2011.10833


The purpose of this work is to study the phenomenon of tidal locking in a pedagogical framework by analyzing the effective gravitational potential of a two-body system with two spinning objects. It is shown that the effective potential of such a system is an example of a fold catastrophe. In fact, the existence of a local minimum and saddle point, corresponding to tidally-locked circular orbits, is regulated by a single dimensionless control parameter which depends on the properties of the two bodies and on the total angular momentum of the system. The method described in this work results in compact expressions for the radius of the circular orbit and the tidally-locked spin/orbital frequency. The limiting case in which one of the two orbiting objects is point-like is studied in detail. An analysis of the effective potential, which in this limit depends on only two parameters, allows one to clearly visualize the properties of the system. The notorious case of the Mars’ moon Phobos is presented as an example of a satellite that is past the no return point and, therefore, will not reach a stable or unstable tidally-locked orbit.

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A. Ferroglia and M. Fiolhais
Tue, 24 Nov 2020
63/83

Comments: 13 pages, 5 figures

The Sun Diver: Combining solar sails with the Oberth effect [CL]

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http://arxiv.org/abs/2009.12659


A highly reflective sail provides a way to propel a spacecraft out of the solar system using solar radiation pressure. The closer the spacecraft is to the Sun when it starts its outward journey, the larger the radiation pressure and so the larger the final velocity. For a spacecraft starting on the Earth’s orbit, closer proximity can be achieved via a retrograde impulse from a rocket engine. The sail is then deployed at the closest approach to the Sun. Employing the so-called Oberth effect, a second, prograde, impulse at closest approach will raise the final velocity further. Here I investigate how a fixed total impulse ({\Delta}v) can best be distributed in this procedure to maximize the sail’s velocity at infinity. Once {\Delta}v exceeds a threshold that depends on the lightness number of the sail (a measure of its sun-induced acceleration), the best strategy is to use all of the {\Delta}v in the retrograde impulse to dive as close as possible to the Sun. Below the threshold the best strategy is to use all of the {\Delta}v in the prograde impulse and thus not to dive at all. Although larger velocities can be achieved with multi-stage impulsive transfers, this study shows some interesting and perhaps counter-intuitive consequences of combining impulses with solar sails.

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C. Bailer-Jones
Tue, 29 Sep 20
97/98

Comments: 10 pages, accepted to the American Journal of Physics

On the effect of the central body small deformations on its satellite trajectory in the problem of the two-body gravitational interaction [EPA]

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http://arxiv.org/abs/2008.02802


The problem of the two-body gravitational interaction has been solved numerically based on the classical mechanics principles. One of the bodies is a deformable three-axis ellipsoid (central body) and the other is a material point (satellite). The relationship of the angular discrepancy between the calculated and actual positions of the satellite pericenter with central body’s gravity anomaly has been established.

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D. Kiryan and G. Kiryan
Mon, 10 Aug 20
-804/53

Comments: 13 pages, 6 figures, 1 table

Special Relativity — Applications to astronomy and the accelerator physics [CL]

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http://arxiv.org/abs/2007.07780


There are many books on the classical subject of special relativity. However, after having spent a number of years, both in relativistic engineering and research with relativity, I have come to the conclusion that there exist a place for a new book. I do believe that the present book is not quite the same as the others, mainly due to attempt to cast light on dark corners. I should make it clear what this little book is not. It is not a textbook on relativity theory. What the book is about is the nature of special relativistic kinematics, its relation to space and time, and the operational interpretation of coordinate transformations. Every theory contains a number of quantities that can be measured by experiment and an expressions that cannot possibly be observed. Whenever we have a theory containing an arbitrary convention, we should examine what parts of the theory depend on the choice of that convention and what parts do not. The distinction is not always made and many authors claim some data to be observable, according to arbitrary conventions, which do not correspond to any physical experiment. This leads to inconsistencies and paradoxes that should be avoided at all cost.

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E. Saldin
Thu, 16 Jul 20
-213/56

Comments: Working draft from July 2020 (still a work-in-progress), 217 pages, 44 figures. arXiv admin note: substantial text overlap with arXiv:1808.07808, arXiv:1903.07452, arXiv:1709.09408, arXiv:1909.03833

On the electrostatic potential and electric field of a uniformly charged disk [CL]

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http://arxiv.org/abs/2004.04540


We calculate the electrostatic potential and electric field of a uniformly charged disk everywhere in space. This electrostatic problem was solved long ago, and its gravitational analogue – even earlier. However, it seems that physics students are not aware of the solution, because it is not presented in textbooks. The purpose of the present article is to fill this gap in the pedagogical literature.

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V. Bochko and Z. Silagadze
Fri, 10 Apr 20
44/56

Comments: 14 pages, 6 figures, to be published in European Journal of Physics

The Geometry of Isochrone Orbits: from Archimedes' parabolae to Kepler's third law [CL]

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http://arxiv.org/abs/2003.13456


In classical mechanics, the Kepler potential and the Harmonic potential share the following remarkable property: in either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum. For this reason, the Kepler and Harmonic potentials are called \it{isochrone}. In this paper, we solve the following general problem: are there any other isochrone potentials, and if so, what kind of orbits do they contain? To answer these questions, we adopt a geometrical point of view initiated by Michel H\’enon in 1959, in order to explore and classify exhaustively the set of isochrone potentials and isochrone orbits. In particular, we provide a geometric generalization of Kepler’s third law, and give a similar law for the apsidal angle, for any isochrone orbit. We also relate the set of isochrone orbits to the set of parabolae in the plane under linear transformations, and use this to derive an analytical parameterization of any isochrone orbit. Along the way we compare our results to known ones, pinpoint some interesting details of this mathematical physics problem, and argue that our geometrical methods can be exported to more generic orbits in potential theory.

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P. Ramond and J. Perez
Tue, 31 Mar 20
57/94

Comments: 54 pages, 18 figures

Emergence of modified Newtonian gravity from thermodynamics [CL]

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http://arxiv.org/abs/1912.00252


Being inspired by Verlinde’s proposal that general relativistic gravity has a thermodynamic origin as an entropic force, Newtonian gravity is reexamined in view of nonequilibrium thermodynamics. Here, firstly, an unspecified scalar field potential is introduced and treated as a thermodynamic variable on an equal footing with the fluid variables. Then, the effects of irreversibility on the field are explored through the analysis of the entropy production rate in the linear regime. Remarkably, the second law of thermodynamics imposes a stringent constraint on the allowable field, which turns out to be of gravity. The resulting field equation for the gravitational potential contains a dissipative term originating from irreversibility. It is found that the system relaxes to the conventional theory of Newtonian gravity up to a certain spatial scale (typically the solar scale), whereas on the larger scale (such as the galaxy scale) a potential needed in Modified Newtonian Dynamics (MOND) naturally appears. A comment is made on an implication of the result to the astrophysical phenomenon regarding dark matter.

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P. Ván and S. Abe
Tue, 3 Dec 19
25/90

Comments: 18 pages, 1 figure

Stellar speckle and correlation functions derived from classical wave expansions for spherical antennas [IMA]

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http://arxiv.org/abs/1910.08113


Michelson phase and Hanbury Brown-Twiss intensity stellar interferometry require expressions for the speckle patterns and the first and second order correlation functions, respectively, of the fields radiated by stars in terms of their diameters and measured quasi-monochromatic wavelengths. Although our sun and most other stars are spherical in shape at optical wavelengths, all previous determinations of speckle and correlation functions have modeled stars as circular discs rather than spheres because of the mathematical tools available for incoherent fields on planar surfaces, and the absence of closed-form expressions for the prerequisite Green’s function on a spherical surface. However, with the incentive that most stars are indeed shaped like spheres and not discs, the present paper avoids the direct use of surface Green’s functions by modeling a star as a spherical antenna composed of a random distribution of uncorrelated volume sources within a thin surface layer (photosphere and chromosphere). Without using van Cittert-Zernicke, central limit, or moment theorems, a self-contained, straightforward, detailed derivation of speckle patterns and correlation functions is given based on angularly symmetric spherical mode expansions with coefficients determined by the assumed Lambertian nature of the star’s radiation and the uniform asymptotic behavior of the spherical Hankel functions.

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A. Yaghjian
Mon, 21 Oct 19
44/54

Comments: 14 pages, 1 figure

Resonant Laplace-Lagrange theory for extrasolar systems in mean-motion resonance [EPA]

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http://arxiv.org/abs/1909.09462


Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the Laplace-Lagrange secular approximation for coplanar systems with two planets by including (near-)resonant harmonics, and realize an expansion at high order in the eccentricities of the resonant Hamiltonian both at orders one and two in the masses. We show that the expansion at first order in the masses gives a qualitative good approximation of the dynamics of resonant extrasolar systems with moderate eccentricities, while the second order is needed to reproduce more accurately their orbital evolutions. The resonant approach is also required to correct the secular frequencies of the motion given by the Laplace-Lagrange secular theory in the vicinity of a mean-motion resonance. The dynamical evolutions of four (near-)resonant extrasolar systems are discussed, namely GJ 876 (2:1 resonance), HD 60532 (3:1), HD 108874 and GJ 3293 (close to 4:1).

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M. Sansottera and A. Libert
Mon, 23 Sep 19
38/46

Comments: 21 pages, 7 figures

A Statistical Solution to the Chaotic, Non-Hierarchical Three-Body Problem [GA]

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http://arxiv.org/abs/1909.05272


The three-body problem is arguably the oldest open question in astrophysics, and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but only where hierarchies of masses or separations exist. Numerical integrations show that bound, non-hierarchical triples of Newtonian point particles will almost always disintegrate into a single escaping star and a stable, bound binary, but the chaotic nature of the three-body problem prevents the derivation of tractable analytic formulae deterministically mapping initial conditions to final outcomes. However, chaos also motivates the assumption of ergodicity, suggesting that the distribution of outcomes is uniform across the accessible phase volume. Here, we use the ergodic hypothesis to derive a complete statistical solution to the non-hierarchical three-body problem, one which provides closed-form distributions of outcomes (e.g. binary orbital elements) given the conserved integrals of motion. We compare our outcome distributions to large ensembles of numerical three-body integrations, and find good agreement, so long as we restrict ourselves to “resonant” encounters (the ~50% of scatterings that undergo chaotic evolution). In analyzing our scattering experiments, we identify “scrambles” (periods in time where no pairwise binaries exist) as the key dynamical state that ergodicizes a non-hierarchical triple. The generally super-thermal distributions of survivor binary eccentricity that we predict have notable applications to many astrophysical scenarios. For example, non-hierarchical triples produced dynamically in globular clusters are a primary formation channel for black hole mergers, but the rates and properties of the resulting gravitational waves depend on the distribution of post-disintegration eccentricities.

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N. Stone and N. Leigh
Fri, 13 Sep 19
32/70

Comments: 54 pages, 8 figures

Electromagnetic Helicity in Classical Physics [HEAP]

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http://arxiv.org/abs/1908.07394


This pedagogical note revisits the concept of electromagnetic helicity in classical systems. In particular, magnetic helicity and its role in mean field dynamo theories is briefly discussed highlighting the major mathematical inconsistency in most of these theories—violation of magnetic helicity conservation. A short review of kinematic dynamo theory and its classic theorems is also presented in the Appendix.

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A. Jafari
Wed, 21 Aug 19
25/78

Comments: N/A

Multiple Scales Asymptotic Solution For The Constant Radial Thrust Problem [EPA]

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http://arxiv.org/abs/1907.09988


An approximate analytical solution for the two body problem perturbed by a radial, low acceleration is obtained, using a regularized formulation of the orbital motion and the method of multiple scales. Formulating the dynamics with the Dromo special perturbation method allows us to separate the two characteristic periods of the problem in a clear and physically significative way, namely the orbital period and a period depending on the magnitude of the perturbing acceleration. This second period becomes very large compared to the orbital one for low thrust cases, allowing us to develop an accurate approximate analytical solution through the method of multiple scales. Compared to a regular expansion, the multiple scales solution retains the qualitative contributions of both characteristic periods and has a longer validity range in time. Looking at previous solutions for this problem, our approach has the advantage of not requiring the evaluation of special functions or an initially circular orbit. Furthermore, the simple expression reached for the long period provides additional insight on the problem. Finally, the behavior of the asymptotic solution is assessed through several test cases, finding a good agreement with high-precision numerical solutions. The results presented not only advance in the study of the two body problem with constant radial thrust, but confirm the utility of the method of multiple scales for tackling problems in orbital mechanics.

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J. Gonzalo and C. Bombardelli
Wed, 24 Jul 19
17/60

Comments: 32 pages, 11 figures. Accepted for publication in Celestial Mechanics and Dynamical Astronomy

Gamow's Cyclist: A New Look at Relativistic Measurements for a Binocular Observer [CL]

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http://arxiv.org/abs/1906.11642


The visualisation of objects moving at relativistic speeds has been a popular topic of study since Special Relativity’s inception. While the standard exposition of the theory describes certain shape-changing effects, such as the Lorentz-contraction, it makes no mention of how an extended object would appear in a snapshot or how apparent distortions could be used for measurement. Previous work on the subject has derived the apparent form of an object, often making mention of George Gamow’s relativistic cyclist thought experiment. Here, a rigorous re-analysis of the cyclist, this time in 3-dimensions, is undertaken for a binocular observer, accounting for both the distortion in apparent position and the relativistic colour and intensity shifts undergone by a fast moving object. A methodology for analysing binocular relativistic data is then introduced, allowing the fitting of experimental readings of an object’s apparent position to determine the distance to the object and its velocity. This method is then applied to the simulation of Gamow’s cyclist, producing self-consistent results.

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E. Cryer-Jenkins and P. Stevenson
Mon, 1 Jul 19
44/52

Comments: 18 pages, 15 figures. Submitted to Proc. Roy. Soc. A

Test of Einstein equivalence principle near the Galactic center supermassive black hole [GA]

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http://arxiv.org/abs/1902.04193


During its orbit around the four million solar mass black hole Sagittarius A* the star S2 experiences significant changes in gravitational potential. We use this change of potential to test one part of the Einstein equivalence principle: the local position invariance (LPI). We study the dependency of different atomic transitions on the gravitational potential to give an upper limit on violations of the LPI. This is done by separately measuring the redshift from hydrogen and helium absorption lines in the stellar spectrum during its closest approach to the black hole. For this measurement we use radial velocity data from 2015 to 2018 and combine it with the gravitational potential at the position of S2, which is calculated from the precisely known orbit of S2 around the black hole. This results in a limit on a violation of the LPI of $|\beta_{He}-\beta_{H}| = (2.4 \pm 5.1) \cdot 10^{-2}$. The variation in potential that we probe with this measurement is six magnitudes larger than possible for measurements on Earth, and a factor ten larger than in experiments using white dwarfs. We are therefore testing the LPI in a regime where it has not been tested before.

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G. Collaboration, A. Amorim, M. Bauböck, et. al.
Wed, 13 Feb 19
18/62

Comments: Accepted for publication in Physical Review Letters

The status of isochrony in the formation and evolution of self-gravitating systems [GA]

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http://arxiv.org/abs/1902.01095


In the potential theory, isochrony was introduced by Michel H\’enon in 1959 to characterize astrophysical observations of some globular clusters. Today, Michel Henon’s isochrone potential is mainly used for his integrable property in numerical simulations, but is generally not really known. In a recent paper [29], we have presented new fundamental and theoretical results about isochrony that have particular importance in self-gravitating dynamics and which are detailed in this paper. In particular, new characterization of the isochrone state has been proposed which are investigated in order to analyze the product of the fast relaxation of a self-gravitating system. The general paradigm consists in considering that this product is a lowered isothermal sphere (King Model). By a detailed numerical study we show that this paradigm fails when the isochrone model succeeds in reproducing the quasi-equilibrium state obtained just after fast relaxation.

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A. Simon-Petit, J. Perez and G. Plum
Tue, 5 Feb 19
51/86

Comments: 23 pages, 7 figures, 1 table, accepted for publication in MNRAS

Comment on Eur. Phys. J. Plus 133, 261 (2018) by Kholmetskii et al [CL]

Posted on by

http://arxiv.org/abs/1808.09815


We show that the YARK theory of gravity, proposed in Eur. Phys. J. Plus 133, 261 (2018) by Kholmetskii et al. and in previous papers of the same research group is wrong.

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C. Corda
Thu, 30 Aug 18
44/61

Comments: 8 pages, accepted for publication in The European Physical Journal Plus

The light speed vs the observer: the Kennedy-Thorndike test from GRAAL-ESRF [CL]

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http://arxiv.org/abs/1807.08551


High precision tests of the light speed constancy for all observers as of empirical basis of the Special Relativity have continuously been among the goals of advanced experimental studies. Based on the Compton Edge method proposed by us [1], a constraint on the one-way light speed isotropy and the Lorentz invariance violation has been obtained at the dedicated GRAAL experiment at European Synchrotron Radiation Facility (ESRF, Grenoble) [2-5]. Using the GRAAL’s data we now get a new constraint on one of key tests of Special Relativity – the Kennedy-Thorndike experiment [6] – in probing the light speed invariance with respect to the velocity of the observer (apparatus). Our analysis takes advantage of GRAAL’s setup where two separate energy scales are involved: first, via the position of the Compton Edge determining the light speed in the reference frame of incident 6 GeV electrons within the tagging system, second, in the calorimeter via the 1.27 MeV photons of the ^22 Na source. The two energy scales are engaged to each other through production of $\eta$ mesons by tagged laser Compton backscattered $\gamma$-rays. Accuracy of the calibration and stability of energies reached in each section enable us to obtain the limit 7 10^-12 for the Kennedy-Thorndike test, which improves the currently existing limits by three orders of magnitude.

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V. Gurzadyan and A. Margaryan
Tue, 31 Jul 18
34/69

Comments: To appear in Eur Phys J C; 6 pages, 3 figures

Small-N collisional dynamics IV: Order in the realm of not-so-small-N [SSA]

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http://arxiv.org/abs/1807.10777


In this paper, the fourth in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We focus once again on the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and interactions that produce direct collisions between any two particles. Our long-term goal is to predict the probability of a given collision event occurring over the course of an interaction, as a function of the numbers and properties of the particles. In previous papers, we varied the number of interacting particles, as well as the distributions of particle radii and masses. Here, we refine the methods developed in these preceding studies, and arrive at a final and robust methodology that can be used to study collisional dynamics in a variety of astrophysical contexts, ranging from stars in star clusters, galaxies in galaxy groups and clusters and even the collisional growth of planetesimals in protoplanetary disks. We further present and refine the concept of a Collision Rate Diagram (CRD), the primary tool we use to quantify the relative rates for different collision scenarios to occur. The agreement between our final theoretical model and the results of numerical scattering simulations is excellent.

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N. Leigh, A. Geller, M. Shara, et. al.
Tue, 31 Jul 18
65/69

Comments: 10 pages, 5 figures, 1 table; accepted for publication in MNRAS

Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole [GA]

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http://arxiv.org/abs/1807.09409


The highly elliptical, 16-year-period orbit of the star S2 around the massive black hole candidate Sgr A* is a sensitive probe of the gravitational field in the Galactic centre. Near pericentre at 120 AU, ~1400 Schwarzschild radii, the star has an orbital speed of ~7650 km/s, such that the first-order effects of Special and General Relativity have now become detectable with current capabilities. Over the past 26 years, we have monitored the radial velocity and motion on the sky of S2, mainly with the SINFONI and NACO adaptive optics instruments on the ESO Very Large Telescope, and since 2016 and leading up to the pericentre approach in May 2018, with the four-telescope interferometric beam-combiner instrument GRAVITY. From data up to and including pericentre, we robustly detect the combined gravitational redshift and relativistic transverse Doppler effect for S2 of z ~ 200 km/s / c with different statistical analysis methods. When parameterising the post-Newtonian contribution from these effects by a factor f, with f = 0 and f = 1 corresponding to the Newtonian and general relativistic limits, respectively, we find from posterior fitting with different weighting schemes f = 0.90 +/- 0.09 (stat) +- 0.15 (sys). The S2 data are inconsistent with pure Newtonian dynamics.

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G. Collaboration, R. Abuter, A. Amorim, et. al.
Thu, 26 Jul 18
10/62

Comments: Accepted for publication in A&A Letters, 29 June 2018, 10 pages, 6 figures, corresponding author: F. Eisenhauer &lt;eisenhau@mpe.mpg.de&gt;

Small & Big (and in between): Ion Traps and Gravitational Waves [CL]

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http://arxiv.org/abs/1807.00765


The Eisenhart lift of a Paul Trap used to store ions in molecular physics is a linearly polarized periodic gravitational wave. A modified version of Dehmelt’s Penning Trap is in turn related to circularly polarized periodic gravitational waves, sought for in inflationary models. Similar equations rule also the Lagrange points in Celestial Mechanics. The explanation is provided by anisotropic oscillators.

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P. Zhang, M. Cariglia, C. Duval, et. al.
Tue, 3 Jul 18
60/95

Comments: 30 pages, many figures

Numerical treatment of the nonconservative product in a multiscale fluid model for plasmas in thermal nonequilibrium: application to solar physics [CL]

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http://arxiv.org/abs/1806.10436


This contribution deals with the modeling of collisional multicomponent magnetized plasmas in thermal and chemical nonequilibrium aiming at simulating and predicting magnetic reconnections in the chromosphere of the sun. We focus on the numerical simulation of a simplified fluid model in order to properly investigate the influence on shock solutions of a nonconservative product present in the electron energy equation. Then, we derive jump conditions based on travelling wave solutions and propose an original numerical treatment in order to avoid non-physical shocks for the solution, that remains valid in the case of coarse-resolution simulations. A key element for the numerical scheme proposed is the presence of diffusion in the electron variables, consistent with the physically-sound scaling used in the model developed by Graille et al. following a multiscale Chapman-Enskog expansion method [M3AS, 19 (2009) 527–599]. The numerical strategy is eventually assessed in the framework of a solar physics test case. The computational method is able to capture the travelling wave solutions in both the highly- and coarsely-resolved cases.

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Q. Wargnier, S. Faure, B. Graille, et. al.
Thu, 28 Jun 18
49/60

Comments: N/A

Motion in time-periodic backgrounds with applications to ultralight dark matter haloes at galactic centers [CL]

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http://arxiv.org/abs/1806.07331


We consider motion in spherically symmetric but time-dependent backgrounds. This problem is of interest, for example, in the context of ultralight dark matter, where galactic haloes produce a time-dependent and periodic gravitational potential. We study the properties of motion of stars in such spacetimes, for different field strengths and frequency, and including dissipative effects. We show that orbital resonances may occur and that spectroscopic emission lines from stars in these geometries exhibit characteristic, periodic modulation patterns. In addition, we work out a fully relativistic and weak-field description of a special class of time-periodic geometries, that of scalar oscillatons. When applied to the galactic center, our results indicate that the motion of S2-like stars may carry distinguishable observational imprints of ultra-light dark matter.

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M. Bošković, F. Duque, M. Ferreira, et. al.
Wed, 20 Jun 18
43/58

Comments: 26 pages, 13 figures. Accepted to Physical Review D

Gravitational Magnus effect [CL]

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http://arxiv.org/abs/1805.01097


It is well known that a spinning body moving in a fluid suffers a force orthogonal to its velocity and rotation axis — it is called the Magnus effect. Recent simulations of spinning black holes and (indirect) theoretical predictions, suggest that a somewhat analogous effect may occur for purely gravitational phenomena. The magnitude and precise direction of this “gravitational Magnus effect” is still the subject of debate. Starting from the rigorous equations of motion for spinning bodies in General Relativity (Mathisson-Papapetrou equations), we show that indeed such an effect takes place and is a fundamental part of the spin-curvature force. The effect arises whenever there is a current of mass/energy, non-parallel to a body’s spin. We compute the effect explicitly for some astrophysical systems of interest: a galactic dark matter halo, a black hole accretion disk, and the FLWR spacetime. It is seen to lead to secular orbital precessions potentially observable by future astrometric experiments and gravitational-wave detectors. Finally, we consider also the reciprocal problem: the “force” exerted by the body on the surrounding matter, and show that (from this perspective) the effect is due to the body’s gravitomagnetic field. We compute it rigorously, showing the matching with its reciprocal, and clarifying common misconceptions in the literature regarding the action-reaction law in post-Newtonian gravity.

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L. Costa, R. Franco and V. Cardoso
Fri, 4 May 18
58/65

Comments: 28 pages, 9 figures

Isochrony in 3D radial potentials. From Michel Hénon ideas to isochrone relativity: classification, interpretation and applications [CL]

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http://arxiv.org/abs/1804.11282


Revisiting and extending an old idea of Michel H\’enon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They appear in spherically symmetrical systems formed by a large amount of charges (electrical or gravitational) of the same type considered in mean-field theory. Such potentials are defined by the fact that the radial period of a test charge in such potentials, provided that it exists, depends only on its energy and not on its angular momentum.
Our characterization of the isochrone set is based on the action of a real affine subgroup on isochrone potentials related to parabolas in the $\mathbb{R}^2$ plane. Furthermore, any isochrone orbits are mapped onto associated Keplerian elliptic ones by a generalization of the Bohlin transformation. This mapping allows us to understand the isochrony property of a given potential as relative to the reference frame in which its parabola is represented. We detail this isochrone relativity in the special relativity formalism.
We eventually exploit the completeness of our characterization and the relativity of isochrony to propose a deeper understanding of general symmetries such as Kepler’s Third Law and Bertrand’s theorem.

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A. Simon-Petit, J. Perez and G. Duval
Tue, 1 May 18
14/78

Comments: 67 pages, 7 theorems, 6 lemmas, 4 propositions and 2 corrolaries

When do star clusters become multiple star systems? II. Toward a half-life formalism with four bodies [SSA]

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http://arxiv.org/abs/1803.05444


We present a half-life formalism for describing the disruption of gravitationally-bound few-body systems, with a focus on binary-binary scattering. For negative total encounter energies, the four-body problem has three possible decay products in the point particle limit. For each decay product and a given set of initial conditions, we obtain directly from numerical scattering simulations the half-life for the distribution of disruption times. As in radioactive decay, the half-lives should provide a direct prediction for the relative fractions of each decay product. We test this prediction with simulated data and find good agreement with our hypothesis. We briefly discuss applications of this feature of the gravitational four-body problem to populations of black holes in globular clusters. This paper, the second in the series, builds on extending the remarkable similarity between gravitational chaos at the macroscopic scale and radioactive decay at the microscopic scale to larger-N systems.

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T. Ibragimov, N. Leigh, T. Ryu, et. al.
Fri, 16 Mar 2018
19/44

Comments: 17 pages, 18 figures, 2 tables; accepted for publication in MNRAS

Exact gravitational potential of a homogeneous torus in toroidal coordinates and a surface integral approach to Poisson's equation [CL]

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http://arxiv.org/abs/1803.00003


New exact solutions are derived for the gravitational potential inside and outside a homogeneous torus as rapidly converging series of toroidal harmonics. The approach consists of splitting the inter- nal potential into a known solution to Poisson’s equation plus some solution to Laplace’s equation. The full solutions are then obtained using two equivalent methods, applying differential boundary conditions at the surface, or evaluating a surface integral derived from Green’s third identity. This surface integral may not have been published before and is general to all geometries and volume density distributions, reducing the problem for the gravitational potential of any object from a volume to a surface integral.

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M. Majic
Fri, 2 Mar 18
37/61

Comments: 5 pages, 2 figures, 2 Matlab files attached as ancillary

Illustrating chaos: A schematic discretization of the general three-body problem in Newtonian gravity [SSA]

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http://arxiv.org/abs/1801.07257


We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular momentum-space. Each time a transformation is applied, the system changes state as the particles re-distribute their energy and angular momenta. These diagrams have the virtue of containing all of the quantitative information needed to fully characterize most bound or unbound interactions through time and space, including the total duration of the interaction, the initial and final stable states in addition to every intervening temporary meta-stable state. As shown via an illustrative example for the bound case, prolonged excursions of one of the particles, which by far dominates the computational cost of the simulations, are reduced to a single discrete transformation in energy- and angular momentum-space, thereby potentially mitigating any computational expense. We further generalize our formalism to sequences of (unbound) three-body interactions, as occur in dense stellar environments during binary hardening. Finally, we provide a method for dynamically evolving entire populations of binaries via three-body scattering interactions, using a purely analytic formalism. In principle, the techniques presented here are adaptable to other three-body problems that conserve energy and angular momentum.

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N. Leigh and S. Wegsman
Wed, 24 Jan 18
23/73

Comments: 9 pages, 4 figures; accepted for publication in MNRAS

Orbital stability in static axisymmetric fields [SSA]

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http://arxiv.org/abs/1801.07106


We investigate the stability of test-particle equilibrium orbits in axisymmetric, but otherwise arbitrary, gravitational and electromagnetic fields. We extend previous studies of this problem to include a toroidal magnetic field. We find that, even though the toroidal magnetic field does not alter the location of the circular orbits, it enters the problem as a gyroscopic force with the potential to provide gyroscopic stability. This is in essence similar to the situation encountered in the reduced three-body problem where rotation enables stability around the local maxima of the effective potential. Nevertheless, we show that gyroscopic stabilization by a toroidal magnetic field is impossible for axisymmetric force fields in source-free regions because in this case the effective potential does not possess any local maxima. As an example of an axisymmetric force field with sources, we consider the classical problem of a rotating, aligned magnetosphere. By analyzing the dynamics of halo and equatorial particle orbits we conclude that axisymmetric toroidal fields that are antisymmetric about the equator are unable to provide gyroscopic stabilization. On the other hand, a toroidal magnetic field that does not vanish at the equator can provide gyroscopic stabilization for positively charged particles in prograde equatorial orbits.

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G. Mohandas, T. Heinemann and M. Pessah
Tue, 23 Jan 18
27/85

Comments: 11 pages, 3 figures, submitted to Celestial Mechanics and Dynamical Astronomy

Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits [CL]

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http://arxiv.org/abs/1711.11267


We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical problem is the stability of Roche–Riemann ellipsoids moving on circular Kepler orbits. However, previous stability studies have to be reassessed. Indeed, they only consider global perturbations of large wavelength or local perturbations of short wavelength. Moreover many planets and stars undergo orbital motions on eccentric Kepler orbits, implying time-dependent ellipsoidal semi-axes. This time dependence has never been taken into account in hydrodynamic stability studies. In this work we overcome these stringent assumptions. We extend the hydrodynamic stability analysis of rotating ellipsoids to the case of eccentric orbits. We have developed two open-source and versatile numerical codes to perform global and local inviscid stability analyses. They give sufficient conditions for instability. The global method, based on an exact and closed Galerkin basis, handles rigorously global ellipsoidal perturbations of unprecedented complexity. Tidally driven and libration-driven elliptical instabilities are first recovered and unified within a single framework. Then we show that new global fluid instabilities can be triggered in ellipsoids by tidal effects due to eccentric Kepler orbits. Their existence is confirmed by a local analysis and direct numerical simulations of the fully nonlinear and viscous problem. Thus a non-zero orbital eccentricity may have a strong destabilising effect in celestial fluid bodies, which may lead to space-filling turbulence in most of the parameters range.

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J. Vidal and D. Cebron
Fri, 1 Dec 17
66/68

Comments: N/A

Classical orbital paramagnetism in non-equilibrium steady state [CL]

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http://arxiv.org/abs/1206.3440


We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be {\it paramagnetic} for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo-Anderson type non-markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr-van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.

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A. Deshpande and N. Kumar
Mon, 25 Sep 17
58/60

Comments: 6 pages, 4 figures, Has appeared in Journal of Astrophysics and Astronomy special issue on ‘Physics of Neutron Stars and Related Objects’, celebrating the 75th birth-year of G. Srinivasan

Exact Analytic Solutions for a Ballistic Orbiting Wind [SSA]

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http://arxiv.org/abs/1707.02505


Much theoretical and observational work has been done on stellar winds within binary systems. We present a new solution for a ballistic wind launched from a source in a circular orbit. Our method emphasizes the curved streamlines in the corotating frame, where the flow is steady-state, allowing us to obtain an exact solution for the mass density at all pre-shock locations. Assuming an initially isotropic wind, fluid elements launched from the interior hemisphere of the wind will be the first to cross other streamlines, resulting in a spiral structure bounded by two shock surfaces. Streamlines from the outer wind hemisphere later intersect these shocks as well. An analytic solution is obtained for the geometry of the two shock surfaces. Although the inner and outer shock surfaces asymptotically trace Archimedean spirals, our tail solution suggests many crossings where the shocks overlap, beyond which the analytic solution cannot be continued. Our solution can be readily extended to an initially anisotropic wind.

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F. Wilkin and H. Hausner
Tue, 11 Jul 17
64/74

Comments: 7 pages, 7 figures, accepted to ApJ

Small-N collisional dynamics III: The battle for the realm of not-so-small-N [SSA]

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http://arxiv.org/abs/1707.01911


In this paper, the third in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We study the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and we focus on interactions that produce direct collisions between any two stars. Our long-term goal is to construct an equation that gives the probability of a given collision event occurring over the course of the interaction, as a function of the total encounter energy and angular momentum as well as the numbers and properties of the particles. In previous papers, we varied the number of interacting particles and the distribution of particle radii, for all equal mass particles. Here, we focus on the effects of different combinations of particle masses.
We develop an analytic formalism for calculating the time-scales for different collision scenarios to occur. Our analytic time-scales reproduce the simulated time-scales when gravitational focusing is included. We present a method for calculating the relative rates for different types of collisions to occur, assuming two different limits for the particle orbits; radial and tangential. These limits yield relative collision probabilities that bracket the probabilities we obtain directly from numerical scattering experiments, and are designed to reveal important information about the (time-averaged) trajectories of the particles as a function of the interaction parameters. Finally, we present a Collision Rate Diagram (CRD), which directly compares the predictions of our analytic rates to the simulations and quantifies the quality of the agreement. The CRD will facilitate refining our analytic collision rates in future work, as we expand in to the remaining parameter space.

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N. Leigh, A. Geller, M. Shara, et. al.
Mon, 10 Jul 17
11/64

Comments: 13 pages, 6 figures, 2 tables; accepted for publication in MNRAS

Superradiance in rotating stars and pulsar-timing constraints on dark photons [CL]

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http://arxiv.org/abs/1704.06151


In the presence of massive bosonic degrees of freedom, rotational superradiance can trigger an instability that spins down black holes. This leads to peculiar gravitational-wave signatures and distribution in the spin-mass plane, which in turn can impose stringent constraints on ultralight fields. Here, we demonstrate that there is an analogous spindown effect for conducting stars. We show that rotating stars amplify low frequency electromagnetic waves, and that this effect is largest when the time scale for conduction within the star is of the order of a light crossing time. This has interesting consequences for dark photons, as massive dark photons would cause stars to spin down due to superradiant instabilities. The time scale of the spindown depends on the mass of the dark photon, and on the rotation rate, compactness, and conductivity of the star. Existing measurements of the spindown rate of pulsars place direct constraints on models of dark sectors. Our analysis suggests that dark photons of mass $m_V \sim 10^{-12}$ eV are excluded by pulsar-timing observations. These constraints also exclude superradiant instabilities triggered by dark photons as an explanation for the spin limit of observed pulsars.

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V. Cardoso, P. Pani and T. Yu
Fri, 21 Apr 17
8/73

Comments: 13 pages, 4 figures

Reversing the irreversible: from limit cycles to emergent time symmetry [CL]

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http://arxiv.org/abs/1703.09696


In 1979 Penrose hypothesized that the arrows of time are explained by the hypothesis that the fundamental laws are time irreversible. That is, our reversible laws, such as the standard model and general relativity are effective, and emerge from an underlying fundamental theory which is time irreversible. In Cort\^{e}s and Smolin (2014a, 2014b, 2016) we put forward a research program aiming at realizing just this. The aim is to find a fundamental description of physics above the planck scale, based on irreversible laws, from which will emerge the apparently reversible dynamics we observe on intermediate scales. Here we continue that program and note that a class of discrete dynamical systems are known to exhibit this very property: they have an underlying discrete irreversible evolution, but in the long term exhibit the properties of a time reversible system, in the form of limit cycles. We connect this to our original model proposal in Cort\^{e}s and Smolin (2014a), and show that the behaviours obtained there can be explained in terms of the same phenomenon: the attraction of the system to a basin of limit cycles, where the dynamics appears to be time reversible. Further than that, we show that our original models exhibit the very same feature: the emergence of quasi-particle excitations obtained in the earlier work in the space-time description is an expression of the system’s convergence to limit cycles when seen in the causal set description.

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M. Cortes and L. Smolin
Thu, 30 Mar 17
67/69

Comments: 22 pages, 8 figures

The Gibbs paradox, the Landauer principle and the irreversibility associated with tilted observers [CL]

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http://arxiv.org/abs/1703.03958


It is well known that, in the context of General Relativity, some spacetimes, when described by a congruence of comoving observers, may consist in a distribution of a perfect (non-dissipative) fluid, whereas the same spacetime as seen by a “tilted”‘ (Lorentz-boosted) congruence of observers, may exhibit the presence of dissipative processes. As we shall see, the appearence of entropy producing processes are related to the tight dependence of entropy on the specific congruence of observers. This fact is well illustrated by the Gibbs paradox. The appearance of such dissipative processes, as required by the Landauer principle, are necessary, in order to erase the different amount of information stored by comoving observers, with respect to tilted ones.

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L. Herrera
Tue, 14 Mar 17
28/74

Comments: 10 pages Latex. Invited contribution for the special issue “Advances in Relativistic Statistical Mechanics” published in Entropy

General invertible transformation and physical degrees of freedom [CL]

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http://arxiv.org/abs/1702.01849


An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.

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K. Takahashi, H. Motohashi, T. Suyama, et. al.
Wed, 8 Feb 17
60/65

Comments: 14 pages

Light radiation pressure upon an optically orthotropic surface [CL]

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http://arxiv.org/abs/1702.01465


In this paper, we discuss the problem of determination of light radiation pressure force upon an anisotropic surface. The anisotropy of optical parameters is considered to have major and minor axes so the model is called as an orthotropic model. We derive the equations for the force components from the emission, absorption, and reflection, utilizing the modified Maxwell specular-diffuse model. The proposed model can be used as a model of flat solar sail with anisotropically-dispersed wrinkles.

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N. Nerovny
Tue, 7 Feb 17
58/64

Comments: 12 pages

Nonlinear reflection from the surface of neutron stars and puzzles of radio emission from the pulsar in the Crab nebula [HEAP]

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http://arxiv.org/abs/1701.02304


Having no any explanations the radiation of high-frequency components of the pulsar in the Crab Nebula can be a manifestation of instability in the nonlinear reflection from the neutron star surface. Reflected radiation it is the radiation of relativistic positrons flying from the magnetosphere to the star and accelerated by the electric field of the polar gap. The discussed instability it is a stimulated scattering by surface waves, predicted more than forty years ago and still nowhere and by no one had been observed.

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V. Kontorovich
Wed, 11 Jan 17
50/64

Comments: 14 pages, 4 figures; The Report on the Conference “XXV Scientific Session of the Council of RAS on the Nonlinear Dynamics-2015”, P.P.Shirshov Institute of Oceanology RAS, Moscow, Russia, 19-20 December 2015; based on publication in LOW TEMPERATURE PHYSICS, 42, #8, 672-678 with author’s corrections

Constraints on Bounded Motion and Mutual Escape for the Full 3-Body Problem [EPA]

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http://arxiv.org/abs/1611.09997


When gravitational aggregates are spun to fission they can undergo complex dynamical evolution, including escape and reconfiguration. Previous work has shown that a simple analysis of the full 2-body problem provides physically relevant insights for whether a fissioned system can lead to escape of the components and the creation of asteroid pairs. In this paper we extend the analysis to the full 3-body problem, utilizing recent advances in the understanding of fission mechanics of these systems. Specifically, we find that the full 3-body problem can eject a body with as much as 0.31 of the total system mass, significantly larger than the 0.17 mass limit previously calculated for the full 2-body problem. This paper derives rigorous limits on a fissioned 3-body system with regards to whether fissioned system components can physically escape from each other and what other stable relative equilibria they could settle in. We explore this question with a narrow focus on the Spherical Full Three Body Problem studied in detail earlier.

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D. Scheeres
Thu, 1 Dec 16
4/75

Comments: Accepted for publication in Celestial Mechanics and Dynamical Astronomy

Dynamics of wide binary stars: A case study for testing Newtonian dynamics in the low acceleration regime [GA]

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http://arxiv.org/abs/1611.08635


Extremely wide binary stars represent ideal systems to probe Newtonian dynamics in the low acceleration regimes (<10e-10 m/s/s) typical of the external regions of galaxies. Here we present a study of 60 alleged wide binary stars with projected separation ranging from 0.004 to 1 pc, probing gravitational accelerations well below the limit were dark matter or modified dynamics theories set in. Radial velocities with accuracy ~100 m/s were obtained for each star, in order to constrain their orbital velocity, that, together with proper motion data, can distinguish bound from unbound systems. It was found that about half of the observed pairs do have velocity in the expected range for bound systems, out to the largest separations probed here. In particular, we identified five pairs with projected separation >0.15 pc that are useful for the proposed test. While it would be premature to draw any conclusion about the validity of Newtonian dynamics at these low accelerations, our main result is that very wide binary stars seem to exist in the harsh environment of the solar neighborhood. This could provide a tool to test Newtonian dynamics versus modified dynamics theories in the low acceleration conditions typical of galaxies. In the near future the GAIA satellite will provide data to increase significantly the number of wide pairs that, with the appropriate follow up spectroscopic observations, will allow the implementation of this experiment with unprecedented accuracy.

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R. Scarpa, R. Ottolina, R. Falomo, et. al.
Tue, 29 Nov 16
22/77

Comments: Accepted for publication on International Journal of Modern Physics D

Analytical approximation to the dynamics of a binary stars system with time depending mass variation [CL]

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http://arxiv.org/abs/1610.05097


We study the classical dynamics of a binary stars when there is an interchange of mass between them. Assuming that one of the star is more massive than the other, the dynamics of the lighter one is analyzed as a function of its time depending mass variation. Within our approximations and models for mass transference, we obtain a general result which establishes that if the lightest star looses mass, its period increases. If the lightest star win mass, its period decreases.

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G. Lopez and E. Lopez
Tue, 18 Oct 16
17/70

Comments: 9 pages, 3 figures

Non-perturbative relativistic guiding center transformation: exact magnetic moment and the gyro-phase proposed as the Kaluza-Klein 5^th dimension [CL]

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http://arxiv.org/abs/1610.00504


The non perturbative guiding center transformation [Di Troia C., Phys. Plasmas 22, 042103 (2015)] is extended to the relativistic regime. The single particle dynamic is described in the Minkowski flat space-time. The main solutions are obtained in covariant form: the gyrating particle solutions and the guiding particle solution, both in gyro-kinetic as in MHD orderings. It is shown the relevance of the ideal Ohm’s law in the context of the guiding center transformation. Moreover, it is also considered the presence of a gravitational field. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the Kaluza-Klein model.

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C. Troia
Tue, 4 Oct 16
64/81

Comments: submitted to ppcf special issue as contribution to the Varenna-Lausanne conference on Theory of Fusion Plasmas

Near-exponential surface densities as hydrostatic, nonequilibrium profiles in galaxy discs [GA]

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http://arxiv.org/abs/1609.08957


Apparent exponential surface density profiles are nearly universal in galaxy discs across Hubble types, over a wide mass range, and a diversity of gravitational potential forms. Several processes have been found to produce exponential profiles, including the actions of bars and spirals, and clump scattering, with star scattering a common theme in these. Based on reasonable physical constraints, such as minimal entropy gradients, we propose steady state distribution functions for disc stars, applicable over a range of gravitational potentials. The resulting surface density profiles are generally a power-law term times a Sersic-type exponential. Over a modest range of Sersic index values, these profiles are often indistinguishable from Type I exponentials, except at the innermost radii. However, in certain parameter ranges these steady states can appear as broken, Type II or III profiles. The corresponding velocity dispersion profiles are low order power-laws. A chemical potential associated with scattering can help understand the effects of long range scattering. The steady profiles are found to persist through constant velocity expansions or contractions in evolving discs. The proposed distributions and profiles are simple and solve the stellar hydrodynamic equations. They may be especially relevant to thick discs, which have settled to a steady form via scattering.

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C. Struck and B. Elmegreen
Thu, 29 Sep 16
58/76

Comments: 12 pages, 4 figures, no tables, accepted for the MNRAS

Experimental Realization of an Achromatic Magnetic Mirror based on Metamaterials [IMA]

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http://arxiv.org/abs/1609.06197


Our work relates to the use of metamaterials engineered to realize a meta-surface approaching the exotic properties of an ideal object not observed in nature, a “magnetic mirror”. Previous realizations were based on resonant structures which implied narrow bandwidths and large losses. The working principle of our device is ideally frequency-independent, it does not involve resonances and it does not rely on a specific technology. The performance of our prototype, working at millimetre wavelengths, has never been achieved before and it is superior to any other device reported in the literature, both in the microwave and optical regions. The device inherently has large bandwidth (144%), low losses (<1 %) and is almost independent of incidence-angle and polarization-state and thus approaches the behaviour of an ideal magnetic mirror. Applications of magnetic mirrors range from low-profile antennas, absorbers to optoelectronic devices. Our device can be realised using different technologies to operate in other spectral regions.

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G. Pisano, P. Ade and C. Tucker
Wed, 21 Sep 16
44/53

Comments: N/A

The chaotic four-body problem in Newtonian gravity I: Identical point-particles [SSA]

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http://arxiv.org/abs/1608.07286


In this paper, we study the chaotic four-body problem in Newtonian gravity. Assuming point particles and total encounter energies $\le$ 0, the problem has three possible outcomes. We describe each outcome as a series of discrete transformations in energy space, using the diagrams first presented in Leigh \& Geller (2012; see the Appendix). Furthermore, we develop a formalism for calculating probabilities for these outcomes to occur, expressed using the density of escape configurations per unit energy, and based on the Monaghan description originally developed for the three-body problem. We compare this analytic formalism to results from a series of binary-binary encounters with identical point particles, simulated using the \texttt{FEWBODY} code. Each of our three encounter outcomes produces a unique velocity distribution for the escaping star(s). Thus, these distributions can potentially be used to constrain the origins of dynamically-formed populations, via a direct comparison between the predicted and observed velocity distributions. Finally, we show that, for encounters that form stable triples, the simulated single star escape velocity distributions are the same as for the three-body problem. This is also the case for the other two encounter outcomes, but only at low virial ratios. This suggests that single and binary stars processed via single-binary and binary-binary encounters in dense star clusters should have a unique velocity distribution relative to the underlying Maxwellian distribution (provided the relaxation time is sufficiently long), which can be calculated analytically.

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N. Leigh, N. Stone, A. Geller, et. al.
Mon, 29 Aug 16
4/41

Comments: 18 pages, 12 figures; accepted for publication in MNRAS

Testing the black hole "no-hair" hypothesis [CL]

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http://arxiv.org/abs/1607.03133


Black holes in General Relativity are very simple objects. This property, that goes under the name of “no-hair,” has been refined in the last few decades and admits several versions. The simplicity of black holes makes them ideal testbeds of fundamental physics and of General Relativity itself. Here we discuss the no-hair property of black holes, how it can be measured in the electromagnetic or gravitational window, and what it can possibly tell us about our universe.

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V. Cardoso and L. Gualtieri
Thu, 28 Jul 16
40/57

Comments: Commissioned by Classical and Quantum Gravity

Benford's distribution in extrasolar world: Do the exoplanets follow Benford's distribution? [EPA]

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http://arxiv.org/abs/1606.05678


In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature in accordance with a logarithmic distribution law, which is referred to as Benford’s law. The existence and applicability of this empirical law have been extensively studied by physicists, accountants, computer scientists, mathematicians, statisticians, etc., and it has been observed that a large number of data-sets related to diverse problems follow this distribution. However, applicability of Benford’s law has been hardly tested for extrasolar objects. Motivated by this fact, this paper investigates the existence of Benford’s distribution in the extrasolar world using Kepler data for exoplanets. The investigation has revealed the presence of Benford’s distribution in various physical properties of these exoplanets. Further, Benford goodness parameters are computed to provide a quantitative measure of coincidence of real data with the ideal values obtained from Benford’s distribution. The quantitative analysis and the plots have revealed that several physical parameters associated with the exoplanets (e.g., mass, volume, density, orbital semi-major axis, orbital period, and radial velocity) nicely follow Benford’s distribution, whereas some physical parameters (e.g., total proper motion, stellar age and stellar distance) moderately follow the distribution, and some others (e.g., longitude, radius, and effective temperature) do not follow Benford’s distribution. Further, some specific comments have been made on the possible generalizations of the obtained result, its potential applications in analyzing data-set of candidate exoplanets, and how interested readers can perform similar investigations on other interesting data-sets.

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A. Shukla, A. Pandey and A. Pathak
Tue, 21 Jun 16
33/75

Comments: 7 pages, 3 figures and one potrait

Near Periodic solution of the Elliptic RTBP for the Jupiter Sun system [CL]

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http://arxiv.org/abs/1606.01819


Let us consider the elliptic restricted three body problem (Elliptic RTBP) for the Jupiter Sun system with eccentricity $e=0.048$ and $\mu=0.000953339$. Let us denote by $T$ the period of their orbits. In this paper we provide initial conditions for the position and velocity for a spacecraft such that after one period $T$ the spacecraft comes back to the same place, with the same velocity, within an error of 4 meters for the position and 0.2 meters per second for the velocity. Taking this solution as periodic, we present numerical evidence showing that this solution is stable. In order to compare this periodic solution with the motion of celestial bodies in our solar system, we end this paper by providing an ephemeris of the spacecraft motion from February 17, 2017 to December 28, 2028.

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O. Perdomo
Tue, 7 Jun 16
4/80

Comments: 1 figure. Youtube Link for the motion described in this paper at this https URL

Relative Equilibria in the Spherical, Finite Density 3-Body Problem [CL]

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http://arxiv.org/abs/1605.01809


The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the 3-body problem and ensures that minimum energy configurations exist for all values of angular momentum.

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D. Scheeres
Mon, 9 May 16
15/48

Comments: Accepted for publication in the Journal of Nonlinear Science

Chaotic Emission from Electromagnetic Systems Considering Self-Interaction [CL]

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http://arxiv.org/abs/0604204


The emission of electromagnetic waves from a system described by the H\’enon-Heiles potential is studied in this work. The main aim being to analyze the behavior of the system when the damping term is included explicitly into the equations of motion. Energy losses at the chaotic regime and at the regular regime are compared. The results obtained here are similar to the case of gravitational waves emission, as long we consider only the energy loss. The main difference being that in the present work the energy emitted is explicitly calculated solving the equation of motion without further approximations. It is expected that the present analysis may be useful when studying the analogous problem of dissipation in gravitational systems.

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F. Kokubun and V. Zanchin
Thu, 31 Mar 16
28/53

Comments: Typos in Refs. corrected. Other minor changes

When does a star cluster become a multiple star system? I. Lifetimes of equal-mass small-N systems [SSA]

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http://arxiv.org/abs/1603.07731


What is the difference between a long-lived unstable (or quasi-stable) multiple star system and a bona fide star cluster? In this paper, we present a possible framework to address this question, by studying the distributions of disruption times for chaotic gravitational encounters as a function of the number of interacting particles. To this end, we perform a series of numerical scattering experiments with the \texttt{FEWBODY} code, to calculate the distributions of disruption times as a function of both the particle number N and the virial coefficient k. The subsequent distributions are fit with a physically-motivated function, consisting of an initial exponential decay followed by a very slowly decreasing tail at long encounter times due to long-lived quasi-stable encounters. We find three primary features characteristic of the calculated distributions of disruption times. These are: (1) the system half-life increases with increasing particle number, (2) the fraction of long-lived quasi-stable encounters increases with increasing particle number and (3) both the system half-life and the fraction of quasi-stable encounters increase with decreasing virial coefficient. We discuss the significance of our results for collisional dynamics, and consider the extrapolation of our results to larger-N systems. We suggest that this could potentially offer a clear and unambiguous distinction between star clusters and (unstable or quasi-stable) multiple star systems. Although we are limited by very small-number statistics, our results tentatively suggest that (for our assumptions) this transition occurs at a critical particle number of order 100.

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N. Leigh, M. Shara and A. Geller
Mon, 28 Mar 16
13/40

Comments: 7 pages, 4 figures, 2 tables; accepted for publication in MNRAS

Gravitation, holographic principle, and extra dimensions [CL]

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http://arxiv.org/abs/1603.00595


Within the context of Newton’s theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a $n$-hypervolume where gravitation takes origin, within a $n$-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and “glue” to the central body via unification of the four known interactions and, in addition, (i) particles can no longer be conceived as point-like but e.g., strings or membranes, and (ii) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.

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R. Caimmi
Thu, 3 Mar 16
20/75

Comments: 13 pages, 2 figures, accepted for publication on Journal of Modern Physics, 2016, vol. 7, pp. 426-434

On the relationship between the modifications to the Raychaudhuri equation and the canonical Hamiltonian structures [CL]

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http://arxiv.org/abs/1512.07473


The problem of obtaining canonical Hamiltonian structures from the equations of motion is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on its sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. Both of the repulsive modifications are found to yield singularity avoidance. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a `generalized polymerized’ canonical phase space. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is non-trigonometric and singularities persist. Our results hint on connections between repulsive/attractive nature of modifications to gravity arising from gravitational sector and polymerized/non-polymerized gravitational phase space.

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P. Singh and S. Soni
Thu, 24 Dec 15
25/28

Comments: 20 pages

Comment on perihelion advance due to cosmological constant [CL]

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http://arxiv.org/abs/1511.04829


We comment on the recent paper “Note on the perihelion/periastron advance due to cosmological constant” by H. Arakida (Int. J. Theor. Phys. 52 (2013) 1408-1414, arXiv:1212.6289) and provide simple derivations both of the main result of this paper and of the Adkins-McDonnell’s precession formula, on which this main result is based.

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S. Ovcherenko and Z. Silagadze
Tue, 17 Nov 15
50/87

Comments: 3 pages, revtex4, to be published in Ukrainian Journal of Physics

Carbon Dioxide in Exoplanetary Atmospheres: Rarely Dominant Compared to Carbon Monoxide and Water [EPA]

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http://arxiv.org/abs/1507.01944


We present a comprehensive study of the abundance of carbon dioxide in exoplanetary atmospheres. We construct analytical models of systems in chemical equilibrium that include carbon monoxide, carbon dioxide, water, methane and acetylene and relate the equilibrium constants of the chemical reactions to temperature and pressure via the tabulated Gibbs free energies. We prove that such chemical systems may be described by a quintic equation for the mixing ratio of methane. By examining the abundances of these molecules across a broad range of temperatures (spanning equilibrium temperatures from 600 to 2500 K), pressures (via temperature-pressure profiles that explore albedo and opacity variations) and carbon-to-oxygen ratios (from 0.1 to 100), we conclude that carbon dioxide is subdominant compared to carbon monoxide and water. Atmospheric mixing does not alter this conclusion if carbon dioxide is subdominant everywhere in the atmosphere. Carbon dioxide and carbon monoxide may attain comparable abundances if the metallicity is greatly enhanced, but this property is negated by temperatures above 1000 K. For hydrogen-dominated atmospheres, our generic result has the implication that retrieval studies need to set the subdominance of carbon dioxide as a prior of the calculation and not let its abundance completely roam free as a fitting parameter, because it directly affects the inferred value of the carbon-to-oxygen ratio and may produce unphysical conclusions. We discuss the relevance of these implications for the hot Jupiter WASP-12b and suggest that some of the previous results are chemically impossible. The relative abundance of carbon dioxide to acetylene is potentially a sensitive diagnostic of the carbon-to-oxygen ratio.

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K. Heng and J. Lyons
Thu, 9 Jul 15
46/50

Comments: Submitted to ApJ. 10 pages, 8 figures, 2 tables

Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O [EPA]

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http://arxiv.org/abs/1506.05501


We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients) and procedures associated with the Gibbs free energy (minimisation, rescaling) have a common physical and mathematical origin. We correct an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and rigorously derive its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. To avoid confusion, we simply term them the dimensionless and dimensional equilibrium constants. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously thought without recourse to tagging on ad hoc functional forms. Our formulation of the evolution equations for chemical kinetics correctly enforces the book-keeping of elemental abundances, reproduces chemical equilibrium in the steady-state limit and is able to explain why photochemistry is an intrinsically disequilibrium effect. Finally, we derive analytical models of chemical systems with only hydrogen and with carbon, hydrogen and oxygen. For the latter, we include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.

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K. Heng, J. Lyons and S. Tsai
Fri, 19 Jun 15
18/51

Comments: Submitted to ApJ. 7 pages, 3 figures

Newtonian wormholes with spherical symmetry and tidal forces on test particles [CL]

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http://arxiv.org/abs/1505.06260


A spherically symmetric wormhole in Newtonian gravitation in curved space, enhanced with a connection between the mass density and the Ricci scalar, is presented. The wormhole, consisting of two connected asymptotically flat regions, inhabits a spherically symmetric curved space. The gravitational potential, gravitational field and the pressure that supports the fluid that permeates the Newtonian wormhole are computed. Particle dynamics and tidal effects in this geometry are studied. The possibility of having Newtonian black holes in this theory is sketched.

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P. Luz and J. Lemos
Tue, 26 May 15
63/67

Comments: 12 pages, 2 figures. Accepted for publication in International Journal of Modern Physics D

Lindblad Zones: resonant eccentric orbits to aid bar and spiral formation in galaxy discs [GA]

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http://arxiv.org/abs/1504.05161


The apsidal precession frequency in a fixed gravitational potential increases with the radial range of the orbit (eccentricity). Although the frequency increase is modest it can have important implications for wave dynamics in galaxy discs, which have not been previously explored in detail. One of the most interesting consequences is that for a given pattern frequency, each Lindblad resonance does not exist in isolation, but rather is the parent of a continuous sequence of resonant radii, a Lindblad Zone, with each radius in this zone characterized by a specific eccentricity. In the epicyclic approximation the precession or epicyclic frequency does not depend on epicycle size, and this phenomenon is not captured. A better approximation for eccentric orbits is provided by p-ellipse curves (Struck 2006), which do exhibit this effect. Here the p-ellipse approximation and precession-eccentricity relation are used as tools for finding the resonant radii generated from various Lindblad parent resonances. Simple, idealized examples, in flat rotation curve and near solid-body discs, are used to show that ensembles of eccentric resonant orbits excited in Lindblad Zones can provide a backbone for generating a variety of (kinematic) bars and spiral waves. In cases balancing radius-dependent circular frequencies and eccentricity-dependent precession, a range of resonant orbits can maintain their form in the pattern frame, and do not wind up. Eccentric resonance orbits require a strong perturbation to excite them, and may be produced mostly in galaxy interactions or by strong internal disturbances.

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C. Struck
Tue, 21 Apr 15
59/69

Comments: 16 pages, 12 figures, MNRAS accepted

Features of the fractional diffusion-advection equation [SSA]

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http://arxiv.org/abs/1504.02999


We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.

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M. Rocca, A. Plastino, A. Plastino, et. al.
Tue, 14 Apr 15
6/87

Comments: 17 pages. 9 figures. arXiv admin note: substantial text overlap with arXiv:1412.0255

Stable Orbits of Rigid, Rotating, Precessing, Massive Rings [CL]

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http://arxiv.org/abs/1412.1881


The dynamics of a rigid, rotating, precessing, massive ring orbiting a point mass within the perimeter of the ring are considered. It is demonstrated that orbits dynamically stable against perturbations in three dimensions exist for a range of rigid body rotation parameters of the ring. Previous analysis and some well-known works of fiction have considered the stability of both rigid and flexible, non-precessing ring systems and found that they are unstable in the plane of the ring unless an active stabilization system is employed. There does not appear to be any analyses previously published considering rigid body precession of such a system or that demonstrate passive stability in three dimensions. Deviations from perfect rigidity and possible applications of such a system are discussed.

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E. Rippert
Mon, 8 Dec 14
33/61

Comments: 29 pages, 10 figures

Non-equilibrium statistical field theory for classical particles: Non-linear structure evolution with first-order interaction [CEA]

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http://arxiv.org/abs/1411.1502


We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by choosing appropriate initial conditions and propagators and show that the non-linear growth of the density power spectrum found in numerical simulations of cosmic structure evolution is reproduced well to redshift zero and for arbitrary wave numbers. The main difference of our approach to ordinary cosmological perturbation theory is that we do not perturb a dynamical equation for the density contrast. Rather, we transport the initial phase-space distribution of a canonical particle ensemble forward in time and extract any collective information from it at the time needed. Since even small perturbations of particle trajectories can lead to large fluctuations in density, our approach allows to reach high density contrast already at first order in the perturbations of the particle trajectories. We argue why the expected asymptotic behaviour of the non-linear power spectrum at large wave numbers can be reproduced in our approach at any order of the perturbation series.

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M. Bartelmann, F. Fabis, D. Berg, et. al.
Fri, 7 Nov 14
53/56

Comments: 9 pages, 2 figures

Non-equilibrium statistical field theory for classical particles: Linear and mildly non-linear evolution of cosmological density power spectra [CEA]

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http://arxiv.org/abs/1411.1153


We use the non-equlibrium statistical field theory for classical particles, recently developed by Mazenko and Das and Mazenko, together with the free generating functional we have previously derived for point sets initially correlated in phase space, to calculate the time evolution of power spectra in the free theory, i.e. neglecting particle interactions. We provide expressions taking linear and quadratic momentum correlations into account. Up to this point, the expressions are general with respect to the free propagator of the microscopic degrees of freedom.
We then specialise the propagator to that expected for particles in cosmology treated within the Zel’dovich approximation and show that, to linear order in the momentum correlations, the linear growth of the cosmological power spectrum is reproduced. Quadratic momentum correlations return a first contribution to the non-linear evolution of the power spectrum, for which we derive a simple closed expression valid for arbitrary wave numbers. This expression is a convolution of the initial density power spectrum with itself, multiplied by a mode-coupling kernel. We also derive the bispectrum expected in this theory within these approximations and show that its connected part reproduces almost, but not quite, the bispectrum expected in Eulerian perturbation theory of the density contrast.

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M. Bartelmann, F. Fabis, D. Berg, et. al.
Thu, 6 Nov 14
25/67

Comments: 9 pages, 1 figure