http://arxiv.org/abs/2102.07815
A couple of dozen Earth-like planets orbiting M dwarfs have been discovered so far. Some of them have attracted interest because of their potential long-term habitability. I show that the General Theory of Relativity (GTR) predicts spin precessions which, to the post-Newtonian (pN) order, may impact the habitability of a fictitious telluric planet orbiting a late M dwarf with $M_\star=0.08\,M_\odot$ at $a=0.02\,\mathrm{au}$, corresponding to an orbital period $P_\mathrm{b}\simeq 4\,\mathrm{d}$, inducing long-term variations of the obliquity $\varepsilon$ of its spin $\boldsymbol S$ which, under certain circumstances, may not be deemed as negligible from the point of view of life’s sustainability. I analytically derive the orbit-averaged equations of the pN precessions of the polar angles $\theta,\,\alpha$ of $\boldsymbol{\hat{S}}$ and of the orbital inclination $I$ and node $\Omega$ entering $\varepsilon$, and numerically integrate them by producing time series of the pN changes $\Delta\varepsilon(t)$ of the obliquity. For rapidly rotating M dwarfs with rotational periods of the order of $P_\star \simeq 0.1-1\,\mathrm{d}$, the planet’s obliquity $\varepsilon$ can undergo pN large variations $\Delta\varepsilon(t)$ up to tens of degrees over timescales $\Delta t \simeq 20-200\,\mathrm{kyr}$, depending on the mutual orientations of the star’s spin ${\boldsymbol J}_\star$, of $\boldsymbol S$, and of the orbital angular momentum $\boldsymbol L$. Instead, $\Delta\varepsilon(t)$ are $\lesssim 1-1.5^\circ$ for the planet b of the Teegarden’s Star. GTR should be considered one of the key factors to be taken into account in compiling budgets of the long-term habitability of rocky planets around fast spinning late M dwarfs. My approach can be extended also to other astronomical scenarios where features of the target bodies other than their habitability are of interest.
L. Iorio
Wed, 17 Feb 21
5/56
Comments: LaTex2e, 24 pages, 5 figures, no tables
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