http://arxiv.org/abs/2212.03233
Context. Large and complete galaxy cluster samples can be used to infer cosmological parameter constraints from number count measurements. Key to their interpretation is the availability of accurately calibrated estimates of the halo mass function from cosmological simulations. Galaxy cluster masses are usually defined as the mass within a spherical region enclosing a given matter overdensity (in units of the critical density). However, this may differ from the mass definition of the numerical halo catalogues that are used to calibrate the halo mass function.
Aims. In this article, we present a generic non parametric formalism that allows one to accurately map the halo mass function between different mass overdensity definitions using the distribution of halo sparsities defined as the ratios of both masses. We show that changing mass definitions reduces to modelling the distribution of halo sparsities.
Methods. Using standard transformation rules of random variates, we derive relations between the halo mass function at different overdensities and the distribution of halo sparsities.
Results. We show that these relations reproduce the N-body halo mass functions from the Uchuu simulation within the statistical errors at a few percent level. Furthermore, these relations allow one to relate the halo mass functions at different overdensities to parametric descriptions of the halo density profile. In particular, we will discuss the case of the concentration-mass relation of the Navarro-Frenk-White profile. Finally, we will show that the use of such relations allows to predict the distribution of sparsities of a sample of haloes of a given mass, thus opening the way to inferring cosmological constraints from individual galaxy cluster sparsity measurements.
T. Richardson and P. Corasaniti
Wed, 7 Dec 22
68/74
Comments: 12 pages, 9 figures, submitted to A&A
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