A Two-Parameter Matching Scheme for Massive Galaxies and Dark Matter Haloes

Abstract

Halo Abundance Matching has been used to construct a one-parameter mapping between galaxies and dark matter haloes by assuming that halo mass and galaxy luminosity (or stellar mass) are monotonically related. While this approach has been reasonably successful, it is known that galaxies must be described by at least two parameters, as can be seen from the two-parameter Fundamental Plane on which massive early-type galaxies lie. In this paper, we derive a connection between initial dark matter density perturbations in the early universe and present-day virialized dark matter haloes by assuming simple spherical collapse combined with conservation of mass and energy. We find that $z=0$ halo concentration, or alternatively the inner slope of the halo density profile $\alpha$, is monotonically and positively correlated with the collapse redshift of the halo. This is qualitatively similar to the findings of some previous works based on numerical simulations, with which we compare our results. We then describe how the halo mass and concentration (or inner slope $\alpha$) can be used as two halo parameters in combination with two parameters of early-type galaxies to create an improved abundance matching scheme.

10 pages, 4 figures. Submitted to MNRAS

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• The Concentration Dependence of the Galaxy-Halo Connection: Modeling Assembly Bias with Abundance Matching
• A flexible subhalo abundance matching model for galaxy clustering in redshift space
• Stellar Velocity Dispersion: Linking Quiescent Galaxies to their Dark Matter Halos
• A question of separation: disentangling tracer bias and gravitational nonlinearity with counts-in-cells statistics
• Rosella: A mock catalogue from the P-Millennium simulation
• The cosmological distribution of compact object mergers from dynamical interactions with SMBH binaries
• Properties beyond mass for unresolved haloes across redshift and cosmology using correlations with local halo environment