Towards a universal model for the density profiles of dark matter haloes

Abstract: It is well established from cosmological simulations that dark matter haloes are not precisely self-similar and an additional parameter, beyond their concentration, is required to accurately describe their spherically-averaged mass density profiles. We present, for the first time, a model to consistently predict both halo concentration, $c$, and this additional shape' parameter, $\alpha$, for a halo of given mass and redshift for a specified cosmology. Following recent studies, we recast the dependency on mass, redshift, and cosmology to a dependence onpeak height'. We show that, when adopting the standard definition of peak height, which employs the so-called spherical top hat (STH) window function, the concentration--peak height relation has a strong residual dependence on cosmology (i.e., it is not uniquely determined by peak height), whereas the $\alpha$--peak height relation is approximately universal when employing the STH window function. Given the freedom in the choice of window function, we explore a simple modification of the STH function, constraining its form so that it produces universal relations for concentration and $\alpha$ as a function of peak height using a large suite of cosmological simulations. It is found that universal relations for the two density profile parameters can indeed be derived and that these parameters are set by the linear power spectrum, $P(k)$, filtered on different scales. We show that the results of this work generalise to any (reasonable) combination of $P(k)$ and background expansion history, $H(z)$, resulting in accurate predictions of the density profiles of dark matter haloes for a wide range of cosmologies.