2009/06/30 by Patrick Valageas, P. Valageas · 1 citation
Physics and Astronomy · #Astrophysics #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Dark matter #Function (biology) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gaussian #Halo #Halo effect #Halo mass function #Non-Gaussianity #Physics #Quantum mechanics #Statistical physics #astro-ph.CO
paper · pdf · doi:10.1051/0004-6361/200912636
published as Astron.Astrophys.514:A46,2010 · 15 pages
openalex publication_date 2010/02/25 · arxiv created 2011/02/09 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
<i>Aims. <i/>We revisit the derivation of the mass function and the bias of dark matter halos for non-Gaussian initial conditions.<i>Methods. <i/>We use a steepest-descent approach to point out that exact results can be obtained for the high-mass tail of the halo mass function and the two-point correlation of massive halos. Focusing on primordial non-Gaussianity of the local type, we check that these results agree with numerical simulations.<i>Results. <i/>The high-mass cutoff of the halo mass function takes the same form as the one obtained from the Press-Schechter formalism, but with a linear threshold <i>δ<i/><sub>L<sub/> that depends on the definition of the halo (i.e. <i>δ<i/><sub>L<sub/> 1.59 for a nonlinear density contrast of 200). We show that a simple formula, which obeys this high-mass asymptotic and uses the fit obtained for Gaussian initial conditions, matches numerical simulations while keeping the mass function normalized to unity. Next, by deriving the real-space halo two-point correlation in the spirit of Kaiser (1984, ApJ, 284, L9) and taking a Fourier transform, we obtain good agreement with simulations for the correction to the halo bias, <i>Δ<i/><i>b<sub>M<sub/><i/>(<i>k<i/>,<i>f<i/><sub>NL<sub/>), due to primordial non-Gaussianity. Therefore, neither the halo mass function nor the bias require an ad-hoc parameter <i>q<i/> (such as <i>δ<i/><sub>c<sub/> <i>δ<i/><sub>c<sub/> ), provided one uses the correct linear threshold <i>δ<i/><sub>L<sub/> and pays attention to halo displacements. The nonlinear real-space expression can be useful for checking that the “linearized” bias is a valid approximation. Moreover, it clearly shows how the baryon acoustic oscillation at ~100 <i>h<i/><sup>-1<sup/> Mpc is amplified by the bias of massive halos and modified by primordial non-Gaussianity. On smaller scales, 30 < <i>x<i/> < 90 <i>h<i/><sup>-1<sup/> Mpc, the correction to the real-space bias roughly scales as <i>f<i/><sub>NL<sub/> <i>b<sub>M<sub/><i/>(<i>f<i/><sub>NL<sub/> = 0) <i>x<sup>2<sup/><i/>. The low-<i>k<i/> behavior of the halo bias does not imply a divergent real-space correlation, so that one does not need to introduce counterterms that depend on the survey size.