Accelerating computation of the densityfield filtering scale σ(R) and nonlinear mass by an order of magnitude
Abstract
The nonlinear mass is a characteristic scale in halo formation that has many applications across cosmology. Naively, computing it requires repeated numerical integration to calculate the variance of the power spectrum on different scales and determine which scales exceed the threshold for nonlinear collapse. We accelerate calculation of both the nonlinear mass and the rms amplitude of the power spectrum σ(R) by working in configuration space and approximating the correlation function as a polynomial at r ≤ 5 h^{1} Mpc. This enables an analytic rather than numerical solution for the nonlinear mass, accurate across a variety of cosmologies to 0.1 $1{{\ \rm per\ cent}}$ in mass (depending on redshift) and 2060× faster than the standard numerical method. We also present a further acceleration of the nonlinear mass (4001000× faster than the standard method) in which we determine the polynomial coefficients using a Taylor expansion in the cosmological parameters rather than refitting a polynomial to the correlation function. Our method is also 500× faster than the standard method for σ(R) for a typical case of N_{R} = 100 desired R values, with timing essentially independent of N_{R}. Our approach can be used for quick calculation of the halo mass function, halo massbias relation, and cosmological calculations involving the nonlinear mass.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 January 2021
 DOI:
 10.1093/mnras/staa3525
 Bibcode:
 2021MNRAS.500.4439K
 Keywords:

 methods: numerical;
 cosmology: theory