Accelerating Computation of the Nonlinear Mass by an Order of Magnitude

The nonlinear mass is a characteristic scale in halo formation that has wide-ranging 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 this calculation 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, accurate across a variety of cosmologies to 0.1$-$1% (depending on redshift) and 10$-$20 times faster than the naive numerical method. We also present a further acceleration (40$-$80 times faster than the naive method) in which we determine the polynomial coefficients using a Taylor expansion in the cosmological parameters rather than re-fitting a polynomial to the correlation function. Our acceleration greatly reduces the cost of repeated calculation of the nonlinear mass. This will be useful for MCMC analyses to constrain cosmological parameters from the highly nonlinear regime, e.g. with data from upcoming surveys.