Cosmological Simulations: Approximate Mass Function Emulator

Mass function model space covered by the emulator. In red we show the 100 models used to build the emulator, in blue 10 test cosmologies to verify the accuracy of the emulator, and in light blue a LCDM cosmology. If the underlying mass function predictions would be "perfect", the emulator performance would be at an accuracy of better than 1%. Since we assume universality, which is only valid at 10%, the approximate emulator will provide results at that accuracy level.
Caption: 

Mass function model space covered by the emulator. In red we show the 100 models used to build the emulator, in blue 10 test cosmologies to verify the accuracy of the emulator, and in light blue a LCDM cosmology. If the underlying mass function predictions would be "perfect", the emulator performance would be at an accuracy of better than 1%. Since we assume universality, which is only valid at 10%, the approximate emulator will provide results at that accuracy level.

Authors: Katrin Heitmann, Earl Lawrence, Salman Habib, Rahul Biswas, Derek Bingham, David Higdon

We release an approximate mass function emulator that is based on the assumption that the halo mass function is universal. The emulator covers the space of w0-wa dark energy models and allows for effects of massive neutrinos up to a mass of ~1eV. Currently, the emulator provides predictions for z=0, a more flexible emulator covering redshifts up to z=2 is currently under construction. The approximations made hold at the 10% level. Over the next year or two this emulator will be replaced by one that is based on full simulations. The models to be simulated have been carefully chosen and as currently carried out as part of a DOE INCITE program with the HACC code. Details on this project will be published in Heitmann et al. (in preparation).

The approximate mass function calculation is based on the universal form developed in Bhattacharya et al. 2011 (ApJ  732, 122). In that paper a very accurate mass function fit was derived from a large number of LCDM simulations. Universality (first rigorously investigated by Jenkins et al. in 2001) assumes that the main cosmology dependence in the mass function is captured by the linear power spectrum, if the mass function is described in terms of the differential mass function f(sigma), where sigma is the variance of the linear matter power spectrum over a length R. In Bhattacharya et al. 2011 universality was tested on a set of wCDM models and was shown to hold at the 10% level. Here we generate a set of ~100 cosmologies in an eight-dimensional parameter space using the universal mass function expression from Bhattacharya et al. 2011 and build an emulator from this. The main advantage of the emulator compared to using the fitting form directly is its ease of use (no additional CAMB runs are needed to generate the lienar power spectrum) and its speed. The code is available on this webpage;  a paper with more details will be published in the very near future.