Alternative Conditional Mass Functions

[daviesje]

Different halo mass functions have been handled previously by rescaling the integrals on the grid, which were calculated using the Extended Press-Schechter conditional mass function, to the mean values of a specified unconditional mass function. This was done separately for ionising emissivity and star formation rate density so that we always had the correct mean.

With a discrete halo catalogue this is not possible. We could apply the same corrections to the HaloBox grids, but then the emissivity grids would be inconsistent with the halo mass catalogues. Alternatives include:

• Implementing Sheth-Tormen (https://arxiv.org/pdf/astro-ph/0105113.pdf) and/or Delos (https://arxiv.org/pdf/2311.17986.pdf) conditional mass functions. In theory these should be much more accurate mass functions which could remove the necessity for mean fixing in all models. There are implementations of these CMFs in the code but they are not working. First samples drawn from them currently fit expected distributions very well, but drawing progenitors from these distributions quickly results huge errors. The Delos paper specifically warns that short timesteps (high delta) cause the conditional mass functions to not match random walk results, however I would still expect samples drawn from the CMF to sum to the unconditional mass function across all conditions, as long as it always integrates to one. I am unsure at the moment if there is a bug in the implementation or if the approach itself is restricted to Extended Press-Schechter somehow.
• Rescaling the EPS mass function: This has been notably done in binary-split merger tree construction (Parkinson+08), where scaling terms are added to the EPS CMF (with condition scale and density) so that the final halo populations match expected results (usually an N-body).
• Rescaling unconditional mass functions: Different forms have been implemented in https://arxiv.org/pdf/0803.1954.pdf, https://arxiv.org/pdf/1702.01788.pdf, which rescale a given unconditional mass function, resulting in a CMF that can be used.