NumCosmoMultiplicityFuncBhattacharya

Dark matter halo — Bhattacharya multiplicity function.

Dark matter halo multiplicity function fitted to LCDM simulations using the friends of friends algorithm, FoF(0.2). See reference arXiv:1005.2239.

$$f(\sigma, z) = A(z) \sqrt{\frac{2}{\pi}} e^{-\frac{a(z) \delta_c^2}{2 \sigma^2}} \left[ 1 + \left( \frac{\sigma^2}{a(z) \delta_c^2} \right)^{p} \right] \left( \frac{\delta_c \sqrt{a(z)}}{\sigma} \right)^{q},$$ where $A(z) = A_0 (1+z)^{-0.11}$, and the default values fitted in the range $0 \leq z \leq 2$ are $A_0 = 0.333$, $a_0 = 0.788$, $p = 0.807$ and $q = 1.795$.

The redshift evolution of the shape parameter $a$ is selected through the NcMultiplicityFuncBhattacharya:convention property: the original Bhattacharya et al. 2011 fit (arXiv:1005.2239) uses $a(z) = a_0 (1+z)^{-0.01}$, while the Heitmann et al. 2019 Outer Rim form (arXiv:1904.11970) keeps $a = a_0$ constant in redshift. The two agree at $z = 0$ and differ by at most $\sim 1\%$ in $a$ over $0 \leq z \leq 2$.