hmf.core._kernels.fits.watson_gamma¶

hmf.core._kernels.fits.watson_gamma(sigma: ArrayLike, delta_halo: ArrayLike, omega_m_z: ArrayLike, C_a: ArrayLike, d_a: ArrayLike, d_b: ArrayLike, p: ArrayLike, q: ArrayLike) → ndarray[tuple[Any, ...], dtype[float64]][source]¶

The overdensity correction \(\Gamma(\Delta, \sigma, z)\) of Watson et al. (2013).

\[\Gamma = C(\Delta)\left(\frac{\Delta}{178}\right)^{d(z)} \exp\left[\frac{p(1 - \Delta/178)}{\sigma^q}\right],\]

with \(C = \exp[C_a(\Delta/178 - 1)]\) and \(d = -d_a\Omega_m(z) - d_b\). delta_halo is relative to the mean density. It is exactly 1 at \(\Delta = 178\).