clenspy.cosmology.concentration.child18_powerlaw¶

clenspy.cosmology.concentration.child18_powerlaw(m_hinv, z, fit='individual_all')[source]¶

Child et al. (2018) Eq. 19: the power-law \(c\)–\(M\) fit.

\[c_{200c} = A\,(1+z)^{d}\,M^{m}\]

NOTE: domain of validity \(0 \le z \le 1\) only – the paper states the power law “is only valid for redshifts \(0 \le z \le 1\), where a power-law dependence on mass and redshift is a reasonable description of our results”. Above \(z = 1\) the true relation flattens and this form keeps falling.

NOTE: \(M\) is dimensionful inside a power law here, so \(A\) carries the units implicitly; \(M\) must be in \(h^{-1}M_\odot\) for the tabulated \(A\) to apply. This is why child18 is preferable where \(M_\star\) is available – there the ratio is dimensionless.

Parameters:

m_hinv (float or array-like) – \(M_{200c}\) in \(h^{-1}M_\odot\).
z (float or array-like) – Redshift, \(0 \le z \le 1\).
fit (str, optional) – Row of CHILD18_TABLE2 (default: "individual_all").

Returns:

np.ndarray – \(c_{200c}\), dimensionless.