pyccl.halos.profiles.pressure_gnfw module

class pyccl.halos.profiles.pressure_gnfw.HaloProfilePressureGNFW(self, *, mass_def, mass_bias=0.8, P0=6.41, c500=1.81, alpha=1.33, alpha_P=0.12, beta=4.13, gamma=0.31, P0_hexp=-1.0, qrange=(0.001, 1000.0), nq=128, x_out=inf)[source]

Bases: HaloProfilePressure

Generalized NFW electron pressure profile by Arnaud et al. 2010.

The parametrization is:

\[P_e(r) = C\times P_0 h_{70}^E (c_{500} x)^{-\gamma} [1+(c_{500}x)^\alpha]^{(\gamma-\beta)/\alpha},\]

where

\[C = 1.65\,h_{70}^2\left(\frac{H(z)}{H_0}\right)^{8/3} \left[\frac{h_{70}\tilde{M}_{500c}} {3\times10^{14}\,M_\odot}\right]^{2/3+\alpha_{\mathrm{P}}},\]

\(x = r/\tilde{r}_{500c}\), \(h_{70}=h/0.7\), and the exponent \(E\) is -1 for SZ-based profile normalizations and -1.5 for X-ray-based normalizations. The biased mass \(\tilde{M}_{500c}\) is related to the true overdensity mass \(M_{500c}\) via the mass bias parameter \((1-b)\) as \(\tilde{M}_{500c}=(1-b)M_{500c}\). \(\tilde{r}_{500c}\) is the overdensity halo radius associated with \(\tilde{M}_{500c}\) (note the intentional tilde!), and the profile is defined for a halo overdensity \(\Delta=500\) with respect to the critical density.

The default arguments (other than mass_bias), correspond to the profile parameters used in the Planck 2013 (XX) paper. The profile is calculated in physical (non-comoving) units of \(\mathrm{eV/cm^3}\).

Parameters:

  • mass_def (MassDef or str) – a mass definition object, or a name string.

  • mass_bias (float) – The mass bias parameter \(1-b\).

  • P0 (float) – Profile normalization.

  • c500 (float) – Concentration parameter.

  • alpha (float) – Profile shape parameters.

  • beta (float) – Profile shape parameters.

  • gamma (float) – Profile shape parameters.

  • alpha_P (float) – Additional mass dependence exponent

  • P0_hexp (float) – Power of \(h\) with which the normalization parameter scales. Equal to \(-1\) for SZ-based normalizations, and \(-3/2\) for X-ray-based normalizations.

  • qrange (tuple) – Tuple of two numbers denoting the limits of integration used when computing the Fourier-space profile template, in units of \(r_{\mathrm{vir}}\).

  • nq (int) – Number of sampling points of the Fourier-space profile template.

  • x_out (float) – Profile threshold, in units of \(r_{\mathrm{500c}}\). Defaults to \(+\infty\).

update_parameters(*, mass_bias=None, P0=None, c500=None, alpha=None, beta=None, gamma=None, alpha_P=None, P0_hexp=None, x_out=None)[source]

Update any of the parameters associated with this profile. Any parameter set to None won’t be updated.

Note

A change in alpha, beta, gamma, c500, or x_out recomputes the Fourier-space template, which may be slow.

Parameters:

  • mass_bias (float) – The mass bias parameter \(1-b\).

  • P0 (float) – Profile normalization.

  • c500 (float) – Concentration parameter.

  • alpha (float) – Profile shape parameters.

  • beta (float) – Profile shape parameters.

  • gamma (float) – Profile shape parameters.

  • alpha_P (float) – Additional mass dependence exponent

  • P0_hexp (float) – Power of \(h\) with which the normalization parameter scales. Equal to \(-1\) for SZ-based normalizations, and \(-3/2\) for X-ray-based normalizations.

  • x_out (float) – Profile threshold, in units of \(r_{\mathrm{500c}}\). Defaults to \(+\infty\).