hmfast.halos.bias.T10HaloBias

class hmfast.halos.bias.T10HaloBias

Bases: HaloBias

Halo bias model from Tinker et al. (2010).

This class implements the large-scale halo bias relation as a function of peak height \(\nu\) and redshift, calibrated for the \(200\mathrm{m}\) halo definition.

Methods

bias(cosmology, m, z[, mass_def, ...])

Compute the halo bias for a given order.

bias(cosmology, m, z, mass_def=<hmfast.halos.massdef.MassDefinition object>, convert_masses=False, order=1)

Compute the halo bias for a given order.

The first-order (linear) and second-order (quadratic) halo bias are given by:

\[ \begin{align}\begin{aligned}b_1(\nu) = 1 - A \frac{\nu^a}{\nu^a + \delta_c^a} + B \nu^b + C \nu^c\\b_2(\nu) = 2(1 + a^2)(\epsilon_1 + E_1) + \epsilon_2 + E_2\end{aligned}\end{align} \]

where

• \(\nu = \delta_c / \sigma(M)\) is the peak height,

• \(\delta_c \approx 1.686\) is the critical density for collapse,

• \(A, a, B, b, C, c\) are given in Tinker et al. (2010), Table 2.

• \(\epsilon_1, E_1, \epsilon_2, E_2\) are given in Hoffmann et al. (2015), Table 5.

Please refer to the original paper for the parameter values and full expressions.

Parameters:

cosmologyCosmology

Cosmology used to evaluate the bias.

marray-like

Halo mass grid in physical \(M_\odot\).

zarray-like

Redshift grid.

mass_defMassDefinition, optional

Halo mass definition at which to evaluate the bias. Defaults to the native \(200\mathrm{m}\) calibration definition.

convert_massesbool, optional

Mass conversions are applied if convert_masses is set to True.

orderint, optional

Bias order to evaluate. Supported values are 1 and 2.

Returns:

float or array-like

Dimensionless halo bias values of the requested order, with shape \((N_m, N_z)\), where singleton dimensions get squeezed before return.