halomod.bias.Tinker10PBSplit

class halomod.bias.Tinker10PBSplit(nu: ~numpy.ndarray, delta_c: float = 1.686, m: ~numpy.ndarray | None = None, mstar: float | None = None, delta_halo: float | None = 200, n: float | None = 1, sigma_8: float | None = 0.8, cosmo: ~astropy.cosmology.flrw.base.FLRW = FlatLambdaCDM(name='Planck15', H0=<Quantity 67.74 km / (Mpc s)>, Om0=0.3075, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.0486), n_eff: None | ~numpy.ndarray = None, z: float = 0.0, **model_parameters)[source]

Bases: Bias

Empirical bias of Tinker et al (2010).

See documentation for Bias for information on input parameters. This model has no free parameters.

Notes

This is form from [1] obeys the peak-background split consistency formalism, which offers some advantages, but also fits well to simulations. It is dependent on the spherical halo definition. See the reference for details on the form.

Parameters:

  • alpha (float, optional) – The fitted parameters. Each of these are available to specify at a certain overdensity. So for example alpha_200 specifies the alpha parameter at a spherical halo overdensity of 200. All default values are taken from Tinker 2010.

  • beta (float, optional) – The fitted parameters. Each of these are available to specify at a certain overdensity. So for example alpha_200 specifies the alpha parameter at a spherical halo overdensity of 200. All default values are taken from Tinker 2010.

  • gamma (float, optional) – The fitted parameters. Each of these are available to specify at a certain overdensity. So for example alpha_200 specifies the alpha parameter at a spherical halo overdensity of 200. All default values are taken from Tinker 2010.

  • phi (float, optional) – The fitted parameters. Each of these are available to specify at a certain overdensity. So for example alpha_200 specifies the alpha parameter at a spherical halo overdensity of 200. All default values are taken from Tinker 2010.

  • eta (float, optional) – The fitted parameters. Each of these are available to specify at a certain overdensity. So for example alpha_200 specifies the alpha parameter at a spherical halo overdensity of 200. All default values are taken from Tinker 2010.

  • beta_exp (float, optional) – The value of beta, phi etc., are functions of redshift via the relation beta = beta0 (1 + z)^beta_exp (and likewise for the other parameters).

  • phi_exp (float, optional) – The value of beta, phi etc., are functions of redshift via the relation beta = beta0 (1 + z)^beta_exp (and likewise for the other parameters).

  • eta_exp (float, optional) – The value of beta, phi etc., are functions of redshift via the relation beta = beta0 (1 + z)^beta_exp (and likewise for the other parameters).

  • gamma_exp (float, optional) – The value of beta, phi etc., are functions of redshift via the relation beta = beta0 (1 + z)^beta_exp (and likewise for the other parameters).

  • max_z (float, optional) – The maximum redshift for which the redshift evolution holds. Above this redshift, the relation flattens. Default 3.

References

[1]

Tinker, J. L. et al., “The Large-scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests”, https://ui.adsabs.harvard.edu/abs/2010ApJ…724..878T, 2010

See also

Tinker10

Bias from the same study but without the constraint of the peak-background split formalism.

bias()[source]

Calculate the first-order, linear, deterministic halo bias.

Returns:

b – The bias as a function of mass, as an array of values corresponding to the instance attributes m and/or nu.

Return type:

array-like

Examples

>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from halomod.bias import Mo96
>>> peak_height = np.linspace(0.1, 2, 100)
>>> bias = Mo96(nu=peak_height)
>>> plt.plot(peak_height, bias.bias())
delta_virs = array([ 200,  300,  400,  600,  800, 1200, 1600, 2400, 3200])
classmethod get_models() → Dict[str, Type]

Get a dictionary of all implemented models for this component.

pair_hmf = (<class 'hmf.mass_function.fitting_functions.Tinker10'>,)

The HMF model that pairs with this bias in the peak-background split