halomod.bias.Tinker10¶

class halomod.bias.Tinker10(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 an empirical form that does not obey the peak-background split consistency formalism, but fits well to simulations. It is dependent on the spherical halo definition. The form from [1] is

\[1 - A\frac{\nu^a}{\nu^a + \delta_c^a} + B \nu^b + C \nu^c\]

with

\[A = 1 + 0.24 y e^{-(4/y)^4},\]

and

\[a = 0.44y - 0.88\]

and

\[C = 0.019 + 0.107y + 0.19 e^{-(4/y)^4}\]

and \(y=\log_{10} \Delta_{\rm halo}\).

The fitted parameters are (B,b,c) = (0.183, 1.5, 2.4).

Parameters:

B (float, optional) – The fitted parameters.
b (float, optional) – The fitted parameters.
c (float, optional) – The fitted parameters.

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

Tinker10PBsplit: Bias from the same study but with 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())

classmethod get_models() → Dict[str, Type]¶: Get a dictionary of all implemented models for this component.

pair_hmf = ()¶: The HMF model that pairs with this bias in the peak-background split