halomod.bias.ST99¶

class halomod.bias.ST99(nu: ndarray, delta_c: float = 1.686, m: ndarray | None = None, mstar: float | None = None, delta_halo: float | None = 200, n: float | None = 1, sigma_8: float | None = 0.8, cosmo: 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 | ndarray = None, z: float = 0.0, **model_parameters)[source]¶

Bases: Bias

Peak-background split bias corresponding to ST99 HMF.

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

Notes

This bias form can be explicitly derived by assuming a Sheth-Tormen form for the HMF, as shown for example in [1]. The form is

\[1 + \frac{q\nu - 1}{\delta_c} + \frac{2p}{\delta_c ( 1 + q^p \nu^p)}\]

with p and q having default values of (0.707, 0.3). They are free in this implementation for the user to modify.

Parameters:

p (float, optional) – The free parameters of the form.
q (float, optional) – The free parameters of the form.

References

[1]

Sheth, R. K.. and Tormen, G., “Large-scale bias and the peak background split”, https://ui.adsabs.harvard.edu/abs/1999MNRAS.308..119S, 1999

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 = (<class 'hmf.mass_function.fitting_functions.SMT'>,)¶: The HMF model that pairs with this bias in the peak-background split