halomod.bias.SMT01¶

class halomod.bias.SMT01(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

Extended Press-Schechter-derived bias function corresponding to SMT01 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 and allowing for ellipsoidal collapse, as shown for example in [1]. The form is

\[1 + \frac{1}{\delta_c \sqrt{a}} \left(\sqrt{a} a \nu + \sqrt{a} b (a\nu)^{1-c} - \frac{(a\nu)^c}{(a\nu)^c + b(1-c)(1 - c/2)}\right)\]

with a, b and c having default values of (0.707, 0.5, 0.6). They are free in this implementation for the user to modify.

Parameters:

a (float, optional) – The free parameters of the form.
b (float, optional) – The free parameters of the form.
c (float, optional) – The free parameters of the form.

References

[1]

Sheth, R. K. and Tormen G., “Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes”, https://ui.adsabs.harvard.edu/abs/2001MNRAS.323….1S, 2001

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