halomod.bias.Tinker10

class halomod.bias.Tinker10(nu: numpy.ndarray, delta_c: float = 1.686, m: Optional[numpy.ndarray] = None, mstar: Optional[float] = None, delta_halo: Optional[float] = 200, n: Optional[float] = 1, sigma_8: Optional[float] = 0.8, cosmo: astropy.cosmology.core.FLRW = FlatLambdaCDM(name="Planck15", H0=67.7 km / (Mpc s), Om0=0.307, Tcmb0=2.725 K, Neff=3.05, m_nu=[0.   0.   0.06] eV, Ob0=0.0486), n_eff: Optional[numpy.ndarray] = None, z: float = 0.0, **model_parameters)

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.

Methods

__init__(nu[, delta_c, m, mstar, …])	Initialize self.
bias()	Calculate the first-order, linear, deterministic halo bias.
get_models()	Get a dictionary of all implemented models for this component.

Attributes

pair_hmf

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