# mrpy.extra.physical_dependence¶

Module containing functions for the dependence of MRP parameters on physical parameters, defined with respect to Behroozi+13.

The values output by the functions in this module were derived as part of the study reported in Murray, Robotham and Power (2016). See that paper for details on the fits used.

In brief, three physical parameters were varied – matter density, rms fluctuation
\(\sigma_8\) and redshift – around the best-fit values from Planck+13, and up
to a redshift of 8. For each, the Behroozi+13 mass function was calculated using
the hmf python package over a range of masses corresponding to (lm-3, lm+2), where
*lm* is the log mass mode. The MRP was fit to each curve, and then the best-fit parameters
were parameterised as a function of the physical parameters using the Eureqa software.

Note

Given the way these parameterisations were determined, it is not advised to trust these values far from the log-mass-mode of each fit.

Functions

`mrp_b13` (m[, z, Om0, sig8, Hs_kw, alpha_kw, …]) |
Return the MRP defined at `m` for the given physical parameters. |

`mrp_params_b13` ([z, Om0, sig8, Hs_kw, …]) |
Return all 4 MRP parameters as a function of physical parameters. |