# SFRBiasedNFWPhaseSpace¶

class halotools.empirical_models.SFRBiasedNFWPhaseSpace(**kwargs)[source] [edit on github]

Model for the phase space distribution of galaxies in isotropic Jeans equilibrium in an NFW halo profile, based on Navarro, Frenk and White (1995), where the concentration of the tracers is permitted to differ from the host halo concentration, independently for red and blue galaxies.

For a review of the mathematics underlying the NFW profile, including descriptions of how the relevant equations are implemented in the Halotools code base, see Source code notes on NFWProfile and NFWPhaseSpace.

Notes

The SFRBiasedNFWPhaseSpace class can only be used to make mocks in concert with some other component model that is responsible for modeling an quiescent property of the galaxy_table.

Parameters: conc_gal_bias_logM_abscissa : array_like, optional Numpy array of shape (num_gal_bias_bins, ) storing the values of log10(Mhalo). For each entry of conc_gal_bias_logM_abscissa, there will be a corresponding parameter in the param_dict allowing you to vary the strength of the galaxy concentration bias, using log-linear interpolation for the intermediate values between these control points. conc_mass_model : string or callable, optional Specifies the function used to model the relation between NFW concentration and halo mass. Can either be a custom-built callable function, or one of the following strings: dutton_maccio14, direct_from_halo_catalog. cosmology : object, optional Instance of an astropy cosmology. Default cosmology is set in sim_defaults. redshift : float, optional Default is set in sim_defaults. mdef: str, optional String specifying the halo mass definition, e.g., ‘vir’ or ‘200m’. Default is set in model_defaults. concentration_key : string, optional Column name of the halo catalog storing NFW concentration. This argument is only relevant when conc_mass_model is set to direct_from_halo_catalog. In such a case, the default value is halo_nfw_conc, which is consistent with all halo catalogs provided by Halotools but may differ from the convention adopted in custom halo catalogs. concentration_bins : ndarray, optional Array storing how halo concentrations will be digitized when building a lookup table for mock-population purposes. The spacing of this array sets a limit on how accurately the concentration parameter can be recovered in a likelihood analysis. conc_gal_bias_bins : ndarray, optional Array storing how biases in galaxy concentrations will be digitized when building a lookup table for mock-population purposes. The spacing of this array sets a limit on how accurately the galaxy bias parameter can be recovered in a likelihood analysis. profile_integration_tol : float, optional Default is 1e-5

Examples

>>> biased_nfw = SFRBiasedNFWPhaseSpace()


The behavior of the SFRBiasedNFWPhaseSpace model is controlled by the values stored in its param_dict. In the above default model, we have two parameters that control the concentration of the satellites, quiescent_conc_gal_bias and star_forming_conc_gal_bias. The value of $$F_{\rm q}$$ = quiescent_conc_gal_bias sets the value for the concentration of quiescent satellites according to $$F_{\rm q} * c_{\rm halo},$$ where $$c_{\rm halo}$$ is the value of the halo concentration specified by the concentration-mass model.

By default, $$F_{\rm q} = F_{\rm sf} = 1$$. Quiescent satellites with larger values of $$F_{\rm q}$$ will be more radially concentrated and have smaller radial velocity dispersions, and likewise for star-forming galaxies.

The SFRBiasedNFWPhaseSpace gives you the option to allow $$F_{\rm q}$$ and $$F_{\rm sf}$$ to vary with halo mass. You can accomplish this via the conc_gal_bias_logM_abscissa keyword:

>>> biased_nfw_mass_dep = SFRBiasedNFWPhaseSpace(conc_gal_bias_logM_abscissa=[12., 15.])


In the above model, the values of $$F_{\rm q} = F_{\rm q}(M_{\rm halo})$$ and $$F_{\rm sf} = F_{\rm sf}(M_{\rm halo})$$ can be independently specified at either of the two control points, $$10^{12}M_{\odot}$$ or $$10^{15}M_{\odot}$$. For every element in the input conc_gal_bias_logM_abscissa, there is a correposponding value in the param_dict controlling the value of $$F_{\rm q}$$ and $$F_{\rm sf}$$ at that mass.

For example, in the biased_nfw_mass_dep defined above, to set the value of $$F_{\rm q}(M_{\rm halo} = 10^{15})$$:

>>> biased_nfw_mass_dep.param_dict['quiescent_conc_gal_bias_param1'] = 2


To triple the value of $$F_{\rm sf}(M_{\rm halo} = 10^{12})$$:

>>> biased_nfw_mass_dep.param_dict['star_forming_conc_gal_bias_param0'] *= 3


Values of $$F_{\rm q}$$ and $$F_{\rm sf}$$ at masses between the control points will be determined by log-linear interpolation. When extrapolating $$F_{\rm q}$$ and $$F_{\rm sf}$$ beyond the specified range, the values will be kept constant at the end point values.

Methods Summary

 calculate_conc_gal_bias([seed]) Calculate the ratio of the galaxy concentration to the halo concentration, $$c_{\rm gal}/c_{\rm halo}$$.

Methods Documentation

calculate_conc_gal_bias(seed=None, **kwargs)[source] [edit on github]

Calculate the ratio of the galaxy concentration to the halo concentration, $$c_{\rm gal}/c_{\rm halo}$$.

Parameters: prim_haloprop : array, optional Array storing the mass-like variable, e.g., halo_mvir. If prim_haloprop is not passed, then table keyword argument must be passed. quiescent : array, optional Boolean array storing whether the galaxy is quiescent. Must be passed together with prim_haloprop argument. table : object, optional Table storing the halo catalog. If your NFW model is based on the virial definition, then halo_mvir must appear in the input table, and likewise for other halo mass definitions. If table is not passed, then prim_haloprop and quiescent keyword arguments must be passed. conc_gal_bias : array_like Ratio of the galaxy concentration to the halo concentration, $$F_{\rm gal} = c_{\rm gal}/c_{\rm halo}$$.

Examples

>>> model = SFRBiasedNFWPhaseSpace()
>>> mass = np.logspace(10, 15, 100)
>>> quiescent = np.zeros(100).astype(bool)
>>> quiescent[::2] = True
>>> conc_gal_bias = model.calculate_conc_gal_bias(prim_haloprop=mass, quiescent=quiescent)