halomod.hod.Leauthaud11

class halomod.hod.Leauthaud11(central: bool = False, cosmo=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), cm_relation: CMRelation | None = None, profile: Profile | None = None, mdef: BaseMassDefinition | None = <hmf.halos.mass_definitions.SOMean object>, **model_parameters)[source]

Bases: HODPoisson

A 16-parameter HOD model based on Leauthaud et al. (2011).

This model was adapted from halotools library: https://halotools.readthedocs.io/.

The following implementation allows for redshift evolution of central occupation parameters, smhm_m0_0, smhm_m1_0, smhm_beta_0, smhm_delta_0 and smhm_gamma_0 (‘0’ indicates redshift, z=0) controlled by the parameters smhm_m0_a, smhm_m1_a, smhm_beta_a, smhm_delta_a and smhm_gamma_a, respectively.

However, it is entirely possible to not use the redshift evolution aspect of this HOD by setting all the parameters ending with “_a” to ‘0’ (default). This results in the basic 11-parameter Leauthaud11 HOD. Then, the parameters like “smhm_delta_0” no longer corresponds to z=0 as mentioned below. The “redshift” parameter also becomes meaningless, in that case.

Lastly, all of the calculations here assume h=1 units. The user can simply convert back to a particular cosmology, for instance, after running an MCMC analysis.

e.g. The characteristic stellar mass, smhm_m0_0 in h=0.7 units corresponds to smhm_m0_0 - 2*(np.log10(0.7)) assuming that the stellar mass scales as 1/(h^2). This inverse-squared scaling is true for stellar masses derived from scaled luminosity. Similarly, the characteristic halo mass, smhm_m1_0 in h=0.7 units is smhm_m1_0 - (np.log10(0.7)) assuming that the halo mass scales as 1/h.

Note that all <Ncen> model parameter defaults are set to the column 2 values in Table 2 of Behroozi et al. (2010). All <Nsat> model parameters set according to the SIG_MOD1 values of Table 5 of arXiv:1104.0928 for the lowest redshift bin.

Parameters:

  • redshift (float, default = 0.0) – Redshift at which the HOD is evaluated. This controls the redshift evolution of the central occupation parameters, smhm_m0_0, smhm_m1_0, smhm_beta_0, smhm_delta_0 and smhm_gamma_0.

  • sm_thresh (float, default = 9.0) – Base-10 logarithm of the stellar mass threshold for the HOD in h=1 units.

  • smhm_m0_0 (float, default = 10.72) – Characteristic Stellar Mass in the SHMR at z=0. <Ncen>

  • smhm_m0_a (float, default = 0.0) – Redshift evolution of the characteristic Stellar Mass. <Ncen>

  • smhm_m1_0 (float, default = 12.35) – Characteristic Halo Mass in the SHMR at z=0. <Ncen>

  • smhm_m1_a (float, default = 0.0) – Redshift evolution of the characteristic Halo Mass. <Ncen>

  • smhm_beta_0 (float, default = 0.43) – Faint end slope in the SHMR at z=0. <Ncen>

  • smhm_beta_a (float, default = 0.0) – Redshift evolution of the faint end slope. <Ncen>

  • smhm_delta_0 (float, default = 0.56) – Controls massive end slope in the SHMR at z=0. <Ncen>

  • smhm_delta_a (float, default = 0.0) – Redshift evolution of the massive end slope. <Ncen>

  • smhm_gamma_0 (float, default = 1.54) – Controls the transition regime in the SHMR at z=0. <Ncen>

  • smhm_gamma_a (float, default = 0.0) – Redshift evolution of the transition. <Ncen>

  • sig_logmstar (float, default = 0.206) – Log-normal scatter in Stellar Mass at fixed Halo Mass. <Ncen>

  • alphasat (float, default = 1.0) – Power law slope of the satellite occupation function. <Nsat>

  • betasat (float, default = 0.859) – Slope of the scaling of Msat. <Nsat>

  • bsat (float, default = 10.62) – Normalization of the scaling of Msat. <Nsat>

  • betacut (float, default = -0.13) – Slope of the scaling of Mcut. <Nsat>

  • bcut (float, default = 1.47) – Normalization of the scaling of Mcut. <Nsat>

central_condition_inherent = False
central_occupation(m)

The occupation function of the central component.

cs_pairs(m)

The average amount of the tracer coupled with itself in haloes of mass m, <T_c T_s>.

classmethod get_models() → dict[str, type]

Get a dictionary of all implemented models for this component.

mean_log_halo_mass(log_stellar_mass)[source]

Return the halo mass of a central galaxy as a function of the stellar mass.

Parameters:

log_stellar_mass (array) – Array of base-10 logarithm of stellar masses in h=1 units.

Returns:

log_halo_mass – Array containing 10-base logarithm of halo mass in h=1 units.

Return type:

array_like

mean_log_stellar_mass(m)[source]

Return the stellar mass of a central galaxy as a function of the input table.

Parameters:

m (array) – Array of halo masses in h=1 units upon which the corresponding stellar masses must be calculated based on the SHMR set by the HOD parameters.

Returns:

log_stellar_mass – Array containing log10 of stellar masses in h=1 units living in the input table.

Return type:

array_like

property mmin

Defines a reasonable minimum mass to set for this HOD to converge when integrated.

nc(m)

Amplitude of central tracer per tracer source.

ns(m)

Amplitude of satellite tracer per tracer source.

satellite_occupation(m)

The occupation function of the satellite (or profile-dependent) component.

sharp_cut = False
sigma_central(m)

The standard deviation of the central tracer amount in haloes of mass m.

sigma_satellite(m)

The standard deviation of the satellite tracer amount in haloes of mass m.

ss_pairs(m)

The average amount of the tracer coupled with itself in haloes of mass m, <T_s T_s>.

total_occupation(m)

The total (average) occupation of the halo.

total_pair_function(m)

The total weight of the occupation paired with itself.

unit_conversion(cosmo, z)

A factor to convert the total occupation to a desired unit.