Parameters for Parameterized QuantitiesΒΆ

Parameterized quantities are most often used in the context of the galaxy luminosity function, where model the efficiency of star formation as a function of halo mass and (perhaps) redshift. See the mirocha2017 option in Parameter Bundles for a concrete example of how these parameters can be used. The basic idea is to provide a framework that enables any parameter to be parameterized more generally as a function of redshift, halo mass, etc. This potential is not yet fully realized, so beware that not all parameters can utilize this functionality!

A more detailed description of the methodology can be found here: The ParameterizedQuantity Framework.

The relevant parameters are:

pq_func

Function adopted. Options include pl, dpl, and many more. See listing below parameter(s) pq_func_par[0-5].

Default: dpl

pq_func_var

Independent variable of pq_func.

Options:

  • mass

  • redshift

Default: mass

pq_func_par[0-5]

Parameters required by pq_func. Their meaning depends on the type of function employed. See below for meaning of each parameter by pq_func and number (\(x\) is either redshift or halo mass in general).

Options:

  • pl: \(p[0] * (x / p[1])^{p[2]}\)

  • dpl: \(p[0] / ((x / p[1])^{-p[2]} + (x / p[1])^{-p[3]})\)

  • dpl_arbnorm: \(p[0](p[4]) / ((x / p[1])^-p[2] + (x / p[1])^-p[3])'\)

  • pwpl: \(p[0] * (x / p[4])^{p[1]}\) if \(x \leq p[4]\) else \(p[2] * (x / p[4])^{p[3]}\)

  • plexp: \(p[0] * (x / p[1])^{p[2]} * np.exp(-x / p[3])\)

  • lognormal: \(p[0] * np.exp(-(logx - p[1])^2 / 2 / p[2]^2)\)

  • astep: \(p[0]\) if \(x \leq p[1]\) else \(p[2]\)

  • rstep: \(p[0] * p[2]\) if \(x \leq p[1]\) else \(p[2]\)

  • plsum: \(p[0] * (x / p[1])^{p[2]} + p[3] * (x / p[4])^{p[5]}\)

Default: None

pq_func_var

Independent variable of pq_faux.

Options:

  • mass

  • redshift

Default: None