Population Parameters

Basic Properties

formation_epoch

Redshift interval over which sources are “on.”

Default: (50, 0)

is_lya_src

Sources contribute to Ly-\(\alpha\) background?

Default: True

is_ion_src_cgm

Sources contribute to growth of HII regions?

Default: True

is_ion_src_igm

Sources contribute ionization in bulk IGM?

If approx_xrb=True, this ionization rate assumes a mean X-ray photon energy of xray_Eavg, which is 500 eV by default.

Default: True

is_heat_src_igm

Sources emit X-rays and heat bulk IGM?

Default: True

solve_rte

Solve the cosmological radiative transfer equation (RTE) in detail?

Options: bool, list, tuple

Default: False

Star formation history

pop_Tmin

Minimum virial temperature of star-forming halos.

Default: \(10^4\) [Kelvin]

pop_Mmin

Minimum mass of star-forming halos. Will override Tmin if set to something other than None.

Default: None [\(M_{\odot}\)]

pop_fstar

Star formation efficiency, \(f_{\ast}\), i.e., fraction of collapsing gas that turns into stars.

Default: 0.1

Note

If you set fstar to None, the strength of radiation backgrounds will be determined by the \(\xi\) parameters, xi_LW, xi_XR, and xi_UV.

pop_sfrd

The star formation rate density (SFRD) as a function of redshift. If provided, will override Tmin and Mmin. For example, a constant (co-moving) SFRD of \(1 \ M_{\odot} \ \text{yr}^{-1} \ \text{cMpc}^{-3}\) would be sfrd=lambda z: 1.0.

Default: None [\(M_{\odot} \ \text{yr}^{-1} \ \text{cMpc}^{-3}\)]

Radiation Fields

pop_yield

How many photons are emitted per unit star formation?

Default: \(2.6 \times 10^{39}\)

pop_yield_units

How to normalize the yield?

Options: erg/s/SFR [i.e., \(\mathrm{erg} \ \mathrm{s}^{-1} \ (M_{\odot} \ \mathrm{yr}^{-1})^{-1}\)], photons/baryon, photons/Msun

Default: erg/s/SFR

Internally, all units are cgs, which means at run-time all yields will be converted to units of \(\mathrm{erg} \ \mathrm{g}^{-1}\).

These parameters of course dictate an amount of energy produced per unit star formation in a particular band. That band is specified by the pop_EminNorm and pop_EmaxNorm parameters.

pop_EminNorm

Minimum photon energy to consider in normalization.

Default: 200 [eV]

pop_EmaxNorm

Maximum photon energy to consider in normalization.

Default: 3e4 [eV]

To be precise,

\[\int_{\texttt{pop_EminNorm}}^{\texttt{pop_EmaxNorm}} \frac{\epsilon_{\nu}}{\dot{\rho}_{\ast}} d\nu = \frac{\texttt{pop_yield}}{\texttt{pop_yield_units}}\]

where \(\epsilon_{\nu}\) is the emissivity of the population and \(\dot{\rho}_{\ast}\) is the star-formation rate density (SFRD).

This range does not necessarily determine the band in which photons are emitted. For example, you might want to normalize the emission in the 0.5-8 keV band (e.g., if you’re adopting the \(L_X\)-SFR relation), but allow sources to emit at all energies. To do so, you must choose an SED, which then gets used to extrapolate the 0.5-8 keV yield to lower/higher energies.

We use square brackets on this page to denote the units of parameters.

pop_type

Options:

• 'bb': blackbody
• 'pl': power-law
• 'mcd'; Multi-color disk (Mitsuda et al. 1984)
• 'simpl': SIMPL Comptonization model (Steiner et al. 2009)
• 'qso': Quasar template spectrum (Sazonov et al. 2004)

pop_Emin

Minimum photon energy to consider in radiative transfer calculation.

Default: 200 [eV]

pop_Emax

Maximum photon energy to consider in radiative transfer calculation.

Default: 3e4 [eV]

For backward compatibility

There are many parameters that do not have the pop_ prefix attached to them, but are nonetheless convenient because they are the most common parameters in fiducial global 21-cm models. In addition, in ares version 0.1, the pop_ formulation was not yet in place, and the following parameters were the norm. They can still be used for problem_type=101 (see Problem Types), but one should be careful otherwise.

cX

Normalization of the X-ray luminosity to star formation rate (\(L_X\)-SFR) relation in band given by pop_EminNorm and pop_EmaxNorm. If approx_xrb=1, this represents the X-ray luminosity density per unit star formation, such that the heating rate density will be equal to \(\epsilon_X = f_{X,h} c_X f_X \times \text{SFR}\).

Default: \(3.4 \times 10^{40}\) [\(\text{erg} \ \text{s}^{-1} \ (M_{\odot} \ \mathrm{yr}^{-1})^{-1}\)]

fX

Constant multiplicative factor applied to cX, which is typically chosen to match observations of nearby star-forming galaxies, i.e., fX parameterizes ignorance in redshift evolution of cX.

Default: 0.2

Nlw

Number of photons emitted in the Lyman-Werner band per baryon of star formation.

If fstar is not None, the co-moving LW luminosity density is given by \(f_{\ast} N_{\mathrm{LW}} \text{SFRD}\).

Default: 9690

Nion

Number of ionizing photons emitted per baryon of star formation.

Default: 4000

fesc

Escape fraction of ionizing radiation.

Default: 0.1

xi_UV

Ionizing efficiency, \(\xi_{\mathrm{UV}}\). If supplied, overrides fesc, Nion, and fstar, as it is defined by:

\(\xi_{\mathrm{UV}} \equiv f_{\ast} f_{\mathrm{esc}} N_{\mathrm{ion}}\)

Default: None

xi_LW

Lyman-Werner efficiency, \(\xi_{\mathrm{LW}}\). If supplied, overrides Nlw, and fstar, as it is defined by:

\(\xi_{\mathrm{LW}} \equiv f_{\ast} N_{\mathrm{LW}}\)

Default: None

xi_XR

X-ray efficiency, \(\xi_{\mathrm{XR}}\). If supplied, overrides fX and fstar, as it is defined by:

\(\xi_{\mathrm{XR}} \equiv f_{\ast} f_X\)

Default: None