Population Parameters

Basic Properties

pop_zform

Redshift when sources “turn on.”

Default: 50

pop_zdead

Population will not contribute to radiation backgrounds after this redshift.

Default: 0

pop_lw_src

Sources contribute to Lyman-Werner background? Only relevant if LW feedback is turned on.

Default: True

pop_lya_src

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

Default: True

pop_ion_src_cgm

Sources contribute to growth of HII regions?

Default: True

pop_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

pop_heat_src_igm

Sources emit X-rays and heat bulk IGM?

Default: True

pop_solve_rte

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

Options: bool, list, tuple

Default: False

Star formation history

The following parameters control the star-formation history of a population. See Models for Star Formation in Galaxies for more information.

pop_sfr_model

Value determines how star-formation history is computed.

Options:
  • fcoll: Relate SFRD to rate of collapse onto halos above minimum virial temperature (pop_Tmin) or mass (pop_Mmin) threshold assuming constant efficiency of star formation (pop_fstar).
  • sfe-func: Model star formation efficiency as function halo mass and (perhaps) redshift. See next section for more details.
  • sfrd-func: User-supplied function of redshift. See pop_sfrd below.
  • link:<ID>: Link the SFRD to population with the given ID number (in <>’s).
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.

Options:
  • Any number between 0 and 1.
  • pq for “parameterized halo property”. Requires pop_model=True. See next section for more details on setting the pq_* parameters. Note that if multiple PQ’s are being used for a single population, you can use square brackets to attach an ID number, e.g., pop_fstar=pq[0] and pop_fesc=pq[1]. The square brackets w/ ID numbers must be appended to each of the corresponding pq_* parameters as well.

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. Also must set ``pop_sfrd_units=’msun/yr/mpc^3’ (see below).

Default: None

pop_sfrd_units

Sets the units of the parametric form for the SFRD (pop_sfrd).

Options:
  • msun/yr/mpc^3 for \(M_{\odot} \ \text{yr}^{-1} \ \text{cMpc}^{-3}\)
  • g/s/cm^3

Default: g/s/cm^3

pop_calib_L1600
If not None, this parameter will guarantee that the \(1600\AA\) luminosity (per unit star formation) is fixed at the provided value. This can be useful if, for example, you’re modeling the galaxy luminosity function (LF) and want to change the stellar population model while preserving the LF. See Section 3.4 of Mirocha, Furlanetto, & Sun (2017) for further discussion of this.

Radiation Fields

pop_sed_model

Treat the SED of this source population in detail? If True, it means that we use parameters like pop_sed, pop_Emin, pop_Emax, etc. in order to set the overall normalization of the emission. If False, parameters like pop_Nlw, pop_Nion, and pop_fX are used instead of pop_rad_yield.

See Models for Radiation Emitted by Galaxies for more information.

Default: True

pop_rad_yield

How many photons are emitted per unit star formation?

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

pop_rad_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_sed

Spectral energy distribution assumed for this population.

Options:

  • 'bb': blackbody. If supplied, pop_temperature sets assumed blackbody temperature.
  • 'pl': power-law. If supplied, pop_alpha parameter sets power-law index.
  • 'mcd'; Multi-color disk (Mitsuda et al. 1984)
  • 'simpl': SIMPL Comptonization model (Steiner et al. 2009)
  • 'qso': Quasar template spectrum (Sazonov et al. 2004)
  • leitherer1999: Stellar population synthesis models from the original starburst99 dataset.
  • eldridge2009: Stellar population synthesis models from BPASS version 1.0 models.
pop_Z

If pop_sed is leitherer1999 or eldridge2009, this is the stellar metallicity assumed for the synthesis models. Can take on values in the range \(0.001 \leq Z \leq 0.04\).

Default: 0.02 (solar)

pop_imf

If pop_sed is leitherer1999 or eldridge2009, this is the stellar initial mass function used.

Default: 2.35 (Salpeter)

pop_nebular

Whether or not to include nebular emission.

Default: False

pop_ssp

Whether or not to assume a “simple stellar population,” i.e., an instantaneous burst of star formation. If False, assumes continuous star formation.

Default: False

pop_binaries

If pop_sed is eldridge2009, this dictates whether binary systems are included in the model.

Default: False

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