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_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 ofxray_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. Seepop_sfrd
below.link:<ID>
: Link the SFRD to population with the givenID
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 thanNone
.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.
php
for “parameterized halo property”. Requirespop_model=True
. See next section for more details on setting thephp_*
parameters. Note that if multiple php’s are being used for a single population, you can use square brackets to attach an ID number, e.g.,pop_fstar=php[0]
andpop_fesc=php[1]
. The square brackets w/ ID numbers must be appended to each of the correspondingphp_*
parameters as well.
Default: 0.1
Note
If you set
fstar
toNone
, the strength of radiation backgrounds will be determined by the \(\xi\) parameters,xi_LW
,xi_XR
, andxi_UV
.pop_sfrd
The star formation rate density (SFRD) as a function of redshift. If provided, will override
Tmin
andMmin
. For example, a constant (co-moving) SFRD of \(1 \ M_{\odot} \ \text{yr}^{-1} \ \text{cMpc}^{-3}\) would besfrd=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 (2016) for further discussion of this.
Radiation Fields¶
pop_sed_model
Treat the SED of this source population in detail?
See Models for Radiation Emitted by Galaxies for more information.
Default:
True
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,
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
isleitherer1999
oreldridge2009
, 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
isleitherer1999
oreldridge2009
, 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
iseldridge2009
, 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]
Parameterized halo properties¶
Parameterized halo properties 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 mirocha2016
option in Parameter Bundles for a concrete example of how these parameters can be used.
php_func
Function adopted. Options include
pl
,dpl
, and many more. See listing below parameter(s)php_func_par[0-5]
.Default:
dpl
php_func_var
Independent variable of
php_func
.- Options:
mass
redshift
Default:
mass
php_func_par[0-5]
Parameters required by
php_func
. Their meaning depends on the type of function employed. See below for meaning of each parameter byphp_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
php_faux
- “Auxiliary function” used to augment
php_func
. php_func_var
Independent variable of
php_faux
.- Options:
mass
redshift
Default:
None
php_faux_meth
Method used to augment
php_func
.- Options:
multiply
add
Default:
multiply
php_faux_par[0-4]
- Parameters required by
php_faux
.
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
andpop_EmaxNorm
. Ifapprox_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 ofcX
.Default: 0.2
Nlw
Number of photons emitted in the Lyman-Werner band per baryon of star formation.
If
fstar
is notNone
, 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
, andfstar
, 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
, andfstar
, 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
andfstar
, as it is defined by:\(\xi_{\mathrm{XR}} \equiv f_{\ast} f_X\)Default: None