rabacus.rad_src package¶

Submodules¶

rabacus.rad_src.background module¶

An isotropic background radiation source module.

class rabacus.rad_src.background.BackgroundSource(q_min, q_max, spectrum_type, Nnu=128, segmented=True, px_fit_type='verner', verbose=False, z=None, T_eff=None, alpha=None, user_E=None, user_shape=None)[source]¶

Bases: rabacus.rad_src.source.Source

An isotropic background radiation source class.

Args:

q_min (float): minimum photon energy / Rydbergs [dimensionless]

q_max (float): maximum photon energy / Rydbergs [dimensionless]

spectrum_type (str): the spectral shape {monochromatic, hm12, thermal, powerlaw, user}

Kwargs:

Nnu (int): number of spectral samples, log spaced in energy

segmented (bool): if True, forces spectral samples at H and He ionization thresholds

px_fit_type (str): source to use for photoionization cross section fits {verner}

verbose (bool): verbose screen output?

z (float): redshift, need if spectrum_type = hm12

T_eff (float): effective temperature, need if spectrum_type = thermal

alpha (float): powerlaw index, need if spectrum_type = powerlaw

user_E (array): energy samples for user defined spectrum. should have units of energy.

user_shape (array): shape of user defined spectrum. should be dimensionless

Attributes:

U (Units)

PC (PhysicalConstants)

H (Hydrogen)

He (Helium)

PX (PhotoXsections)

E (array): Spectrum energy samples

lam (array): Spectrum wavelength samples

nu (array): Spectrum frequency samples

q (array): Spectrum energy samples / Rydbergs

Inu (array): Specific intensity $I_{\nu}$

monochromatic (bool): True for monochromatic spectra otherwise False

grey (object): Grey photoionization cross sections and energies. Only created if segmented = True.

log (object): Convenience object storing the log of other attributes

sigma (object): photoionization cross sections and ratios

th (object): all quantities evaluated at ionization thresholds

thin (object): all optically thin quantities

Notes:

The fundamental characterization of the radiation field for this class is the specific intensity $I_{\nu}$ with units of erg/(s cm^2 sr Hz) or units of erg/(s cm^2 sr) for monochromatic spectra. Integrating over frequency and solid angle yields several other useful characterizations of the radiation field which we summarize below.

$F_{u} = 4 \pi \int I_{\nu} d\nu \rightarrow \frac{dF_{u}}{d\nu} = 4 \pi I_{\nu}$

$u = \frac{4 \pi}{c} \int I_{\nu} d\nu \rightarrow \frac{du}{d\nu} = \frac{4 \pi}{c} I_{\nu}$

$F_{n} = 4 \pi \int \frac{I_{\nu}}{h\nu} d\nu \rightarrow \frac{dF_{n}}{d\nu} = 4 \pi \frac{I_{\nu}}{h\nu}$

$n = \frac{4 \pi}{c} \int \frac{I_{\nu}}{h\nu} d\nu \rightarrow \frac{dn}{d\nu} = \frac{4 \pi}{c} \frac{I_{\nu}}{h\nu}$

Variable Description Units Symbol

Inu specific intensity [erg/(s cm^2 sr Hz)] $I_{\nu}$

thin.Fu energy flux [erg/(s cm^2)] $F_{u}$

thin.u energy density [erg/(cm^3)] $u$

thin.Fn photon flux [1/(s cm^2)] $F_{n}$

thin.n photon density [1/(cm^3)] $n$

The photoionization and photoheating rates are also integrals over the specific intensity.

$\Gamma_{\rm _{X}} = 4 \pi \int \frac{ I_{\nu} \sigma_{\rm _{X}} }{h \nu} d\nu \rightarrow \frac{ d\Gamma_{\rm _{X}} }{d\nu} = 4 \pi \frac{ I_{\nu} \sigma_{\rm _{X}} }{h \nu}$

$H_{\rm _{X}} = 4 \pi \int \frac{ I_{\nu} \sigma_{\rm _{X}} }{h \nu} h(\nu - \nu_{\rm _{X}}) d\nu \rightarrow \frac{ dH_{\rm _{X}} }{d\nu} = 4 \pi \frac{ I_{\nu} \sigma_{\rm _{X}} }{h \nu} h(\nu-\nu_{\rm _{X}})$

where $\scriptstyle{\rm X}$ is one of $\{ {\scriptstyle{\rm HI, \, HeI, \, HeII }} \}$ . Note that the $\sigma_{\rm _{X}}$ are frequency dependent photoionization cross sections and the $\nu_{\rm _{X}}$ are (scalar) frequencies that correspond to the ionization energies for a given species. In many applications, we prefer to use energy as a variable instead of frequency. The above equations can easily be recast with a change of variable $E=h\nu$ .

$\Gamma_{\rm _{X}} = 4 \pi \int \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E} dE \rightarrow \frac{ d\Gamma_{\rm _{X}} }{dE} = 4 \pi \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E}$

$H_{\rm _{X}} = 4 \pi \int \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E} (E - E_{\rm _{X}}) dE \rightarrow \frac{ dH_{\rm _{X}} }{dE} = 4 \pi \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E} (E - E_{\rm _{X}})$

where the $E_{\rm _{X}}$ are (scalar) ionization energies.

Variable Description Units Symbol

thin.H1i H1 photo ion. rate [1/s] $\Gamma_{\rm _{HI}}$

thin.He1i He1 photo ion. rate [1/s] $\Gamma_{\rm _{HeI}}$

thin.He2i He2 photo ion. rate [1/s] $\Gamma_{\rm _{HeII}}$

thin.H1h H1 photo heat rate [erg/s] $H_{\rm _{HI}}$

thin.He1h He1 photo heat rate [erg/s] $H_{\rm _{HeI}}$

thin.He2h He2 photo heat rate [erg/s] $H_{\rm _{HeII}}$

In addition, the class provides methods for calculating the shielded photoionization/heating rates given an optical depth.

$\Gamma_{\rm _{X}} = 4 \pi \int \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E} e^{-\tau} dE \rightarrow \frac{ d\Gamma_{\rm _{X}} }{dE} = 4 \pi \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E} e^{-\tau}$

$H_{\rm _{X}} = 4 \pi \int \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E} (E - E_{\rm _{X}}) e^{-\tau} dE \rightarrow \frac{ dH_{\rm _{X}} }{dE} = 4 \pi \frac{ I_{\nu} \sigma_{\rm _{X}} }{h E} (E - E_{\rm _{X}}) e^{-\tau}$

where $\tau = \sum_{\rm _X} \tau_{\rm _X}$ , $\tau_{\rm _X} = N_{\rm _X} \sigma_{\rm _X}$ , $N_{\rm _X}$ are column densities, and $\sigma_{\rm _X}$ are energy dependent photoionization cross sections.

Note

The $\tau_{\rm _X}$ are energy dependent optical depths while the parameters to the shielding functions (shld_H1i(), shld_H1h(), shld_He1i(), shld_He1h(), shld_He2i(), shld_He2h()) are the $\tau_{\rm _X}$ evaluated at the species threhold energy (i.e. scalars).

Function	Description	Units	Symbol
shld_H1i	H1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HI}}$
shld_He1i	He1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeI}}$
shld_He2i	He2 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeII}}$
shld_H1h	H1 photo heat rate	[erg/s]	$H_{\rm _{HI}}$
shld_He1h	He1 photo heat rate	[erg/s]	$H_{\rm _{HeI}}$
shld_He2h	He2 photo heat rate	[erg/s]	$H_{\rm _{HeII}}$

See also

PlaneSource, PointSource

normalize_H1i(H1i)[source]¶

Normalize the spectrum such that the H1 photoionization rate integral yields H1i.

Args:: H1i (float): target photoionization rate

normalize_n(n)[source]¶

Normalize the spectrum such that the number density of photons between q_min and q_max is n.

Args:: n (float): target photon number density

return_attenuation(tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Calculate the attenuation array. First the energy dependence of tau for each absorbing species (H1, He1, He2) is calculated using the input scalar optical depths at the ionization thresholds. Next an energy dependent total tau is calculated and exponentiated to arrive at the attenuation array atten = np.exp(-tau).

Args:

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

atten (array): attenuation as a function of energy

scale_spectrum(fac)[source]¶

Changes normalization of spectrum and recalculates spectral integrands.

Args:: fac (float): multiplicative factor

set_integrands()[source]¶: Defines tabulated functions of photon energy/frequency which represent integrands for optically thin quantities. All attributes defined in this function are integrands of the fundamental quantity, specific intensity or Inu which has units [erg/(s Hz cm^2 sr)].

shld_H1h(tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Integrates spectrum to calculate the HI photoheating rate after passing through a column with optical depth tau

Args:

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

H1h (float): attenuated H1 photoheating rate

shld_H1i(tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Integrates spectrum to calculate the HI photoionization rate after passing through a column with optical depth tau

Args:

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

H1i (float): attenuated H1 photoionization rate

shld_He1h(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeI photoheating rate after passing through a column with optical depth tau.

See also

shld_H1h()

shld_He1i(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeI photoionization rate after passing through a column with optical depth tau.

See also

shld_H1i()

shld_He2h(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeII photoheating rate after passing through a column with optical depth tau.

See also

shld_H1h()

shld_He2i(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeII photoionization rate after passing through a column with optical depth tau.

See also

shld_H1i()

write_to_file(fname, top_group='/')[source]¶

rabacus.rad_src.hm12 module¶

A module for loading the Haardt and Madau 2012 spectral model (see HM12_UVB_Table). The returned spectrum will be normalized as in the HM12 model. Further adjustments to normalization are handled through classes derived from Source.

class rabacus.rad_src.hm12.HM12Spectrum(source, z)[source]¶

Provides the HM12 spectral shape.

Args:

source: a class derived from (Source)

z (float): redshift

rabacus.rad_src.monochromatic module¶

A module for loading monochromatic spectra. This module is only here to conform to the style of the other spectral shapes. Normalization is handled through classes derived from Source.

class rabacus.rad_src.monochromatic.MonochromaticSpectrum(source)[source]¶

Provides a monochromatic shape.

Args:: source: a class derived from (Source)

rabacus.rad_src.plane module¶

An plane parallel radiation source class.

class rabacus.rad_src.plane.PlaneSource(q_min, q_max, spectrum_type, Nnu=128, segmented=True, px_fit_type='verner', verbose=False, z=None, T_eff=None, alpha=None, user_E=None, user_shape=None)[source]¶

Bases: rabacus.rad_src.source.Source

A plane parallel radiation source class.

Args:

q_min (float): minimum photon energy / Rydbergs [dimensionless]

q_max (float): maximum photon energy / Rydbergs [dimensionless]

spectrum_type (str): the spectral shape {monochromatic, hm12, thermal, powerlaw, user}

Kwargs:

Nnu (int): number of spectral samples, log spaced in energy

segmented (bool): if True, forces spectral samples at H and He ionization thresholds

px_fit_type (str): source to use for photoionization cross section fits {verner}

verbose (bool): verbose screen output?

z (float): redshift, need if spectrum_type = hm12

T_eff (float): effective temperature, need if spectrum_type = thermal

alpha (float): powerlaw index, need if spectrum_type = powerlaw

user_E (array): energy samples for user defined spectrum. should have units of energy.

user_shape (array): shape of user defined spectrum. should be dimensionless

Attributes:

U (Units)

PC (PhysicalConstants)

H (Hydrogen)

He (Helium)

PX (PhotoXsections)

E (array): Spectrum energy samples

lam (array): Spectrum wavelength samples

nu (array): Spectrum frequency samples

q (array): Spectrum energy samples / Rydbergs

dFu_over_dnu (array): Energy flux density $dF_{u}/d\nu$

monochromatic (bool): True for monochromatic spectra otherwise False

grey (object): Grey photoionization cross sections and energies. Only created if segmented = True.

log (object): Convenience object storing the log of other attributes

sigma (object): photoionization cross sections and ratios

th (object): all quantities evaluated at ionization thresholds

thin (object): all optically thin quantities

Notes:

The fundamental characterization of the radiation field for this class is the energy flux density $dF_{u}/d\nu$ with units of erg/(s cm^2 Hz) or energy flux $F_{u}$ with units of erg/(s cm^2) for monochromatic spectra. Integrating over frequency yields several other useful characterizations of the radiation field which we summarize below.

$F_{u} = \int \frac{dF_{u}}{d\nu} d\nu$

$u = \frac{1}{c} \int \frac{dF_{u}}{d\nu} d\nu \rightarrow \frac{du}{d\nu} = \frac{1}{c} \frac{dF_{u}}{d\nu}$

$F_{n} = \int \frac{1}{h \nu} \frac{dF_{u}}{d\nu} d\nu \rightarrow \frac{dF_{n}}{d\nu} = \frac{1}{h \nu} \frac{dF_{u}}{d\nu}$

$n = \frac{1}{c} \int \frac{1}{h \nu} \frac{dF_{u}}{d\nu} d\nu \rightarrow \frac{dn}{d\nu} = \frac{1}{c} \frac{1}{h \nu} \frac{dF_{u}}{d\nu}$

Variable	Description	Units	Symbol
dFu_dnu	energy flux density	[erg/(s cm^2 Hz)]	$dF_{u}/d\nu$
thin.Fu	energy flux	[erg/(s cm^2)]	$F_{u}$
thin.u	energy density	[erg/(cm^3)]	$u$
thin.Fn	photon flux	[1/(s cm^2)]	$F_{n}$
thin.n	photon density	[1/(cm^3)]	$n$

The photoionization and photoheating rates are also integrals over the energy flux density.

$\Gamma_{\rm _{X}} = \int \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dF_{u}}{d\nu} d\nu \rightarrow \frac{ d\Gamma_{\rm _{X}} }{d\nu} = \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dF_{u}}{d\nu}$

$H_{\rm _{X}} = \int \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dF_{u}}{d\nu} h(\nu - \nu_{\rm _{X}}) d\nu \rightarrow \frac{ dH_{\rm _{X}} }{d\nu} = \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dF_{u}}{d\nu} h(\nu - \nu_{\rm _{X}})$

where $\scriptstyle{\rm X}$ is one of $\{ {\scriptstyle{\rm HI, \, HeI, \, HeII }} \}$ . Note that the $\sigma_{\rm _{X}}$ are frequency dependent photoionization cross-sections and the $\nu_{\rm _{X}}$ are (scalar) frequencies that correspond to the ionization energies for a given species. In many applications, we prefer to use energy as a variable instead of frequency. The above equations can easily be recast with a change of variable $E=h\nu$ .

$\Gamma_{\rm _{X}} = \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE} dE \rightarrow \frac{ d\Gamma_{\rm _{X}} }{dE} = \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE}$

$H_{\rm _{X}} = \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE} (E - E_{\rm _{X}}) dE \rightarrow \frac{ dH_{\rm _{X}} }{dE} = \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE} (E - E_{\rm _{X}})$

where the $E_{\rm _{X}}$ are (scalar) ionization energies.

Variable	Description	Units	Symbol
thin.H1i	H1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HI}}$
thin.He1i	He1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeI}}$
thin.He2i	He2 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeII}}$
thin.H1h	H1 photo heat rate	[erg/s]	$H_{\rm _{HI}}$
thin.He1h	He1 photo heat rate	[erg/s]	$H_{\rm _{HeI}}$
thin.He2h	He2 photo heat rate	[erg/s]	$H_{\rm _{HeII}}$

In addition, the class provides methods for calculating the shielded photoionization/heating rates given an optical depth.

$\Gamma_{\rm _{X}} = \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE} e^{-\tau} dE \rightarrow \frac{ d\Gamma_{\rm _{X}} }{dE} = \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE}e^{-\tau}$

$H_{\rm _{X}} = \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE} (E - E_{\rm _{X}}) e^{-\tau} dE \rightarrow \frac{ dH_{\rm _{X}} }{dE} = \frac{ \sigma_{\rm _{X}} }{E} \frac{dF_{u}}{dE} (E - E_{\rm _{X}}) e^{-\tau}$

where $\tau = \sum_{\rm _X} \tau_{\rm _X}$ , $\tau_{\rm _X} = N_{\rm _X} \sigma_{\rm _X}$ , $N_{\rm _X}$ are column densities, and $\sigma_{\rm _X}$ are energy dependent photoionization cross sections.

Note

The $\tau_{\rm _X}$ are energy dependent optical depths while the parameters to the shielding functions (shld_H1i(), shld_H1h(), shld_He1i(), shld_He1h(), shld_He2i(), shld_He2h()) are the $\tau_{\rm _X}$ evaluated at the species threhold energy (i.e. scalars).

Function	Description	Units	Symbol
shld_H1i	H1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HI}}$
shld_He1i	He1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeI}}$
shld_He2i	He2 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeII}}$
shld_H1h	H1 photo heat rate	[erg/s]	$H_{\rm _{HI}}$
shld_He1h	He1 photo heat rate	[erg/s]	$H_{\rm _{HeI}}$
shld_He2h	He2 photo heat rate	[erg/s]	$H_{\rm _{HeII}}$

See also

BackgroundSource, PointSource

normalize_Fn(Fn)[source]¶

Normalize the spectrum such that the photon flux between q_min and q_max is Fn.

Args:: Fn (float): target photon flux

normalize_H1i(H1i)[source]¶

Normalize the spectrum such that the H1 photoionization rate integral yields H1i.

Args:: H1i (float): target photoionization rate

normalize_n(n)[source]¶

Normalize the spectrum such that the number density of photons between q_min and q_max is n.

Args:: n (float): target photon number density

return_attenuation(tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Calculate the attenuation array. First the energy dependence of tau for each absorbing species (H1, He1, He2) is calculated using the input scalar optical depths at the ionization thresholds. Next an energy dependent total tau is calculated and exponentiated to arrive at the attenuation array atten = np.exp(-tau).

Args:

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

atten (array): attenuation as a function of energy

scale_spectrum(fac)[source]¶

Changes normalization of spectrum and recalculates spectral integrands.

Args:: fac (float): multiplicative factor

set_integrands()[source]¶: Defines tabulated functions of photon energy/frequency which represent integrands for optically thin quantities. All attributes defined in this function are integrands of the fundamental quantity, energy flux density or dFu_over_dnu which has units [erg/(s cm^2 Hz)].

shld_H1h(tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Integrates spectrum to calculate the HI photoheating rate after passing through a column with optical depth tau

Args:

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

H1h (float): attenuated H1 photoheating rate

shld_H1i(tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Integrates spectrum to calculate the HI photoionization rate after passing through a column with optical depth tau

Args:

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

H1i (float): attenuated H1 photoionization rate

shld_He1h(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeI photoheating rate after passing through a column with optical depth tau.

See also

shld_H1h()

shld_He1i(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeI photoionization rate after passing through a column with optical depth tau.

See also

shld_H1i()

shld_He2h(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeII photoheating rate after passing through a column with optical depth tau.

See also

shld_H1h()

shld_He2i(tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeII photoionization rate after passing through a column with optical depth tau.

See also

shld_H1i()

rabacus.rad_src.point module¶

A point radiation source class.

class rabacus.rad_src.point.PointSource(q_min, q_max, spectrum_type, Nnu=128, segmented=True, px_fit_type='verner', verbose=False, z=None, T_eff=None, alpha=None, user_E=None, user_shape=None)[source]¶

Bases: rabacus.rad_src.source.Source

A point radiation source class.

Args:

q_min (float): minimum photon energy / Rydbergs [dimensionless]

q_max (float): maximum photon energy / Rydbergs [dimensionless]

spectrum_type (str): the spectral shape {monochromatic, hm12, thermal, powerlaw, user}

Kwargs:

Nnu (int): number of spectral samples, log spaced in energy

segmented (bool): if True, forces spectral samples at H and He ionization thresholds

px_fit_type (str): source to use for photoionization cross section fits {verner}

verbose (bool): verbose screen output?

z (float): redshift, need if spectrum_type = hm12

T_eff (float): effective temperature, need if spectrum_type = thermal

alpha (float): powerlaw index, need if spectrum_type = powerlaw

user_E (array): energy samples for user defined spectrum. should have units of energy.

user_shape (array): shape of user defined spectrum. should be dimensionless

Attributes:

U (Units)

PC (PhysicalConstants)

H (Hydrogen)

He (Helium)

PX (PhotoXsections)

E (array): Spectrum energy samples

lam (array): Spectrum wavelength samples

nu (array): Spectrum frequency samples

q (array): Spectrum energy samples / Rydbergs

dLu_over_dnu (array): Energy luminosity density $dL_{u}/d\nu$

monochromatic (bool): True for monochromatic spectra otherwise False

grey (object): Grey photoionization cross sections and energies. Only created if segmented = True.

log (object): Convenience object storing the log of other attributes

sigma (object): photoionization cross sections and ratios

th (object): all quantities evaluated at ionization thresholds

thin (object): all optically thin quantities

Notes:

The fundamental characterization of the radiation field for this class is the energy luminosity density $dL_{u}/d\nu$ with units of erg/(s Hz) or energy luminosity $L_{u}$ with units of erg/s for monochromatic spectra. All quantities except for the luminosity are dependent on radius. We summarize them below,

$F_{u}(r) = \frac{1}{4 \pi r^2} \int \frac{dL_{u}}{d\nu} d\nu$

$u(r) = \frac{1}{c} \frac{1}{4 \pi r^2} \int \frac{dL_{u}}{d\nu} d\nu$

$F_{n}(r) = \frac{1}{4 \pi r^2} \int \frac{1}{h \nu} \frac{dL_{u}}{d\nu} d\nu$

$n(r) = \frac{1}{c} \frac{1}{4 \pi r^2} \int \frac{1}{h \nu} \frac{dL_{u}}{d\nu} d\nu$

Variable	Description	Units	Symbol
dLu_dnu	energy lum. density	[erg/(s Hz)]	$dL_{u}/d\nu$
thin.Fu	energy flux	[erg/(s cm^2)]	$F_{u}$
thin.u	energy density	[erg/(cm^3)]	$u$
thin.Fn	photon flux	[1/(s cm^2)]	$F_{n}$
thin.n	photon density	[1/(cm^3)]	$n$

The photoionization and photoheating rates are also integrals over the energy luminosity density.

$\Gamma_{\rm _{X}}(r) = \frac{1}{4 \pi r^2} \int \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dL_{u}}{d\nu} d\nu \rightarrow \frac{ d\Gamma_{\rm _{X}} }{d\nu} = \frac{1}{4 \pi r^2} \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dL_{u}}{d\nu}$

$H_{\rm _{X}}(r) = \frac{1}{4 \pi r^2} \int \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dL_{u}}{d\nu} h(\nu - \nu_{\rm _{X}}) d\nu \rightarrow \frac{ dH_{\rm _{X}} }{d\nu} = \frac{1}{4 \pi r^2} \frac{ \sigma_{\rm _{X}} }{h \nu} \frac{dL_{u}}{d\nu} h(\nu - \nu_{\rm _{X}})$

where $\scriptstyle{\rm X}$ is one of $\{ {\scriptstyle{\rm HI, \, HeI, \, HeII }} \}$ . Note that the $\sigma_{\rm _{X}}$ are frequency dependent photoionization cross-sections and the $\nu_{\rm _{X}}$ are (scalar) frequencies that correspond to the ionization energies for a given species. In many applications, we prefer to use energy as a variable instead of frequency. The above equations can easily be recast with a change of variable $E=h\nu$ .

$\Gamma_{\rm _{X}}(r) = \frac{1}{4 \pi r^2} \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE} dE \rightarrow \frac{ d\Gamma_{\rm _{X}} }{dE} = \frac{1}{4 \pi r^2} \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE}$

$H_{\rm _{X}}(r) = \frac{1}{4 \pi r^2} \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE} (E - E_{\rm _{X}}) dE \rightarrow \frac{ dH_{\rm _{X}} }{dE} = \frac{1}{4 \pi r^2} \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE} (E - E_{\rm _{X}})$

where the $E_{\rm _{X}}$ are (scalar) ionization energies.

Variable	Description	Units	Symbol
thin.H1i	H1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HI}}$
thin.He1i	He1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeI}}$
thin.He2i	He2 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeII}}$
thin.H1h	H1 photo heat rate	[erg/s]	$H_{\rm _{HI}}$
thin.He1h	He1 photo heat rate	[erg/s]	$H_{\rm _{HeI}}$
thin.He2h	He2 photo heat rate	[erg/s]	$H_{\rm _{HeII}}$

In addition, the class provides methods for calculating the shielded photoionization/heating rates given an optical depth.

$\Gamma_{\rm _{X}}(r) = \frac{1}{4 \pi r^2} \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE} e^{-\tau} dE \rightarrow \frac{ d\Gamma_{\rm _{X}} }{dE} = \frac{1}{4 \pi r^2} \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE} e^{-\tau}$

$H_{\rm _{X}}(r) = \frac{1}{4 \pi r^2} \int \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE} (E - E_{\rm _{X}}) e^{-\tau} dE \rightarrow \frac{ dH_{\rm _{X}} }{dE} = \frac{1}{4 \pi r^2} \frac{ \sigma_{\rm _{X}} }{E} \frac{dL_{u}}{dE} (E - E_{\rm _{X}}) e^{-\tau}$

where $\tau = \sum_{\rm _X} \tau_{\rm _X}$ , $\tau_{\rm _X} = N_{\rm _X} \sigma_{\rm _X}$ , $N_{\rm _X}$ are column densities, and $\sigma_{\rm _X}$ are energy dependent photoionization cross sections.

Note

The $\tau_{\rm _X}$ are energy dependent optical depths while the parameters to the shielding functions (shld_H1i(), shld_H1h(), shld_He1i(), shld_He1h(), shld_He2i(), shld_He2h()) are the $\tau_{\rm _X}$ evaluated at the species threhold energy (i.e. scalars).

Function	Description	Units	Symbol
shld_H1i	H1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HI}}$
shld_He1i	He1 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeI}}$
shld_He2i	He2 photo ion. rate	[1/s]	$\Gamma_{\rm _{HeII}}$
shld_H1h	H1 photo heat rate	[erg/s]	$H_{\rm _{HI}}$
shld_He1h	He1 photo heat rate	[erg/s]	$H_{\rm _{HeI}}$
shld_He2h	He2 photo heat rate	[erg/s]	$H_{\rm _{HeII}}$

See also

BackgroundSource, PlaneSource

normalize_Ln(Ln)[source]¶

Normalize spectrum such that the photon luminosity is Ln.

Args:: Ln (float): target photon luminosity

normalize_Lu(Lu)[source]¶

Normalize spectrum such that the energy luminosity is Lu.

Args:: Lu (float): target energy luminosity

return_attenuation(tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Calculate the attenuation array. First the energy dependence of tau for each absorbing species (H1, He1, He2) is calculated using the input scalar optical depths at the ionization thresholds. Next an energy dependent total tau is calculated and exponentiated to arrive at the attenuation array atten = np.exp(-tau).

Args:

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

atten (array): attenuation as a function of energy

scale_spectrum(fac)[source]¶

Changes normalization of spectrum and recalculates spectral integrands.

Args:: fac (float): multiplicative factor

set_integrands()[source]¶: Defines tabulated functions of photon energy/frequency which represent integrands for optically thin quantities. All attributes defined in this function are integrands of the fundamental quantity, energy luminosity density or dLu_over_dnu which has units [erg/(s Hz)].

shld_H1h(r, tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Integrates spectrum to calculate the HI photoheating rate after passing through a column with optical depth tau

Args:

r (float): radial distance from point source

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

H1h (float): attenuated H1 photoheating rate

shld_H1i(r, tauH1_th, tauHe1_th, tauHe2_th)[source]¶

Integrates spectrum to calculate the HI photoionization rate after passing through a column with optical depth tau

Args:

r (float): radial distance from point source

tauH1_th (float): H1 optical depth at the H1 ionizing threshold

tauHe1_th (float): He1 optical depth at the He1 ionizing threshold

tauHe2_th (float): He2 optical depth at the He2 ionizing threshold

Returns:

H1i (float): attenuated H1 photoionization rate

shld_He1h(r, tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeI photoheating rate after passing through a column with optical depth tau.

See also

shld_H1h()

shld_He1i(r, tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeI photoionization rate after passing through a column with optical depth tau.

See also

shld_H1i()

shld_He2h(r, tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeII photoheating rate after passing through a column with optical depth tau.

See also

shld_H1h()

shld_He2i(r, tauH1_th, tauHe1_th, tauHe2_th)[source]¶: Integrates spectrum to calculate the HeII photoionization rate after passing through a column with optical depth tau.

See also

shld_H1i()

rabacus.rad_src.powerlaw module¶

A module for loading powerlaw spectra. This module is only concerned with the shape of the spectrum. Normalization is handled through classes derived from Source.

class rabacus.rad_src.powerlaw.PowerlawSpectrum(source, alpha)[source]¶

Provides a powerlaw shape.

Args:

source: a class derived from (Source)

alpha (float): powerlaw index

rabacus.rad_src.source module¶

Module for source base class.

class rabacus.rad_src.source.Source[source]¶

Base class for radiation sources. Derive specific radiation source classes from this class. Cannot be directly instantiated. Note that all derived source classes call initialize() when they are instanciated.

initialize(q_min, q_max, spectrum_type, Nnu, segmented, px_fit_type, verbose, z, T_eff, alpha, user_E, user_shape)[source]¶

Perform general initialization.

Args:

q_min (float): minimum photon energy / Rydbergs [dimensionless]

q_max (float): maximum photon energy / Rydbergs [dimensionless]

spectrum_type (str): the spectral shape {monochromatic, hm12, thermal, powerlaw, user}

Nnu (int): number of spectral samples, log spaced in energy

segmented (bool): if True, forces spectral samples at H and He ionization thresholds

px_fit_type (str): source to use for photoionization cross section fits {verner}

verbose (bool): verbose screen output?

z (float): redshift, need if spectrum_type = hm12

T_eff (float): effective temperature, need if spectrum_type = thermal

alpha (float): powerlaw index, need if spectrum_type = powerlaw

user_E (array): energy samples for user defined spectrum. should have units of energy.

user_shape (array): shape of user defined spectrum. should be dimensionless

set_photon_arrays(q_min, q_max, Nnu, segmented)[source]¶

Creates wavelength, frequency, and energy arrays for the spectrum.

Args:

q_min (float): minimum photon energy / Rydbergs [dimensionless]

q_max (float): maximum photon energy / Rydbergs [dimensionless]

Nnu (int): number of spectral samples, log spaced in energy

segmented (bool): if True, forces spectral samples at H and He ionization thresholds

validate_spectrum_type()[source]¶: Performs check to make sure the input is compatible with the source type.

rabacus.rad_src.species module¶

A module supplying containers for groups of ions.

class rabacus.rad_src.species.AbsorbingSpecies[source]¶: Photoabsorbing species in primordial chemistry models, $\{ {\scriptstyle{\rm HI, \, HeI, \, HeII }} \}$ .

class rabacus.rad_src.species.RecombiningSpecies[source]¶: Recombining species in primoridial chemistry model, $\{ {\scriptstyle{\rm HII, \, HeII, \, HeIII }} \}$ .

rabacus.rad_src.thermal module¶

A module for loading blackbody spectra. This module is only concerned with the shape of the spectrum. Normalization is handled through classes derived from Source.

class rabacus.rad_src.thermal.ThermalSpectrum(source, T_eff)[source]¶

Provides a blackbody shape.

Args:

source: a class derived from (Source)

T_eff (float): blackbody temperature

Module contents¶

A package containing classes which represent sources of radiation. To create a source, one needs to choose a geometry class and a spectral shape. The choices for geometry are:

(PointSource)
(PlaneSource)
(BackgroundSource)

When creating a source, instantiate a geometric source class and indicate the spectral shape by setting the argument spectrum_type equal to one of {monochromatic, powerlaw, thermal, hm12}. Note that the spectral shape does not determine the normalization of the spectrum, therefore classes will be returned with an arbitrary normalization. The exception is the Haardt & Madau 2012 model which is returned with the normalization native to the model. Each geometric class contains methods to (re)normalize the spectrum.

Segmented Spectra¶

By default, the spectra created for sources will be segmented. This means that an exactly uniform spacing of the energy samples in log energy space will be sacrificed to guarantee that samples exist at the ionization thresholds of neutral hydrogen, neutral helium, and singly ionized helium ( $E_{\rm _{HI}}$ , $E_{\rm _{HeI}}$ , $E_{\rm _{HeII}}$ ). If one tries to create a segmented spectrum in which the energy samples do not cover the range between $E_{\rm _{HI}}$ and $E_{\rm _{HeII}}$ (see the q_min and q_max variables) an error will occur.

Grey Quantities¶

Frequency averaged or “grey” quantities will be calculated for any segmented spectrum. We show an example for the BackgroundSource class here, but the principle is the same for all source types. The grey photoionization cross sections are defined as follows,

$\sigma_{\rm _{HI}}^{\rm grey} = \frac{ \int_{\nu_{\rm HI}}^{\nu_{\rm HeI}} I_{\nu} \sigma_{\rm _{HI}} \frac{d\nu}{\nu} }{ \int_{\nu_{\rm HI}}^{\nu_{\rm HeI}} I_{\nu} \frac{d\nu}{\nu} }, \quad \sigma_{\rm _{HeI}}^{\rm grey} = \frac{ \int_{\nu_{\rm HeI}}^{\nu_{\rm HeII}} I_{\nu} \sigma_{\rm _{HeI}} \frac{d\nu}{\nu} }{ \int_{\nu_{\rm HeI}}^{\nu_{\rm HeII}} I_{\nu} \frac{d\nu}{\nu} }, \quad \sigma_{\rm _{HeII}}^{\rm grey} = \frac{ \int_{\nu_{\rm HeII}}^{\nu_{\rm max}} I_{\nu} \sigma_{\rm _{HeII}} \frac{d\nu}{\nu} }{ \int_{\nu_{\rm HeII}}^{\nu_{\rm max}} I_{\nu} \frac{d\nu}{\nu} }$

We can implicitly define a grey frequency and therefore a grey energy,

$\sigma_{\rm _{HI}}( \nu_{\rm _{HI}}^{\rm grey} ) = \sigma_{\rm _{HI}}^{\rm grey}, \quad E_{\rm _{HI}}^{\rm grey} = h \nu_{\rm _{HI}}^{\rm grey}$

where similar relationships hold for the helium ions.

Examples¶

The following code will create a point source with a photon luminosity of 5.0e48 photons per second and a 1.0e5 K blackbody spectrum between 1 and 5 Rydbergs:

import rabacus as ra
q_min = 1.0; q_max = 5.0; T_eff = 1.0e5 * ra.U.K
pt_t1e5 = ra.rad_src.PointSource( q_min, q_max, 'thermal', T_eff=T_eff )
pt_t1e5.normalize_Ln( 5.0e48 / ra.U.s )

The following code will create a uniform background source with a spectral shape given by the model of Haardt and Madau 2012 at redshift 3 between 1 and 400 Rydbergs:

import rabacus as ra
q_min = 1.0; q_max = 4.0e2; z=3.0
bgnd_hm12 = ra.rad_src.BackgroundSource( q_min, q_max, 'hm12', z=z ) 