zeus21.T21coefficients

Bulk of the Zeus21 calculation:

Determines Lyman-alpha and X-ray fluxes,
Evolves the cosmic-dawn IGM state (WF coupling and heating),
Computes the 21-cm global signal and the effective biases gammaR to determine the 21-cm power spectrum.

Authors: zeus21 v2 collaboration - June 2026

Emily Bregou ; Hector Afonso G. Cruz ; Sarah Libanore ; Julian B. Muñoz ; Yonny Sklansky ; Emilie Thélie ; Alessandra Venditti

arXiv:2302.08506, arXiv:2306.09403, arXiv:2407.18294, Sklansky et al. (in prep)

Classes

`LyAlpha_class`	Determines Lyman-alpha properties and fluxes.
`Xrays_class`	Determines X-ray properties and fluxes.
`get_T21_coefficients`	Loops through SFRD integrals and accounts for LyA coupling and Xray heating to obtain the average T21 and the coefficients for its power spectrum

Module Contents

class zeus21.T21coefficients.LyAlpha_class(UserParams, CosmoParams, AstroParams, HMFinterp, z_Init=None, SFRD_Init=None)[source]

Determines Lyman-alpha properties and fluxes.

Parameters:

UserParams (UserParams class)
CosmoParams (CosmoParams class)
AstroParams (AstroParams class)
HMFinterp (HMFinterp class)
z_Init (Z_init class, optional) – Initial redshift matrices for the calculation (see sfrd.py for details). Default is None.
SFRD_Init (SFRD_class class, optional) – Initial star formation rate density for the calculation (see sfrd.py for details). Default is None.

coeff1LyAzp[source]

Redshift-dependent coefficient in the J_alpha flux computation, see Eq. 29 in arXiv:2302.08506.

Type:: array

coeff2LyAzpRR_II[source]

Coefficient that multiplies the SFRD in the integral for J_alpha for Pop II stars, see Eq. 30 of arXiv:2302.08506.

Type:: array

coeff2LyAzpRR_III

Coefficient that multiplies the SFRD in the integral for J_alpha for Pop III stars.

Type:: array

coeff1LyAzp[source]

coeff2LyAzpRR_II[source]

class zeus21.T21coefficients.Xrays_class(UserParams, CosmoParams, AstroParams, HMFinterp, z_Init=None, SFRD_Init=None)[source]

Determines X-ray properties and fluxes.

Parameters:

UserParams (UserParams class)
CosmoParams (CosmoParams class)
AstroParams (AstroParams class)
HMFinterp (HMFinterp class)
z_Init (Z_init class, optional) – Initial redshift matrices for the calculation (see sfrd.py for details). Default is None.
SFRD_Init (SFRD_class class, optional) – Initial star formation rate density for the calculation (see sfrd.py for details). Default is None.

atomfractions[source]

Fraction of baryons in HI and HeI, assumed to just be the avg cosmic. Used to compute X-ray absorption.

Type:: array

atomEnIon[source]

Threshold energies for HI and HeI, in eV.

Type:: array

TAUMAX[source]

Maximum optical depth, cut to 0 after to avoid overflows.

Type:: float

coeff1Xzp[source]

Redshift-dependent coefficient in the X-ray flux computation, with extra factors to account for adiabatic cooling and the fact that we compute the integral in redshift instead of time.

Type:: array

coeff2XzpRR_II[source]

Coefficient that multiplies the SFRD in the integral for the X-ray flux for Pop II stars

Type:: array

coeff2XzpRR_III

Coefficient that multiplies the SFRD in the integral for the X-ray flux for Pop III stars

Type:: array

_GammaXray_II[source]

X-ray ionization rate for Pop II stars, in s^-1, see Eq. 37 in arXiv:2302.08506

Type:: array

_GammaXray_III[source]

X-ray ionization rate for Pop III stars, in s^-1

Type:: array

coeff_Gammah_Tx_II[source]

Coefficient that multiplies the X-ray ionization rate to get the X-ray heating rate for Pop II stars, in K/s, see Eq. 41 in arXiv:2302.08506.

Type:: array

coeff_Gammah_Tx_III[source]

Coefficient that multiplies the X-ray ionization rate to get the X-ray heating rate for Pop III stars, in K/s

Type:: array

Gammaion_II[source]

X-ray ionization rate for Pop II stars, in s^-1

Type:: array

Gammaion_III[source]

X-ray ionization rate for Pop III stars, in s^-1

Type:: array

_xe_avg_ad

Average ionization fraction of the IGM from adiabatic cooling and recombinations

Type:: array

_xe_avg

Average ionization fraction of the IGM, including both the contribution from UV photons and the partial ionization from X-rays

Type:: array

_fheat[source]

Fraction of X-ray energy that goes into heating, as opposed to ionization

Type:: array

Gammaheat_II[source]

X-ray heating rate for Pop II stars, in K/s

Type:: array

Gammaheat_III[source]

X-ray heating rate for Pop III stars, in K/s

Type:: array

Tk_xray[source]

Average kinetic temperature of the IGM from X-ray heating, in K

Type:: array

Tk_ad[source]

Average kinetic temperature of the IGM from adiabatic cooling only, in K

Type:: array

Tk_avg[source]

Average kinetic temperature of the IGM, including both adiabatic cooling and X-ray heating, in K

Type:: array

sigma_HI[source]

Cross section for X-ray absorption by HI, as a function of energy in eV, in cm^2

Type:: function

sigma_HeI[source]

Cross section for X-ray absorption by HeI, as a function of energy in eV, in cm^2

Type:: function

atomfractions[source]

atomEnIon[source]

TAUMAX = 100.0[source]

coeff1Xzp[source]

coeff2XzpRR_II[source]

coeff_Gammah_Tx_II[source]

coeff_Gammah_Tx_III[source]

Gammaion_II[source]

Gammaion_III[source]

xe_avg_ad[source]

xe_avg[source]

Gammaheat_II[source]

Gammaheat_III[source]

Tk_xray[source]

Tk_ad[source]

Tk_avg[source]

sigma_HI(Energyin)[source]

Cross section for Xray absorption for neutral HI, from astro-ph/9601009

Parameters:: Energyin (float) – Energy in eV
Returns:: Cross section in cm^2.
Return type:: float

sigma_HeI(Energyin)[source]

Cross section for Xray absorption for neutral HI

Parameters:: Energyin (float) – Energy in eV
Returns:: Cross section in cm^2.
Return type:: float

class zeus21.T21coefficients.get_T21_coefficients(UserParams, CosmoParams, AstroParams, HMFinterp, z_Init=None, SFRD_Init=None)[source]

Loops through SFRD integrals and accounts for LyA coupling and Xray heating to obtain the average T21 and the coefficients for its power spectrum

Parameters:

UserParams (object) – User-defined parameters
CosmoParams (object) – Cosmological parameters
AstroParams (object) – Astrophysical parameters
HMFinterp (object) – Halo mass function interpolator

z_Init

Redshift tables for the calculation (see sfrd.py for details)

Type:: object

SFRD_Init

Initial star formation rate density for the calculation (see sfrd.py for details)

Type:: object

USE_POPIII[source]

Whether to include Pop III stars in the calculation or not, determined by AstroParams

Type:: bool

relvel

Relative velocity between baryons and dark matter, which affects the SFRD and therefore the LyA and X-ray fluxes. Only computed if USE_POPIII is True

Type:: object or None

LyA[source]

Lyman-alpha anisotropies, which depend on the SFRD and the redshift tables; see LyAlpha_class for details

Type:: object

Xrays[source]

X-ray anisotropies, which depend on the SFRD and the redshift tables; see Xrays_class for details

Type:: object

ReioGlobal[source]

Global reionization history, which depends on the SFRD and the redshift tables; see reionization.py for details

Type:: object

xHI_avg[source]

Average neutral hydrogen fraction volume-weighted, computed from the global reionization history

Type:: array

T21avg[source]

Average 21cm brightness temperature

Type:: array

tau_reio_val[source]

Optical depth to reionization, computed from the global reionization history and the average neutral hydrogen fraction

Type:: float

__ getattr__

This method allows us to access the attributes of the classes that we initialized directly from the get_T21_coefficients class, without having to specify which class they come from

Type:: method

evolve_T21_fields[source]

Compute evolution of the LyA flux, LyA coupling coefficient, color temperature and spin temperature

Type:: method

Jalpha_avg

Average LyA flux at all redshifts and radii

Type:: array

_coeff_Ja_xa_0

Normalization of the LyA flux at all redshifts

Type:: array

coeff_Ja_xa

LyA flux corrected with Hirata2006 prescription

Type:: array

xa_avg

LyA coupling coefficient

Type:: array

TCMB

CMB temperature at all redshifts

Type:: array

invTcol_avg

Inverse of the color temperature (equal 1/Tk)

Type:: array

_invTs_avg

Inverse of the spin temperature

Type:: array

tau_reio[source]

Compute the optical depth to reionization

Type:: method

Salpha_exp[source]

Hirata2006 correction to the LyA flux (Eq 55 in astro-ph/0608032)

Type:: method

USE_POPIII[source]

LyA[source]

Xrays[source]

ReioGlobal[source]

xHI_avg[source]

T21avg[source]

tau_reio_val[source]

evolve_T21_fields(UserParams, CosmoParams)[source]

Compute evolution of the LyA flux, LyA coupling coefficient, color temperature and spin temperature

Parameters:

UserParams (object) – User-defined parameters
CosmoParams (object) – Cosmological parameters

Return type:

None

tau_reio(CosmoParams, zlist, xHI)[source]

Compute the optical depth to reionization

Parameters:

CosmoParams (object) – Cosmological parameters
zlist (list) – Redshifts
xHI (array) – Neutral fraction as function of redshift

Returns:

tau_reio

Return type:

list

Salpha_exp(z, T, xe)[source]

Hirata2006 correction to the LyA flux (Eq 55 in astro-ph/0608032). This function is used to initialize the xalpha computation, but then overwritten. Only used if FLAG_WF_ITERATIVE == False

Parameters:

z (float) – Redshifts
T (float) – Temperature in K
xe (float) – Free electron fraction with small reionization (xe << 1)

Returns:

Salpha – Correction to the LyA flux

Return type:

float