HyRex.helium module

class HyRex.helium.helium_model(lna_axis_4Heequil, integration_spacing=0.0005, Nsteps=800, Nsteps_postSahaHe=4000, z0=8000.0, z1=20.0)[source]

Bases: Module

Helium recombination model implementation.

Computes helium ionization fraction evolution through multiple phases: HeII+III equilibrium, post-Saha HeII expansion, and full HeII recombination.

Attributes:

integration_spacing float
Step size in log scale factor for integration
lna_axis_4Heequil array
Log scale factor grid for HeII+III equilibrium phase
concrete_axis_size array
Pre-allocated array for HeII full recombination phase
concrete_axis_size_postSahaHe array
Pre-allocated array for post-Saha HeII expansion phase

Methods:

get_helium_history :
Compute full helium recombination history (units: dimensionless)
xesaha_HeII_III :
Compute HeII+III equilibrium phase (units: dimensionless)
post_saha_xHeII :
Compute post-Saha HeII expansion (units: dimensionless)
solve_HeII_full :
Solve full HeII recombination (units: dimensionless)
xHeII_post_Saha :
Compute HeII fraction in post-Saha regime (units: dimensionless)
xH1_Saha :
Compute neutral hydrogen fraction in Saha equilibrium (units: dimensionless)
helium_dxHeIIdlna :
Compute HeII recombination rate (units: dimensionless)
xe_derivative_HeII :
Compute HeII derivative for ODE integration (units: dimensionless)

get_helium_history(h, omega_b, omega_cdm, Neff, YHe, rtol=1e-06, atol=1e-09, solver=Kvaerno3(), max_steps=1024)[source]

Compute complete helium recombination history through all phases.

Sequentially computes helium ionization fraction through HeII+III equilibrium, post-Saha HeII expansion, and full HeII recombination phases.

Parameters:

h float
Hubble parameter
omega_b float
The baryon density Omega_b h^2
omega_cdm float
The density of Cold Dark Matter Omega_cdm h^2
Neff float
Effective number of neutrinos
YHe float
Helium fraction
rtol float, optional
Relative tolerance for ODE solver (default: 1e-6)
atol float, optional
Absolute tolerance for ODE solver (default: 1e-9)
solver diffrax.Solver, optional
ODE solver instance (default: Kvaerno3())
max_steps int, optional
Maximum solver steps (default: 1024)

Returns:

tuple: (xe_4He, lna_4He) containing helium ionization fraction evolution and log scale factor grid

helium_dxHeIIdlna(xe, lna, h, omega_b, omega_cdm, Neff, YHe)[source]

Compute HeII recombination rate.

Calculates rate of change of HeII ionization fraction including detailed atomic physics and escape probabilities.

Parameters:

xe float
Current total ionization fraction
lna float
Log scale factor
h float
Hubble parameter
omega_b float
The baryon density Omega_b h^2
omega_cdm float
The density of Cold Dark Matter Omega_cdm h^2
Neff float
Effective number of neutrinos
YHe float
Helium fraction

Returns:

float: HeII recombination rate dxHeII/dlna (units: dimensionless)

post_saha_xHeII(starting_lna, h, omega_b, omega_cdm, Neff, YHe, threshold=1e-05)[source]

Compute post-Saha HeII expansion phase.

Calculates ionization fraction including corrections to Saha equilibrium until deviations exceed threshold.

Parameters:

starting_lna float
Initial log scale factor
h float
Hubble parameter
omega_b float
The baryon density Omega_b h^2
omega_cdm float
The density of Cold Dark Matter Omega_cdm h^2
Neff float
Effective number of neutrinos
YHe float
Helium fraction
threshold float, optional
Threshold for deviation from Saha (default: 1e-5)

Returns:

tuple: (xe_output, lna_output) - ionization fraction and log scale factor arrays

solve_HeII_full(starting_lna, xe0, h, omega_b, omega_cdm, Neff, YHe, rtol=1e-06, atol=1e-09, solver=Kvaerno3(), max_steps=1024)[source]

Solve full HeII recombination evolution.

Integrates HeII recombination including detailed atomic physics until HeII fraction becomes negligible.

Parameters:

starting_lna float
Initial log scale factor
xe0 float
Initial ionization fraction
h float
Hubble parameter
omega_b float
The baryon density Omega_b h^2
omega_cdm float
The density of Cold Dark Matter Omega_cdm h^2
Neff float
Effective number of neutrinos
YHe float
Helium fraction
rtol float, optional
Relative tolerance (default: 1e-6)
atol float, optional
Absolute tolerance (default: 1e-9)
solver diffrax.Solver, optional
ODE solver (default: Kvaerno3())
max_steps int, optional
Maximum steps (default: 1024)

Returns:

tuple: (xe_output, lna_output) - ionization fraction and log scale factor arrays

xH1_Saha(lna, omega_b, YHe)[source]

Compute neutral hydrogen fraction in Saha equilibrium.

Calculates neutral hydrogen fraction assuming Saha equilibrium between hydrogen ionization and recombination.

Parameters:

lna float
Log scale factor
omega_b float
The baryon density Omega_b h^2
YHe float
Helium fraction

Returns:

float: Neutral hydrogen fraction (units: dimensionless)

xHeII_post_Saha(lna, omega_b, YHe)[source]

Compute HeII fraction in post-Saha regime.

Calculates HeII fraction using Saha equilibrium between HeI and HeII.

Parameters:

lna float
Log scale factor
h float
Hubble parameter
omega_b float
The baryon density Omega_b h^2
omega_cdm float
The density of Cold Dark Matter Omega_cdm h^2
Neff float
Effective number of neutrinos
YHe float
Helium fraction

Returns:

float: HeII fraction (units: dimensionless)

xe_derivative_HeII(lna, state, args)[source]

Compute HeII derivative for ODE integration.

Derivative function for HeII ionization fraction evolution used in ODE integration with diffrax.

Parameters:

lna float
Log scale factor
state float
Current HeII ionization state
args tuple
h, omega_b, omega_cdm, Neff, YHe, omega_rad; the Hubble parameter, the baryon denisty Omega_b h^2, the CDM density Omega_cdm h^2, the effecgive number of neutrinos, the helium fraction, and the radiation energy density (determined by Neff and can be computed by cosmology.omega_rad0(Neff))

Returns:

float: Time derivative of HeII fraction (units: dimensionless)

xesaha_HeII_III(lna_axis, omega_b, YHe, threshold=1e-09)[source]

Compute xe in HeII+III equilibrium phase.

Calculates ionization fraction assuming equilibrium between HeII and HeIII until HeIII fraction drops below threshold.

Parameters:

lna_axis array
Log scale factor grid
omega_b float
The baryon density Omega_b h^2
YHe float
Helium fraction
threshold float, optional
Threshold for HeIII fraction to stop calculation (default: 1e-9)

Returns:

tuple: (xe_output, lna_output) - ionization fraction and log scale factor arrays