HyRex.recomb_functions module

HyRex.recomb_functions.Gamma_compton(xe, TCMB, YHe)

Computes the Compton scattering rate. See Eq.(2) of 1904.09296

Dimensions: s^{-1}

Parameters:

• xe float

  Free electron fraction.

• TCMB float

  CMB temperature, in eV.

• YHe float

  Helium mass fraction.

Returns:

• GammaC float

  The Compton scattering rate

HyRex.recomb_functions.alpha_H(Tm)

Case-B recombination coefficient for hydrogen.

Dimensions: cm^3 s^{-1}

WARNING: Assumes input Tm to be in eV.

Parameters:

• Tm float

  Matter temperature.

Returns:

• alpha_H float

  Case B recombination coefficient for hydrogen at given matter temperature.

HyRex.recomb_functions.beta_H(TCMB)

Case-B photoionization coefficient for hydrogen.

Dimensions: s^{-1}

WARNING: Assumes input TCMB to be in eV.

Parameters:

• TCMB float

  CMB temperature.

Returns:

• beta_H float

  Case B photoionization coefficient for hydrogen at given CMB (radiation) temperature.

HyRex.recomb_functions.effective_coefficients(TCMB, Tm, H, nH, x1s)

Computes the effective coefficients for, Case-B recombination (A2s, A2p), Case-B photoionization (B2s, B2p), and Generalized Peebles factors (C2s, C2p) in the effetive four-level-atom strategy outlined by arXiv:1011.3758.

Dimensions: A2s, A2p : cm^3 s^{-1} B2s, B2p : s^{-1} C2s, C2p : None

Parameters:

• TCMB float

  Current CMB temperature, in eV.

• Tm float

  Current matter temperature, in eV.

• H float

  Current Hubble parameter, in s^{-1}.

• nH float

  Current proton (free+bound) number density, in cm^{-3}.

• x1s float

  Fraction of proton in the 1s bound state.

Returns:

• coefficients tuple (float, float, float, float, float, float, float, float)

  A tuple of the six relevant effective coefficients for the four-level-atom.

HyRex.recomb_functions.peebles_C(z, xHII, H, nH)

Peebles C factor, probability for an n=2 hydrogen atom to reach the ground state before becoming photoionized, a function of redshift and ionized proton fraction.

Dimensions: None

Parameters:

• z float/jnp.array

  Requested redshift(s).

• xHII float

  Ionized hydrogen fraction.

• H float/jnp.array

  Value(s) of Hubble at given redshift(s).

• nH float/jnp.array

  Value(s) of hydrogen number density at given redshift(s)

Returns:

• C float/jnp.array

  Peebles C factor.

HyRex.recomb_functions.xe_Saha(TCMB, nH)

Computes the free electron fraction in the Saha equilibrium approximation, valid at early times when matter and photons are in Chemical Equilibrium.

Parameters:

• TCMB float

  CMB temperature, in eV

• nH float

  Current Hydrogen number density, in cm^{-3}

Returns:

• xe_saha float

  Saha equilibrium prediction of free electron fraction.

• s float

  xe_saha^2/(1-xe_saha)