Module bremsstrahlung

Bremsstrahlung (free-free) emission and absorption.

Photon-number-changing process: e + ion → e + ion + γ. Dominates over double Compton at lower redshifts (z < few × 10⁵).

The BR emission coefficient: K_BR(x, θ_e) = (α λ_e³ / (2π√(6π))) θ_e^{-7/2} e^{-xφ}/φ³ Σ_i Z_i² N_i g_ff(Z_i, x, θ_e)

In the code, we express this as a rate per Thomson scattering time τ: K_BR(x) = prefactor × Σ_i Z_i² (N_i/N_e) g_ff(Z_i, x, θ_e)

References:

• Karzas & Latter (1961) — original Gaunt factors
• Itoh et al. (2000) — relativistic thermal BR fits
• Chluba & Sunyaev (2012), MNRAS 419, 1294 [Eq. 14]
• Chluba, Ravenni & Bolliet (2020), MNRAS 492, 177 (BRpack)

Structs

BrPrecomputed

Precomputed x-independent BR factors for use in the grid loop.

Functions

br_emission_coefficient

BR emission coefficient K_BR at frequency x.

br_emission_coefficient_fast

Fast BR emission coefficient using precomputed x-independent factors.

br_emission_coefficient_fast_preln

Fast BR emission coefficient with precomputed ln(x).

br_emission_coefficient_with_he

BR emission coefficient with pre-computed He ionization fractions.

br_heating_integral

BR emission rate integrated over frequency (for electron temperature equation).

br_precompute

Precompute x-independent BR factors.

gaunt_ff_nr

Non-relativistic thermally-averaged free-free Gaunt factor.