Module double_compton

Double Compton (DC) scattering: γ + e → γ + γ + e

Photon-number-changing process that dominates at z > few × 10⁵. In the soft photon limit, DC emission creates low-frequency photons that drive the spectrum toward a Planck distribution.

The DC emission coefficient: K_DC(x, θ_z, θ_e) = (4α/3π) θ_z² g_dc(x, θ_z, θ_e)

where g_dc is the DC Gaunt factor including relativistic corrections.

References:

• Lightman (1981) — original DC coefficient
• Chluba, Sazonov & Sunyaev (2007), A&A 468, 785 [arXiv:0705.3033]
• Chluba & Sunyaev (2012), MNRAS 419, 1294 [Eq. 10-13]

Functions

dc_emission_coefficient

DC emission coefficient K_DC(x, θ_z, θ_e).

dc_emission_coefficient_fast

Fast DC emission coefficient using precomputed x-independent prefactor.

dc_gaunt_factor

DC Gaunt factor in the soft photon limit with relativistic corrections.

dc_heating_integral

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

dc_high_freq_suppression

High-frequency suppression factor for DC emission.

dc_prefactor

Precompute the x-independent DC prefactor: (4α/3π) θ_z² × I₄^pl / (1 + 14.16 θ_z)