Module dark_photon

Helpers for dark photon (γ ↔ A’) conversion in the narrow-width approximation.

The canonical way to model γ ↔ A’ resonant conversion in the PDE solver is crate::energy_injection::InjectionScenario::DarkPhotonResonance, which takes (ε, m_{A’}) and internally calls gamma_con / resonance_redshift to install the impulsive depletion Δn(x) = -[1 - exp(-γ_con/x)] × n_pl(x) at z_start = z_res.

The 1/x factor in that IC captures the frequency dependence of the conversion probability P(x) ∝ 1/ω for ultrarelativistic photons.

References:

• Mirizzi, Redondo & Sigl (2009), JCAP 0903, 026
• Chluba, Cyr & Johnson (2024), MNRAS 535, 1874
• Arsenadze et al. (2025), JHEP 03, 018

Functions

dln_omega_pl_sq_dlna

|d ln ω_pl² / d ln a| at redshift z. Centered finite difference in z.

gamma_con

NWA dark-photon conversion parameter γ_con (dimensionless).

plasma_frequency_ev

Photon plasma frequency ω_pl (in eV) at redshift z.

resonance_redshift

Resonance redshift z_res where ω_pl(z_res) = m.