Resonant Photon-Axion Mixing Driven by Dark Matter Oscillations

TL;DR

This work identifies a new driven resonance in photon–axion mixing induced by coherently oscillating axion dark matter. Using Floquet theory, the authors show that a periodic axion background in a magnetic field generates a series of sidebands, enabling resonant transitions when $Δ_γ-Δ_a≈n m_a$, even away from static level crossing. The analysis reduces to effective two-level, driven systems with Rabi oscillations and yields polarization signatures, notably stochastic circular polarization, that emerge from the driven mixing. Numerical applications to blazar 3C 279 illustrate observable imprints and provide illustrative bounds on $g_{aγ}$ across a range of $m_a$, highlighting the banded resonance structure as a hallmark of the mechanism and suggesting a general framework for wave propagation in time-dependent backgrounds.

Abstract

Wave propagation in periodically time-dependent media can exhibit driven mode conversion that is absent in static or adiabatic descriptions. We show that photon propagation through a coherent axion dark matter background provides a natural realization of such driven dynamics. In the presence of a magnetic field, the oscillating axion field acts as a coherent temporal drive, inducing resonant photon-axion conversion when the mismatch between their dispersion relations is compensated by integer harmonics of the axion oscillation frequency, $Δ_γ- Δ_a \approx n m_a$ with $n \in \mathbb{Z}$. This driven resonance enables efficient mixing far from the conventional level-crossing regime and disappears entirely upon time averaging, explaining why it is missed in standard treatments. The process constitutes a unitary mode-conversion phenomenon that preserves the axion dark matter number density and is distinct from parametric instabilities or axion decay. A systematic description is naturally provided by Floquet theory. We develop a general framework for photon propagation in oscillating axion backgrounds and show that the resulting resonant mixing leads to characteristic polarization signatures, with potential implications for astrophysical observations such as blazar polarization.

Figures (4)

• Figure 1: Photon--axion conversion probability $P_{\gamma \to a}$ along a representative blazar jet. The blue line shows the case of driven Floquet mixing with oscillating DM background, while the orange line indicates standard adiabatic conversion with static DM background. Vertical red dashed lines mark locations where $\Delta_\gamma(r) - \Delta_a \approx n m_a$.
• Figure 2: Illustrative bound on the axion--photon coupling $g_{a\gamma}$ derived from 3C 279 optical polarimetry. The shaded region indicates parameters excluded by the non-observation of excess circular polarization. The driven mixing mechanism gives rise to a distinctive band structure in parameter space, directly reflecting the discrete Floquet resonance condition $\Delta_\gamma - \Delta_a \approx n m_a$.
• Figure S1: Empirical cumulative distribution function (ECDF) of the photon-to-axion conversion probability $P_{\gamma\to a}$. The colors represent different fluctuation correlation lengths $L_{\rm fluc}$, ranging from $10^{-3}$ to $1$ pc. Panels (a) and (b) correspond to stochastic fluctuations in the electron density and magnetic field, respectively. Solid and dashed lines distinguish between driven Floquet mixing with oscillating DM background and adiabatic conversion with static DM background. Each curve is generated from $N=1000$ random realizations. Note that the $x$-axis is on a logarithmic scale.
• Figure S2: Probability density of induced circular polarization for various axion masses $m_a$ (assuming $g_{a\gamma}=5\times10^{-11}\,\mathrm{GeV}^{-1}$), estimated via Kernel Density Estimation (KDE) by uniformly sampling the axion phase $\varphi_a\in[0,2\pi]$. The shaded profiles are generated using Gaussian kernels with Scott’s rule bandwidths. The transition from single-peaked to double-peaked distributions illustrates the varying sensitivity of the conversion process to the axion phase across different mass regimes.