Photon-dark photon oscillation in M87 and Crab Nebula environments

TL;DR

This work studies resonant photon-DP oscillations in magnetized, inhomogeneous plasmas around compact objects to bound the DP-photon kinetic mixing $\epsilon$ without assuming DP DM. It develops a two-state formalism, including vacuum, monotonic, and non-monotonic potentials, with a special treatment for coalescing resonances via Airy-based methods. Applying the framework to M87* (LOFAR data) and the Crab Nebula (radio SED), it shows that non-monotonic density structures can amplify conversion, yielding $\epsilon\sim7\times10^{-6}$ at $m_{A'}\sim5\times10^{-7}$ eV for M87* and $\epsilon\sim8\times10^{-7}$ at $m_{A'}\sim4\times10^{-9}$ eV for the Crab Nebula; these bounds surpass many existing astrophysical limits in realistic plasmas. While laboratory and cosmological bounds remain stronger at comparable masses, the results highlight the discovery potential of structured plasma environments, especially in systems with strong magnetic fields such as magnetars. The approach also has broader implications for other two-state oscillation phenomena in astrophysical plasmas and could extend to multiple spectral bands and angular resonances.

Abstract

Compact astrophysical systems such as neutron stars and black holes provide powerful laboratories for testing feebly coupled dark photons (DPs). We investigate light DPs kinetically mixed with the visible photon that need not be the dark matter, focusing on resonant photon-DP oscillations in magnetized, modeled plasma environments. We show that realistic non-monotonic plasma density profiles generically enhance resonant conversion relative to monotonic models, leading to substantially stronger constraints on the photon-DP kinetic mixing parameter ($ε$). Using spectral data from the supermassive black hole (SMBH) M87*, extending to the LOFAR band, we derive a bound $ε\simeq 7\times10^{-6}$ at the DP mass $m_{A'} \simeq 5\times10^{-7}\,\mathrm{eV}$ for oscillation distance $3r_{\rm ph}$, where $r_{\rm ph}$ denotes the photon sphere radius. From the Crab pulsar-wind Nebula, we obtain an even stronger constraint, $ε\simeq 8\times10^{-7}$ at $m_{A'} \simeq 4\times10^{-9}\,\mathrm{eV}$ for oscillation baselines of order $10^{3}\,\mathrm{km}$, surpassing existing astrophysical limits in realistic plasma backgrounds. While laboratory and cosmological bounds remain slightly stronger at comparable masses, observation of compact objects with larger surface magnetic fields and measurements of photon spectra at lower frequencies would enhance the limits on the photon-DP coupling by orders of magnitude.

Figures (5)

• Figure 1: Conversion probability $P_{a\leftrightarrow n}/\epsilon^{2}$ for photon-DP mixing. Left Panel: Probability as a function of distance for a monotonic power-law plasma profile (red) showing a single resonance near the photon-sphere radius, and for a non-monotonic log-normal profile (blue) exhibiting two resonant locations. Right Panel: Probability plotted against the mass-deviation parameter $\delta m$, computed using the multiple-level-crossing approximation Eq. \ref{['app39']} and evaluated at the plasma peak $r_m=z_{c}$.
• Figure 2: DP-photon conversion probability $P_{a\leftrightarrow n}$ as a function of the deviation parameter $\delta m$ in the Crab pulsar magnetosphere. The curves correspond to oscillation distances of $r_{0}=250\,\mathrm{km}$ (red) and $r_{0}=500\,\mathrm{km}$ (blue), computed for $m_{\rm crit}=10^{-7}\,\mathrm{eV}$ and a photon energy of $4\times10^{-5}\,\mathrm{eV}$. The pronounced oscillatory structure originates from the non-monotonic magnetospheric potential, whereas in the $\delta m \ll 1$ regime, the probability approaches a constant value, reflecting the need for the approximate expression Eq. \ref{['app39']} in the multiple-level crossing scenario.
• Figure 3: Left panel: Intrinsic and DP-modified radio spectrum of the M87* SMBH environment, using LOFAR data. The solid curve shows the distorted spectrum for the benchmark parameters $m_{A'} = 1.38\times10^{-13}\,\mathrm{eV}$ and $\epsilon = 2\times10^{-3}$. Right Panel: Intrinsic and DP-modified spectrum of the Crab Nebula. The red curve corresponds to the benchmark point $m_{A'} = 5\times10^{-7}\,\mathrm{eV}$ and $\epsilon = 10^{-7}$. Both panels illustrate how DP-photon conversion alters the radio continuum relative to the intrinsic emission models.
• Figure 4: Constraints on the kinetic mixing parameter $\epsilon$ as a function of the DP mass $m_{A'}$. The purple dashed and dot-dashed curves correspond to the cases where the DP-photon oscillation occurs near the photon sphere $(r_0 = 5\,r_{\rm ph})$ and at $1$ kpc scales, respectively, assuming a monotonic plasma profile. The dotted purple curve shows the limits obtained using the large-scale plasma density from the TNG300 simulation. The filled purple region indicates the parameter space excluded at the $95\%$ C.L. from the LOFAR radio observations. The red solid curve represents the constraint for a non-monotonic plasma profile near the SMBH, where multiple level crossings enhance the conversion probability. For comparison, other astrophysical and laboratory bounds are shown which are taken from the AxionLimits database AxionLimits.
• Figure 5: Constraints on the kinetic mixing parameter $\epsilon$ from the Crab pulsar: Left panel: The $95\%$ exclusion limits for an oscillation distance of $z = 200\,\mathrm{km}$. Right panel: The $95\%$ exclusion limits for an oscillation distance of $z = 1000\,\mathrm{km}$. The solid blue curves represent the bounds obtained using the non-monotonic effective potential generated by the combined plasma and QED contributions in the Crab magnetosphere. Dashed and dot-dashed curves denote projected sensitivities for enhanced magnetic field strengths $B_0 = 10\,B_c$ and $B_0 = 1000\,B_c$, respectively. Existing astrophysical limits from stellar cooling and CAST, very high energy gamma-ray observations from Crab Nebula, together with laboratory constraints as well as cosmological bounds from COBE/FIRAS, are included for comparison and are taken from the AxionLimits database AxionLimits.