Constraining Dark Photon Dark Matter with Radio Silence from Soliton Mergers around Supermassive Black Holes

We place the first constraints on the dark matter fraction contained within dark photon solitons using the absence of their predicted radio-frequency signatures, or radio silence, following mergers around supermassive black holes. In these dense environments, spiky dark matter density profiles can form that enhance the soliton merger rate. We present a novel estimate of this rate by incorporating both the steepened dark matter profile and the soliton velocity dispersion via the Jeans equation. For galaxies with an initial profile $\rho_\mathrm{DM} \propto r^{-1}$, we find the total merger rate across redshifts $0 \leq z \leq 4$ to be $\Gamma_{\text{merg}}^{\text{TOTAL}} \lesssim 10^{-7}f^2_{\text{DM}}\,\text{Mpc}^{-3}\,\text{day}^{-1}$, where $f_\mathrm{DM}$ is the solitonic fraction of dark matter. This enhanced rate leads to more major merger events in which the generated soliton has a mass exceeding a critical threshold, leading to its decay via the parametric resonance phenomenon that produces brief, narrowband, and energetic radio bursts detectable by fast radio burst surveys. Comparing our predictions with the non-observation of such events, we already obtain $f_\mathrm{DM} \lesssim 10^{-1}$ from the first fast radio burst study. This constraint is strengthened to $f_\mathrm{DM} \lesssim 10^{-2}$ from the Parkes HTRU survey, with CHIME projected to tighten this to $f_\mathrm{DM} \lesssim 10^{-3}$. For larger $f_\mathrm{DM}$, we instead constrain the effective coupling strength between the dark and visible sectors to lie outside $10^{-18}\,\mathrm{GeV^{-1}} \lesssim g \lesssim 10^{-8}\,\mathrm{GeV^{-1}}$ for dark photon masses in the range $10^{-6}\,\mathrm{eV} \lesssim m \lesssim 10^{-4}\,\mathrm{eV}$. Our results establish astrophysical transients as powerful probes of dark sectors, opening a window onto the detectability of ultralight vector fields.