Synchrotron emission from virial shocks around stacked OVRO-LWA galaxy clusters

Galaxy clusters accrete mass through large scale, strong, structure-formation shocks. Such a virial shock is thought to deposit fractions ${\xi }_e$ and ${\xi }_B$ of the thermal energy in cosmic-ray electrons (CREs) and magnetic fields, respectively, thus generating a leptonic virial ring. However, the expected synchrotron signal was not convincingly established until now. We stack low-frequency radio data from the OVRO-LWA around the 44 most massive, high latitude, extended MCXC clusters, enhancing the ring sensitivity by rescaling clusters to their characteristic, $R_{500}$ radii. Both high (73 MHz) and co-added low ($36\text{–}68\text{ MHz}$) frequency channels separately indicate a significant ($4\text{–}5\sigma$) excess peaked at $(2.4\text{–}2.6)R_{500}$, coincident with a previously stacked Fermi $\gamma$-ray signal interpreted as inverse-Compton emission from virial-shock CREs. The stacked radio signal is well fit (TS-test: $4$–$6\sigma$ at high frequency, $4$–$8\sigma$ at low frequencies, and $8$–$10\sigma$ joint) by virial-shock synchrotron emission from the more massive clusters, with $\dot{m}{\xi }_e{\xi }_B\simeq (1\text{–}4)\times {10}^{-4}$, where $\dot{m}\equiv \dot{M}\mathrm{/}(MH)$ is the dimensionless accretion rate for a cluster of mass $M$ and a Hubble constant $H$. The inferred CRE spectral index is flat, $p\simeq 2.0\pm 0.2$, consistent with acceleration in a strong shock. Assuming equipartition or using $\dot{m}{\xi }_e\sim 0.6\mathrm{\%}$ inferred from the Fermi signal yields ${\xi }_B\simeq (2\text{–}9)\mathrm{\%}$, corresponding to $B\simeq (0.1\text{–}0.3)\mu \text{G}$ magnetic fields downstream of typical virial shocks. Preliminary evidence suggests non-spherical shocks, with factor $2$–$3$ elongations.