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 $\dot{m}\equiv \dot{M}/(MH)$ 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 $\dot{m}\xi_e\sim0.6\%$ inferred from the Fermi signal yields $\xi_B\simeq (2\text{--}9)\%$, 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.