Are Odd Radio Circles virial shocks around massive galaxies? Implications for cosmic-ray diffusion in the circumgalactic medium

Recently, a new population of circular radio ($\sim$GHz) objects have been discovered at high Galactic latitudes, called the Odd Radio Circles (ORCs). A fraction of the ORCs encircles massive galaxies in the sky with stellar mass $\sim 10^{11}\, M_\odot$ situated at $z=0.2$-$0.6$, suggesting a possible physical connection. In this work, we explore the possibility that these radio circles originate from the accretion shocks/virial shocks around massive ($\gtrsim10^{13}\, M_\odot$) dark matter halo at $z\sim0.5$. We found that the radio flux density of the emitting shell is marginally consistent with the ORCs. We also find that pure advection of electrons from the shock results in a radio-emitting shell that is considerably narrower than the observed one due to strong inverse-Compton cooling of electrons. Instead, we show that the diffusion of cosmic-ray (CR) electrons plays a significant role in increasing the width of the shell. We infer a diffusion coefficient, $D_{\rm cr} \sim 10^{30}\ {\rm cm^2\,s^{-1}}$, consistent with the values expected for low-density circumgalactic medium (CGM). If ORCs indeed trace virial shocks, then our derived CR diffusion coefficient represents one of the few estimations available for the low-density CGM. Finally, we show that the apparent discrepancy between ORC and halo number density can be mitigated by considering an incomplete halo virialization and the limited radiation efficiency of shocks. This study, therefore, opens up new avenues to probe such shocks and non-thermal particle acceleration within them. Furthermore, our results suggest that low-mass galaxies ($\lesssim 10^{13}\, M_\odot$) may not show ORCs due to their significantly lower radio surface brightness.