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Recently, a new population of circular radio ($\sim$GHz) objects have beendiscovered at high Galactic latitudes, called the Odd Radio Circles (ORCs). Afraction 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 possiblephysical connection. In this work, we explore the possibility that these radiocircles originate from the accretion shocks/virial shocks around massive($\gtrsim10^{13}\, M_\odot$) dark matter halo at $z\sim0.5$. We found that theradio flux density of the emitting shell is marginally consistent with theORCs. We also find that pure advection of electrons from the shock results in aradio-emitting shell that is considerably narrower than the observed one due tostrong inverse-Compton cooling of electrons. Instead, we show that thediffusion of cosmic-ray (CR) electrons plays a significant role in increasingthe width of the shell. We infer a diffusion coefficient, $D_{\rm cr} \sim10^{30}\ {\rm cm^2\,s^{-1}}$, consistent with the values expected forlow-density circumgalactic medium (CGM). If ORCs indeed trace virial shocks,then our derived CR diffusion coefficient represents one of the few estimationsavailable for the low-density CGM. Finally, we show that the apparentdiscrepancy between ORC and halo number density can be mitigated by consideringan incomplete halo virialization and the limited radiation efficiency ofshocks. This study, therefore, opens up new avenues to probe such shocks andnon-thermal particle acceleration within them. Furthermore, our results suggestthat low-mass galaxies ($\lesssim 10^{13}\, M_\odot$) may not show ORCs due totheir significantly lower radio surface brightness.

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