Weak Radio and Bright Early Optical Emission in EP260321a: A Comparative Study with XRO 080109 Reveals the Role of Circumstellar Material Mass

Shock breakout (SBO) occurs when a radiation-mediated shock wave, formed during a core-collapse supernova (SN) explosion, breaks out from the stellar surface of the progenitor or from the circumstellar material (CSM), if the CSM is optically thick. The X-ray outburst XRO 080109, associated with a Type Ib/c SN 2008D, has been suggested to be an SBO event from a regular supernova. The recent detection of EP260321a, associated with a broad-lined Type Ic SN 2026gzf, by the Einstein Probe adds a new SBO event. However, the two SBO events differ markedly in their spectra, energetics, late-time radio emission and early optical emission within the first day. We show that the non-detections in radio follow-up observations of EP260321a imply a shock velocity $\lesssim 0.1c$, whereas the radio data of XRO 080109 suggest a shock velocity of $\simeq 0.2c$. These velocities are consistent with those inferred from the properties of the X-ray outbursts and explain the difference in their X-ray spectra. The X-ray energy and duration of EP260321a indicate that the shock breaks out from the CSM at a radius of $\sim 2\times {10}^{13}\mathrm{c}\mathrm{m}$. Its bright optical emission at $t\lesssim 1\mathrm{d}$ can be explained by cooling emission from a dense, extended CSM shell heated by the radiation-mediated shock, requiring a total CSM mass of $\sim 0.06M_{\odot }$, substantially larger than that inferred for XRO 080109. Finally, the lower shock velocity and larger CSM mass can be unified in a picture in which a more massive CSM decelerates the radiation-mediated shock more significantly before it breaks out.