Testing the Shock-cooling Emission Model from Star-Disk Collisions for Quasiperiodic Eruptions

Quasiperiodic eruptions (QPEs), the repeated outbursts observed in soft X-ray bands, have attracted broad interest, but their physical origin is under debate. One of the popular models, the star-disk collision model, suggests that QPEs can be produced through periodic collisions of an orbiting star with the accretion disk of a central black hole (BH). However, previous tests of the star-disk collision model mainly focus on the timing analysis. Other observed properties, such as peak luminosities $L_{\rm{p}}$, durations $t_{\rm{e}}$, and radiation temperatures $T_{\rm{p}}$ of the eruptions, are not systematically investigated. For a sample of six QPE sources and two QPE-like sources, we test the shock-cooling emission model from star-disk collisions by using these observables to derive the constraints on the stellar radius $R_\star$. We find that, except for two sources (eRO-QPE3 and eRO-QPE4), the rest of the sample either has no allowed $R_\star$ to simultaneously reproduce the observed $L_{\rm{p}}$ and $t_{\rm{e}}$, or the required $R_\star$ is too large to avoid being disrupted by the central BH. For the two exceptions, a stellar radius of the order of $1\ R_{\rm{\odot}}$ is necessary to satisfy all the constraints. Another issue with the simplest version of this model is that it predicts $k T_{\rm{p}} \sim 10\ \rm{eV}$, one order of magnitude lower than the observed value.