Contribution of magnetar burst pulsed emission to X-ray detectability of fast radio burst counterparts

In this note we discuss the possibility of detecting accompanying X-ray emission from sources of fast radio bursts with the eROSITA telescope onboard the Spektr-RG observatory. In the previous paper we have shown that during the four years of the survey program about 300 bursts are expected to appear in the field of view of eROSITA. About 1\% of them will be detected by ground based radio telescopes. For the total energy release $\sim~10^{46}$~ergs depending on spectral characteristics and absorption in the interstellar and intergalactic media, an X-ray flare can be detected from distances from $\sim 1$~Mpc (thermal spectrum with $kT=200$~keV and strong absorption) up to $\sim1$~Gpc (power-law spectrum with photon index $\Gamma=2 $ and realistic absorption). In this paper, we refine the model of hyperflares by adding to the main pulse a so-called ``pulsating tail" whose radiation has a relatively soft thermal spectrum ($kT=10$ keV), and the total energy release is $\sim 10^{44}$~erg. This supplement allows to significantly increase the maximum distance at which a burst is registered for some parameters of the flares. Thus, eROSITA observations might help to provide important constraints on parameters of sources of fast radio bursts, or may even allow identification of X-ray transient counterparts, which will help to constrain models of fast radio bursts generation.