General relativistic analysis of the periodicity uncovered by Leibowitz in X-ray flare sequences from Sgr A*

In a recent series of papers, Leibowitz revealed two pacemaker frequencies associated with flares observed near the Sgr A* location: one for X-ray flares and the other for IR (infrared) flares. He proposed an astrophysical model to account for these two frequencies, involving a unique body orbiting the Sgr A* black hole (supposed nonrotating) close to its last stable circular orbit. In the framework of this model, the Roche lobe contacts the star’s surface near the periastrons, which generates matter pullouts. The resulting X events are then separated by time intervals that are close to integer multiples of the radial orbital frequency, which explains the X pacemaker. One revisits this X sequence orbiting-body interpretation but in a full general relativistic framework, which is more appropriate than the pseudo-Newtonian Paczyński-Wiita potential approach used by Leibowitz. One concludes that no main sequence (or giant) star can survive the tidal effects, whereas no pullout matter is possible for white dwarfs (or neutron stars), on the orbits compatible with the X pacemaker frequency, even if large eccentricities are allowed. This confirms the result obtained by Leibowitz (on the impossibility of a main sequence or usual compact star, since the only solution he found involves an “unusual internal structure star”) but (1) in the framework of full relativistic calculations and (2) extending the result to the eccentric case.