SDSS~J075217.84+193542.2: X-ray weighing of a secondary BH

Precise measurements of black hole (BHs) masses are necessary to understand the coevolution of these sources and their host galaxies. Sometimes in the center of a galaxy there is not one, but two BHs. The BH duality of the quasar nucleus SDSS~J075217.84+193542.2 (herein SDSS~J0752) was recently proposed based on the observed strict periodicity of optical emission from the source. We tested this assumption using X-ray observations with Swift/XRT (2008–2010). We fitted the SDSS~J075217 spectrum using a Comptonization model and discovered soft X-ray variability in the 0.3–10~keV energy range. We pursued a scenario in which two supermassive BHs at the center of SDSS~J0752 form a pair; and the less massive (secondary) BH periodically crosses/punctures the disk around the more massive (primary) BH. We associate these periodic crossings with tidal disruptions of the disk and, as a consequence, with an increase in X-rays seen as a flare in SDSS~J0752. During such an X-ray flare event (2008–2010), we discovered a change in the source spectral states and the photon index saturation at the $\mathrm{\Gamma }\sim 3$ level with mass accretion rate $\dot{M}$. For BH mass scaling we used sources: OJ~287, M101 ULX–1 and HLX–1 ESO~243–49, as a reference ones, and found that M${}_{SDSS}=9\times {10}^7$ solar masses, assuming $d_{SDSS}=500$ Mpc. Thus, we obtained a lower limit to a BH mass due the unknown inclination. In addition, we used the virial mass of the secondary BH based on $H_{\alpha }$-line measurements and we estimated the binary’s inclination at SDSS~J0752, $i={80}^{\circ }$, using a scaling technique.