Abstract :

The inner regions of an accretion disk around a black hole produce X-rays which sometimes vary in time as Quasi-periodic Oscillations (QPOs), whose frequencies must correspond to some characteristic time-scale of the system associated with perhaps the inner truncated disk radius. These time-scales probe the strong gravitational field of the black hole. However, this identification has been difficult since one needs to simultaneously measure the inner radius (through broadband spectral studies) and the QPO frequency. With AstroSat, HXMT, and NICER observation of three black hole X-ray binary sources, GRS 1915+105, MAXI J1535-571, and H1743-322, we report on the variation of the QPO frequency with inner radius and accretion rate inferred by fitting relativistic spectral models. We find that the frequency varies just as the dynamic frequency ( i.e. the inverse of the sound crossing time r/c s (r)) as predicted decades ago by the relativistic standard accretion disk theory.