Measuring the Innermost Stable Circular Orbits of Supermassive Black Holes

Abstract

We present a promising new technique, the g-distribution method, for measuring the inclination angle (i), the innermost stable circular orbit (ISCO), and the spin of a supermassive black hole. The g-distribution method uses measurements of the energy shifts in the relativistic iron line emitted by the accretion disk of a supermassive black hole due to microlensing by stars in a foreground galaxy relative to the g-distribution shifts predicted from microlensing caustic calculations. We apply the method to the gravitationally lensed quasars RX J1131−1231 (z s = 0.658, z l = 0.295), QJ 0158−4325 (z s = 1.294, z l = 0.317), and SDSS 1004+4112 (z s = 1.734, z l = 0.68). For RX J1131−1231 our initial results indicate that r ISCO < ∼ 8.5 gravitational radii (r g ) and i > ∼ 76• . We detect two shifted Fe lines, in several observations, as predicted in our numerical simulations of caustic crossings. The current ∆E-distribution of RX J1131−1231 is sparsely sampled but further X-ray monitoring of RX J1131−1231 and other lensed quasars will provide improved constraints on the inclination angles, ISCO radii and spins of the black holes of distant quasars.

Constraining X-Ray Coronal Size with Transverse Motion of AGN Ultra-fast Outflows

“…It has been reported by observations of micro-lensed QSOs that X-ray-emitting (coronal) region in QSOs is indeed compact (r/R g < ∼ 10; e.g. Morgan et al 2008;MacLeod et al 2015;Chartas et al 2017) consistent with our result. More specifically, the observed broad iron lines of Seyfert 1s seem to require a very steep emissivity (e.g.…”

A dynamic black hole corona in an active galaxy through X-ray reverberation mapping

“…It is unique in that the shape of the variability (visualised as power spectral density -PSD) is also time-dependent, varying on days timescales 7,8 . This short-timescale variability is observed in most AGN, which -along with gravitational microlensing observations of quasars 16 -indicates that the X-rays are emerging from a region within the central ~15 + (where + = "# / 0 is the gravitational radius, G is the gravitational constant and c is the speed of light). At a distance of nearly a billion light years, such regions have an angular size on the sky too small to be resolved using present or planned instruments.…”

“…We produce background-subtracted light curves in the 0.3-1.0 keV (soft) and 1.2-5.0 keV (hard) bands (see 7 for more details). Details of the broadband spectral analysis can be found in 11,16 . The spectral modelling includes a component for the observed ultrafast outflow.…”

Confirmation of Planet-mass Objects in Extragalactic Systems

“…Thus, SDSS J1004+4112 and Q J0158−4325 are the best targets to model the line shift rates induced by microlensing after the well-monitored lens RX J1131−1231. These line energy shifts can be ascribed to a differential magnification of a section of the emission region bearing a range of g values as a caustic transits the innermost disk, thereby resulting in the variation of observed Fe Kα line profile (Popović et al 2003(Popović et al , 2006Chartas et al 2017;Ledvina et al 2018). To calculate the line shift rate, we first identify the peak (g peak ) of the g distribution by a fitting a Gaussian to the distribution, yielding g peak = 0.923 for SDSS J1004+4112 and g peak = 1.017 for Q J0158−4325 ( Figure 1).…”

“…To calculate the line shift rate, we first identify the peak (g peak ) of the g distribution by a fitting a Gaussian to the distribution, yielding g peak = 0.923 for SDSS J1004+4112 and g peak = 1.017 for Q J0158−4325 ( Figure 1). For this purpose, we use the lines detected at > 90% confidence level (See Table 6 and Table 7 of Chartas et al (2017)). The significance of the line energy shift from the peak is determined for each detected lines using their respective measured energies and uncertainties.…”