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Register a new userSizes and Temperature Profiles of Quasar Accretion Disks from Chromatic Microlensing
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Jeffrey A. Blackburne
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Microlensing perturbations to the flux ratios of gravitationally lensed quasar images can vary with wavelength because of the chromatic dependence of the accretion disks apparent size. Multiwavelength observations of microlensed quasars can thus constrain the temperature profiles of their accretion disks, a fundamental test of an important astrophysical process which is not currently possible using any other method. We present single-epoch broadband flux ratios for 12 quadruply lensed quasars in eight bands ranging from 0.36 to 2.2 microns, as well as Chandra 0.5--8 keV flux ratios for five of them. We combine the optical/IR and X-ray ratios, together with X-ray ratios from the literature, using a Bayesian approach to constrain the half-light radii of the quasars in each filter. Comparing the overall disk sizes and wavelength slopes to those predicted by the standard thin accretion disk model, we find that on average the disks are larger than predicted by nearly an order of magnitude, with sizes that grow with wavelength with an average slope of ~0.2 rather than the slope of 4/3 predicted by the standard thin disk theory. Though the error bars on the slope are large for individual quasars, the large sample size lends weight to the overall result. Our results present severe difficulties for a standard thin accretion disk as the main source of UV/optical radiation from quasars.
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Microlensing observations indicate that quasar accretion discs have half-light radii larger than expected from standard theoretical predictions based on quasar fluxes or black hole masses. Blackburne and colleagues have also found a very weak wavelength dependence of these half-light radii. We consider disc temperature profile models that might match these observations. Nixon and colleagues have suggested that misaligned accretion discs around spinning black holes will be disrupted at radii small enough for the Lense-Thirring torque to overcome the discs viscous torque. Gas in precessing annuli torn off a disc will spread radially and intersect with the remaining disc, heating the disc at potentially large radii. However, if the intersection occurs at an angle of more than a degree or so, highly supersonic collisions will shock-heat the gas to a Compton temperature of T~10^7 K, and the spectral energy distributions (SEDs) of discs with such shock-heated regions are poor fits to observations of quasar SEDs. Torn discs where heating occurs in intermittent weak shocks that occur whenever the intersection angle reaches a tenth of a degree pose less of a conflict with observations, but do not have significantly larger half-light radii than standard discs. We also study two phenomenological disc temperature profile models. We find that discs with a temperature spike at relatively large radii and lowered temperatures at radii inside the spike yield improved and acceptable fits to microlensing sizes in most cases. Such temperature profiles could in principle occur in sub-Keplerian discs partially supported by magnetic pressure. However, such discs overpredict the fluxes from quasars studied with microlensing except in the limit of negligible continuum emission from radii inside the temperature spike.
We compare the microlensing-based continuum emission region size measurements in a sample of 15 gravitationally lensed quasars with estimates of luminosity-based thin disk sizes to constrain the temperature profile of the quasar continuum accretion region. If we adopt the standard thin disk model, we find a significant discrepancy between sizes estimated using the luminosity and those measured by microlensing of $log(r_{L}/r_{mu})=-0.57pm0.08,text{dex}$. If quasar continuum sources are simple, optically thick accretion disks with a generalized temperature profile $T(r) propto r^{-beta}$, the discrepancy between the microlensing measurements and the luminosity-based size estimates can be resolved by a temperature profile slope $0.37 < beta < 0.56$ at $1,sigma$ confidence. This is shallower than the standard thin disk model ($beta=0.75$) at $3,sigma$ significance. We consider alternate accretion disk models that could produce such a temperature profile and reproduce the empirical continuum size scaling with black hole mass, including disk winds or disks with non-blackbody atmospheres.
We present accretion disk size measurements for 15 luminous quasars at $0.7 leq z leq 1.9$ derived from $griz$ light curves from the Dark Energy Survey. We measure the disk sizes with continuum reverberation mapping using two methods, both of which are derived from the expectation that accretion disks have a radial temperature gradient and the continuum emission at a given radius is well-described by a single blackbody. In the first method we measure the relative lags between the multiband light curves, which provides the relative time lag between shorter and longer wavelength variations. From this, we are only able to constrain upper limits on disk sizes, as many are consistent with no lag the 2$sigma$ level. The second method fits the model parameters for the canonical thin disk directly rather than solving for the individual time lags between the light curves. Our measurements demonstrate good agreement with the sizes predicted by this model for accretion rates between 0.3-1 times the Eddington rate. Given our large uncertainties, our measurements are also consistent with disk size measurements from gravitational microlensing studies of strongly lensed quasars, as well as other photometric reverberation mapping results, that find disk sizes that are a factor of a few ($sim$3) larger than predictions.
We present three complete seasons and two half-seasons of SDSS r-band photometry of the gravitationally lensed quasar SBS 0909+532 from the U.S. Naval Observatory, as well as two seasons each of SDSS g-band and r-band monitoring from the Liverpool Robotic Telescope. Using Monte Carlo simulations to simultaneously measure the systems time delay and model the r-band microlensing variability, we confirm and significantly refine the precision of the systems time delay to Delta t_{AB} = 50^{+2}_{-4} days, where the stated uncertainties represent the bounds of the formal 1sigma confidence interval. There may be a conflict between the time delay measurement and a lens consisting of a single galaxy. While models based on the Hubble Space Telescope astrometry and a relatively compact stellar distribution can reproduce the observed delay, the models have somewhat less dark matter than we would typically expect. We also carry out a joint analysis of the microlensing variability in the r- and g-bands to constrain the size of the quasars continuum source at these wavelengths, obtaining log[(r_{s,r}/cm) [cos{i}/0.5]^{1/2}] = 15.3 pm 0.3 and log[(r_{s,g}/cm) [cos{i}/0.5]^{1/2}] = 14.8 pm 0.9, respectively. Our current results do not formally constrain the temperature profile of the accretion disk but are consistent with the expectations of standard thin disk theory.
Microlensing perturbations to the magnification of gravitationally lensed quasar images are dependent on the angular size of the quasar. If quasar variability at visible wavelengths is caused by a change in the area of the accretion disk, it will affect the microlensing magnification. We derive the expected signal, assuming that the luminosity scales with some power of the disk area, and estimate its amplitude using simulations. We discuss the prospects for detecting the effect in real-world data and for using it to estimate the logarithmic slope of the luminositys dependence on disk area. Such an estimate would provide a direct test of the standard thin accretion disk model. We tried fitting six seasons of the light curves of the lensed quasar HE 0435-1223 including this effect as a modification to the Kochanek et al. (2006) approach to estimating time delays. We find a dramatic improvement in the goodness of fit and relatively plausible parameters, but a robust estimate will require a full numerical calculation in order to correctly model the strong correlations between the structure of the microlensing magnification patterns and the magnitude of the effect. We also comment briefly on the effect of this phenomenon for the stability of time delay estimates.
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