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Register a new userA Stochastic Model for the Luminosity Fluctuations of Accreting Black Holes
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Brandon C. Kelly
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In this work we have developed a new stochastic model for the fluctuations in lightcurves of accreting black holes. The model is based on a linear combination of stochastic processes and is also the solution to the linear diffusion equation perturbed by a spatially correlated noise field. This allows flexible modeling of the power spectral density (PSD), and we derive the likelihood function for the process, enabling one to estimate the parameters of the process, including break frequencies in the PSD. Our statistical technique is computationally efficient, unbiased by aliasing and red noise leak, and fully accounts for irregular sampling and measurement errors. We show that our stochastic model provides a good approximation to the X-ray lightcurves of galactic black holes, and the optical and X-ray lightcurves of AGN. We use the estimated time scales of our stochastic model to recover the correlation between characteristic time scale of the high frequency X-ray fluctuations and black hole mass for AGN, including two new `detections of the time scale for Fairall 9 and NGC 5548. We find a tight anti-correlation between the black hole mass and the amplitude of the driving noise field, which is proportional to the amplitude of the high frequency X-ray PSD, and we estimate that this parameter gives black hole mass estimates to within ~ 0.2 dex precision, potentially the most accurate method for AGN yet. We also find evidence that ~ 13% of AGN optical PSDs fall off flatter than 1 / f^2, and, similar to previous work, find that the optical fluctuations are more suppressed on short time scales compared to the X-rays, but are larger on long time scales, suggesting the optical fluctuations are not solely due to reprocessing of X-rays.
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I outline the theory of accretion onto black holes, and its application to observed phenomena such as X-ray binaries, active galactic nuclei, tidal disruption events, and gamma-ray bursts. The dynamics as well as radiative signatures of black hole accretion depend on interactions between the relatively simple black-hole spacetime and complex radiation, plasma and magnetohydrodynamical processes in the surrounding gas. I will show how transient accretion processes could provide clues to these interactions. Larger global magnetohydrodynamic simulations as well as simulations incorporating plasma microphysics and full radiation hydrodynamics will be needed to unravel some of the current mysteries of black hole accretion.
A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the X-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit (ISCO), whose radius depends only on the mass and spin of the black hole. In the Fe K method, which applies to both classes of black holes, one models the profile of the relativistically-broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuum-fitting method, which has so far only been applied to stellar-mass black holes, one models the thermal X-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the continuum-fitting method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.
We present the publicly available model textsc{reltrans} that calculates the light-crossing delays and energy shifts experienced by X-ray photons originally emitted close to the black hole when they reflect from the accretion disk and are scattered into our line-of-sight, accounting for all general relativistic effects. Our model is fast and flexible enough to be simultaneously fit to the observed energy-dependent cross-spectrum for a large range of Fourier frequencies, as well as to the time-averaged spectrum. This not only enables better geometric constraints than only modelling the relativistically broadened reflection features in the time-averaged spectrum, but additionally enables constraints on the mass of supermassive black holes in active galactic nuclei and stellar-mass black holes in X-ray binaries. We include a self-consistently calculated radial profile of the disk ionization parameter and properly account for the effect that the telescope response has on the predicted time lags. We find that a number of previous spectral analyses have measured artificially low source heights due to not accounting for the former effect and that timing analyses have been affected by the latter. In particular, the magnitude of the soft lags in active galactic nuclei may have been under-estimated, and the magnitude of lags attributed to thermal reverberation in X-ray binaries may have been over-estimated. We fit textsc{reltrans} to the lag-energy spectrum of the Seyfert galaxy Mrk 335, resulting in a best fitting black hole mass that is smaller than previous optical reverberation measurements ($sim 7$ million compared with $sim14-26$ million $M_odot$).
The role of bremsstrahlung in the emission from hot accretion flows around slowly accreting supermassive black holes is not thoroughly understood. In order to appraise the importance of bremsstrahlung relative to other radiative processes, we compute spectral energy distributions (SEDs) of accretion disks around slowly accreting supermassive black holes including synchrotron radiation, inverse Compton scattering, and bremsstrahlung. We compute SEDs for (i) four axisymmetric radiative general relativistic magnetohydrodynamics (RadGRMHD) simulations of $10^{8}M_{odot}$ black holes with accretion rates between $10^{-8}dot{M}_{text{Edd}}$ and $10^{-5}dot{M}_{text{Edd}}$, (ii) four axisymmetric RadGRMHD simulations of M87$^ast$ with varying dimensionless spin $a_ast$ and black hole mass, and (iii) a 3D GRMHD simulation scaled for Sgr A$^ast$. At $10^{-8}dot{M}_{text{Edd}}$, most of the luminosity is synchrotron radiation, while at $10^{-5}dot{M}_{text{Edd}}$ the three radiative processes have similar luminosities. In most models, bremsstrahlung dominates the SED near $512text{ keV}$. In the M87$^ast$ models, bremsstrahlung dominates this part of the SED if $a_{ast} = 0.5$, but inverse Compton scattering dominates if $a_{ast}= 0.9375$. Since scattering is more variable than bremsstrahlung, this result suggests that $512text{ keV}$ variability could be a diagnostic of black hole spin. In the appendix, we compare some bremsstrahlung formulae found in the literature.
The `fundamental plane of black hole accretion (FP), a relation between the radio luminosities ($L_R$), X-ray luminosities ($L_X$), and masses ($M_{BH}$) of hard/quiescent state black hole binaries and low-luminosity active galactic nuclei, suggests some aspects of black hole accretion may be scale invariant. However, key questions still exist concerning the relationship between the inflow/outflow behaviour in the `classic hard state and quiescence, which may impact this scaling. We show that the broadband spectra of A0620-00 and~sgra~(the least luminous stellar mass/supermassive black holes on the FP) can be modelled simultaneously with a physically-motivated outflow-dominated model where the jet power and all distances are scaled by the black hole mass. We find we can explain the data of both A0620-00 and~sgra~(in its non-thermal flaring state) in the context of two outflow-model scenarios: (1) a synchrotron-self-Compton dominated state in which the jet plasma reaches highly sub-equipartition conditions (for the magnetic field with respect to that of the radiating particles), and (2) a synchrotron dominated state in the fast-cooling regime in which particle acceleration occurs within the inner few gravitational radii of the black hole and plasma is close to equipartition. We show that it may be possible to further discriminate between models (1) and (2) through future monitoring of its submm/IR/X-ray emission, in particular via time lags between the variable emission in these bands.
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