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Register a new userThe Fundamental Plane of Black Hole Accretion and its Use as a Black Hole-Mass Estimator
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We present an analysis of the fundamental plane of black hole accretion, an empirical correlation of the mass of a black hole ($M$), its 5 GHz radio continuum luminosity ($ u L_{ u}$), and its 2-10 keV X-ray power-law continuum luminosity ($L_X$). We compile a sample of black holes with primary, direct black hole-mass measurements that also have sensitive, high-spatial-resolution radio and X-ray data. Taking into account a number of systematic sources of uncertainty and their correlations with the measurements, we use Markov chain Monte Carlo methods to fit a mass-predictor function of the form $log(M/10^{8},M_{scriptscriptstyle odot}) = mu_0 + xi_{mu R} log(L_R / 10^{38},mathrm{erg,s^{-1}}) + xi_{mu X} log(L_X / 10^{40},mathrm{erg,s^{-1}})$. Our best-fit results are $mu_0 = 0.55 pm 0.22$, $xi_{mu R} = 1.09 pm 0.10$, and $xi_{mu X} = -0.59^{+0.16}_{-0.15}$ with the natural logarithm of the Gaussian intrinsic scatter in the log-mass direction $lnepsilon_mu = -0.04^{+0.14}_{-0.13}$. This result is a significant improvement over our earlier mass scaling result because of the increase in active galactic nuclei sample size (from 18 to 30), improvement in our X-ray binary sample selection, better identification of Seyferts, and improvements in our analysis that takes into account systematic uncertainties and correlated uncertainties. Because of these significant improvements, we are able to consider potential influences on our sample by including all sources with compact radio and X-ray emission but ultimately conclude that the fundamental plane can empirically describe all such sources. We end with advice for how to use this as a tool for estimating black hole masses.
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We put active galactic nuclei (AGNs) with low-mass black holes on the fundamental plane of black hole accretion---the plane that relates X-ray emission, radio emission, and mass of an accreting black hole---to test whether or not the relation is universal for both stellar-mass and supermassive black holes. We use new Chandra X-ray and Very Large Array radio observations of a sample of black holes with masses less than $10^{6.3} M_{scriptscriptstyle odot}$, which have the best leverage for determining whether supermassive black holes and stellar-mass black holes belong on the same plane. Our results suggest that the two different classes of black holes both belong on the same relation. These results allow us to conclude that the fundamental plane is suitable for use in estimating supermassive black hole masses smaller than $sim 10^7 M_{scriptscriptstyle odot}$, in testing for intermediate-mass black holes, and in estimating masses at high accretion rates.
We perform a detailed study of the location of brightest cluster galaxies (BCGs) on the fundamental plane of black hole (BH) accretion, which is an empirical correlation between a BH X-ray and radio luminosity and mass supported by theoretical models of accretion. The sample comprises 72 BCGs out to $zsim0.3$ and with reliable nuclear X-ray and radio luminosities. These are found to correlate as $L_mathrm{X} propto L_mathrm{R}^{0.75 pm 0.08}$, favoring an advection-dominated accretion flow as the origin of the X-ray emission. BCGs are found to be on average offset from the fundamental plane such that their BH masses seem to be underestimated by the $M_mathrm{BH}-M_mathrm{K}$ relation a factor $sim$10. The offset is not explained by jet synchrotron cooling and is independent of emission process or amount of cluster gas cooling. Those core-dominated BCGs are found to be more significantly offset than those with weak core radio emission. For BCGs to on average follow the fundamental plane, a large fraction ($sim40%$) should have BH masses $> 10^{10}$ M$_{odot}$ and thus host ultramassive BHs. The local BH-galaxy scaling relations would not hold for these extreme objects. The possible explanations for their formation, either via a two-phase process (the BH formed first, the galaxy grows later) or as descendants of high-z seed BHs, challenge the current paradigm of a synchronized galaxy-BH growth.
We investigate a mechanism for a super-massive black hole at the center of a galaxy to wander in the nucleus region. A situation is supposed in which the central black hole tends to move by the gravitational attractions from the nearby molecular clouds in a nuclear bulge but is braked via the dynamical frictions by the ambient stars there. We estimate the approximate kinetic energy of the black hole in an equilibrium between the energy gain rate through the gravitational attractions and the energy loss rate through the dynamical frictions, in a nuclear bulge composed of a nuclear stellar disk and a nuclear stellar cluster as observed from our Galaxy. The wandering distance of the black hole in the gravitational potential of the nuclear bulge is evaluated to get as large as several 10 pc, when the black hole mass is relatively small. The distance, however, shrinks as the black hole mass increases and the equilibrium solution between the energy gain and loss disappears when the black hole mass exceeds an upper limit. As a result, we can expect the following scenario for the evolution of the black hole mass: When the black hole mass is smaller than the upper limit, mass accretion of the interstellar matter in the circum-nuclear region, causing the AGN activities, makes the black hole mass larger. However, when the mass gets to the upper limit, the black hole loses the balancing force against the dynamical friction and starts spiraling downward to the gravity center. From simple parameter scaling, the upper mass limit of the black hole is found to be proportional to the bulge mass and this could explain the observed correlation of the black hole mass with the bulge mass.
We examine the origin and evolution of correlations between properties of supermassive black holes (BHs) and their host galaxies using simulations of major galaxy mergers, including the effects of gas dissipation, cooling, star formation, and BH accretion and feedback. We demonstrate that the simulations predict the existence of a BH fundamental plane (BHFP), of the form M_BH sigma^(3.0+-0.3)*R_e^(0.43+-0.19) or M_BH M_bulge^(0.54+-0.17)*sigma^(2.2+-0.5), similar to relations found observationally. The simulations indicate that the BHFP can be understood roughly as a tilted intrinsic correlation between BH mass and spheroid binding energy, or the condition for feedback coupling to power a pressure-driven outflow. While changes in halo circular velocity, merger orbital parameters, progenitor disk redshifts and gas fractions, ISM gas pressurization, and other parameters can drive changes in e.g. sigma at fixed M_bulge, and therefore changes in the M_BH-sigma or M_BH-M_bulge relations, the BHFP is robust. Given the empirical trend of decreasing R_e for a given M_bulge at high redshift, the BHFP predicts that BHs will be more massive at fixed M_bulge, in good agreement with recent observations. This evolution in the structural properties of merger remnants, to smaller R_e and larger sigma (and therefore larger M_BH, conserving the BHFP) at a given M_bulge, is driven by the fact that bulge progenitors have characteristically larger gas fractions at high redshifts. Adopting the observed evolution of disk gas fractions with redshift, our simulations predict the observed trends in both R_e(M_bulge) and M_BH(M_bulge).
Over the last decade, the evidence is mounting that several aspects of black hole accretion physics proceed in a mass-invariant way. One of the best examples of this scaling is the empirical Fundamental Plane of Black Hole Accretion relation linking mass, radio and X-ray luminosity over eight orders of magnitude in black hole mass. The currently favored theoretical interpretation of this relation is that the physics governing power output in weakly accreting black holes depends more on relative accretion rate than on mass. In order to test this theory, we explore whether a mass-invariant approach can simultaneously explain the broadband spectral energy distributions from two black holes at opposite ends of the mass scale but at similar Eddington accretion fractions. We find that the same model, with the same value of several fitted physical parameters expressed in mass-scaling units to enforce self-similarity, can provide a good description of two datasets from V404 Cyg and M81*, a stellar and supermassive black hole, respectively. Furthermore, only one of several potential emission scenarios for the X-ray band is successful, suggesting it is the dominant process driving the Fundamental Plane relation at this accretion rate. This approach thus holds promise for breaking current degeneracies in the interpretation of black hole high-energy spectra, and for constructing better prescriptions of black hole accretion for use in various local and cosmological feedback applications.
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