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Register a new userWandering of the central black hole in a galactic nucleus and correlation of the black hole mass with the bulge mass
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Hajime Inoue
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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.
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We simulate the star cluster, made of stars in the main sequence and different black hole (BH) remnants, around SgrA* at the center of the Milky Way galaxy. Tracking stellar evolution, we find the BH remnant masses and construct the BH mass function. We sample 4 BH species and consider the impact of the mass-function in the dynamical evolution of system. Starting from an initial 6 dimensional family of parameters and using an MCMC approach, we find the best fits to various parameters of model by directly comparing the results of the simulations after $t = 10.5$ Gyrs with current observations of the stellar surface density, stellar mass profile and the mass of SgrA*. Using these parameters, we study the dynamical evolution of system in detail. We also explore the mass-growth of SgrA* due to tidally disrupted stars and swallowed BHs. We show that the consumed mass is dominated for the BH component with larger initial normalization as given by the BH mass-function. Assuming that about 10% of the tidally disrupted stars contribute in the growth of SgrA* mass, stars make up the second dominant effect in enhancing the mass of SgrA*. We consider the detectability of the GW signal from inspiralling stellar mass BHs around SgrA* with LISA. Computing the fraction of the lifetime of every BH species in the LISA band, with signal to noise ratio $gtrsim 8$, to their entire lifetime, and rescaling this number with the total number of BHs in the system, we find that the total expected rate of inspirals per Milky-Way sized galaxy per year is $10^{-5}$. Quite interestingly, the rate is dominated for the BH component with larger initial normalization as dictated by the BH mass-function. We interpret it as the second signature of the BH mass-function.
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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A calibration is made for the correlation between the X-ray Variability Amplitude (XVA) and Black Hole (BH) mass. The correlation for 21 reverberation-mapped Active Galactic Nuclei (AGN) appears very tight, with an intrinsic dispersion of 0.20 dex. The intrinsic dispersion of 0.27 dex can be obtained if BH masses are estimated from the stellar velocity dispersions. We further test the uncertainties of mass estimates from XVAs for objects which have been observed multiple times with good enough data quality. The results show that the XVAs derived from multiple observations change by a factor of 3. This means that BH mass uncertainty from a single observation is slightly worse than either reverberation-mapping or stellar velocity dispersion measurements; however BH mass estimates with X-ray data only can be more accurate if the mean XVA value from more observations is used. Applying this relation, the BH mass of RE J1034+396 is found to be $4^{+3}_{-2} times 10^6$ $M_{odot}$. The high end of the mass range follows the relationship between the 2$f_0$ frequencies of high-frequency QPO and the BH masses derived from the Galactic X-ray binaries. We also calculate the high-frequency constant $C= 2.37 M_odot$ Hz$^{-1}$ from 21 reverberation-mapped AGN. As suggested by Gierlinski et al., $M_{rm BH}=C/C_{rm M}$, where $C_{rm M}$ is the high-frequency variability derived from XVA. Given the similar shape of power-law dominated X-ray spectra in ULXs and AGN, this can be applied to BH mass estimates of ULXs. We discuss the observed QPO frequencies and BH mass estimates in the Ultra-Luminous X-ray source M82 X-1 and NGC 5408 X-1 and favor ULXs as intermediate mass BH systems (abridged).
In the past two decades, high amplitude electromagnetic outbursts have been detected from dormant galaxies and often attributed to the tidal disruption of a star by the central black hole. X-ray emission from the Seyfert 2 galaxy GSN 069 (2MASX J01190869-3411305) at redshift z = 0.018 was first detected in 2010 July and implies an X-ray brightening of more than a factor of 240 over ROSAT observations performed 16 years earlier. The emission has smoothly decayed over time since 2010, possibly indicating a long-lived tidal disruption event. The X-ray spectrum is ultra-soft and can be described by accretion disc emission with luminosity proportional to the fourth power of the disc temperature during long-term evolution. Here we report observations of X-ray quasi-periodic eruptions from the nucleus of GSN 069 over the course of 54 days, 2018 December onwards. During these eruptions, the X-ray count rate increases by up to two orders of magnitude with event duration of just over 1 hour and recurrence time of about 9 hours. These eruptions are associated with fast spectral transitions between a cold and a warm phase in the accretion flow around a low-mass black hole (of approximately 4x10$^5$ solar masses) with peak X-ray luminosity of ~ 5x10$^{42}$ ergs per second. The warm phase has a temperature of about 120 eV, reminiscent of the typical soft X-ray excess, an almost universal thermal-like feature in the X-ray spectra of luminous active nuclei. If the observed properties are not unique to GSN 069, and assuming standard scaling of timescales with black hole mass and accretion properties, typical active galactic nuclei with more massive black holes can be expected to exhibit high-amplitude optical to X-ray variability on timescales as short as months or years.
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