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Register a new userThe scaling of the X-ray variability with black hole mass in AGN
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I. E. Papadakis
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The relation between the 2-10 keV, long term, excess variance and AGN black hole mass is considered in this work. A significant anti-correlation is found between these two quantities in the sense that the excess variance decreases with increasing black hole mass. This anti-correlation is consistent with the hypothesis that the 2-10 keV power spectrum in AGN follows a power law of slope -2 at high frequencies. It then flattens to a slope of -1 below a break frequency until a second break frequency below which it flattens to a slope of zero. The ratio of the two break frequencies is equal to 10-30, similar to the ratio of the respective frequencies in Cyg X-1. The power spectrum amplitude in the frequency x power space does not depend on black hole mass. Instead it is roughly equal to 0.02 in all objects. The high frequency break decreases with increasing black hole mass according to the relation 1.5x(10^-6)/(BHmass/(10^7) solar masses) Hz, in the case of classical Seyfert 1 galaxies. The excess variance of NGC4051, a Narrow Line Seyfert 1 object, is larger than what is expected for its black hole mass and X-ray luminosity. This can be explained if its high frequency break is 20 times larger than the value expected in the case of a classical Seyfert 1 with the same black hole mass. Finally, the excess variance vs X-ray luminosity correlation is a byproduct of the excess variance vs black hole mass correlation, with AGN accreting at ~ 0.1-0.15 the Eddington limit. These results are consistent with recent results from the power spectral analysis of AGN.
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We propose a new method of estimation of the black hole masses in AGN based on the normalized excess variance, sigma_{nxs}^2. We derive a relation between sigma_{nxs}^2, the length of the observation, T, the light curve bin size, Delta t, and the black hole mass, assuming that (i) the power spectrum above the high frequency break, f_{bf}, has a slope of -2, (ii) the high frequency break scales with black hole mass, (iii) the power spectrum amplitude (in frequency x power space) is universal and (iv) sigma_{nxs}^2 is calculated from observations of length T < 1/f_{bf}. Values of black hole masses in AGN obtained with this method are consistent with estimates based on other techniques such as reverberation mapping or the Mbh-stellar velocity dispersion relation. The method is formally equivalent to methods based on power spectrum scaling with mass but the use of the normalized excess variance has the big advantage of being applicable to relatively low quality data.
We have investigated the relationship between the 2-10 keV X-ray variability amplitude and black hole mass for a sample of 46 radio-quiet active galactic nuclei observed by ASCA. Thirty-three of the objects in our sample exhibited variability over a time-scale of ~40 ks, and we found a significant anti-correlation between excess variance and mass. Unlike most previous studies, we have quantified the variability using nearly the same time-scale for all objects. Moreover, we provide a prescription for estimating the uncertainties in excess variance which accounts both for measurement uncertainties and for the stochastic nature of the variability. We also present an analytical method to predict the excess variance from a model power spectrum accounting for binning, sampling and windowing effects. Using this, we modelled the variance-mass relation assuming all objects have a universal twice-broken power spectrum, with the position of the breaks being dependent on mass. This accounts for the general form of the relationship but there is considerable scatter. We investigated this scatter as a function of the X-ray photon index, luminosity and Eddington ratio. After accounting for the dependence of excess variance on mass, we find no significant correlation with either luminosity or X-ray spectral slope. We do find an anti-correlation between excess variance and the Eddington ratio, although this relation might be an artifact owing to the uncertainties in the mass measurements. It remains to be established that enhanced X-ray variability is a property of objects with steep X-ray slopes or large Eddington ratios.
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 decades, the phenomenology of fast time variations of high-energy flux from black-hole binaries has increased, thanks to the availability of more and more sophisticated space observatories, and a complex picture has emerged. Recently, models have been developed to interpret the observed signals in terms of fundamental frequencies connected to General Relativity, which has opened a promising way to measure the prediction of GR in the strong-field regime. I review the current standpoint both from the observational and theoretical side and show that these systems are the most promising laboratories for testing GR and the observations available today suggest that the next observational facilities can lead to a breakthrough in the field.
We present the results from a detailed X-ray variability analysis of 66 AGN in the Lockman Hole, which have optical spectroscopic identifications. We compare, quantitatively, their variability properties with the properties of local AGN, and we study the variability-luminosity relation as a function of redshift, and the variability-redshift relation in two luminosity bins. We use archival data from the last 10 XMM observations of the Lockman Hole field to extract light curves in the rest frame, 2-10 keV band. We use the normalized excess variance to quantify the variability amplitude. Using the latest results regarding the AGN power spectral shape and its dependence on black hole mass and accretion rate, we are able to compute model variability-luminosity curves, which we compare with the relations we observe. When we consider all the sources in our sample, we find that their variability amplitude decreases with increasing redshift and luminosity. These global anti-correlations are less pronounced when we split the objects in various luminosity and redshift bins. We do not find a significant correlation between variability amplitude and spectral slope. The variability-luminosity relation that we detect has a larger amplitude when compared to that of local AGN. We also find that, at a given luminosity, the variability amplitude increases with redshift up to z~1, and then stays roughly constant. Our results imply that the AGN X-ray mechanism operates in the same way at all redshifts. Among objects with the same luminosity in our sample, the black hole mass decreases and the accretion rate increases with larger redshift.
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