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Register a new userIs the anti-correlation between the X-ray variability amplitude and black hole mass of AGNs intrinsic?
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Aims. Both the black hole mass and the X-ray luminosity of AGNs have been found to be anti-correlated with the normalized excess variance ($sigma_{rm rms}^2 $) of the X-ray light curves. We investigate which correlation with $sigma_{rm rms}^2 $ is the intrinsic one. Methods. We divide a full sample of 33 AGNs (O Neill et al. 2005) into two sub-samples. The black hole masses of 17 objects in sub-sample 1 were determined by the reverberation mapping or the stellar velocity dispersion. The black hole masses of the remaining 16 objects were estimated from the relationship between broad line region radius and optical luminosity (sub-sample 2). Then partial correlation analysis, ordinary least squares regression and K-S tests are performed on the full sample and the sub-samples, respectively. Results. We find that $sigma_{rm rms}^2 $ seems to be intrinsically correlated with the black hole mass in the full sample. However, this seems to be caused by including the sub-sample 2 into the analysis, which introduces an extra correlation between the black hole mass and the luminosity and strengthens any correlation with the black hole mass artificially. Therefore, the results from the full sample may be misleading. The results from the sub-sample 1 show that the correlation between $sigma_{rm rms}^2 $ and the X-ray luminosity may be the intrinsic one and therefore the anti-correlation between $sigma_{rm rms}^2 $ and the black hole mass is doubtful.
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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).
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.
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.
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 investigate the X-ray variability characteristics of hard X-ray selected AGNs (based on Swift/BAT data) in the soft X-ray band using the RXTE/ASM data. The uncertainties involved in the individual dwell measurements of ASM are critically examined and a method is developed to combine a large number of dwells with appropriate error propagation to derive long duration flux measurements (greater than 10 days). We also provide a general prescription to estimate the errors in variability derived from rms values from unequally spaced data. Though the derived variability for individual sources are not of very high significance, we find that, in general, the soft X-ray variability is higher than those in hard X-rays and the variability strengths decrease with energy for the diverse classes of AGN. We also examine the strength of variability as a function of the break time scale in the power density spectrum (derived from the estimated mass and bolometric luminosity of the sources) and find that the data are consistent with the idea of higher variability at time scales longer than the break time scale.
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