Recent studies of active galactic nuclei (AGN) found a statistical inverse linear scaling between the X-ray normalized excess variance $sigma_{rm rms}^2$ (variability amplitude) and the black hole mass spanning over $M_{rm BH}=10^6- 10^9 M_{odot}$. B
eing suggested to have a small scatter, this scaling relation may provide a novel method to estimate the black hole mass of AGN. However, a question arises as to whether this relation can be extended to the low-mass regime below $sim10^6 M_{odot}$. If confirmed, it would provide an efficient tool to search for AGN with low-mass black holes using X-ray variability. This paper presents a study of the X-ray excess variances for a sample of AGN with black hole masses in the range of $10^5- 10^6 M_{odot}$ observed with {it XMM-Newton} and {it ROSAT}, including data both from the archives and from newly preformed observations. It is found that the relation is no longer a simple extrapolation of the linear scaling; instead, the relation starts to flatten at $sim10^6 M_{odot}$ toward lower masses. Our result is consistent with the recent finding of citet{L15}. Such a flattening of the $M_{rm BH}-sigma_{rm rms}^2$ relation is actually expected from the shape of the power spectrum density of AGN, whose break frequency is inversely scaled with the mass of black holes.
We discuss further observational support of an idea formulated a decade ago by Abramowicz, Klu{z}niak, McClintock and Remillard. They demonstrated that the 3:2 pairs of frequencies of the twin-peak black hole (BH) high-frequency quasi-periodic oscill
ations (QPOs) scale inversely with the BH masses and that the scaling covers the entire range from stellar to supermassive BHs. For this reason, they believed that the QPOs may be used for accurate measurements of masses and spins of BHs.
Ultra-luminous X-ray sources (ULXs) are off-nuclear X-ray sources in nearby galaxies with X-ray luminosities $geq$ 10$^{39}$ erg s$^{-1}$. The measurement of the black hole (BH) masses of ULXs is a long-standing problem. Here we estimate BH masses in
a sample of ULXs with XMM-Newton observations using two different mass indicators, the X-ray photon index and X-ray variability amplitude based on the correlations established for active galactic nuclei (AGNs). The BH masses estimated from the two methods are compared and discussed. We find that some extreme high-luminosity ($L_{rm X} >5times10^{40}$ erg s$^{-1}$) ULXs contain the BH of 10$^{4}$-10$^{5}$ $M_odot$. The results from X-ray variability amplitude are in conflict with those from X-ray photon indices for ULXs with lower luminosities. This suggests that these ULXs generally accrete at rates different from those of X-ray luminous AGNs, or they have different power spectral densities of X-ray variability. We conclude that most of ULXs accrete at super-Eddington rate, thus harbor stellar-mass BH.
Risks threatening modern societies form an intricately interconnected network that often underlies crisis situations. Yet, little is known about how risk materializations in distinct domains influence each other. Here we present an approach in which
expert assessments of risks likelihoods and influence underlie a quantitative model of the global risk network dynamics. The modeled risks range from environmental to economic and technological and include difficult to quantify risks, such as geo-political or social. Using the maximum likelihood estimation, we find the optimal model parameters and demonstrate that the model including network effects significantly outperforms the others, uncovering full value of the expert collected data. We analyze the model dynamics and study its resilience and stability. Our findings include such risk properties as contagion potential, persistence, roles in cascades of failures and the identity of risks most detrimental to system stability. The model provides quantitative means for measuring the adverse effects of risk interdependence and the materialization of risks in the network.
We discuss two methods to estimate black hole (BH) masses using X-ray data only: from the X-ray variability amplitude and from the photon index Gamma. The first method is based on the anti-correlation between BH mass and X-ray variability amplitude.
Using a sample of AGN with BH masses from reverberation mapping, we show that this method shows small intrinsic scatter. The second method is based on the correlation between Gamma and both the Eddington ratio L_{bol}/L_{Edd} and the bolometric correction L_{bol}/L_{2-10keV}.
We study the radial ionization structure at the surface of an X-ray illuminated accretion disk. We plot the expected iron K$alpha$ line energy as a function of the Eddington ratio and of the distance of the emitting matter from the central source, fo
r a non-rotating and a maximally-rotating black hole. We compare the predicted disk line energies with those measured in an archival sample of active galactic nuclei observed with {it Chandra}, {it XMM-Newton} and {it Suzaku}, and discuss whether the line energies are consistent with the radial distances inferred from reverberation studies. We also suggest using rapidly-variable iron K$alpha$ lines to estimate the viscosity parameter of an accretion disk. There is a forbidden region in the line energy versus Eddington ratio plane, at low Eddington ratios, where an accretion disk cannot produce highly-ionized iron K$alpha$ lines. If such emission is observed in low-Eddington-ratio sources, it is either coming from a highly-ionized outflow, or is a blue-shifted component from fast-moving neutral matter.
We propose the rest-frame 2-10 keV photon index, ga, acting as an indicator of the bolometric correction, lb/$L_{rm 2-10keV}$ (where lb~ is the bolometric luminosity and $L_{rm 2-10keV}$ is the rest-frame 2-10 keV luminosity), in radio-quiet active g
alactic nuclei (AGNs). Correlations between ga~ and both bolometric correction and Eddington ratio are presented, based on simultaneous X-ray, UV, and optical observations of reverberation -mapped AGNs. These correlations can be compared with those for high-redshift AGNs to check for any evolutionary effect. Assuming no evolutionary effect in AGNs spectral properties, together with the independent estimates of $L_{rm 2-10keV}$, the bolometric correction, Eddington ratio, and black hole (BH) mass can all be estimated from these correlations for high-redshift AGNs, with the mean uncertainty of a factor of 2-3. If there are independent estimates of BH masses, ga~ for high-redshift AGNs can be used to determine their true lb~ and $L_{rm 2-10keV}$, and in conjunction with the redshift, can be potentially used to place constraints on cosmology by comparison with the rest-frame 2-10 keV flux. We find that the true $L_{rm 2-10keV}$ estimated from ga~ for the brightest Type I AGNs with $z<1$ in the Lockman Hole is generally in agreement with the observed $L_{rm 2-10keV}$. However, there are still many uncertainties, such as the accurate determination of the intrinsic ga~ for distant AGNs and the large uncertainty in the luminosities obtained, which call for significant further study before ``AGN cosmology can be considered a viable technique.
We use publicly available XMM-Newton data to systematically compare the hard X-ray photon indices, $Gamma_{rm 2-10 keV}$ and the iron K$alpha$ emission lines of narrow-line (NL) and broad-line Seyfert 1 (BLS1) galaxies. We compile a flux-limited ($f_
{rm 2-10 keV} geq 1 times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$) sample including 114 radio-quiet objects, with the 2-10 keV luminosity ranging from 10$^{41}$ to 10$^{45}$ erg s$^{-1}$. Our main results are: 1) NLS1s and BLS1s show similar luminosity distributions; 2) The weighted mean of $Gamma_{rm 2-10 keV}$ of NLS1s, BLS1s and the total sample is $2.04pm0.04$, $1.74pm0.02$, $1.84pm0.02$, respectively; a significant anti-correlation between ga and FWHMH$beta$ suggests that $Gamma_{rm 2-10 keV} > 2.0$ may be taken to indicate X-ray luminous NLS1 type; 3) The 6.4 keV narrow iron K$alpha$ lines from NLS1s are generally weaker than that from BLS1s; this would indicate a smaller covering factor of the dusty tori in NLS1s, if the line emission originates from the inner boundary region of the dusty torus in an AGN; 4) all the broadened iron K$alpha$ lines with intrinsic width $sigma>0.5$ keV correspond to FWHMhb $leq 4000 ~kms$.
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. T
he 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).
