We represent Eddington luminosity probably a good estimator of m, 48 A. Figure 1. Upper limits are marked with arrows, different symbols indicate objects belonging to different spectral classes. The thick solid upper line gives the maximum core radio power as calculated by Ho for sources accreting at the Eddington rate. Figure 2. Radio core luminosity at 5 GHz vs. Upper limits are marked with arrows, different symbols indicate objects belonging to different spectral classes and different colors objects in different mass bins.
The color-coding of the different mass bins makes the mass segregation more evident. It is clear that, when the data points are grouped into mass bins, objects in different bins tend to lie on parallel tracks. The presence of a mass segregation suggests that the radio luminosity of an object likely depends both on its accretion rate and on its mass.
We can proceed to quantify the degree of correlation between our three observables radio luminosity at 5 GHz, L R , X-ray luminosity in the 2—10 keV band, L X and black hole mass. Scale Invariance and Jet Dominance in Black Hole Accretors In a recent paper, Heinz and Sunyaev have demonstrated that, under the general assumption that the jet formation process is not qualitatively different among SMBH of different mass or between SMBH and GBH, it is in fact possible to derive a universal scaling between the jet radio luminosity at a given frequency and both mass and accretion rate.
L R scales with the physical accretion rate only. This is tantalizingly close to the predicted dependence of Eq. Heinz et al. They should therefore depart from the observed correlations. For GBHs, it has indeed been shown that the correlation between radio and X-ray luminosity breaks down as the sources switch to their high states Maccarone, ; Gallo et al. Abramowicz et al. In fact, Maccarone et al. Let us consider, for example, a recent paper by Fender et al. Can we extend this result to the larger family of radio loud AGN?
As expected, by rescaling the radio luminosity in such a way all the different tracks corresponding to different 52 A. The radio luminosity log L R , divided by M 1. In between, possibly lies the restricted region of the parameter space where pure discs accretion is allowed HSS. At low accretion rates, black holes seem to follow the more regular behavior circumscribed by the fundamental plane of Eq. In this regime, no dichotomy need be expected, as already suggested by Nagar et al. Moreover, the relation itself is perfectly consistent with the scaling relations predicted by standard synchrotron theory under a scale invariance assumption.
The main scaling parameters are the mass of the black hole and its accretion rate. References Abramowicz, M. Franceschini, A. Merloni, S. Nayakshin and R. Sunyaev eds. Magorrian, J. Nagar N. Rawlings, S. Early models accomplished this loading by centrifugal action from a thin disk, but more recent studies suggest that the primary means is thermal, heating the plasma to roughly the virial temperature; Meier, The jet is accelerated to the local Alfven speed by the rotational Alfven wave and beyond that to the local magnetosonic speed by the toroidal magnetic pressure gradient.
The plasma loading is more problematical. It is the rapid rotation of the core that is suddenly and rapidly generated, by the collapse of that iron core to protoneutron star densities. The plasma loading itself is a relatively easy problem to solve. However, a strongly charged black hole will induce charge separation in any surrounding plasma, accreting charges opposite in sign to that on the hole and expelling those of like sign.
This will effectively discharge the hole in a few light-crossing times. This conclusion itself presents a problem, however. How does a global, well-ordered rotating magnetosphere develop naturally from a turbulent accretion disk? In addition, even if a global magnetosphere can be constructed, there is a question as to how that magnetosphere can couple to black hole rotation to produce a strong jet.
Radio galaxies and quasars that have similar optical properties, and therefore similar accretion disks, can differ in their radio jet luminosities by factors of —6. This is most easily explained by tying jet production to rotation of the central object, just as it is done in stellar jet-producing systems. Basics of Magnetically Dominated Accretion Flows 2. So, if the interior of an ADAF becomes magnetically dominated, the transition region will be rather narrow in radius. Figure 1 shows a schematic of our low-state model and will be discussed more fully below.
However, inside this radius electrons radiate copiously by synchrotron, pair production, and other relativistic processes. It is often assumed that such cooling would lead once again to a geometrically thin, optically thick disk. It, therefore, is extremely important to begin performing MRI simulations with a real energy equation, including separate evolution of the ions and electrons. It is a nearly radial in-spiral, geometrically thick because of magnetic pressure support Meier, Power spectrum data are taken from Morgan et al. The input and output powers Pi, j correspond to those in the Malzac et al.
The plasma experiences only compressional heating and radiative cooling by electrons and could remain quite cool; the majority of the gravitational energy released is converted into radial infall kinetic energy, not heat. The behavior of SgrA at the Galactic center Genzel et al. Discussion 3. It is natural to associate the non-thermal photon spectrum and bandwidth-limited noise with the optically thin, turbulent ADAF that has formed in the center of the disk. The inner MDAF model provides natural answers to these questions. The slope of this cutoff may represent the high frequency tail of the turbulence spectrum near R1.
The power spectrum at each disk radius should be dominated by a rather narrowly peaked local spectrum Maron and Blackman, The jet velocity from equation 62 D. MEIER 5 increases as the disk truncation radius decreases. It is this fast jet that creates the shock and outburst that we observe. Malzac et al. The output power is the jet production that occurs at this radius. The MDAF model provides a physical reason why this ad hoc scaling of the break in different systems is a reasonable black hole mass indicator.
AGN also display another property similar to that shown by X-ray binaries, and the MDAF model provides the same explanation there as well. Jets produced by quasars and many Seyferts tend to be quite relativistic, even within only a parsec from the black hole core. They therefore may be launched and accelerated rather close to the central black hole. This suggestion is supported by semi-analytic jet acceleration models, which suggest a magnetic foot point only a few gravitational radii from the hole for 3C Vlahakis and Konigl, Yet, at kiloparsec distances, M87 shows superluminal motions up to 6 c.
It appears possible, then, that the jet-production region in LLAGN and FR I objects also may look like that in Figure 1, with the launch point lying many tens of gravitational radii from the black hole. As in previous models, the outer region of the disk is a geometrically thin, optically thick, and cool turbulent disk, driven by the MRI. In particular, extension of this model to include an MDAF inside all truncated disks naturally predicts the variation in jet speed with inner radius deduced by Fender et al.
The spectral slopes are due not to the physics of the turbulence itself but rather to variations in disk structure with radius. Only the cutoff at a few Hz is indicative of the high frequency end of the local power spectrum there. Acknowledgements The author is especially grateful to T. Macarone and R. Fender for organizing this conference on black hole accretion on all mass scales. Emphasizing the similarities and scaling of black hole systems contributes greatly to their overall understanding. References Balbus, S. Biretta, J. Esin, A. Gammie, C. Genzel, R.
Goldreich, P. Koide, S. Lovelace, R. Maron, J. Migliari, S. Misner, C. Morgan, E. Abramowicz, G. Bjornsson and J. Pringle eds. Papadakis, I. Ruderman, M. Shakura, N. Thorne, K. Vlahakis, N. Wheeler, J. High-resolution Chandra and XMM-Newton X-ray spectroscopic studies of stellar and supermassive black holes have revealed that these phenomenologically different systems share many common physical characteristics. Introduction Despite major advances in our understanding of black hole systems over the past several decades, many questions relating to the structure and dynamics of accretion onto black holes remain unanswered.
Taking advantage of the high-resolution spectroscopic capabilities of Chandra and XMM-Newton, we can improve our understanding through plasma diagnostics of the observed absorption and emission lines. In particular, it has been found that black hole types differing by six to seven orders of magnitude in mass scale, from the stellar to supermassive black holes, display many similar phenomena.
References will be limited. One way to do so is to assess the similar phenomena governing these systems. Astrophysics and Space Science 67—70, Black hole mass. Also reported by Sako et al. For these systems, the relevant comparisons of their properties are listed in Table I. O U T F L OW S Narrow absorption and emission lines are fairly ubiquitous in the astrophysical sources we see at high spectral resolution, and give important information about the state of the plasma, be it X-ray hot or X-ray cold.
- Nights In Black Lace.
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For the sources of interest in this article, the plasma is photoionized due to its proximity to the black hole. Kaspi et al. Of these, the most remarkable are those which show relativistic velocities, e. One surprising thing which has emerged from some of these studies is the remarkable amount of material that is being ejected, modulo a covering factor, compared to the mass accretion rate. This is a topic worthy of further investigation. The Role of High-Resolution X-ray Spectroscopy for Building the Phenomenology Towards Self-Consistent Physical Models of Black Hole Systems The high-resolution spectral capabilities of the Chandra and XMM-Newton grating spectrometers will help in answering some of the outstanding questions relating to energetic accretion systems by allowing us to apply atomic physics techniques to the study of astrophysical plasma.
A clear understanding of the line diagnostics will allow an accurate assessment of the physics, environment, and geometry governing the regions from nearest to the black hole to those which are the most distant. Ultimately, this might help us 1 It should be noted that the high-velocity blueshifts observed in some of these sources Section 2. References Brandt, W. Chartas, G. Greiner, J. Kaspi, S. Lee, J. Lopez, L. Marshall, H.
Pounds, K. Reeves, J. Sako, M. Schulz, N. Turner, A. Received 1 October ; accepted 1 June Abstract. We discuss constraints on black hole spin and spin-related astrophysics as derived from X-ray spectroscopy. After a brief discussion about the robustness with which X-ray spectroscopy can be used to probe strong gravity, we summarize how these techniques can constrain black hole spin.
Furthermore, these XMM-Newton data are already providing evidence for exotic spin-related astrophysics in the central regions of this object. We conclude with a discussion of the impact that Constellation-X will have on the study of strong gravity and black hole spin. Keywords: accretion disks, black hole physics 1. At the current time, the best evidence for the effects of black hole spin come from X-ray observations, both timing and spectroscopy. X-ray variability studies, particularly investigations of quasi-periodic oscillations QPOs have produced tantalizing hints that we might be witnessing the effects of black hole spin Stella et al.
However, the lack of any agreed upon theoretical framework for the high-frequency QPOs prevents us from drawing robust conclusions at this Astrophysics and Space Science 71—79, For this reason, the most compelling studies of black hole spin have originated from X-ray spectroscopy. In this contribution, we describe constraints on black hole spin from X-ray spectroscopy. The essential physics underlying this phenomenon is straightforward.
It is important to stress, however, that the role of photoionized absorption in masking or mimicking broad iron lines is knowable, and will be elucidated by the high-resolution and high count-rate spectra that Astro-E2 will be obtaining on a regular basis starting in early To summarize this section, there are robust examples of broad iron emission lines that are giving us a clean probe of the strong gravity region around both stellar and supermassive black holes. However, while broad iron lines are not rare, the precise fraction of objects in the various classes of accreting black holes that display these features is still uncertain.
Constraining Black Hole Spin with X-ray Spectroscopy Having established that at least some accreting black holes display broad iron lines that cleanly probe the strong gravity region, we now ask whether we can constrain the black hole spin using these features.
To sharpen the discussion, we will address whether one can rule out a Schwarzschild metric i. Even with XMM-Newton, we cannot probe the iron line on the dynamical timescale of the very centralmost regions of the accretion disk where spin effects 74 C. There is a common misconception that rapidly spinning black holes invariably produce broader and more highly redshifted emission lines than slowly spinning black holes. Hence, the line broadening will increase with black hole spin if the line emission is always truncated at the ISCO. But it is important to realize that we can produce arbitrarily redshifted and broadened emission lines from around even a non-rotating black hole if nature had the freedom to produce line emission from any radius beyond the horizon Reynolds and Begelman, This would be an overly bleak assessment of our ability to constrain black hole spin.
Even the application of some rather weak i. The June observation of this source reported by Wilms et al. The systematic exploration of these constraints has only just begun and is still a work in progress. The user may therefore tune the spectral resolution and numerical accuracy of the model to suit the data at hand, a feature that is not available in the tabular models such as laor that have been extensively employed to date. Current work is focused on obtaining spin constraints once that assumption is relaxed.
The Exotic Astrophysics of Spinning Black Holes Rapidly spinning black holes are undoubtedly amongst the most exotic objects in the current-day universe. In this section, we focus on one particular facet of their behaviour — the magnetic interactions between the spinning black hole and surrounding matter including the accretion disk. We argue that XMM-Newton data are already hinting at evidence for the magnetic extraction of spin energy from the black hole in MCG Analytic Krolik, ; Gammie, and numerical Hawley and Krolik, ; Reynolds and Armitage, studies have shown that magnetic forces can couple material within the plunging region to the body of the accretion disk, thereby extracting energy and angular momentum from that region.
In an extreme limit, a Penrose process1 might be realized in which the innermost regions of the 1 We note that Williams has also argued for the importance of a non-magnetic, particle—particle and particle—photon scattering mediated Penrose process. Note that all of this behaviour is in stark contrast to standard black hole disk models Shakura and Sunyaev, ; Novikov and Thorne, ; Page and Thorne, in which material follows conservative orbits once inside the ISCO. Can we see evidence for any of these processes in the current data? Again, we return to the Deep Minimum State of MCG which displays one of the broadest and most highly redshifted iron lines known.
One can attempt to rescue the standard disk model by supposing that a larger portion of the total dissipation in the disk is channeled into the X-ray emitting corona as one moves to smaller radii. If this is really the correct description of the physics at play, the data argue that the accretion disk is in an extreme torque-dominated state, i. MHD simulations suggest that magnetic connections between the plunging region and the body of an accretion disk tend to be rather sporadic.
However, the enhanced returning radiation associated with the torque-induced emission will strongly Compton cool the X-ray corona leading to a steepening of the X-ray continuum and possibly a large-scale condensation-driven collapse of the corona. It is also possible that the local-corona approximation is not valid. Aspects of this scenario have been explored by many authors including Martocchia and Matt , Reynolds and Begelman and Miniutti and Fabian We note that this scenario does not diminish the need for exotic spin-related astrophysics — the base of a spin-driven magnetic jet is an obvious candidate for this elevated continuum X-ray source.
The enormous throughput of Constellation-X will allow us to probe detailed time variability of the iron line. Dynamical timescale line variability, an easy goal for ConstellationX, will allow us to follow non-axisymmetric structures in the disk as they orbit Armitage and Reynolds, ; also see Iwasawa et al. This gives us a direct probe of an almost Keplerian orbit close into a black hole. Furthermore, line variability on the light crossing time will allow us to probe relativistic reverberation signatures Reynolds et al.
There is no compelling reason to believe that GR fails on the macroscopic scales probed by either X-ray or gravitational wave studies of astrophysical black holes. X-ray spectroscopy with Constellation-X provides a crucial parallel track of study in which we can obtain measurements of black hole spin across the whole mass range of astrophysical black holes i. Only then can the demographics and astrophysical relevance of black hole spin truly be gauged. Acknowledgement We thank the conference organizers for a stimulating and highly enjoyable meeting.
References Agol, E. Armitage, P. Dovciak, M. Fabian, A. Hawley, J. Iwasawa, K. Iwasawa, I. Krolik, J. Marconi, A. Miller, J. Miniutti, G. Novikov, I. DeWitt and D. DeWitt eds. Page, D. Reynolds, C. Schurch, N. Speith, R. Stella, L. Strohmayer, T. Vaughan, S. Wang, J. Williams, R.
Wilms, J. Young, A. PAGE2 , G. Received 29 September ; accepted 30 November Abstract. This supports the notion of a continuous sequence of X-ray properties from the Galactic Centre through LINER galaxies to Seyferts, likely determined by the amount of material available for accretion in the central regions. Introduction Low-ionisation nuclear emission-line region LINER galaxies are characterised by optical emission-line ratios which indicate a low level of ionisation Heckman, The origin of these emission lines is still the subject of debate: the lines are attributed either to shock heating Baldwin et al.
FH84 argue that this emission comes from photoionisation by the AGN of clouds spanning a range of densities and velocities. Since its discovery as a low luminosity X-ray source Marshall et al. Astrophysics and Space Science 81—86, Identifying the physical mechanisms producing the X-ray emission may help to reveal the origin of the optical emission lines where at present neither shock heating nor photoionisation by the AGN can be ruled out. The source is piled up in MOS2.
The MOS1 and pn spectra were combined using the method of Page et al. The features at The O VII lines are reproduced well by the 0. The model and data are shown in Figure 1. Wavelength in A. Therefore, it is likely that if there is an accretion disc in NGC , its inner edge is truncated at a larger radius than is typical in Seyfert galaxies. It appears then that the low luminosities and therefore accretion rates of LINER-AGN are a consequence of a shortage of material in their central regions. Accretion rate onto the black hole with respect to the Eddington rate is likely to be the overriding factor, with LINER galaxies accreting at much lower rates than Seyfert galaxies Ho et al.
References Baganoff, F. Baldwin, J. Bianchi, S. Blustin, A. Dickey, J. Ferland, G. Filippenko, A. Halpern, J. Heckman, T. Kinkhabwala, A. Marshall, F. Nelson, C. Page, M. Phillips, M. Porquet, D. Siemiginowska, A. Tanaka, Y. Turner, T. The current paradigm of high energy spectroscopy tells us that light emitted from a wide variety of objects has its origin close to the black hole event horizon.
As such, these photons are subject to general relativistic effects such as light-bending, gravitational lensing and redshift, time-dilation, etc. To this end, we have developed a new semi-analytic strong gravity code, capable of describing the contribution of photons that perform multiple orbits of the hole. Introduction Black holes are the ultimate test of strong gravity, spacetime so warped that not even light can escape.
Photons emitted in this region are subjected to general relativistic effects such as light-bending, gravitational lensing and redshift, as well as special relativistic effects as the emitting material will be moving rapidly e. Fabian et al. Calculations of the relativistic corrections to photon properties have been ongoing for nearly three decades, starting with the classic work of Cunningham who calculated the distortions expected on the spectrum of a geometrically thin, optically thick, Keplerian accretion disc orbiting a Kerr black hole. Interest in these calculations dramatically increased with the realisation that the accretion disc could emit line as well as continuum radiation.
DONE irradiation of the accretion disc can give a narrow feature, on which the relativistic distortions are much more easily measured than on the broad accretion disc continuum Fabian et al. Since then, several groups have developed numerical codes that are capable of determining these effects both for standard discs Dovciak et al. More recent data from XMM are interpreted as showing that the line is even wider than expected from an extreme Kerr disk, requiring direct extraction of the spin energy from the central black hole as well as the immense gravitational potential Wilms et al.
Complex ionised absorption also affects AGN spectra e. However, in MCG these issues have been examined in detail, and the results on the dramatic line width appear robust Fabian and Vaughan, ; Reynolds et al. Thus, there is a clear requirement that the extreme relativistic effects are well modelled. Also, it does not include the effects of light-bending although Fabian et al. The choice of the angular dependence is far more complex however, as it depends on the poorly understood vertical structure of the accretion disc, in particular, the ionisation state of the material and so the choice of this dependence is not unique.
Left panel The coordinate system used for the disc. This disc frame can be connected to the frame which co-rotates with the black hole spacetime via a simple boost which depends on the velocity. DONE Figure 2. However, such a limited range of radii is probably not very realistic. The disc should extend out to much greater distances from the black hole, where the relativistic effects including light-bending are less extreme. However, realistic emissivities strongly weight the contribution from the innermost regions, so the effective dilution of the relativistic effects by including the outer disc is not overwhelming.
Despite the expectation of an extended disc, some recent observational studies e. Reynolds et al. This enhances the importance of light-bending. A zeroth-order approximation to spacetimes with different spins is to use the maximal Kerr results but with a disc with inner radius given by the minimum stable orbit for the required value of a e. Laor, This is roughly on the same order as the effect of changing the angular emissivity, which is much reduced here compared to Figure 2 due to the larger Figure 3. DONE rmin. Assumptions about both spin and angular emissivity become somewhat more important for smaller outer disc radii.
Figure 3 right-hand panel shows this for a disc between 6 and 20rg. The contribution of orbiting photons higher order images to a distant observers image of a geometrically thin, optically thick, Keplerian accretion disc around Schwazschild top row and extreme Kerr bottom row black holes.
The principle effect of black hole spin for the accretion disk dynamics is to move the location of the marginally stable orbit, rms and hence the location of the inner edge of the accretion disc. In the case of the Schwarzschild hole, the inner edge of the accretion disc is located at 6rg , above the radius of the unstable photon orbits 3rg so higher order image photons which cross the equatorial plane below 6rg are not absorbed by the disc and may be able to freely propagate to the observer. This is because these photons are strongly bent, i.
However, there is some new behaviour for the limb brightened emissivity. This has the largest change in emissivity with angle, and this combined with the exquisite sensitivity of lensed paths means that this picks out only a small area on the disc, leading to a discrete feature in the spectrum. The discrete features are completely dominant for all emissivities at secondorder.
These have the standard blue peak enhancement. However, the two strong features redward of this are a pair of lensed features, from the near and far side of the disc. Here the principle effect of changes in the angular emissivity is to alter the height of the blue wing, relative to the rest of the line. Lubinski and Zdziarski, , there are some objects where the line implies that there is material down to the last stable orbit in a maximally spinning Kerr spacetime most notably MCG Wilms et al.
However, the strong gravity codes generally used to model these effects are now over a decade old. Increased computer power means that it is now possible to improve on these models. This emissvity law is not only dependent on the location of the emitter within the disc, but also the initial direction that a photon is emitted in. Light-bending means that a range of initial photon directions contribute to the observed radiation spectrum at a given inclination. By contrast, the spectra of the second-order image is dominated by discrete spectral features in both cases. References Ballantyne, D.
Beckwith, K. Bursa, M. Cunningham, C. Laor, A. Lubinski, P. Nayakshin, S. Ross, R. Zycki, P. Several AGN and black hole X-ray binaries show a clear very broad iron line, which is strong evidence that the black holes are rapidly spinning. The strong gravitational light bending in these regions then explains the power-law variability as due to changes in height of the primary X-ray source above the disc.
Keywords: accretion, accretion disks, black hole physics, x-rays: galaxies 1. For a spinning Kerr black hole it reduces as the spin increases Bardeen et al. Broad iron lines seen in the spectrum of several active galaxies and galactic black hole binaries are reviewed here. The cases for relativistic lines in the Seyfert galaxy MCG and the X-ray binary GX are very strong, indicating that those black holes are rapidly spinning. The puzzling spectral variability of such sources is now beginning to be understood within the context of emission from the strong gravity regime Miniutti and Fabian, This is discussed within the context of state changes and jetted emission observed in the galactic black holes.
This raises the exciting possibility that the spin energy of the hole is being tapped Wilms et al. Right panel: The light curve in Figure 3. Centre panel: Iron line variability in the last orbit of from Iwasawa et al. Iwasawa et al. Figure 3 , but that the general amplitude of the variations was considerably less than expected and not directly correlated with the observed continuum. Left panel: The two component model in which the PLC solid line varies considerably in amplitude while the RDC dashed line varies little. Right panel: RDC vs. PLC normalizations for The model consists of a highly variable power-law component PLC plus a much less variable harder component carrying the iron line RDC, Figure 2a.
It is a power-law from 3 to 10 keV with no iron-K features. On the assumption that this power-law continues to lower energies, where attenuation at low energies due to both galactic absorption and the warm absorber in MCG is seen. Small variations in the amplitide of the RDC are seen. Since however, both show the effects of the warm absorber they must originate in a similar location. How bright the PLC appears depends strongly on its height above the disc. Much of the radiation is bent down to the disc and black hole when the PLC is at a height of a few rg but less so above 20rg Figure 5a.
Part of the source variability can thus be explained by an intrinsically constant PLC changing height above the disc. Intrinsic variability of the PLC might also be present. The RDC is expected to change little during PLC variations due to source position but will change with intrinsic variability. The lines in GX Figure 6a, Miller et al. That in GX shows a very broad red wing indicating that the black hole is rapidly spinning.
Changes in the strength of the iron line as the power-law continuum varied during the outburst of XTE J Rossi et al. Narrow Line Seyfert 1 galaxies tend to show steep soft X-ray spectra and sometimes broad iron emission features. One extreme such object is 1H which has a marked drop in its spectrum above 7 keV. This is either an absorption edge A. Figure 7. Broad-Line-Free Sources Some objects show no evidence for a broad line. There are also intermediate sources where the data are either poor or there are complex absorption components so that one cannot argue conclusively that there is a relativistic line present.
Generalization of the Light-Bending Model Our interpretation of the spectral behaviour of MCG and some other sources means that we are observing the effects of very strong gravitational light bending within a few gravitational radii of a rapidly spinning black hole. The short term 10— ks behaviour is explained, without large intrinsic luminosity variability, through small variations in the position of the emitting region in a region where spacetime is strongly curved.
This implies that some of the rapid variability is due to changes in the source position. Cyg X-1, Uttley and McHardy, This picture suggests a possible generalization of the light-bending model to unify the AGN and BHC in their different states. Note the work of Fender et al. The key parameter may be the height of the main coronal activity above the black hole. Assume that much of the power of the inner disc passes into the corona Merloni and Fabian, and that the coronal activity is magnetically focussed close to the central axis.
Beloborodov, Any jet is weak. The objects with the highest spin and highest accretion rate give the most extreme behaviour. Summary A relativistically-broadened iron line is unambiguous in the spectra and behaviour of a few objects. Studies in the near future with ASTRO-E2 followed by XEUS and Constellation-X in the next decade will continue to open up the immediate environment of accreting black holes, within just a few gravitational radii, to detailed study.
Acknowledgements Thanks to G. Miniutti, S. Vaughan, K. Iwasawa and J. Miller for collaboration and many discussions. The generalization of the light bending modelling was developed with them and A. The Royal Society is thanked for support. Bardeen, J. Beloborodov, A. Boller, T. Branduardi-Raymont, G. Dabrowski, Y. Gallo, L. Martocchia, A. Matt, G. Rossi, S. Shih, D.
Taylor, R. Uttley, P. We discuss the evolution of black hole transients on the basis of a few systems that were intensively observed with the Rossi X-ray Timing Explorer rxte. We focus on the global evolution and the observed state transitions. Rather than giving a numerical recipe for classifying observations, we try to identify times during outbursts at which clear changes occur in the X-ray variability, X-ray spectral, or multi-wavelength properties. Keywords: accretion, accretion disks, black hole physics, X-rays: stars, X-rays: binaries 1. These observations have provided a wealth of information and have already led to a considerable increase in our understanding of these systems.
In this paper we approach the issue from an other angle, focusing on the observed transitions, the overall evolution during an outburst, and how X-ray changes relate to changes at other wavelengths. Esin et al. Homan et al. Astrophysics and Space Science —, The three types can be distinguished on the basis of strength, coherence, phase lags, energy dependence, harmonic content, and frequency stability on a time scale of days. Recent observations of H— Homan et al. Global Evolution Hardness—intensity diagrams HIDs , in which the X-ray count rate is plotted versus an X-ray color, provide a quick way to study the global evolution of black hole transients during outburst.
The HIDs are similar to each other in that all four sources seem to trace out part of a counter-clockwise q-shaped track. Below a certain count rate the spectrum is always very hard i. This means, as was noted by other authors as well see e. Complete references for our discussion can be found in those works. A Detailed Look at the States 4. In Figure 2 we show the early evolution of GX —4. During the rise the frequencies of the noise components and the occasional QPO increased gradually.
An example of a power-density spectrum from this state in GX —4 is shown in Figure 3. The two gray lines show the presence of two different time scales during the early rise. At this point the source entered an intermediate state see Section 4. Examples of power-density spectra of GX —4 from the four states discussed in the text. The different behavior for the different states is evident.
In our view the hard state is limited to only the hardest power-law dominated spectra with indices around 1. In the HID this can be nicely seen as the lower horizontal branch bending down to start running parallel to, and in fact nearly on top of, the hard state branch that was traced out during the rise. We are not aware of any exception to this. This state is different from the hard state in several aspects.
All these properties evolve smoothly from and to the hard state. In the timing domain, the broad-band variability components seen in the power-density spectrum increase their characteristic frequencies, showing an evolution that clearly links them to the corresponding components in the hard state. A clear type C QPO appears, also with a characteristic frequency increasing with time and decreasing hardness see Belloni et al. A typical power-density spectrum from the intermediate state is shown in Figure 3.
After passing through the intermediate GX —4 continued to brighten in the soft sate during its outburst. In most sources the change from type C to type B QPOs seems to take place when the power-law index has a value around 2. In fact, power-laws with such indices are accompanied by a great variety of timing properties: not only type A, B or C QPOs, but also very weak variability like that seen in the soft state.
The part of the transition where the power-law index is relatively constant around a value of 2. It is important to note that the change from the hard intermediate to the soft intermediate state was repeated again in the outburst at the same spectral hardness. It is possible however that the high frequency QPOs in soft intermediate state evolve from broader features in the hard intermediate state, as is suggested by observations of XTE J— Homan et al.
The energy spectrum of the soft state is dominated by a strong thermal component, with the presence of a weak steep power-law component, which was not observed to show a high-energy cutoff see Grove et al. Variability in the soft state is weak compared to the other states, with typical rms amplitudes of at most a few percent root mean square. Unfortunately, by the time most transients reach the soft state they are usually in the decay phase and observations have become shorter and less frequent, so detailed studies of its variability properties are rare.
Surprisingly, the QPO and break frequencies of these power spectra fall on top of the Wijnands—van der Klis relation Wijnands and van der Klis for black holes in the hard and hard intermediate states. This suggests not only that these might be type C QPOs, but more importantly, that variability properties that once were thought to be characteristic of the hard and hard intermediate states are still present in the soft state, although in a much weaker form. As shown above, the hard intermediate and soft intermediate states are kept separate, as both spectral and timing evolution show marked differences.
The hard state and the hard intermediate states have much in common. Spectrally, they are dominated by a hard component for which a high-energy cutoff is observed Grove et al. In the timing domain, the components observed in the powerdensity spectrum in these two states are clearly related, as can be seen from the evolution of their characteristic frequencies Belloni et al.
Clear transitions are marked by gray segments. The branches corresponding to the four basic states in the q-track are labeled Belloni et al. The soft state and soft intermediate state are spectrally somewhat related. The energy spectrum is dominated by the thermal disk component, with a steep hard component with no evidence of a high-energy cutoff. The power density spectrum lacks band-limited components and shows only QPOs superimposed on a power-law component. No radio emission is observed i. In terms of variability however, the soft state shares some properties with the hard state and hard intermediate state, with the typical variability time scales following the same relation as seen in those states.
If the hard-state variability properties are linked to jet production, the presence of related but much weaker variability in the soft state could indicate a very weak i. In addition to these general properties, there is a number of important topics whose detailed discussion is beyond the scope of the present paper. Most notably, the fast transitions observed between different states never involving the hard state, which is only reserved for the beginning and the end of an outburst need to be studied in detail, as they probably hold the key for a deeper understanding of the physics of the states and their association to the jet.
Also, some sources can have bright outbursts without ever leaving the hard state, indicating that once again the instantaneous mass accretion rate is not what determines the transitions. For example, delays between a fast i. The picture presented here, scaled to longer time scales, should also be valid for AGNs. In these sources, there is no contribution of the optically thick accretion disk in the X-ray band, but the path shown in Figure 5 is qualitatively similar if the disk contribution is removed.
References Bailyn, C. Casella, P. Cui, W. Grove, J. Kalemci, E. Meyer-Hofmeister, E. Miyamoto, S. Rossi, R. Smith, D. Wijnands, R. Received 23 September ; accepted 1 June Abstract. Observations with XMM-Newton have changed this. Particular attention will be given to the remarkable similarity found between the timing properties of Seyferts and black hole X-ray binaries, including the power spectrum and the cross spectrum time delays and coherence , and their implications for the physical processes at work in Seyferts.
Keywords: X-rays, variability, active galaxies 1. Introduction X-ray variability appears to be ubiquitous in active galactic nuclei AGN. It was noted early on Lawrence et al. In recent years long RXTE monitoring observations have detected these breaks e. Uttley et al. Figure 1 shows an example of a broad-band 0. Several Seyfert 1 galaxies have been studied with long XMM-Newton observations and yielded interesting power spectra. Figure 2 shows the power spectra for three of these. The XMM-Newton results clearly reveal similar high frequency breaks in the power spectra also measured Figure 1.
XMM-Newton light curve of Mrk binned to sec resolution. XMM-Newton power spectra of three Seyfert 1 galaxies. This is necessarily a model-dependent procedure and is not advisable if sharp features are present in the spectrum. However, for these rather broad, smooth spectra unfolding does provide a clear, if slightly crude, impression of the shape of the underlying spectrum free from sampling effects. These XMM-Newton observations have also demonstrated the energy dependence of the power spectrum.
The cross spectrum compares the variations in one band with those in another as a function of frequency. The amplitude of the cross spectrum gives the coherence Vaughan and Nowak, while the argument gives the phase lag time delay; Nowak et al. The observations typically show high coherence at the lowest frequencies i. At low frequencies, where the coherence is high, the data also exhibit small time delays, with the soft leading the hard variations Vaughan et al. The magnitude of the time delay decreases with increasing frequency although the functional form of the relation is poorly constrained.
The timing studies have revealed: — Similar broken power spectra in Seyferts but object-to-object differences in normalisation variability amplitude and high frequency slope. Figure 3 shows the available data for 11 Seyferts. The connection between Seyferts and GBHCs is reinforced by the similarity between their cross spectra. It is well known that GBHCs show highly coherent variations at low frequencies with the coherence fading away at the highest frequencies plus frequency dependent time lags similar to those measured in Seyferts Nowak et al.
One may ask what advantage is gained by studying Seyferts in X-rays if GBHCs operate with the same physics but provide much higher quality data? The masses are from reverberation mapping experiments except for the four objects marked using dotted error bars. In the simplest models harder photons are expected to lag behind the softer photons due to the larger number of scatterings required to produce harder photons; the delay should be of order the light-crossing time of the corona. The direction and magnitude of the observed time lags in Seyfert 1s are consistent with an origin in a Comptonising corona.
However, if the lags are frequency dependent as expected by analogy with Cygnus X-1 S. Alternatively, the time delay between soft and hard bands could be due to the spectral evolution of individual X-ray events Poutanen and Fabian, or propagation of accretion rate variations through a extended emission region Kotov et al.
ACF is supported by the Royal Society. References Barr, P. Green, A. Jansen, F. Kotov, O. Lawrence, A. Markowitz, A. McHardy, I. Hunt and B. Battrick eds. Nandra, K. Nowak, M. Poutanen, J. Press, W. Revnivtsev, M. Ogelman, and E. Vignali, C. We present and discuss a short and simple derivation of orbital epicyclic frequencies for circular geodesic orbits in stationary and axially symmetric spacetimes. Such spacetimes include as special cases analytically known black hole Kerr and Schwarzschild spacetimes, as well as the analytic Hartle-Thorne spacetime and all numerically constructed spacetimes relevant for rotating neutron stars.
Our derivation follows directly from energy and angular momentum conservation and it uses the concept of the effective potential. Keywords: black holes, neutron stars, orbital motion, epicyclic frequencies 1. Introduction Properties of congruences of nearly circular geodesic orbits in stationary and axially symmetric spacetimes are studied because of their fundamental role in the theory of accretion disks around compact objects with strong gravity.
Analytic formulae for the three frequencies in Schwarzschild, Kerr and Hartle-Thorne metrics have been published many times by several authors see e. Wald, ; Okazaki et al. This fully relativistic derivation is remarkably simple: just four short lines of very transparent, easy to check algebra. The reader who is interested only in our four-line derivation may skip the next two sections and start reading from Section 4.
The red curve represents the stationary model and the green dots show local values of the temperature for the time-dependent computation. In this section, we focus on the numerical computations of the full time-dependent model. We perform the full computations of the radiation pressure instability models since the stability curves give us only the information about the local disk stability. However, the viscous transport Eq. Figures 2 and 3 present the stability curves red and the global solutions of the dynamical model plotted at the same single radius green.
The time-dependent solution never sets on the stability curve, the covered area in Fig. This part of the evolution describes the prolonged period between the outbursts. The models present a strongly developed instability, leading to huge outbursts. The red curve represents the stationary solution and the green dots show local values of the temperature and density in the dynamical model. The points occupy both the upper and lower branches of the S-curve. For comparison with the observed data we need to know the global time behaviour of the disk for a broad parameter range.
For each mass, we present the relations between period, amplitude, and duration divided by period. According to Czerny et al. For our models, the critical value of accretion rate is at the level of 0. Here we define different characteristic modes of the flares. Since we have a dynamical system described by a set of non-linear partial differential equations, we expect that the flares will form different patterns of variability, which should be comparable to the observed patterns.
For that non-linear system we can distinguish between the flickering behaviour and the strong flares. In Figs. The difference between the flickering and outburst modes lies not only in their amplitudes; as we can see in Fig. The latter, corresponds to the temperature and density variations presented in Fig.
In contrast, Fig. In the case of flickering we can distinguish two phases of the cycle: i heating, when the temperature in the inner regions of the disk is growing rapidly, and ii advective, when the inner annuli cool down significantly, and are then extinguished when the disk is sufficiently cool. Now, after a strong decrease of advection, the heating phase repeats again. In the case of the burst, the phases i and ii are much more developed and advection is able to achieve instantaneous thermal equilibrium of the disk, in contradiction to flickering, where the disk is always unstable.
Then, the phase of heating repeats. The black area corresponds to cases of stable solutions without periodic flares. The violet area corresponds to a small flickering, and red and yellow areas correspond to bright outbursts. Thus, the stabilising influence of a magnetic field is more pronounced for the microquasars, than for AGNs.
Our results include different variability patterns. As shown in Fig. To preserve the average luminosity on sub-Eddington level, also the light curve shape should change with at least one of these parameters. To preserve the average luminosity L , the energy emitted during the flare plus energy emitted during quiescence between the flares should be lower than the energy emitted during one period.
Since the radiation pressure instability reaches only the inner parts of the disk, the outer stable parts of the disk radiate during the entire cycle, maintaining the luminosity at the level of L min. This level can be computed from Eq. Black regions represent no flares and a lack of instability. In Figure 7 , we present the dependence between period and amplitude for the microquasars, intermediate mass black holes and AGN, respectively. Figure 7 was made for the three grids of these models which result in significant limit-cycle oscillations i.
In our work we used regular and rectangular grids. Nevertheless, the observed properties of the sources see, e. Table 5 in Sect.
The results shown by points in Fig. The above general relation gains the following forms, if we want to use it for the sources with different black hole mass scales: 32 for the microquasars see fit on Fig. From the formula 31 we can estimate the values of masses of objects, if the values of P and A are known. The positive correlation between period and amplitude indicates that those observables originate in one non-linear process, operating on a single timescale. Although the variability patterns can vary for different accretion rates, for a given mass, the period and amplitude are strongly correlated and can describe the range of instability development.
It can, in general, be adjusted by the specific model parameters, but the basic disk variability pattern is universal in that picture. We note that the scatter is now larger than in Fig. One triangle represents one model. Lines represent fits for each mass. In Fig. Both values are dimensionless and show similar reciprocal behaviour for the black hole accretion disks flares across many orders of magnitude. The timescale of flare scales is approximately inversely proportional to the mass.
According to Fig. We note that Eq. This effect is even more pronounced for larger black hole masses. From those figures, we get the following fitting formulae: Equations 36 and 37 result in the following estimation for P and A 38 In Figs. From those figures, we can derive the following formulae: Equations 39 and 40 result in the following estimation for P and A : 41 In Figs.
We get the following formulae from those figures: Equations 42 and 43 result in the following estimation for P and A : The grids of models deliver some information about the correlation between the observed light curve features and the model parameters. From the Eq.
Those objects are not the product of collapse of single massive stars Davis et al. The exact value of the bolometric correction is strongly model-dependent. The fits of the thermal state with the diskbb model Servillat et al. The use of the diskbb model for larger black hole mass, 10 5 , implies an inner temperature, T in of 0. Thus the overall disk emission may not be significantly modified for the outer radii, and the hottest tail can still extend up to the soft X-ray band.
A factor of 5 qualitatively accounts for that trend Maccarone et al. The inclination angle is not well constrained by the observations. As we see from Eq. These values are close to the model parameters, which are necessary to reproduce the light curve. Therefore, we conclude that our model of an accretion disk with the modified viscosity law gives a proper explanation of HLX-1 outbursts. The model to data comparison, being the result of our analysis, is presented in the Fig.
The observation presented in Fig. In Wu et al. In particular, we tested the large parameter space of our computations, and verified their influence on the observable characteristics of the sources. We also slightly better determined the mass of the black hole in this source. According to Eqs. The results are presented in Table 3. We compare the allowed parameters of duration to period ratios Cols.
We get three values of relative amplitude for each source to present possible limitations for periods and duration times. The timescales presented in the Tables are on the order of minutes for the microquasars, of months for the HLXs, and of millenia for the AGN, which correspond to their viscous timescale. The period is strongly dependent on the amplitude and can change by several orders of magnitude for each mass. Exact duration values from the fit presented in Eq. For microquasars, the values included in Table 3 correspond to the typical values for small and intermediate flares, the same for the case of IMBHs.
In case of AGN, the appearance of big flares is necessary to verify our model with the observational data presented in the Fig. Table 3 Outburst duration values for three kinds of source. Table 4 Outburst duration values for three kinds of source. In this work, we studied the accretion disk instability induced by the dominant radiation pressure, with the use of the generalised prescription for the stress tensor.
We computed a large grid of time-dependent models of accretion disks, parameterised by the black hole mass, and mass accretion rate. We used the values of these parameters, which are characteristic for the microquasars, intermediate black holes, or AGN.
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One of our key findings is that this model can be directly applicable for determination of the black hole mass and accretion rate values, for example, for the Ultraluminous X-ray source HLX-1, and possibly also for other sources. The flare period grows monotonously with its amplitude, for any value of mass see Fig. The outburst width remains in a well-defined relationship with its amplitude see Fig. Our results present different variability modes Figs. The flickering mode is presented in Fig.
In this mode the relative amplitude is small, and flares repeat after one another. In the burst mode the amplitude is large, and the maximum luminosity can be hundreds of times greater than minimal. An exemplary light curve is shown in Fig. In this mode we observe long separation between the flares i. A slow rise of the luminosity is the characteristic property of the disk instability model. The formulae describing fits in Fig. The results are given in Table 5. Our model thus works properly for the periodic and regular oscillations, which are produced in the accretion disk for a broad range of parameters, if only the instability appears.
In general, the method is correct for estimation of the order of magnitude, although not perfect for exact determination of the parameters due to the nonlinearity of the model. For a source with known mass, such as GRS Greiner et al. Steeghs et al. From the high-frequency QPO comparison method used by Rebusco et al. Combining the results of Rebusco et al.
Results of Iyer et al. In our current model we neglect the presence of the accretion disk corona. If we follow the mass estimation done by Iyer et al.
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We get the above results under the assumption of negligible influence of coronal emission on the light curve. From the grid of models performed in Czerny et al. If we combine Eqs. Combining Eqs. Thick lines represent the best fit from Wu et al. Thin lines represent Eq. We assumed that the Eddington accretion rate and the accretion efficiency are roughly independent for different BH masses. The proportionality coefficient in Eq. It should be possible to study the evolution of those sources statistically.
Based on the known masses, accretion rates, and timescales for AGN, the luminosity distribution for the samples of AGN with similar masses or accretion rates can be acquired. This should allow us to reproduce an average light curve for a range of masses and accretion rates for a survey of the known AGNs Wu The averaged light curve for a big ensemble of AGN will help us to provide expected luminosity distributions or luminosity-mass, luminosity-duration relations for the AGNs existing in the universe.
However, high-amplitude outbursts may complicate the study since the detection of the sources between the flares may be strongly biased as the sources become very dim. Although most AGN have a variability timescale on the order of thousands of years, the shape of model light curves sharp and rapid luminosity increases could suggest that, for some cases, luminosity changes can be observed. The light curve of HLX-1, presented in the upper panel of Fig.
To our knowledge, the only explanation for such a phenomenon is variation in the input parameters. The variability of the central object mass is too faint approx. According to Eq. We propose a possible application of the modified viscosity model as a description of a regular variability pattern heartbeat states of black hole accretion disks for the microquasars, IMBHs and AGNs.
The model works for optically thick, geometrically thin disks and determines the range and scale of the radiation pressure instability. Nonlinearity of the models causes appearance of different modes of the disk state stable disk, flickering, outbursts. Thanks to the computation of computing a large grid of models we are able to present quantitative estimations for the variability periods and amplitudes, and our model light curves reproduce several different variability patterns. Finally, our model can be successfully applied to the mass and accretion rate determination for the intermediate black hole HLX-1 at the level of 1.
The prospects of further applications to microquasars and AGNs are promising. We thank Petra Sukova for helpful discussions, Conor Wildy for the language corrections and the anonymous referee for constructive comments. Correlation between the bolometric luminosity and the outburst duration for different-scale BHs. Data correspond to usage on the plateform after The current usage metrics is available hours after online publication and is updated daily on week days.