Sergei Nayakshin

Thermal instability and photoionized X-ray reflection in accretion disks

We study the illumination of accretion disks in the vicinity of compact objects by an overlying X-ray source. Our approach differs from previous works of the subject in that we relax the simplifying assumption of constant gas density used in these studies; instead we determine the density from hydrostatic balance which is solved simultaneously with the ionization balance and the radiative transfer in a plane-parallel geometry. We calculate the temperature profile of the illuminated layer and the reprocessed X-ray spectra for a range of physical conditions, values of photon index Γ for the illuminating radiation, and the incident and viewing angles. In accordance with some earlier studies, we find that the self-consistent density determination makes evident the presence of a thermal ionization instability well known in the context of quasar emission line studies. The main effect of this instability is to prevent the illuminated gas from attaining temperatures at which the gas is unstable to thermal perturbations. Thus, in sharp contrast to the constant density calculations that predict a continuous and rather smooth variation of the gas temperature in the illuminated material, we find that the temperature profile consists of several well defined thermally stable layers. Transitions between these stable layers are very sharp and can be treated as discontinuities as far as the reprocessed spectra are concerned. In particular, the uppermost layers of the X-ray illuminated gas are found to be almost completely ionized and at the local Compton temperature (~107-108 K); at larger depths, the gas temperature drops abruptly to form a thin layer with T ~ 106 K, while at yet larger depths it decreases sharply to the disk effective temperature. For a given X-ray spectral index, this discontinuous temperature structure is governed by just one parameter, A, which characterizes the strength of the gravitational force relative to the incident X-ray flux. We find that most of the Fe Kα line emission and absorption edge are produced in the coolest, deepest layers, while the Fe atoms in the hottest, uppermost layers are generally almost fully ionized, hence making a negligible contribution to reprocessing features in the ~6.4-10 keV energy range. We also find that the Thomson depth of the top hot layers is pivotal in determining the fraction of the X-ray flux which penetrates to the deeper cooler layers, thereby affecting directly the strength of the Fe line, edge and reflection features. Due to the interplay of these effects, for Γ 2, the equivalent width (EW) of the Fe features decreases monotonically with the magnitude of the illuminating flux, while the line centroid energy remains at 6.4 keV. We provide a summary of the dependence of the reprocessing features in the X-ray reflected spectra on the gravity parameter A, the spectral index Γ, and other parameters of the problem. We emphasis that the results of our self-consistent calculations are both quantitatively and qualitatively different from those obtained using the constant density assumption. Therefore, we propose that future X-ray reflection calculations should always utilize hydrostatic balance in order to provide a reliable interpretation of X-ray spectra of active galactic nuclei and galactic black hole candidates.

Accretion Disk Models and Their X-Ray Reflection Signatures. I. Local Spectra

X-ray illumination of accretion disks is an invaluable diagnostic of the structure of these disks because of the associated iron Kα emission. Here we point out that the resulting reflected spectra depend very sensitively on the geometry of the X-ray source and that this fact can be efficiently used to test these models observationally. In particular, we discuss three different accretion disk geometries: the lamppost model, accretion disks with magnetic flares, and the model with a full corona overlaying a cold thin disk. We show that in the case of the lamppost model, unless the X-ray luminosity of the central source is larger than that of the cold disk by a factor of 10 or more, a significant fraction of iron in the ionized skin of the disk is in the hydrogen and helium-like ions. Because these ions have large fluorescence yields, the resulting reflected spectra look strongly ionized, with equivalent width (EW) of the line increasing with X-ray luminosity LX up to the maximum of ~500 eV. This situation contrasts to the magnetic flare model, where the large X-ray flux near flares completely ionizes the skin of the disk and thus the resulting spectra appear to be that from a neutral material. The line EW in this model anticorrelates with X-ray luminosity and becomes arbitrarily small when LX is a good fraction of the Eddington luminosity. Finally, in the full corona case, due to the additional pressure and weight of the corona, the gas pressure (and its density) below the corona is always large enough to make the gas very cool and effectively neutral. No highly ionized skin forms in such a model. If the corona is Thomson thin, then EW of the line does not depend on the accretion disk or corona luminosities for the full corona model.

Time-dependent Disk Models for the Microquasar GRS 1915+105

During the past three years, the Galactic black hole microquasar GRS 1915)105 has exhibited a bewildering diversity of large-amplitude, chaotic variability in X-rays. Although it is generally accepted that the variability in this source results from an accretion disk instability, the exact nature of the insta- bility remains unknown. Here we investigate diUerent accretion disk models and viscosity prescriptions in order to provide a basic explanation for some of the exotic temporal behavior in GRS 1915)105. We discuss a range of possible accretion —ow geometries. Any geometrically thick disk (e.g., an advection- dominated accretion —ow (ADAF) or a ii slim ˇˇ accretion disk) has trouble explaining the very long cycle times unless the a-parameter is exceedingly small (D10~4). In addition, the rise/fall timescales in GRS 1915)105 can be a factor of 100 shorter than the cycle times, whereas thick disks predict that these two timescales should be comparable. We thus concentrate on geometrically thin (though not necessarily standard) Shakura-Sunyaev type disks. We argue that X-ray observations clearly require a quasi-stable accretion disk solution at a high accretion rate at which radiation pressure begins to dominate, which excludes the standard a-viscosity prescription. We have therefore devised a simpli—ed model of a disk with a corona and a modi—ed viscosity law that has a quasi-stable upper branch, and we have developed a code to solve the time-dependent equations to study the evolution of this con—guration. Via numerical simulations, we show that the model does account for several gross observational features of GRS 1915)105, including its overall cyclic behavior on timescales of D100¨1000 s. On the other hand, the rise/fall timescales are not as short as those observed, no rapid oscillations on timescales s emerge (10 naturally from the model, and the computed cycle-time dependence on the average luminosity is stronger than is found in GRS 1915)105. We then consider, and numerically test, a more elaborate model that includes the ii cold ˇˇ disk, a corona, and plasma ejections from the inner disk region that occur when the luminosity of the source is near the Eddington luminosity. The inclusion of a jet allows us to reproduce several additional observed features of GRS 1915)105. We conclude that the most likely structure of the accretion —ow in this source is that of a cold disk with a modi—ed viscosity law, plus a corona that accounts for much of the X-ray emission and unsteady plasma ejections that occur when the luminosity of the source is high. The disk is geometrically thin (as required by the data) because most of the accre- tion power is drained by the corona and the jet. Subject headings: accretion, accretion disksblack hole physics ¨ quasars: individual (GRS 1915)105) ¨ X-rays: general

On the X-Ray-heated Skin of Accretion Disks

We present a simple analytical formula for the Thomson depth of the X-ray-heated skin of accretion disks valid at any radius and for a broad range of spectral indices of the incident X-rays, accretion rates, and black hole masses. We expect that this formula may find useful applications in studies of geometry of the inner part of accretion flows around compact objects, and in several other astrophysically important problems, such as the recently observed X-ray Baldwin effect (i.e., monotonic decrease of the Fe lines equivalent width with the X-ray luminosity of active galactic nuclei [AGNs]), the problem of the missing Lyman edge in AGNs, and line and continuum variability studies in accretion disks around compact objects. We compute the reflected X-ray spectra for several representative cases and show that for hard X-ray spectra and large ionizing fluxes the skin represents a perfect mirror that does not produce any Fe lines or absorption features. At the same time, for soft X-ray spectra or small ionizing fluxes, the skin produces a very strong ionized absorption edge and highly ionized Fe lines that should be observable in the reflected spectra.

Self-consistent Fokker-Planck treatment of particle distributions in astrophysical plasmas

High-energy, multicomponent plasmas in which pair creation and annihilation, lepton-lepton scattering, lepton-proton scattering, and Comptonization all contribute to establishing the particle and photon distributions are present in a broad range of compact astrophysical objects. The different constituents are often not in equilibrium with each other, and this mixture of interacting particles and radiation can produce substantial deviations from a Maxwellian profile for the lepton distributions. Earlier work has included much of the microphysics needed to account for electron-photon and electron-proton interactions, but little has been done to handle the redistribution of the particles as a result of their Coulomb interaction with themselves. The most detailed analysis thus far for finding the exact electron distribution appears to have been done within the framework of nonthermal models, where the electron distribution is approximated as a thermal one at low energy with a nonthermal tail at higher energy. Recent attention, however, has been focused on thermal models. Our goal here is to use a Fokker-Planck approach in order to develop a fully self-consistent theory for the interaction of arbitrarily distributed particles and radiation to arrive at an accurate representation of the high-energy plasma in these sources. We derive Fokker-Planck coefficients for an arbitrary electron distribution and correct an earlier expression for the diffusion coefficient used by previous authors. We conduct several tests representative of two dominant segments of parameter space. For high source compactness of the total radiation field, l ~ 102, we find that although the electron distribution deviates substantially from a Maxwellian, the resulting photon spectra are insensitive to the shape of the exact electron distribution, in accordance with some earlier results. For low source compactness, l ~ few, and an optical depth 0.2, however, we find that both the electron distribution and the photon spectra differ strongly from what they would be in the case of a Maxwellian distribution. In addition, for all values of compactness, we find that different electron distributions lead to different positron number densities and proton equilibrium temperatures. This means that the ratio of radiation pressure to proton pressure is strongly dependent on the lepton distribution, which might lead to different configurations of hydrostatic equilibrium. This, in turn, may change the compactness, optical depth, and heating and cooling rates and therefore lead to an additional change in the spectrum. An important result of our analysis is the derivation of useful, approximate analytical forms for the electron distribution in the case of strongly non-Maxwellian plasmas.

On Time-dependent X-Ray Reflection by Photoionized Accretion Disks: Implications for Fe Kα Line Reverberation Studies of Active Galactic Nuclei

We perform the first study of time-dependent X-ray reflection in photoionized accretion disks. We assume a step-functional change in the X-ray flux and use a simplified prescription to describe the time evolution of the illuminated gas density profile in response to changes in the flux. We find that the dynamical time for readjustment of the hydrostatic balance is an important relaxation timescale of the problem since it affects the evolution of the ionization state of the reflector. If the variations of the X-ray flux occur on timescales shorter than this time, then the Fe Kα line emissivity is not a function of the instantaneous illuminating spectrum since it depends on the shape and intensity of the illuminating flux in prior times. Moreover, during the transition, a prominent Helium-like component of the Fe Kα line may appear. As a result, the Fe Kα line flux may appear to be completely uncorrelated with X-ray continuum flux on timescales shorter than the dynamical time. In addition, the time dependence of the illuminating flux may leave imprints even on the time-averaged Fe Kα line spectra, which may be used as an additional test of accretion disk geometry. Our findings appear to be important for the proposed Fe Kα line reverberation studies in lamppost-like geometries for accretion rates exceeding about ~1% of the Eddington value. However, most active galactic nuclei do not show Helium-like lines that are prominent in such models, probably indicating that these models are not applicable to real sources.

Observational Signatures of X-Ray-irradiated Accretion Disks

Reflection of X‐rays from cool material around a black hole is one of the few observational diagnostics of the accretion flow geometry. Models of this reflected spectru m generally assume that the accretion disk can be characterized by material in a single ionization state. H owever, several authors have recently stressed the importance of the classic ionization instability for X‐ray irradiated gas in hydrostatic balance. This instability leads to a discontinuous transition in the vertical structure of the disk, resulting in a hot ionized skin above much cooler material. If the Compton temperature of the skin is high then even iron is completely ionized, and the skin does not produce any spectral features. These new models, where the ionization structure of the disk is calculated self‐consistently, require an excessive amount of computing power and so are difficult to use in directly fitting observed X‐ray spectra. Instead, we invert the probl em by simulating X‐ray spectra produced by the new reflection models, and then fit these with the old, single zone reflection models, to assess the extent to which the derived accretion geometry depends on the reflection model u sed. We find that the single zone ionization models can severely underestimate the covering fraction of the “cold” material as seen from the X‐ray source if the optical depth in the ionized skin is of order unity, and that this can p roduce an apparent correlation between the covering +∞

Magnetic Flare Origin of X-Rays in Active Galactic Nuclei: Photoionization Evidence

We present full-disk X-ray reflection spectra for two currently popular accretion flow geometries for active galactic nuclei (AGNs): (1) the lamppost model, which is frequently used to discuss the iron-line reverberation in AGNs, and (2) the model in which X-rays are produced in magnetic flares above a cold accretion disk. The lamppost spectra contain several spectroscopic features that are characteristic of highly ionized material that is not seen in the X-ray spectra of most AGNs. The magnetic flare model, on the other hand, produces reflected spectra that are roughly a superposition of a power law and a neutral-like reflection and an iron Kα line; thus, these spectra are more in line with typical AGN X-ray spectra. Furthermore, because of the difference in the ionization structure of the illuminated material in the two models, the line equivalent width increases with the X-ray luminosity LX for the lamppost and decreases with LX for the flare model. In light of these theoretical insights, the recent iron-line reverberation studies of AGNs, the X-ray Baldwin effect, and the general lack of X-ray reflection features in distant quasars all suggest that, for high accretion rates, the cold accretion disk is covered by a thick, completely ionized Thomson skin. Because the latter is only possible when the X-rays are concentrated in small emitting regions, we believe that this presents strong evidence for the magnetic flare origin of X-rays in AGNs.

Modeling the X-Ray-Optical Correlations in NGC 3516

We test the reprocessing paradigm of the optical -- UV AGN variability by detailed modeling of the correlated X-ray -- optical (3590 and 5510 Angstrem) variability of the recent multiwavelength campaign of NGC 3516. We produce model optical light curves by convolving the observed X-ray flux with the response function of an infinite, thin accretion disk, illuminated by a point-like X-ray source at a given height above the compact object (the lamp-post model) and compare their properties to those observed. Special attention is given to the correct computation of the X-ray albedo of the disk. We further compute the X-ray reflection response at two energies (E = 1 and 20 keV) and argue for the possibility of hard lags in their cross spectra. We also compute the continuum Optical -- UV and the X-ray reflection spectra as well as the Fe K-alpha fluorescent line profiles which we also compare to observations. Despite the large (~50 percent) amplitude excursions of the X-ray flux, the model optical light curves exhibit variability amplitudes of 3 -- 4 percent, not unlike those observed. However, the model CCF between the X-ray and the model optical variations show clear lags of 0.1 and 0.25 days for black hole masses M = 10^7 and 10^8 Solar masses, respectively, not apparent in the data. The synchrony of X-ray - optical variations points toward the BH mass 10^8. Our conclusion is that the combination of the observed optical/UV/X-ray spectral and timing observations are inconsistent with the lamp-post model geometry for NGC 3516.

Testing models of X-ray reflection from irradiated discs

We model the reflected spectrum expected from localized magnetic flares above an ionized accretion disc. We concentrate on the case of very luminous magnetic flares above a standard accretion disc extending down to the last stable orbit, and use a simple parametrization to allow for an X-ray-driven wind. Full disc spectra including relativistic smearing are calculated. When fitted with the constant-density reflection models, these spectra give both a low reflected fraction and a small linewidth as seen in the hard spectra from galactic black hole binaries and active galactic nuclei. We fit our calculated spectra to real data from the low/hard state of Nova Muscae and Cyg X-1 and show that these models give comparable χ2 to those obtained from the constant-density reflection models, which implied a truncated disc. This explicitly demonstrates that the data are consistent either with magnetic flares above an ionized disc extending down to the last stable orbit around a black hole, or with non-ionized, truncated discs.