Line Centroid Energy Research Articles

Reverse Shock Revisited in Cassiopeia A with Chandra

Using data from the Chandra X-ray Observatory, we revisit the reverse shock in the supernova remnant (SNR) Cassiopeia A. Based on spectroscopy of a series of annuli in the northwest (NW) and southeast (SE), we get the radial profiles of the S/Si Kα line flux ratio and Fe Kα line centroid energy. They both show monotonic increase, confirming that the Si- and Fe-rich ejecta are heated by the reverse shock. The abrupt change of the S and Si line flux ratio is clearly observed in Cassiopeia A, leading to the determination of the reverse-shock location (∼1.′71 ± 0.′16 and ∼1.′35 ± 0.′18 in the NW and SE, with respect to the central source). By comparing the radial profiles of the S and Si line flux, we find that the reverse shock is moving outward in the frame of the observer, and the velocities are ∼3950 ± 210 km s−1 and ∼2900 ± 260 km s−1 in the NW and SE, respectively. In contrast, the velocities become ∼1150 km s−1 (NW) and ∼1300 km s−1 (SE) in the ejecta frame. Our measured reverse-shock velocities are quite consistent with those obtained from the X-ray and/or optical images. They therefore supply a cross-check of the accuracy for the two available methods for measuring the reverse-shock velocity in SNRs. Both the location and the velocity of the reverse shock show apparent asymmetry, suggesting that the asymmetric explosion of the progenitor plays a key role in the interaction between the reverse shock and the ejecta, ultimately shaping the complex features observed in SNRs.

Discovery of two cyclotron resonance scattering features in X-ray pulsar cen X-3 by Insight-HXMT

ABSTRACT We present the results of the neutron star X-ray binary system Cen X-3 performed by Insight-HXMT with two observations during 2017 and 2018. During these two observations, the source reached a X-ray luminosity of ∼1038 erg s−1 from 2–105 keV. The analysis of the broadband X-ray spectrum reports the presence of two cyclotron resonance scattering features (CRSFs) with the fundamental line at ∼ 28 keV and the harmonic line at ∼47 keV. The multiple lines exist by fittings with different continuum models, like the absorbed negative and positive power-law with an exponential cutoff (NPEX) model and a power-law with high energy exponential cutoff model. This is the first time that both fundamental and harmonic lines are detected in Cen X-3. We also show evidence of two cyclotron lines in the phase-resolved spectrum of Cen X-3. The CRSF and continuum spectral parameters show evolution with the pulse profile, and the two line centroid energy ratio does not change significantly and locates in a narrow value range of 1.6−1.7 over the pulse phase. The implications of the discovering two cyclotron absorption features and phase-resolved spectral properties are discussed.

Variations of cyclotron resonant scattering features in Vela X-1 revealed with Insight-HXMT

ABSTRACT We present a detailed study of the high-mass X-ray binary Vela X-1, using observations performed by Insight-HXMT in 2019 and 2020, concentrating on timing analysis and spectral studies including pulse phase-resolved spectroscopy. The cyclotron line energy is found to be ∼21–27 and 43–50 keV for the fundamental and first harmonic, respectively. We present the evolution of spectral parameters and find that the two line centroid energy ratio E2/E1 evolved from ∼2 before MJD 58900 to ∼1.7 after that. The harmonic cyclotron line energy has no relation to the luminosity but the fundamental line energy shows a positive correlation with X-ray luminosity, suggesting that Vela X-1 is located in the sub-critical accreting regime. In addition, the pulse phase-resolved spectroscopy in Vela X-1 is performed. Both the cyclotron resonant scattering feature and continuum parameters show strong variability over the pulse phase with the ratio of two line energies about 2 near the peak phases and down to ∼1.6 around off-peak phases. Long-term significant variations of the absorption column density and its evolution over the pulse phase may imply the existence of the clumpy wind structure near the neutron star.

Phase-resolved spectroscopy of a quasi-periodic oscillation in the black hole X-ray binary GRS 1915+105 with NICER and NuSTAR

ABSTRACT Quasi-periodic oscillations (QPOs) are often present in the X-ray flux from accreting stellar-mass black holes (BHs). If they are due to relativistic (Lense–Thirring) precession of an inner accretion flow which is misaligned with the disc, the iron emission line caused by irradiation of the disc by the inner flow will rock systematically between red and blue shifted during each QPO cycle. Here, we conduct phase-resolved spectroscopy of an ∼2.2 Hz type-C QPO from the BH X-ray binary GRS 1915+105, observed simultaneously with NICER and NuSTAR. We apply a tomographic model in order to constrain the QPO phase-dependent illumination profile of the disc. We detect the predicted QPO phase-dependent shifts of the iron line centroid energy, with our best fit featuring an asymmetric illumination profile (>2σ confidence). The observed line energy shifts can alternatively be explained by the spiral density waves of the accretion-ejection instability model. However, we additionally measure a significant (>3σ) modulation in reflection fraction, strongly favouring a geometric QPO origin. We infer that the disc is misaligned with previously observed jet ejections, which is consistent with the model of a truncated disc with an inner precessing hot flow. However, our inferred disc inner radius is small (rin ∼ 1.4 GM/c2). For this disc inner radius, Lense–Thirring precession cannot reproduce the observed QPO frequency. In fact, this disc inner radius is incompatible with the predictions of all well-studied QPO models in the literature.

Relation of Cyclotron Resonant Energy and Luminosity in a Strongly Magnetized Neutron Star GRO J1008-57 Observed by Insight-HXMT

Abstract Cyclotron line scattering features are detected in a few tens of X-ray pulsars (XRPs) and used as direct indicators of a strong magnetic field at the surface of accreting neutron stars (NSs). In a few cases, cyclotron lines are known to be variable with the accretion luminosity of XRPs. It is accepted that the observed variations of cyclotron line scattering features are related to variations of geometry and dynamics of accretion flow above the magnetic poles of an NS. A positive correlation between the line centroid energy and luminosity is typical for subcritical XRPs, where the accretion results in hot spots at the magnetic poles. The negative correlation was proposed to be a specific feature of bright supercritical XRPs, where radiation pressure supports accretion columns above the stellar surface. The cyclotron line in the spectra of the Be-transient XRP GRO J1008-57 is detected at energies from ∼75 to 90 keV, the highest observed energy of a cyclotron line feature in XRPs. We report the peculiar relation of cyclotron line centroid energies with luminosity in GRO J1008-57 during the Type II outburst in 2017 August observed by Insight-HXMT. The cyclotron line energy was detected to be negatively correlated with the luminosity at 3.2 × 1037 erg s−1 < L < 4.2 × 1037 erg s−1 and positively correlated at L ≳ 5 × 1037 erg s−1. We speculate that the observed peculiar behavior of a cyclotron line would be due to variations of accretion channel geometry.

Accretion torque reversals in GRO J1008-57 revealed by Insight-HXMT

GRO J1008-57, as a Be/X-ray transient pulsar, is considered to have the highest magnetic field in known neutron star X-ray binary systems. Observational data of the X-ray outbursts in GRO J1008-57 from 2017 to 2020 were collected by the Insight-HXMT satellite. In this work, the spin period of the neutron star in GRO J1008-57 was determined to be about 93.28 seconds in August 2017, 93.22 seconds in February 2018, 93.25 seconds in June 2019 and 93.14 seconds in June 2020. GRO J1008-57 evolved in the spin-up process with a mean rate of −(2.10±0.05)×10−4 s/d from 2009 – 2018, and turned into a spin down process with a rate of (6.7±0.6)×10−5 s/d from Feb 2018 to June 2019. During the type II outburst of 2020, GRO J1008-57 had the spin-up torque again. During the torque reversals, the pulse profiles and continuum X-ray spectra did not change significantly, and the cyclotron resonant scattering feature around 80 keV was only detected during the outbursts in 2017 and 2020. Based on the observed mean spin-up rate, we estimated the inner accretion disk radius in GRO J1008-57 (about 1 - 2 times of the Alfvén radius) by comparing different accretion torque models of magnetic neutron stars. During the spin-down process, the magnetic torque should dominate over the matter accreting inflow torque, and we constrained the surface dipole magnetic field B≥6×1012 G for the neutron star in GRO J1008-57, which is consistent with the magnetic field strength obtained by cyclotron line centroid energy.

Asymmetric expansion of the Fe ejecta in Kepler’s supernova remnant

Abstract The ejecta kinematics of supernova remnants (SNRs) is one of the crucial clues to understanding the explosion mechanism of type Ia supernovae (SNe). In particular, the kinematic asymmetry of iron-peak elements provides the key to understanding the physical processes taking place in the core of the exploding white dwarfs (WDs), although it has been poorly understood by observations. In this paper, we show for the first time the asymmetric expansion structure in the line-of-sight direction of Fe ejecta in Kepler’s SNR revealed by spectral and imaging analysis using the Chandra archival data. We found that the Kα line centroid energy and line width is relatively lower (<6.4 keV) and narrower (∼80 eV) around the center of the remnant, which implies that the majority of the Fe ejecta in the central region is redshifted. At the outer regions, we identify bright blueshifted structures as have been ejected as high-velocity dense clumps. Taking into account the broad population of the Fe charge states, we estimate the redshifted velocity of ∼2000 km s−1 and the blueshifted velocity of ∼3000 km s−1 for each velocity structure. We also present the possibility that a portion of the Fe ejecta near the center are interacting with the dense circumstellar medium (CSM) on the near side of the remnant. For the origin of the asymmetric motion of the Fe ejecta, we suggest three scenarios; (1) the asymmetric distribution of the CSM, (2) the “shadow” in Fe cast by the companion star, and (3) the asymmetric explosion.

Fe K and ejecta emission in SNR G15.9+0.2 withXMM-Newton

Aims: We present a study of the Galactic supernova remnant SNR G15.9+0.2 with archival XMM-Newton observations. Methods: EPIC data are used to investigate the morphological and spectral properties of the remnant, searching in particular for supernova ejecta and Fe K line emission. By comparing the SNR's X-ray absorption column density with the atomic and molecular gas distribution along the line of sight, we attempt to constrain the distance to the SNR. Results: Prominent line features reveal the presence of ejecta. Abundance ratios of Mg, Si, S, Ar, and Ca strongly suggest that the progenitor of SNR G15.9+0.2 was a massive star with a main sequence mass likely in the range 20-25 $M_{\odot}$, strengthening the physical association with a candidate central compact object detected with Chandra. Using EPIC's collective power, Fe K line emission from SNR G15.9+0.2 is detected for the first time. We measure the line properties and find evidence for spatial variations. We discuss how the source fits within the sample of SNRs with detected Fe K emission and find that it is the core-collapse SNR with the lowest Fe K centroid energy. We also present some caveats regarding the use of Fe K line centroid energy as a typing tool for SNRs. Only a lower limit of 5 kpc is placed on the distance to SNR G15.9+0.2, constraining its age to $t_{SNR} \gtrsim 2$ kyr.

A quasi-periodic modulation of the iron line centroid energy in the black hole binary H1743−322

Accreting stellar-mass black holes often show a `Type-C' quasi-periodic oscillation (QPO) in their X-ray flux, and an iron emission line in their X-ray spectrum. The iron line is generated through continuum photons reflecting off the accretion disk, and its shape is distorted by relativistic motion of the orbiting plasma and the gravitational pull of the black hole. The physical origin of the QPO has long been debated, but is often attributed to Lense-Thirring precession, a General Relativistic effect causing the inner flow to precess as the spinning black hole twists up the surrounding space-time. This predicts a characteristic rocking of the iron line between red and blue shift as the receding and approaching sides of the disk are respectively illuminated. Here we report on XMM-Newton and NuSTAR observations of the black hole binary H 1743-322 in which the line energy varies systematically over the ~4 s QPO cycle (3.70 sigma significance), as predicted. This provides strong evidence that the QPO is produced by Lense-Thirring precession, constituting the first detection of this effect in the strong gravitation regime. There are however elements of our results harder to explain, with one section of data behaving differently to all the others. Our result enables the future application of tomographic techniques to map the inner regions of black hole accretion disks.

Continued decay in the cyclotron line energy in Hercules X-1

The centroid energy Ecyc of the cyclotron line in the spectrum of the binary X-ray pulsar Her X-1 had been found to decrease with time on a time scale of a few tens of years - surprisingly short astrophysically. This was found for the pulse phase averaged line centroid energy using observational data from various X-ray satellites over the time frame 1996 to 2012, establishing a reduction of about 4 keV. Here we report on the result of a new observation by NuSTAR performed in August 2015. The earlier results are confirmed and strengthened, with respect to both, the dependence of Ecyc on flux (it is still present after 2006) and the dependence on time: the long-term decay continued with the same rate, corresponding to a reduction of about 5 keV in 20 years.

Positive correlation between the cyclotron line energy and luminosity in sub-critical X-ray pulsars: Doppler effect in the accretion channel

Cyclotron resonance scattering features observed in the spectra of some X-ray pulsars show significant changes of the line centroid energy with the pulsar luminosity. Whereas for bright sources above the so called critical luminosity these variations are established to be connected with the appearance of the high accretion column above the neutron star surface, at low, sub-critical luminosities the nature of the variations (but with the opposite sign) has not been discussed widely. We argue here that the cyclotron line is formed when the radiation from a hotspot propagates through the plasma falling with a mildly relativistic velocity onto the neutron star surface. The position of the cyclotron resonance is determined by the Doppler effect. The change of the cyclotron line position in the spectrum with luminosity is caused by variations of the velocity profile in the line-forming region affected by the radiation pressure force. The presented model has several characteristic features: (i) the line centroid energy is positively correlated with the luminosity; (ii) the line width is positively correlated with the luminosity as well; (iii) the position and the width of the cyclotron absorption line are variable over the pulse phase; (iv) the line has a more complicated shape than widely used Lorentzian or Gaussian profiles; (v) the phase-resolved cyclotron line centroid energy and the width are negatively and positively correlated with the pulse intensity, respectively. The predictions of the proposed theory are compared with the variations of the cyclotron line parameters in the X-ray pulsar GX 304-1 over a wide range of sub-critical luminosities as seen by the INTEGRAL observatory.

Detection of radial velocity shifts due to black hole binaries near merger

Abstract The barycenter of a massive black hole binary will lie outside the event horizon of the primary black hole for modest values of mass ratio and binary separation. Analogous to radial velocity shifts in stellar emission lines caused by the tug of planets, the radial velocity of the primary black hole around the barycenter can leave a tell-tale oscillation in the broad component of FeKα emission from accreting gas. Near-future X-ray telescopes such as Astro-H and Athena will have the energy resolution (δE/E ≲ 10−3) to search nearby active galactic nuclei (AGN) for the presence of binaries with mass ratios q ≳ 0.01, separated by several hundred gravitational radii. The general-relativistic and Lense–Thirring precession of the periapse of the secondary orbit imprints a detectable modulation on the oscillations. The lowest mass binaries in AGN will oscillate many times within typical X-ray exposures, leading to a broadening of the line wings and an overestimate of black hole spin in these sources. Detection of periodic oscillations in the AGN line centroid energy will reveal a massive black hole binary close to merger and will provide an early warning of gravitational radiation emission.

On the origin of cyclotron lines in the spectra of X-ray pulsars

Cyclotron resonance scattering features are observed in the spectra of some X-ray pulsars and show significant changes in the line energy with the pulsar luminosity. In a case of bright sources, the line centroid energy is anti-correlated with the luminosity. Such a behaviour is often associated with the onset and growth of the accretion column, which is believed to be the origin of the observed emission and the cyclotron lines. However, this scenario inevitably implies large gradient of the magnetic field strength within the line-forming region, and it makes the formation of the observed line-like features problematic. Moreover, the observed variation of the cyclotron line energy is much smaller than could be anticipated for the corresponding luminosity changes. We argue that a more physically realistic situation is that the cyclotron line forms when the radiation emitted by the accretion column is reflected from the neutron star surface. The idea is based on the facts that a substantial part of column luminosity is intercepted by the neutron star surface and the reflected radiation should contain absorption features. The reflection model is developed and applied to explain the observed variations of the cyclotron line energy in a bright X-ray pulsar V 0332+53 over a wide range of luminosities.

Ripple effects and oscillations in the broad Fe Kα line as a probe of massive black hole mergers

When a sufficiently massive satellite (or secondary) black hole is embedded in a gas disc around a (primary) supermassive black hole, it can open an empty gap in the disc. A gap-opening secondary close to the primary will leave an imprint in the broad component of the Fe Kα emission line, which varies in a unique and predictable manner. If the gap persists into the innermost disc, the effect consists of a pair of dips in the broad line which ripple blue-ward and red-ward from the line centroid energy, respectively, as the gap moves closer to the primary. This ripple effect could be unambiguously detectable and allow an electromagnetic monitoring of massive black hole mergers as they occur. As the mass ratio of the secondary to primary black hole increases to q ≳ 0.01, we expect the gap to widen, possibly clearing a central cavity in the inner disc, which shows up in the broad Fe Kα line component. If the secondary stalls at ≥ 102rg in its in-migration, due to low corotating gas mass, a detectable ripple effect occurs in the broad line component on the disc viscous time-scale as the inner disc drains and the outer disc is dammed. If the secondary maintains an accretion disc within a central cavity, due to dam bursting or leakage, a periodic ‘see-saw’ oscillation effect is exhibited in the observed line profile. Here, we demonstrate the range of ripple effect signatures potentially detectable with Astro-H and IXO/Athena, and oscillation effects potentially detectable with XMM–Newton or LOFT for a wide variety of merger and disc conditions, including gap width (or cavity size), disc inclination angle and emissivity profile, damming of the accretion flow by the secondary, and a minidisc around the satellite black hole. A systematic study of ripple effects would require a telescope effective area substantially larger than that planned for IXO/Athena. Future mission planning should take this into account. Observations of the ripple effect and periodic oscillations can be used to provide an early warning of gravitational radiation emission from the AGN. Once gravitational waves consistent with massive black hole mergers are detected, an archival search for the Fe Kα ripple effect or periodic oscillations will help in localizing their origin.

Cr-K EMISSION LINE AS A CONSTRAINT ON THE PROGENITOR PROPERTIES OF SUPERNOVA REMNANTS

We perform a survey of the Cr, Mn and Fe-K emission lines in young supernova remnants (SNRs) with the Japanese X-ray astronomy satellite {\sl Suzaku}. The Cr and/or Mn emission lines are detected in 3C\,397 and 0519-69.0 for the first time. We also confirm the detection of these lines in Kepler, W49B, N103B and Cas A. We derive the line parameters (i.e., the line centroid energy, flux and equivalent width [EW]) for these six sources and perform a correlation analysis for the line center energies of Cr, Mn and Fe. Also included in the correlation analysis are Tycho and G344.7-0.1 for which the Cr, Mn and Fe-K line parameters were available in the literature through {\sl Suzaku} observations. We find that the line center energies of Cr correlates very well with that of Fe and that of Mn. This confirms our previous findings that the Cr, Mn and Fe are spatially co-located, share a similar ionization state, and have a common origin in the supernova nucleo-synthesis. We find that the ratio of the EW of the Cr emission line to that of Fe ($\EWR\equiv \EWCr/\EWFe$) provides useful constraints on the SNR progenitors and on the SN explosion mechanisms: for SNRs with $\EWR > 2%$, a type Ia origin is favored (e.g., N103B, G344.7-0.1, 3C\,397 and 0519-69.0); for SNRs with $\EWR < 2%$, they could be of either core-collpase origin or carbon-deflagration Ia origin.

THE DIFFERENCE IN NARROW Fe Kα LINE EMISSION BETWEEN SEYFERT 1 AND SEYFERT 2 GALAXIES

We compile a sample of 89 Seyfert galaxies with both [OIV] 25.89 um line luminosities observed by Spitzer IRS and X-ray spectra observed by XMM EPIC. Using [OIV] emission as proxy of AGN intrinsic luminosity, we find that although type 2 AGNs have higher line equivalent width, the narrow Fe Kalpha line in Compton-Thin and Compton-Thick Seyfert 2 galaxies are 2.9 +0.8 -0.6 and 5.6 +1.9 -1.4 times weaker in terms of luminosity than Seyfert 1 galaxies respectively. This indicates different correction factors need to be applied for various types of AGNs before the narrow Fe Kalpha line luminosity could serve as intrinsic AGN luminosity indicator. We also find Seyfert 1 galaxies in our sample have on average marginally larger line width and higher line centroid energy, suggesting contamination from highly ionized Fe line or broader line emission from much smaller radius, but this effect is too weak to explain the large difference in narrow Fe Kalpha line luminosity between type 1 and type 2 AGNs. This is the first observational evidence showing the narrow Fe Kalpha line emission in AGNs is anisotropic. The observed difference is consistent with theoretical calculations assuming a smoothly distributed obscuring torus, and could provide independent constraints on the clumpiness of the torus.

THE CORES OF THE Fe Kα LINES IN ACTIVE GALACTIC NUCLEI: AN EXTENDED CHANDRA HIGH ENERGY GRATING SAMPLE

We extend the study of the core of the Fe K$\alpha$ emission line at \sim 6.4 keV in Seyfert galaxies reported in Yaqoob & Padmanabhan (2004) using a larger sample observed by the Chandra High Energy Grating (HEG). Whilst heavily obscured active galactic nuclei (AGNs) are excluded from the sample, these data offer some of the highest precision measurements of the peak energy of the Fe K$\alpha$ line, and the highest spectral resolution measurements of the width of the core of the line in unobscured and moderately obscured ($N_{H}<10^{23} \ \rm cm^{-2}$) Seyfert galaxies to date. The Fe K$\alpha$ line is detected in 33 sources, and its centroid energy is constrained in 32 sources. In 27 sources the statistical quality of the data is good enough to yield measurements of the FWHM. We find that the distribution in the line centroid energy is strongly peaked around the value for neutral Fe, with over 80% of the observations giving values in the range 6.38--6.43 keV. Including statistical errors, 30 out of 32 sources ($\sim 94%$) have a line centroid energy in the range 6.35--6.47 keV. The mean equivalent width, amongst the observations in which a non-zero lower limit could be measured, was $53 \pm 3eV. The mean FWHM from the subsample of 27 sources was $2060 \pm 230 \ \rm km \ s^{-1}$. The mean EW and FWHM are somewhat higher when multiple observations for a given source are averaged. From a comparison with the H$\beta$ optical emission-line widths (or, for one source, Br$\alpha$), we find that there is no universal location of the Fe K$\alpha$ line-emitting region relative to the optical BLR. We confirm the presence of the X-ray Baldwin effect, an anti-correlation between the Fe K$\alpha$ line EW and X-ray continuum luminosity. The HEG data have enabled isolation of this effect to the narrow core of the Fe K$\alpha$ line.

An Extreme, Blueshifted Iron‐Line Profile in the Narrow‐Line Seyfert 1 PG 1402+261: An Edge‐on Accretion Disk or Highly Ionized Absorption?

We report on a short XMM-Newton observation of the radio-quiet narrow-line Seyfert 1 galaxy PG 1402+261. The EPIC X-ray spectrum of PG 1402+261 shows a strong excess of counts between 6 and 9 keV in the rest frame. This feature can be modeled by an unusually strong (equivalent width 2 keV) and very broad (FWHM velocity of 110,000 km s-1) iron K-shell emission line. The line centroid energy at 7.3 keV appears blueshifted with respect to the iron Kα emission band between 6.4 and 6.97 keV, while the blue wing of the line extends to 9 keV in the quasar rest frame. The line profile can be fitted by reflection from the inner accretion disk, but an inclination angle of >60° is required to model the extreme blue wing of the line. Furthermore, the extreme strength of the line requires a geometry whereby the hard X-ray emission from PG 1402+261 above 2 keV is dominated by the pure-reflection component from the disk, while little or none of the direct hard power law is observed. Alternatively, the spectrum above 2 keV may be explained by an ionized absorber, if the column density is sufficiently high (NH > 3 × 1023 cm-2) and if the matter is ionized enough to produce a deep (τ ~ 1) iron K-shell absorption edge at 9 keV. This absorber could originate in a large column density, high-velocity outflow, perhaps similar to those that appear to be observed in several other high accretion rate active galactic nuclei. Further observations, especially at higher spectral resolution, are required to distinguish between the accretion disk reflection and outflow scenarios.

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.

Reverberation by a relativistic accretion disc

We calculate the response of a line emitted from a relativistic accretion disk to a continuum variation of the central illuminating source. This model might be relevant to the very broad and sometimes redshifted emission lines which have been observed at optical and X-ray energies in Active Galactic Nuclei and X-ray binaries. We consider separately the cases of a point-like and of an extended central source. Based on the first three moments of the line energy distribution (i.e. the line intensity, centroid energy and width) and the two-dimensional transfer function, we identify a number of characteristic features, which can help assessing the presence of a relativistic accretion disk and estimating its parameters. In particular, by combining an absolute time measurement of the maximum of line response function with a relative measurement in units of light crossing time the mass of the central object can be derived.