arXiv subjects

Chris Shrader

Publications and source records attributed to Chris Shrader.

At least 19 recordsLinked to original sources

arXiv2024

Dual Role of Accretion Disk Winds as X-ray Obscurers and UV Line Absorbers in AGN

X-ray obscuration of active galactic nuclei (AGNs) is considered in the context of ionized winds of stratified structure launched from accretion disks. We argue that a Compton-thick layer of a large-scale disk wind can obscure continuum X-rays and also lead to broad UV absorption such as in the blue wing of Civ; the former originates from the inner wind while the latter from the outer wind as a dual role. Motivated by a number of observational evidence showing strong AGN obscuration phenomena in Seyfert 1 AGNs such as NGC 5548, we demonstrate in this work, by utilizing a physically-motivated wind model coupled to post-process radiative transfer calculations, that an extended disk wind under certain physical conditions (e.g. morphology and density) could naturally cause a sufficient obscuration qualitatively consistent with UV/X-ray observations. Predicted UV/X-ray correlation is also presented as a consequence of variable spatial size of the wind in this scenario.

astro-ph.HE↗

arXiv2023

OJ~287: a new BH mass estimate of the secondary

We presented a study of outburst activity in the BL Lacertae source OJ~287, observed extensively with the X-ray telescope (XRT) onboard Neil Gehrels Swift Observatory. We demonstrated that the results of our analysis of X-ray flaring activity using the Swift/XRT data allow to refine the key characteristics of the OJ~287 secondary (its nature and mass). We discovered that the energy spectra in all spectral states can be fitted using the XSPEC Bulk Motion Comptonization (BMC) model. As a result we found that the X-ray photon index of the BMC model, Gamma correlates with the mass accretion rate, dot. We established that Gamma increases monotonically with dot from the low-hard state, Gamma~ 1.5 to the high-soft state, Gamma~2.8 and finally saturates. The index behavior was similar to that in a number of black hole (BH) candidates in which we showed that its saturation was an observational evidence of the presence of a BH. Based on this correlation, we applied a scaling method and determined that a secondary BH mass in OJ~287 is about ~1.25x10^8 solar masses, using the well-studied X-ray BH binaries XTE~1550--564, H~1743--322, 4U~1630--47, GRS~1915+105 as well as extragalactic BHs ESO~243--49 and M101~ULX--1, as reference sources. Also using the power spectrum analysis we inferred the size of the Compton cloud L_{CC}~ 10^{13} cm where X-ray spectra were formed. Using this value of L_{CC} we confirmed that a BH mass of the secondary in OJ~287 was of order of 10^8 solar masses as we derived using the index, Gamma-correlation (the scaling method) with respect of the mass accretion rate.

astro-ph.HE↗

arXiv2022

Tell-Tale Spectral Signatures of MHD-driven Ultra-Fast Outflows in AGNs

We aim to explore spectral signatures of the predicted multi-ion UFOs in the broadband X-ray spectra of active galactic nuclei (AGNs) by exploiting an accretion disk wind model in the context of a simple magnetohydrodynamic (MHD) framework. We are focused primarily on examining the spectral dependences on a number of key properties; (1) ionizing luminosity ratio $λ_{\rm ion}$, (2) line-of-sight wind density slope $p$, (3) optical/UV-to-X-ray strength $α_{\rm OX}$, (4) inclination $θ$, (5) X-ray photon index $Γ$ and (6) wind density factor $f_D$. With an emphasis on radio-quiet Seyferts in sub-Eddington regime, multi-ion UFO spectra are systematically calculated as a function of these parameters to show that MHD-driven UFOs imprint a unique asymmetric absorption line profile with a pronounced blue tail structure on average. Such a characteristic line signature is generic to the simplified MHD disk-wind models presented in this work due to their specific kinematics and density structure. The properties of these absorption line profiles could be utilized as a diagnostics to distinguish between different wind driving mechanisms or even the specific values of a given MHD wind parameters. We also present high fidelity microcalorimeter simulations in anticipation of the upcoming {\it XRISM}/Resolve and {\it Athena}/X-IFU instruments to demonstrate that such a "tell-tale" sign may be immune to a spectral contamination by the presence of additional warm absorbers and partially covering gas.

astro-ph.HE↗

arXiv2021

Modeling Magnetic Disk-Wind State Transitions in Black Hole X-ray Binaries

We analyze three prototypical black hole (BH) X-ray binaries (XRBs), \4u1630, \gro1655\ and \h1743, in an effort to systematically understand the intrinsic state transition of the observed accretion-disk winds between \windon\ and \windoff\ states by utilizing state-of-the-art {\it Chandra}/HETGS archival data from multi-epoch observations. We apply our magnetically-driven wind models in the context of magnetohydrodynamic (MHD) calculations to constrain their (1) global density slope ($p$), (2) their density ($n_{17}$) at the foot point of the innermost launching radius and (3) the abundances of heavier elements ($A_{\rm Fe,S,Si}$). Incorporating the MHD winds into {\tt xstar} photoionization calculations in a self-consistent manner, we create a library of synthetic absorption spectra given the observed X-ray continua. Our analysis clearly indicates a characteristic bi-modal transition of multi-ion X-ray winds; i.e. the wind density gradient is found to steepen (from $p \sim 1.2-1.4$ to $\sim 1.4-1.5$) while its density normalization declines as the source transitions from \windon\ to \windoff\ state. The model implies that the ionized wind {\it remains physically present} even in \windoff\ state, despite its absent appearance in the observed spectra. Super-solar abundances for heavier elements are also favored. Our global multi-ion wind models, taking into account soft X-ray ions as well as Fe K absorbers, show that the internal wind condition plays an important role in wind transitions besides photoionization changes. % Simulated {\it XRISM}/Resolve and {\it Athena}/X-IFU spectra are presented to demonstrate a high fidelity of the multi-ion wind model for better understanding of these powerful ionized winds in the coming decades.

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arXiv2020

VTXO: the Virtual Telescope for X-ray Observations

The Virtual Telescope for X-ray Observations (VTXO) will use lightweight Phase Frensel Lenses (PFLs) in a virtual X-ray telescope with 1 km focal length and with nearly 50 milli-arcsecond angular resolution. Laboratory characterization of PFLs have demonstrated near diffraction-limited angular resolution in the X-ray band, but they require long focal lengths to achieve this quality of imaging. VTXO is formed by using precision formation flying of two SmallSats: a smaller, 6U OpticsSat that houses the PFLs and navigation beacons while a larger, ESPA-class DetectorSat contains an X-ray camera, a charged-particle radiation monitor, a precision star tracker, and the propulsion for the formation flying. The baseline flight dynamics uses a highly-elliptical supersynchronous geostationary transfer orbit to allow the inertial formation to form and hold around the 90,000 km apogee for 10 hours of the 32.5-hour orbit with nearly a year mission lifetime. The guidance, navigation, and control (GN&C) for the formation flying uses standard CubeSat avionics packages, a precision star tracker, imaging beacons on the OpticsSat, and a radio ranging system that also serves as an inter-satellite communication link. VTXO's fine angular resolution enables measuring the environments nearly an order of magnitude closer to the central engines of bright compact X-ray sources compared to the current state of the art. This X-ray imaging capability allows for the study of the effects of dust scattering nearer to the central objects such as Cyg X-3 and GX 5-1, for the search for jet structure nearer to the compact object in X-ray novae such as Cyg X-1 and GRS 1915+105, and for the search for structure in the termination shock of in the Crab pulsar wind nebula. The VTXO development was supported as one of the selected 2018 NASA Astrophysics SmallSat Study (AS3) missions.

astro-ph.IM↗

arXiv2019

Positron Annihilation in the Galaxy

The 511 keV line from positron annihilation in the Galaxy was the first $γ$-ray line detected to originate from outside our solar system. Going into the fifth decade since the discovery, the source of positrons is still unconfirmed and remains one of the enduring mysteries in $γ$-ray astronomy. With a large flux of $\sim$10$^{-3}$ $γ$/cm$^{2}$/s, after 15 years in operation INTEGRAL/SPI has detected the 511 keV line at $>50σ$ and has performed high-resolution spectral studies which conclude that Galactic positrons predominantly annihilate at low energies in warm phases of the interstellar medium. The results from imaging are less certain, but show a spatial distribution with a strong concentration in the center of the Galaxy. The observed emission from the Galactic disk has low surface brightness and the scale height is poorly constrained, therefore, the shear number of annihilating positrons in our Galaxy is still not well know. Positrons produced in $β^+$-decay of nucleosynthesis products, such as $^{26}$Al, can account for some of the annihilation emission in the disk, but the observed spatial distribution, in particular the excess in the Galactic bulge, remains difficult to explain. Additionally, one of the largest uncertainties in these studies is the unknown distance that positrons propagate before annihilation. In this paper, we will summarize the current knowledge base of Galactic positrons, and discuss how next-generation instruments could finally provide the answers.

astro-ph.HE↗

arXiv2018

Variable Nature of Magnetically-Driven Ultra-Fast Outflows

Among a number of active galactic nuclei (AGNs) that drive ionized outflows in X-rays, a low-redshift (z = 0.184) quasar, PDS 456, is long known to exhibit one of the exemplary ultra-fast outflows (UFOs). However, the physical process of acceleration mechanism is yet to be definitively constrained. In this work, we model the variations of the Fe K UFO properties in PDS 456 over many epochs in X-ray observations in the context of magnetohydrodynamic (MHD) accretion-disk winds employed in our earlier studies of similar X-ray absorbers. We applied the model to the 2013/2014 XMM-Newton/NuSTAR spectra to determine the UFO's condition; namely, velocity, ionization parameter, column density and equivalent width (EW). Under some provisions on the dependence of X-ray luminosity on the accretion rate applicable to near-Eddington state, our photoionization calculations, coupled to a 2.5-dimensional MHD-driven wind model, can further reproduce the observed correlations of the UFO velocity and the anti-correlation of its EW with X-ray strength of PDS 456. This work demonstrates that UFOs, even without radiative pressure, can be driven as an extreme case purely by magnetic interaction while also producing the observed spectrum and correlations.

astro-ph.HE↗

arXiv2017

Magnetized Disk-Winds in NGC 3783

We analyze a 900-ks stacked Chandra/HETG spectrum of NGC 3783 in the context of magnetically-driven accretion-disk wind models in an effort to provide tight constraints on the global conditions of the underlying absorbers. Motivated by the earlier measurements of its absorption measure distribution (AMD) indicating X-ray-absorbing ionic columns that decrease slowly with decreasing ionization parameter, we employ 2D magnetohydrodynamic (MHD) disk-wind models to describe the global outflow. We compute its photoionization structure along with the wind kinematic properties allowing us to further calculate in a self-consistent fashion the shapes of the major X-ray absorption lines. With the wind radial density profile determined by the AMD, the profiles of the ensemble of the observed absorption features are determined by the two global parameters of the MHD wind; i.e. disk inclination θ_obs and wind density normalization n_o. Considering the most significant absorption features in the (~1.8A-20A) range, we show that the MHD-wind is best described by n(r)~6.9e11(r/ro)^-1.15 [cm^-3] and θ_obs=44deg. We argue that winds launched by X-ray heating, radiation pressure or even MHD winds but with steeper radial density profiles are strongly disfavored by data. Considering the properties of Fe K band absorption features (i.e. Fe xxv and Fe xxvi), while typically prominent in the AGN X-ray spectra, they appear to be weak in NGC 3783. For the specific parameters of our model obtained by fitting the AMD and the rest of absorption features, these features are found to be weak in agreement with observation.

astro-ph.HE↗

arXiv2017

Magnetic Origin of Black Hole Winds Across the Mass Scale

Black hole accretion disks appear to produce invariably plasma outflows that result in blue-shifted absorption features in their spectra. The X-ray absorption-line properties of these outflows are quite diverse, ranging in velocity from non-relativistic ($\sim 300$ km/sec) to sub-relativistic ($\sim 0.1c$ where $c$ is the speed of light) and a similarly broad range in the ionization states of the wind plasma. We report here that semi-analytic, self-similar magnetohydrodynamic (MHD) wind models that have successfully accounted for the X-ray absorber properties of supermassive black holes, also fit well the high-resolution X-ray spectrum of the accreting stellar-mass black hole, GRO J1655-40. This provides an explicit theoretical argument of their MHD origin (aligned with earlier observational claims) and supports the notion of a universal magnetic structure of the observed winds across all known black hole sizes.

astro-ph.HE↗

arXiv2015

BEPPOSAX and RXTE spectral study of the low-mass X-ray binary 4u~1705-44. Spectral hardening during the banana branch

We analyze the X-ray spectra of the atoll 4U~1705-44 when the source undergoes the island-banana state transition. We use the Rossi X-ray Timing Explorer (RXTE) and BeppoSAX observations for this analysis. We demonstrate that the broad-band energy spectral distributions for all evolutinary states can be fitted by a model, consisting two Comptonized components. One arises from the seed photons coming from a neutron star (NS) atmosphere at a temperature kT_{s1}<1.5 keV (herein Comptb) and a second resulting from the seed photons of T_{s2}~1.1-1.3 keV coming from the disk (herein Comptb2). We found that we needed to add a low-temperature blackbody and an iron-line ({Gaussian}) component to the model in order to obtain high-quality fits. The data analysis using this model indicates that the power-law photon index Gamma_{1} of our model is always about 2, independently of the spectral state. Another parameter, Gamma_{2} demonstrates a two-phase behavior depending on the spectral state. Gamma_{2} is quasi-constant at Gamma_{2}~ 2 when the electron temperature kT^{(2)}_e<80 keV and Gamma_{2} is less than 2, in the range of 1.3 80 keV. This phase is similar to that was previously found in the Z-source Sco X-1. We interpret the decreasing index phase using a model in which a super-Eddington radiation pressure from the neutron star causes an expansion of the Compton cloud similar to that found previously in Sco~X-1 during the Flaring branch.

astro-ph.SR↗

arXiv2015

Magnetically-Driven Accretion-Disk Winds and Ultra-Fast Outflows in PG1211+143

We present a study of X-ray ionization of magnetohydrodynamic (MHD) accretion-disk winds in an effort to constrain the physics underlying the highly-ionized ultra-fast outflows (UFOs) inferred by X-ray absorbers often detected in various sub-classes of Seyfert active galactic nuclei (AGNs). Our primary focus is to show that magnetically-driven outflows are indeed physically plausible candidates for the observed outflows accounting for the AGN absorption properties of the present X-ray spectroscopic observations. Employing a stratified MHD wind launched across the entire AGN accretion disk, we calculate its X-ray ionization and the ensuing X-ray absorption line spectra. Assuming an appropriate ionizing AGN spectrum, we apply our MHD winds to model the absorption features in an {\it XMM-Newton}/EPIC spectrum of the narrow-line Seyfert, \pg. We find, through identifying the detected features with Fe K$α$ transitions, that the absorber has a characteristic ionization parameter of $\log (ξ_c [erg~cm~s$^{-1}$]) \simeq 5-6$ and a column density on the order of $N_H \simeq 10^{23}$ cm$^{-2}$, outflowing at a characteristic velocity of $v_c/c \simeq 0.1-0.2$ (where $c$ is the speed of light). The best-fit model favors its radial location at $r_c \simeq 200 R_o$ ($R_o$ is the black hole innermost stable circular orbit), with an inner wind truncation radius at $R_{\rm t} \simeq 30 R_o$. The overall K-shell feature in the data is suggested to be dominated by \fexxv\ with very little contribution from \fexxvi\ and weakly-ionized iron, which is in a good agreement with a series of earlier analysis of the UFOs in various AGNs including \pg.

astro-ph.HE↗

arXiv2014

X-ray spectral and timing behavior of Scorpius X-1. Spectral hardening during the flaring branch

We present an analysis of the spectral and timing properties of X-ray emission from the Z-source Sco~X-1 during its evolution between the Horizontal (HB) and Flaring(FB) branches observed with the RXTE during the 1996 -- 2002 period. We find that the broad-band (3 - 250 keV) energy spectra during all spectral states can be adequately reproduced by a model, consisting of two Comptonized components and an iron-line. We suggest that the seed photons of kT_s1~0.7 keV coming from the disk and of temperature kT_s2~1.8 keV coming from the neutron star (NS) are each upscattered by hot electrons of a "Compton cloud" (herein Comptb1 and Comptb2 components respectively with which are associated similarly subscripted parameters). The photon power-law index Gamma_{2} is almost constant (Gamma_{2}~2) for all spectral states. In turn, Gamma_{1} demonstrates a two-phase behavior with the spectral state: Gamma_{1} is quasi-constant at the level Gamma_{1}~2 for the HB-NB and Gamma_{1} is less than 2, namely in the range of 1.3<Gamma_1<2, when source traces the FB. We also detect a decrease kT_{s2} from 1.8 keV to 0.7 keV during the FB. We interpret this apparent quasi-stability of the indices during the HB-NB in the framework of the model in which the spectrum is determined by the Comptonized thermal components. This established for the Comptonized spectral components of the Z-source Sco~X-1 is similar to that was previously found in the atoll sources 4U~1728-34, GX~3+1 and 4U~1820-30 and the Z-source GX~340+0 through all spectral states. However we interpret the index reduction phase detected during the FB in Sco~X-1 within the framework of a model in which the spectrum at the FB is determined by high radiation pressure from the NS surface.

astro-ph.SR↗

arXiv2013

Stratified Magnetically-Driven Accretion-Disk Winds and Their Relations to Jets

We explore the poloidal structure of two-dimensional (2D) MHD winds in relation to their potential association with the X-ray warm absorbers (WAs) and the highly-ionized ultra-fast outflows (UFOs) in AGN, in a single unifying approach. We present the density $n(r,θ)$, ionization parameter $ξ(r,θ)$, and velocity structure $v(r,θ)$ of such ionized winds for typical values of their fluid-to-magnetic flux ratio, $F$, and specific angular momentum, $H$, for which wind solutions become super-\Alfvenic. We explore the geometrical shape of winds for different values of these parameters and delineate the values that produce the widest and narrowest opening angles of these winds, quantities necessary in the determination of the statistics of AGN obscuration. We find that winds with smaller $H$ show a poloidal geometry of narrower opening angles with their \Alfven\ surface at lower inclination angles and therefore they produce the highest line of sight (LoS) velocities for observers at higher latitudes with the respect to the disk plane. We further note a physical and spatial correlation between the X-ray WAs and UFOs that form along the same LoS to the observer but at different radii, $r$, and distinct values of $n$, $ξ$ and $v$ consistent with the latest spectroscopic data of radio-quiet Seyfert galaxies. We also show that, at least in the case of 3C 111, the winds' pressure is sufficient to contain the relativistic plasma responsible for its radio emission. Stratified MHD disk-winds could therefore serve as a unique means to understand and unify the diverse AGN outflows.

astro-ph.HE↗

arXiv2012

Toward a Unified AGN Structure

We present a unified model for the structure and appearance of accretion powered sources across their entire luminosity range from galactic X-ray binaries to luminous quasars, with emphasis on AGN and their phenomenology. Central to this model is the notion of MHD winds launched from the accretion disks that power these objects. These winds provide the matter that manifests as blueshifted absorption features in the UV and X-ray spectra of a large fraction of these sources; furthermore, their density distribution in the poloidal plane determines the "appearance" (i.e. the column and velocity structure of these absorption features) as a function of the observer inclination angle. This work focuses on just the broadest characteristics of these objects; nonetheless, it provides scaling laws that allow one to reproduce within this model the properties of objects spanning a very wide luminosity range and viewed at different inclination angles, and trace them to a common underlying dynamical structure. Its general conclusion is that the AGN phenomenology can be accounted for in terms of three parameters: The wind mass flux in units of the Eddington value, $\dot m$, the observer's inclination angle $θ$ and the logarithmic slope between the O/UV and X-ray fluxes $α_{OX}$. However, because of a significant correlation between $α_{OX}$ and UV luminosity, we conclude that the AGN structure depends on only two parameters. Interestingly, the correlations implied by this model appear to extend to and consistent with the characteristics of galactic X-ray sources, suggesting the presence of a truly unified underlying structure for accretion powered sources.

astro-ph.HE↗

arXiv2010

New Evidence for a Black Hole in the Compact Binary Cygnus X-3

The bright and highly variable X-ray and radio source known as Cygnus X-3 was among the first X-ray sources discovered, yet it remains in many ways an enigma. Its known to consist of a massive, Wolf-Rayet primary in an extremely tight orbit with a compact object. Yet one of the most basic of parameters - the mass of the compact object - is not known. Nor is it even clear whether its is a neutron star or a black hole. In this Paper we present our analysis of the broad-band high-energy continua covering a substantial range in luminosity and spectral morphology. We apply these results to a recently identified scaling relationship which has been demonstrated to provide reliable estimates of the compact object mass in a number of accretion powered binaries. This analysis leads us to conclude that the compact object in Cygnus X-3 has a mass greater than $4.2M_\odot$ thus clearly indicative of a black hole and as such resolving a long-standing issue. The full range of uncertainty in our analysis and from using a range of recently published distance estimates constrains the compact object mass to lie between $4.2M_\odot$ and $14.4M_\odot$. Our favored estimate, based on a 9.0 kpc distance estimate is $\sim 10 M_\odot$ with the error margin of 3.2 solar masses. This result may thus pose challenges to shared-envelope evolutionary models of compact binaries, as well as establishing Cygnus X-3 as the first confirmed accretion-powered galactic gamma-ray source.

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arXiv2004

Downscattering due to Wind Outflows in Compact X-ray Sources: Theory and Interpretation

A number of recent lines of evidence point towards the presence of hot, out-flowing plasma from the central regions of compact Galactic and extragalactic X-ray sources. Additionally, it has long been noted that many of these sources exhibit an ``excess'' continuum component, above 10 keV, usually attributed to Compton Reflection from a static medium. Motivated by these facts, as well as by recent observational constraints on the Compton reflection models - specifically apparently discrepant variability timescales for line and continuum components in some cases -- we consider possible effects of out-flowing plasma on the high-energy continuum spectra of accretion powered compact objects. We present a general formulation for photon downscattering diffusion which includes recoil and Comptonization effects due to divergence of the flow. We then develop an analytical theory for the spectral formation in such systems that allows us to derive formulae for the emergent spectrum. Finally we perform the analytical model fitting on several Galactic X-ray binaries. Objects which have been modeled with high-covering-fraction Compton reflectors, such as GS1353-64 are included in our analysis. In addition, Cyg X-3, is which is widely believed to be characterized by dense circumstellar winds with temperature of order 10^6 K, provides an interesting test case. Data from INTEGRAL and RXTE covering the 3-300 keV range are used in our analysis. We further consider the possibility that the widely noted distortion of the power-law continuum above 10 keV may in some cases be explained by these spectral softening effects.

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arXiv2003

A Method for Black Hole Mass Determination in Accretion Powered X-Ray Sources

We describe a method for the determination of black-hole masses based on information inferred from high-energy spectra. It is required that the spectral energy distribution consist of thermal and Comptonized components. One can then, in principle, infer the depth of the gravitational potential well for sources of known distance. The thermal component is inferred by the integration of a blackbody spectral form over the disk. We assume that the color temperature distribution in the disk has a specific shape given by the Shakura-Sunyaev (1973) disk model which goes to zero at the inner disk radius and at infinity and has a maximum at 4.2 Schwarzchild radii. In this formulation there is only one parameter, the so called color correction factor, relating the apparent temperature to effective temperature which characterizes the thermal emission component. We have made use of improved Galactic black hole binary dynamical mass determinations to derive, in effect, an empirical calibration of this factor. We then present our analysis of observational data for representative objects of several classes; Galactic black hole X-ray binaries, narrow line Seyfert galaxies (NLS1), and ``ultra-luminous'' extragalactic X-ray sources (ULX). We then apply our mass determination calculation and present our results. We argue that this approach can potentially fill a void in the current knowledge of NLS1 and ULX properties, and discuss how a deeper understanding of both classes has relevance to the broader issues of how cosmic black holes, beyond the stellar-mass realm, are formed and what is their overall mass distribution.

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arXiv2001

Observational Signatures of Black Holes: Spectral and Temporal Features of XTE J1550-564

The theoretical predictions of the converging inflow, or Bulk-Motion Comptonization model are discussed and some predictions are compared to X- and gamma-ray observations of the high/soft state of Galactic black hole candidate XTE J1550+564. The 100 Hz QPO phenomenon tends to be detected in the high-state at times when the bolometric luminosity surges and the hard-power-law spectral component is dominant. Furthermore, the power in these features increases with energy. We offer interpretation of this phenomenon, as oscillations of the innermost part of the accretion disk, which in turn supplies the seed photons for the converging inflow where the hard power-law is formed through Bulk Motion Comptonization (BMC). We further argue that the noted lack of coherence between intensity variations of the high-soft-state low and high energy bands is a natural consequence of our model, and that a natural explanation for the observed hard and soft lag phenomenon is offered. In addition, we address some criticisms of the BMC model supporting our claims with observational results.

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