Progress toward development of a predictive dynamic compaction model framework
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shock compaction, predictive↗
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(U) PRAD0697 & PRAD0698: Complex Loading of CeO₂ Powder
Cerium(IV) oxide (CeO₂) powder is shock compressed using the Precision High Energy-density Liner Implosion eXperiment (PHELIX) platform. Experimental results are compared against several modeling approaches. Compaction behavior is best captured with a P-∝ model, which calculates CeO₂ powder bulk densities within 80-99% of experimental values but overpredicts densi cation at the cylindrical target's outer radius and center by up to 20%. Preliminary calculations suggest that accuracy could be increased with the inclusion of a coupled strength model. Several common computational modeling approaches for the shock compression response of granular materials and the magnetohydrodynamic (MHD) force upon the impactor/liner in pulsed power compression experiments are investigated and analyzed for their validity. The Bi-linear Ramp, P-∝ PACXP, and P-∝ Menikoff-Kober continuum compaction models are calibrated to planar impact Hugoniot data for CeO₂ powder and used to predict the powder's shock compaction response under non-planar shock wave compression. MHD calculations of the PHELIX pulsed power driver are performed using an idealized resistor-inductor-capacitor (RLC) circuit calibrated to previous experiments. All simulations are performed using the LANL code FLAG. Two validation experiments are computationally designed using the calibrated compaction and circuit models, executed using the PHELIX platform on CeO₂ targets with initial porous densities of 3.95 and 4.03 g/cm³, measured with proton radiography, and analyzed against the model predictions. The two P-∝ models more accurately describe CeO₂ powder densi cation than the Bi-linear Ramp model. However, the two P-∝ models overpredict bulk density of the shock compressed CeO₂ powder by up to 20% when the appropriate impact velocities are applied. MHD calculations for both validation experiments underpredict liner impact velocities by 4-11% when using the idealized RLC circuit model calibrated to previous experiments. Compensating underpredictions of impact velocity and overpredictions of powder densication lead to a false accuracy in pre-shot calculations compared to experimental data. To improve correlation between simulations and experiments, the following improvements are suggested: 1. A coupled strength model for CeO₂ powder that updates strength as a function of porosity and applied stress. 2. An improved MHD circuit model that more accurately captures the PHELIX machine.
36 MATERIALS SCIENCE↗
Dynamic crushing of metal lattice metamaterials: Shock mode diagrams and transition to topology-independent compaction regime
Additively manufactured lattice metamaterials offer design versatility in strength and energy absorption and provide an additional degree of freedom through the selection of the lattice topology. Under quasistatic loading, the unit cell structure can strongly affect the stiffness, yield, and post-yield behavior, but whether and to what degree the effect of lattice topology persists into dynamic loading scenarios, up to the compaction shock regime, has not been established. LLNL’ s ALE3D hydrocode was used to perform a computational investigation of dynamic loading in multiple lattice types, including the gyroid, octet, Schwarz D, and rhombic dodecahedron, under impact velocities from 0.25 to 2.25 km/s. Shock Hugoniots for each lattice topology are generated and compared, suggesting that above a critical velocity, distinctions between architectures may not persevere and compacted lattices behave similarly. Here, to investigate the transition between topology-dependent quasistatic compression and the topology-independent regime above the critical velocity, a one-dimensional elastic-linear hardening plasticity-densified solid (E-LHP-DS) shock model for lattice materials was developed that relies upon confined compression to link the quasistatic and shock mechanics. Unlike similar works, the model does not assume rigid behavior prior to yield or locking behavior at densification, allowing a richer exploration of lattice mechanics. With only six parameters, the analytical model simultaneously fit quasistatic confined compression simulations for relative densities 0.1 $≤ \bar{ρ} ≤$ 0.9 and predicted dynamic compaction behavior to traverse several distinct shock modes, each defined by a critical impact speed (equivalently, critical stresses). Comparing the numerical results to the one-dimensional E-LHP-DS shock model predictions suggests that the topology-independence under strong shocks is linked to the onset of densification, which can be predicted based on quasistatic confined compression results.
Cellular material↗
Active galaxies and the diffuse gamma-ray background
Active galaxies are shown to account for the observed gamma ray background radiation if a steepening of the spectra above about 100 keV is present. An analytical model is discussed in which protons undergo Fermi acceleration at a shock in a spherical accretion flow onto a massive black hole. Relativistic protons with power law spectra, nuclear interactions producing gamma rays from neutal pion decay and electrons from pion-mu meson-electron decay, with a power law spectrum above several hundred MeV, synchrotron and inverse Compton losses steepening the electron spectrum, a photon spectrum close to the pion gamma spectrum and a high-energy gamma ray spectrum steepened by photon-photon pair production interactions with X rays are covered in the model. Comparisons are made with HEAO 2 data on active galaxies, which have estimated luminosities and radii consistent with the compactness necessary for producing the steepening predicted by the model. The active galaxies spectra would be described by a spherical accretion-shock model.
Kazanas, D.↗
Neutrino heating in 1D, 2D, and 3D core-collapse supernovae: characterizing the explosion of high-compactness stars
Massive stars can end their lives with a successful supernova explosion (leaving behind a neutron star or, more rarely, a black hole), or a failed explosion that leaves behind a black hole. The density structure of the pre-collapse progenitor star already encodes much of the information regarding the outcome and properties of the explosion. However, the complexity of the collapse and subsequent shock expansion phases prevents drawing a straightforward connection between the pre-collapse and post-explosion properties. In order to derive such a connection several explodability studies have been performed in recent years. However, different studies can predict different explosion outcomes. In this article, we show how compactness, which is related to the average density of the star’s core, has an important role in determining the efficiency of neutrino heating, and therefore the outcome of the explosion. Commonly, high-compactness progenitors are assumed to yield failed explosions, due to their large mass accretion rates, preventing the shock from expanding. We show by analysing ~150 2D flash and F ornax simulations and 20 3D F ornax simulations that this is not the case. Instead, due to the rapid increase of neutrino heating with compactness, high-compactness progenitors lead to successful shock revival. We also show that 1D+ simulations that include v-driven convection using a mixing-length theory approach correctly reproduce this trend. Finally, we compare 1D+ models, which we show can reproduce some aspects of multi-D simulations with reasonable accuracy, with other widely used 1D models in the literature.
neutrinos↗
Computational models for the viscous/inviscid analysis of jet aircraft exhaust plumes
Computational models which analyze viscous/inviscid flow processes in jet aircraft exhaust plumes are discussed. These models are component parts of an NASA-LaRC method for the prediction of nozzle afterbody drag. Inviscid/shock processes are analyzed by the SCIPAC code which is a compact version of a generalized shock capturing, inviscid plume code (SCIPPY). The SCIPAC code analyzes underexpanded jet exhaust gas mixtures with a self-contained thermodynamic package for hydrocarbon exhaust products and air. A detailed and automated treatment of the embedded subsonic zones behind Mach discs is provided in this analysis. Mixing processes along the plume interface are analyzed by two upgraded versions of an overlaid, turbulent mixing code (BOAT) developed previously for calculating nearfield jet entrainment. The BOATAC program is a frozen chemistry version of BOAT containing the aircraft thermodynamic package as SCIPAC; BOATAB is an afterburning version with a self-contained aircraft (hydrocarbon/air) finite-rate chemistry package. The coupling of viscous and inviscid flow processes is achieved by an overlaid procedure with interactive effects accounted for by a displacement thickness type correction to the inviscid plume interface.
Dash, S. M.↗
Relativistic particle acceleration in plerions
We discuss recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is either pure electrons and positrons or primarily electrons and positrons with an admixture of heavy ions. Particle-in-cell simulation techniques as well as analytic theory have been used to show that such shocks in pure pair plasmas are fully thermalized -- the downstream particle spectra are relativistic Maxwellians at the temperature expected from the jump conditions. On the other hand, shocks containing heavy ions which are a minority constituent by number but which carry most of the energy density in the upstream medium do put approximately 20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) varies as E(exp -2), where N(E)dE is the number of particles with energy between E and E+dE. The mechanism of thermalization and particle acceleration is found to be synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front. The synchrotron maser modes radiated by the heavy ions are absorbed by the pairs at their (relativistic) cyclotron frequencies, allowing the maximum energy achievable by the pairs to be gamma(sub +/-)m(sub +/-)c squared = m(sub i)c squared gamma(sub 1)/Z(sub i), where gamma(sub 1) is the Lorentz factor of the upstream flow and Z(sub i) is the atomic number of the ions. The shock's spatial structure is shown to contain a series of 'overshoots' in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value. This shock model is applied to an interpretation of the structure of the inner regions of the Crab Nebula, in particular to the 'wisps,' surface brightness enhancements near the pulsar. We argue that these surface brightness enhancements are the regions of magnetic overshoot, which appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar's wind in the Crab Nebula is spatially resolved, and allows one to measure gamma(sub 1) and a number of other properties of the pulsar's wind. We also discuss applications of the shock theory to the termination shocks of the winds from rotation-powered pulsars embedded in compact binaries. We show that this model adequately accounts for (and indeed predicted) the recently discovered X-ray flux from PSR 1957+20, and we discuss several other applications to other examples of these systems.
Arons, Jonathan↗
Shock compaction of molybdenum powder
Shock recovery experiments which were carried out in the 9 to 12 GPa range on 1.4 distension Mo and appear adequate to compact to full density ( 45 (SIGMA)m) powders were examined. The stress levels, however, are below those calculated to be from 100 to approx. 22 GPa which a frictional heating model predicts are required to consolidate approx. 10 to 50 (SIGMA)m particles. The model predicts that powders that have a distension of m=1.6 shock pressures of 14 to 72 GPa are required to consolidate Mo powders in the 50 to 10 (SIGMA)m range.
Ahrens, T. J.↗
Cometary compact H II regions are stellar-wind bow shocks
Comet-shaped H II regions, like G34.3 + 0.2, are easily explained as bow shocks created by wind-blowing massive stars moving supersonically through molecular clouds. The required velocities of the stars through dense clumps are less than about 10 km/s, comparable to the velocity dispersion of stars in OB associations. An analytic model of bow shocks matches the gross characteristics seen in the radio continuum and the velocity structure inferred from hydrogen recombination and molecular line observations. The champagne flow model cannot account for these structures. VLBI observations of masers associated with the shells of cometary compact H II regions should reveal tailward proper motions predominantly parallel to the shell, rather than perpendicular. It is predicted that over a decade baseline, high signal-to-noise VLA observations of this class of objects will show headward pattern motion in the direction of the symmetry axis, but not expansion. Finally, shock-generated and coronal infrared lines are also predicted.
Van Buren, Dave↗
Uncovering The Properties of Young Neutron Stars and Their Surrounding Supernova A Remnants
In the third year of this program, the following studies have been undertaken in support of this effort: G292.0+1.8: In our previous work on this SNR, we discovered a young neutron star and its associated pulsar wind nebula. Radio observations by Camilo et al. (2002) have identified a young 136 ms pulsar in the direction of G292.0+1.8. We have used Chandra HRC observations of the central source to identify X-ray pulsations at the same period, thus establishing the neutron star as the radio pulsar counterpart. We have also set limits on the cooling of this young neutron star based on the unpulsed component of the X-ray emission. We find that the limit falls slightly below standard cooling models in which the modified Urca process is responsible for the bulk of the interior neutrino emission. A paper summarizing these results is currently being circulated amongst co-authors for review prior to publication. 3c 58: Our Chandra observations of this Crab-like SNR revealed the presence of a young, rapidly rotating pulsar as well as a central compact nebula which we interpret as a toroidal structure associated with the pulsar wind termination shock. Our modeling of this structure has allowed us to establish a temperature upper limit for the neutron star which falls well below predictions from standard cooling models, and implies the presence of exotic particles (such as pion condensates) or other processes that increase the neutrino production rate in the interior. A paper summarizing this work has been published in the Astrophysical Journal (Slane, Helfand, & Murray 2002, ApJ, 571, L45), and the results were the subject of a NASA Space Science Update (4/10/2002) which led to extensive media coverage. Based upon our initial observations, we submitted a successful Chandra Large Project proposal for a 350 ks observation of this young neutron star and its wind nebula. Kes 79: Our Chandra observations of this SNR reveal a compact central source which appears to be the neutron star formed in the explosion that produced the remnant. There is no evidence for a surrounding pulsar wind nebula. The source properties are similar to the central source in Cas A even though the Kes 79 remnant is considerably older. The results have been published in the Astrophysical Journal (Seward, Slane, Smith, and Sun 2003, ApJ, 584,414). Chandra Survey for Compact Objects in Supernova Remnants: We have formed a collaboration to carry out an extensive search for young neutron stars in nearby supernova remnants. Using X-ray observations from an approved Chandra Large Project, as well as from additional approved XMM observations, we are investigating a volume-limited sample of SNRs for which there is currently no evidence of associated neutron stars. We have obtained extensive optical and 1R data to complement the project, and analysis of these data is currently underway.
Slane, Patrick O.↗
Determining the Structure of Rotating Massive Stellar Cores with Gravitational Waves
The gravitational wave (GW) signal resulting from stellar core collapse encodes a wealth of information about the physical parameters of the progenitor star and the resulting core-collapse supernova (CCSN). We present a novel approach to constrain CCSN progenitor properties at collapse using two of the most detectable parts of the GW signal: the core-bounce signal and evolution of the dominant frequency mode from the protoneutron star. We focus on the period after core bounce but before explosion and investigate the predictive power of GWs from rotating CCSNe to constrain properties of the progenitor star. We analyze 34 2D and four 3D neutrino-radiation-hydrodynamic simulations of stellar core collapse in progenitors of varied initial mass and rotation rate. Extending previous work, we verify the compactness of the progenitor at collapse to correlate with the early ramp-up slope, and in rotating cases, also with the core angular momentum. Combining this information with the bounce signal, we present a new analysis method to constrain the pre-collapse core compactness of the progenitor. Because these GW features occur less than a second after core bounce, this analysis could allow astronomers to predict electromagnetic properties of a resulting CCSN even before shock breakout.
Astronomy & Astrophysics↗
The effects of mixture preburning on detonation wave propagation
Pressure gain combustion in the form of continuous detonations can provide a significant increase in the efficiency of a variety of propulsion and energy conversion devices. In this regard, rotating detonation engines (RDEs) that utilize an azimuthally-moving detonation wave in annular systems are increasingly seen as a viable approach to realizing pressure gain combustion. However, practical RDEs that employ non- premixed fuel and oxidizer injection need to minimize losses through a number of mechanisms, including turbulence-induced shock-front variations, incomplete fuel-air mixing, and premature deflagration. In this study, a canonical stratified detonation configuration is used to understand the impact of preburning on detonation efficiency. It was found that heat release ahead of the detonation wave leads to weaker shock fronts, delayed combustion of partially-oxidized fuel-air mixture, and non-compact heat release. Furthermore, large variations in wave speeds were observed, which is consistent with wave behavior in full-scale RDEs. Peak pressures in the compression region or near triple points were considerably lower than the theoretically-predicted values for ideal detonations. Analysis of the detonation structure indicates that this deflagration process is parasitic in nature, reducing the detonation efficiency but also leading to heat release far behind the wave that cannot directly strengthen the shock wave. As a result, this parasitic combustion leads to commensal combustion (heat release far downstream of the wave), indicating that it is the root cause of combustion efficiency losses.
42 ENGINEERING↗
Creating and studying a scaled interplanetary coronal mass ejection
The Sun, being an active star, undergoes eruptions of magnetized plasma that reach the Earth and cause the aurorae near the poles. These eruptions, called coronal mass ejections (CMEs), send plasma and magnetic fields out into space. CMEs that reach planetary orbits are called interplanetary coronal mass ejections (ICMEs) and are a source of geomagnetic storms, which can cause major damage to our modern electrical systems with limited warning. To study ICME propagation, we devised a scaled experiment using the Big Red Ball (BRB) plasma containment device at the Wisconsin Plasma Physics Laboratory. These experiments inject a compact torus of plasma as an ICME through an ambient plasma inside the BRB, which acts as the interplanetary medium. Magnetic and temperature probes provide three-dimensional magnetic field information in time and space, as well as temperature and density as a function of time. Using this information, we can identify features in the compact torus that are consistent with those in real ICMEs. We also identify the shock, sheath, and ejecta similar to the structure of an ICME event. This experiment acts as a first step to providing information that can inform predictive models, which can give us time to shield our satellites and large electrical systems in the event that a powerful ICME were to strike.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Using limited neural networks to assess relative mechanistic influence on shock heating in granular solids
The rapid compaction of granular media results in localized heating that can induce chemical reactions, phase transformations, and melting. However, there are numerous mechanisms in play that can be dependent on a variety of microstructural features. Machine learning techniques such as neural networks offer a ubiquitous method to develop models for physical processes. Limiting what kind of microstructural information is used as an input and assessing normalized changes in network error, the relative importance of different mechanisms can be inferred. Here we utilize binned, initial density information as network inputs to predict local shock heating in a granular high explosive trained from large-scale molecular dynamics simulations. In this study, the spatial extent of the density field used in the network is altered to assess the importance and relevant length scales of the physical mechanisms in play, where different microstructural features result in different predictive capabilities.
36 MATERIALS SCIENCE↗
Particle Acceleration in Active Galactic Nuclei
The high efficiency of energy generation inferred from radio observations of quasars and X-ray observations of Seyfert active galactic nuclei (AGNs) is apparently achieved only by the gravitational conversion of the rest mass energy of accreting matter onto supermassive black holes. Evidence for the acceleration of particles to high energies by a central engine is also inferred from observations of apparent superluminal motion in flat spectrum, core-dominated radio sources. This phenomenon is widely attributed to the ejection of relativistic bulk plasma from the nuclei of active galaxies, and accounts for the existence of large scale radio jets and lobes at large distances from the central regions of radio galaxies. Reports of radio jets and superluminal motion from galactic black hole candidate X-ray sources indicate that similar processes are operating in these sources. Observations of luminous, rapidly variable high-energy radiation from active galactic nuclei (AGNs) with the Compton Gamma Ray Observatory show directly that particles are accelerated to high energies in a compact environment. The mechanisms which transform the gravitational potential energy of the infalling matter into nonthermal particle energy in galactic black hole candidates and AGNs are not conclusively identified, although several have been proposed. These include direct acceleration by static electric fields (resulting from, for example, magnetic reconnection), shock acceleration, and energy extraction from the rotational energy of Kerr black holes. The dominant acceleration mechanism(s) operating in the black hole environment can only be determined, of course, by a comparison of model predictions with observations. The purpose of the work proposed for this grant was to investigate stochastic particle acceleration through resonant interactions with plasma waves that populate the magnetosphere surrounding an accreting black hole. Stochastic acceleration has been successfully applied to the problem of ion and electron energization in solar flares, and is capable of accounting for a wide range of both neutral and charged particle emissions. It is also a component in diffusive shock acceleration, since pitch-angle scattering (which is necessary for multiple shock crossings) is accompanied by diffusion in momentum space, which in turn yields a net systematic energy gain; however, stochastic energization will dominate the first-order shock process only in certain parameter regimes. Although stochastic acceleration has been applied to particle energization in the lobes of radio galaxies, its application to the central regions of AGNs has only recently been considered, but not in detail. We proposed to systematically investigate the plasma processes responsible for stochastic particle acceleration in black hole magnetospheres along with the energy-loss processes which impede particle energization. To this end we calculated acceleration rates and escape time scales for protons and electrons resonating with Alfven waves, and for electrons resonating with whistlers. Assuming either a Kolmogorov or Kraichnan wave spectrum, accretion at the Eddington limit, magnetic field strengths near equipartition, and turbulence energy densities approx. 10% of the total magnetic field energy density, we find that Alfven waves accelerate protons to Lorentz factors approx, equals 10(exp 4) - 10(exp 6) before they escape from the system. Acceleration of electrons by fast mode and whistler waves can produce a nonthermal population of relativistic electrons whose maximum energy is determined by a competition with radiation losses.
Miller, James A.↗
HST imaging of hydrogen-poor ejecta in Abell 30 and Abell 78 - Wind-blown cometary structures
HST Faint Object Camera images of hydrogen-poor gas in the planetary nebulae A30 and A78 have revealed remarkable 'cometary' structures in the O III 5007-A forbidden line. Most of these cometary structures, consisting of compact (0.15-0.5 arcsec) knots with radial tails several arcsec in length, are located in an equatorial plane in both nebulae. In addition, two bright, compact (0.3 arcsec) polar knots are present in A30, one of them forming a bow shock. Corresponding polar features in A78 are more diffuse. The central stars of both nebulae have energetic winds which are most likely responsible for the 'cometary' knot morphology. We interpret this morphology in terms of dense (several thousand electrons per cu cm) H-poor condensations whose outer expanding layers are swept outward by stellar winds. Photoionization modeling indicates that while dense knot cores are mostly heated by atomic photoionization, expanding tenuous gas is heated by photoelectrons ejected from abundant dust grains. Our models predict steep temperature gradients for which there is observational evidence and possible abrupt phase transitions in the expanding gas.
Borkowski, Kazimierz J.↗
Spectral Index and Quasi-Periodic Oscillation Frequency Correlation in Black Hole (BH) Sources: Observational Evidence of Two Phases and Phase Transition in BHs
Recent studies have shown that strong correlations are observed between the low frequencies (1-10 Hz) of quasiperiodic oscillations (QPOs) and the spectral power law index of several Black Hole (BH) candidate sources, in low hard states, steep power-law (soft) states and in transition between these states. The observations indicate that the X-ray spectrum of such state (phases) show the presence of a power-law component and are sometimes related to simultaneous radio emission indicated the probable presence of a jet. Strong QPOs (less than 20% rms) are present in the power density spectrum in the spectral range where the power-law component is dominant ( i.e. 60-90% ). This evidence contradicts the dominant long standing interpretation of QPOs as a signature of the thermal accretion disk. We present the data from the literature and our own data to illustrate the dominance of power-law index-QPO frequency correlations. We provide a model, that identifies and explains the origin of the QPOs and how they are imprinted on the properties of power-law flux component. We argue the existence of a bounded compact coronal region which is a natural consequence of the adjustment of Keplerian disk flow to the innermost sub-Keplerian boundary conditions near the central object and that ultimately leads to the formation of a transition layer (TL) between the adjustment radius and the innermost boundary. The model predicts two phases or states dictated by the photon upscattering produced in the TL: (1) hard state, in which the TL is optically thin and very hot (kT approx. greater than 50 keV) producing photon upscattering via thermal Componization; the photon spectrum index Gamma appprox.1.5 for this state is dictated by gravitational energy release and Compton cooling in an optically thin shock near the adjustment radius; (2) a soft state which is optically thick and relatively cold (approx. less than 5 keV); the index for this state, Gamma approx. 2.8 is determined by soft-photon upscattering and photon trapping in converging flow into BH. In the TL model for corona the QPO frequency vnu(sub high) is related to the gravitational (close to Keplerian) frequency nu(sub K) at the outer (adjustment) radius and nu(sub low) is related to the TL s normal mode (magnetoacoustic) oscillation frequency nu(sub MA). The observed correlations between index and low and high QPO frequencies are readily explained in terms of this model. We also suggest a new method for evaluation of the BH mass using the index-frequency correlation.
Titarchuk, Lev↗
Spectral Index and Quasi-Periodic Oscillation Frequency Correlation in Black Hole Sources: Observational Evidence of Two Phases and Phase Transition in Black Holes
Recent studies have shown that strong correlations are observed between the low frequencies (1-10 Hz) of quasi-periodic oscillations (QPOs) and the spectral power law index of several black hole (BH) candidate sources, in low (hard) states, steep power law (soft) states, and transitions between these states. The observations indicate that the X-ray spectra of such state (phases) show the presence of a power-law component and are sometimes related to simultaneous radio emission, indicating the probable presence of a jet. Strong QPOs (>20% rms) are present in the power density spectrum in the spectral range where the power-law component is dominant (i.e., 60%90%). This evidence contradicts the dominant, long-standing interpretation of QPOs as a signature of the thermal accretion disk. We present the data from the literature and our own data to illustrate the dominance of power-law index-QPO frequency correlations. We provide a model that identifies and explains the origin of the QPOs and how they are imprinted on the properties of the power-law flux component. We argue for the existence of a bounded compact coronal region that is a natural consequence of the adjustment of the Keplerian disk flow to the innermost sub-Keplerian boundary conditions near the central object and that ultimately leads to the formation of a transition layer (TL) between the adjustment radius and the innermost boundary. The model predicts two phases or states dictated by the photon upscattering produced in the TL: (1) a hard state, in which the TL is optically thin and very hot (kT approximately greater than 50 keV), producing photon upscattering via thermal Comptonization (the photon spectrum index Gamma approximates 1.7 for this state is dictated by gravitational energy release and Compton cooling in an optically thin shock near the adjustment radius), and (2) a soft state that is optically thick and relatively cold (kT approximately less than 5 keV the index for this state, Gamma approximates 2.8, is determined by soft-photon upscattering and photon trapping in a converging flow into the BH). In the TL model for the corona, the QPO frequency V(sub high) is related to the gravitational (close to Keplerian) frequency V(sub K) at the outer (adjustment) radius and v(sub low) is related to the TL's normal mode (magnetoacoustic) oscillation frequency v(sub MA) . The observed correlations between index and low and high QPO frequencies are readily explained in terms of this model. We also suggest a new method for evaluation of the BH mass using the index-frequency correlation.
Titarchuk, Lev↗