Bulk Comptonization Research Articles

Spectral evolution of RX J0440.9+4431 during the 2022–2023 giant outburst observed with Insight-HXMT

In 2022–2023, the Be/X-ray binary X-ray pulsar RX J0440.9+4431 underwent a Type II giant outburst, reaching a peak luminosity of LX ∼ × 1037 erg s−1. In this work, we utilized Insight-HXMT data to analyze the spectral evolution of RX J0440.9+4431 during the giant outburst. By analyzing the variation in the X-ray spectrum during the outburst using standard phenomenological models, we find that as the luminosity approaches the critical luminosity, the spectrum becomes flatter, with the photon enhancement predominantly concentrated around ∼2 keV and 20–40 keV. The same behavior has also been noted in Type II outbursts from other sources. While the phenomenological models provide good fits to the spectrum, it is sometimes difficult to gain insight into details of the fundamental accretion physics using this approach. Hence, we also analyzed spectra obtained during high and low phases of the outburst using a new, recently developed physics-based theoretical model that allows us to study the variations in the physical parameters during the outburst, such as the temperature, density, and magnetic field strength. Application of the theoretical model reveals that the observed spectrum is dominated by Comptonized bremsstrahlung emission emitted from the column walls in both the high and low states. We show that the spectral flattening observed at high luminosities results from a decrease in the electron temperature, combined with a compactification of the emission zone, which reduces the efficiency of bulk Comptonization. We also demonstrate that when the source is at maximum luminosity, the spectrum tends to harden around the peak of the pulse profile, and we discuss possible theoretical explanations for this behavior. We argue that the totality of the behavior in this source can be explained if the accretion column is in a quasi-critical state at the time of maximum luminosity during the outburst.

A theoretical Fourier-transformation model for the formation of X-ray time lags from black hole accretion discs

ABSTRACT X-ray emission from active galactic nuclei (AGNs) often displays complex and rapid variability, which may provide a glimpse into the detailed thermal and dynamical structure of the accreting gas near the event horizon of the central black hole. The observed variability can be analysed using Fourier transforms of the light curves in multiple energy channels, which can be used to generate Fourier phase lags, corresponding to lags in the time domain. The X-ray time lags may be either soft lags or hard lags, depending on whether the variability in the hard energy channel precedes that in the soft channel or vice versa. The physical explanation for the observed X-ray time lags from AGNs has been puzzling, and several scenarios have been proposed. In this paper, we explore the hypothesis that the X-ray time lags are produced as a result of the reprocessing of iron L-line and K-line seed photons generated via fluorescence, which is driven by a variable incident radiation field. The seed photons are reprocessed by a combination of thermal and bulk Comptonization and spatial reverberation. We assume that the inner region of the accretion flow can be approximated as a hot, geometrically thick ADAF disc. The outer radius of the ADAF region is equal to the shock formation radius, which is located just outside the centrifugal barrier. The time-dependent radiative transfer in the disc is analysed using a Fourier-transformed, vertically averaged transport equation in cylindrical coordinates. We demonstrate that the new model can successfully reproduce the complex X-ray variability data for the Seyfert 1 galaxies 1H 0707–495 and Ark 564.

Radiative Particle-in-Cell Simulations of Turbulent Comptonization in Magnetized Black-Hole Coronae.

We report results from the first radiative particle-in-cell simulations of strong Alfvénic turbulence in plasmas of moderate optical depth. The simulations are performed in a local 3D periodic box and self-consistently follow the evolution of radiation as it interacts with a turbulent electron-positron plasma via Compton scattering. We focus on the conditions expected in magnetized coronae of accreting black holes and obtain an emission spectrum consistent with the observed hard state of Cyg X-1. Most of the turbulence power is transferred directly to the photons via bulk Comptonization, shaping the peak of the emission around 100keV. The rest is released into nonthermal particles, which generate the MeV spectral tail. The method presented here shows promising potential for abinitio modeling of various astrophysical sources and opens a window into a new regime of kinetic plasma turbulence.

A relativistic outflow model of the X-ray polarization in Cyg X-1

ABSTRACT We propose that the polarization of the emission from the X-ray binary Cygnus X-1, measured using the Imaging X-ray Polarimetry Explorer, is imprinted by bulk Comptonization of coronal emission in a mildly relativistic wind or jet with a hollow-cone geometry. Models based on scattering in a static corona overlying a thin accretion disc have difficulty reproducing the relatively high-polarization degree (PD $\sim 4~{{\ \rm per\ cent}}$) concurrently with the low inclination (∼30°) of the binary orbit. We show that bulk outflow with a Lorentz factor ≳1.5 is adequate to reproduce the observed PD, with position angle parallel to the large-scale jet, provided that the scattering occurs in a conical sheath offset from the jet axis and our line of sight aligns roughly with the opening angle of the cone. Physically, this flow geometry could represent the entrainment of dense material near the base of an accelerating jet as it passes through the disc corona, or a slow (but still relativistic) sheath around a fast jet. If similar outflows are present in other X-ray binaries at higher inclination, we might expect to see still higher degrees of linear polarization ${\lesssim} 10~{{\ \rm per\ cent}}$ with an orientation perpendicular to the jet direction.

A Generalized Analytical Model for Thermal and Bulk Comptonization in Accretion-powered X-Ray Pulsars

We develop a new theoretical model describing the formation of the radiation spectrum in accretion-powered X-ray pulsars as a result of bulk and thermal Comptonization of photons in the accretion column. The new model extends the previous model developed by the authors in four ways: (1) we utilize a conical rather than cylindrical geometry; (2) the radiation components emitted from the column wall and the column top are computed separately; (3) the model allows for a nonzero impact velocity at the stellar surface; and (4) the velocity profile of the gas merges with Newtonian freefall far from the star. We show that these extensions allow the new model to simulate sources over a wide range of accretion rates. The model is based on a rigorous mathematical approach in which we obtain an exact series solution for the Green’s function describing the reprocessing of monochromatic seed photons. Emergent spectra are then computed by convolving the Green’s function with bremsstrahlung, cyclotron, and blackbody photon sources. The range of the new model is demonstrated via applications to the high-luminosity source Her X-1, and the low-luminosity source X Per. The new model suggests that the observed increase in spectral hardness associated with increasing luminosity in Her X-1 may be due to a decrease in the surface impact velocity, which increases the PdV work done on the radiation field by the gas.

An Analytical Fourier Transformation Model for the Production of Hard and Soft X-Ray Time Lags in Active Galactic Nuclei: Application to 1H 0707-495

The variability of the X-ray emission from active galactic nuclei is often characterized using time lags observed between soft and hard energy bands in the detector. The time lags are usually computed using the complex cross-spectrum, which is based on the Fourier transforms of the hard and soft time series data. It has been noted that some active galactic nuclei display soft X-ray time lags, in addition to the more ubiquitous hard lags. Hard time lags are thought to be produced via propagating fluctuations, spatial reverberation, or via the thermal Comptonization of soft seed photons injected into a hot electron cloud. The physical origin of the soft lags has been a subject of debate over the last decade. Currently, the reverberation interpretation is recognized as a leading theory. In this paper, we explore the alternative possibility that the soft X-ray time lags result partially from the thermal and bulk Comptonization of monochromatic seed photons which, in the case of the narrow-line Seyfert 1 galaxy 1H 0707-495, may correlate with fluorescence of iron L-line emission. In our model, the seed photons are injected into a hot, quasi-spherical corona in the inner region of the accretion flow. We develop an exact, time-dependent analytical model for the thermal and bulk Comptonization of the seed photons based on a Fourier-transformed radiation transport equation, and we demonstrate that the model successfully reproduces both the hard and soft time lags observed from 1H 0707-495.

An Efficient Method for Fitting Radiation-mediated Shocks to Gamma-Ray Burst Data: The Kompaneets RMS Approximation

Abstract Shocks that occur below a gamma-ray burst (GRB) jet photosphere are mediated by radiation. Such radiation-mediated shocks (RMSs) could be responsible for shaping the prompt GRB emission. Although well studied theoretically, RMS models have not yet been fitted to data owing to the computational cost of simulating RMSs from first principles. Here we bridge the gap between theory and observations by developing an approximate method capable of accurately reproducing radiation spectra from mildly relativistic (in the shock frame) or slower RMSs, called the Kompaneets RMS approximation (KRA). The approximation is based on the similarities between thermal Comptonization of radiation and the bulk Comptonization that occurs inside an RMS. We validate the method by comparing simulated KRA radiation spectra to first-principle radiation hydrodynamics simulations, finding excellent agreement both inside the RMS and in the RMS downstream. The KRA is then applied to a shock scenario inside a GRB jet, allowing for fast and efficient fitting to GRB data. We illustrate the capabilities of the developed method by performing a fit to a nonthermal spectrum in GRB 150314A. The fit allows us to uncover the physical properties of the RMS responsible for the prompt emission, such as the shock speed and the upstream plasma temperature.

Minute-timescale Variability in the X-ray Emission of the Highest Redshift Blazar*

Abstract We report on two Chandra observations of the quasar PSO J0309+27, the most distant blazar observed so far (z = 6.1), performed eight months apart, in 2020 March and November. Previous Swift-XRT observations showed that this object is one of the brightest X-ray sources beyond redshift 6.0 ever observed so far. This new dataset confirmed the high flux level and unveiled a spectral change that occurred on a very short timescale (250 s rest frame), caused by a significant softening of the emission spectrum. This kind of spectral variability, on such a short interval, has never been reported in the X-ray emission of a flat-spectrum radio quasar. A possible explanation for this is given by the emission produced by the inverse Compton scatter of the quasar UV photons by the cold electrons present in a fast shell moving along the jet. Although this bulk Comptonization emission should be an unavoidable consequence of the standard leptonic jet model, this would be the first time that it has been observed.

Probing the physical properties of the intergalactic medium using blazars

ABSTRACT We use Swift blazar spectra to estimate the key intergalactic medium (IGM) properties of hydrogen column density ($\mathit {N}\small {\rm HXIGM}$), metallicity, and temperature over a redshift range of 0.03 ≤ z ≤ 4.7, using a collisional ionization equilibrium model for the ionized plasma. We adopted a conservative approach to the blazar continuum model given its intrinsic variability and use a range of power-law models. We subjected our results to a number of tests and found that the $\mathit {N}\small {\rm HXIGM}$ parameter was robust with respect to individual exposure data and co-added spectra for each source, and between Swift and XMM–Newton source data. We also found no relation between $\mathit {N}\small {\rm HXIGM}$ and variations in source flux or intrinsic power laws. Though some objects may have a bulk Comptonization component that could mimic absorption, it did not alter our overall results. The $\mathit {N}\small {\rm HXIGM}$ from the combined blazar sample scales as (1 + z)1.8 ± 0.2. The mean hydrogen density at z = 0 is n0 = (3.2 ± 0.5) × 10−7 cm−3. The mean IGM temperature over the full redshift range is log(T/K) =6.1 ± 0.1, and the mean metallicity is [X/H] = −1.62 ± 0.04(Z ∼ 0.02). When combining with the results with a gamma-ray burst (GRB) sample, we find the results are consistent over an extended redshift range of 0.03 ≤ z ≤ 6.3. Using our model for blazars and GRBs, we conclude that the IGM contributes substantially to the total absorption seen in both blazar and GRB spectra.

Three-dimensional modelling of accretion columns: spatial asymmetry and self-consistent simulations

ABSTRACT The paper presents the results of three-dimensional (3D) modelling of the structure and the emission of accretion columns formed above the surface of accreting strongly magnetized neutron stars under the circumstances when a pressure of the photons generated in the column base is enough to determine the dynamics of the plasma flow. On the foundation of numerical radiation hydrodynamic simulations, several 3D models of accretion column are constructed. The first group of the models contains spatially 3D columns. The corresponding calculations lead to the distributions of the radiation flux over the sidewalls of the columns which are not characterized by axial symmetry. The second group includes the self-consistent modelling of spectral radiative transfer and two-dimensional spatial structure of the column, with both thermal and bulk Comptonization taken into account. The changes in the structure of the column and the shape of X-ray continuum are investigated depending on physical parameters of the model.

Subphotospheric Turbulence as a Heating Mechanism in Gamma-Ray Bursts

Abstract We examine the possible role of turbulence in feeding the emission of gamma-ray bursts (GRBs). Turbulence may develop in a GRB jet as the result of hydrodynamic or current-driven instabilities. The jet carries dense radiation and the turbulence cascade can be damped by Compton drag, passing kinetic fluid energy to photons through scattering. We identify two regimes of turbulence dissipation: (1) “Viscous”—the turbulence cascade is Compton-damped on a scale greater than the photon mean free path . Then turbulence energy is passed to photons via bulk Comptonization by smooth shear flows on scale . (2) “Collisionless”—the cascade avoids Compton damping and extends to microscopic plasma scales much smaller than . The collisionless dissipation energizes plasma particles, which radiate the received energy; how the dissipated power is partitioned between particles needs further investigation with kinetic simulations. We show that the dissipation regime switches from viscous to collisionless during the jet expansion, at a critical value of the jet optical depth, which depends on the amplitude of turbulence. Turbulent GRB jets are expected to emit nonthermal photospheric radiation. Our analysis also suggests revisions of turbulent Comptonization in black hole accretion disks discussed in previous works.

Radiation-mediated Shocks in Gamma-Ray Bursts: Subshock Photon Production

Abstract Internal shocks provide a plausible heating mechanism in the jets of gamma-ray bursts (GRBs). Shocks occurring below the jet photosphere are mediated by radiation. It was previously found that radiation-mediated shocks (RMSs) inside GRB jets are inefficient photon producers, and the photons that mediate the RMS must originate from an earlier stage of the explosion. We show that this conclusion is valid only for nonmagnetized jets. RMSs that propagate in moderately magnetized plasma develop a collisionless subshock that locally heats the plasma to a relativistic temperature, and the hot electrons emit copious synchrotron photons inside the RMS. We find that this mechanism is effective for mildly relativistic shocks and may be the main source of photons observed in GRBs. We derive a simple analytical estimate for the generated photon number per proton, Z, which gives Z = 105–106, consistent with observations. The number is controlled by two main factors: (1) the abundance of electron–positron pairs created in the shock, which is self-consistently calculated, and (2) the upper limit on the brightness temperature of soft radiation set by induced Compton scattering. The photons are initially injected with low energies that are well below the observed GRB peak. The injected soft photons that survive induced downscattering and free–free absorption gain energy in the RMS via bulk Comptonization and shape its nonthermal spectrum.

Spectral Distortions in CMB by the Bulk Comptonization Due to Zeldovich Pancakes

If the large scale structure of the Universe was created, even partially, via Zeldovich pancakes, than the fluctuations of the CMB radiation should be formed due to bulk comptonization of black body spectrum on the contracting pancake. Approximate formulas for the CMB energy spectrum after bulk comptonization are obtained. The difference between comptonized energy spectra of the CMB due to thermal and bulk comptonization may be estimated by comparison of the plots for the spectra in these two cases.

An XMM-Newton look at the strongly variable radio-weak BL Lac Fermi J1544–0639

Context. Fermi J1544–0639/ASASSN-17gs/AT2017egv was identified as a gamma-ray/optical transient on May 15, 2017. Subsequent multiwavelength observations suggest that this source may belong to the new class of radio-weak BL Lacs. Aims. We studied the X-ray spectral properties and short-term variability of Fermi J1544–0639 to constrain the X-ray continuum emission mechanism of this peculiar source. Methods. We present the analysis of an XMM-Newton observation, 56 ks in length, performed on February 21, 2018. Results. The source exhibits strong X-ray variability, both in flux and spectral shape, on timescales of ∼10 ks, with a harder-when-brighter behaviour typical of BL Lacs. The X-ray spectrum is nicely described by a variable broken power law, with a break energy of around 2.7 keV consistent with radiative cooling due to Comptonization of broad-line region photons. We find evidence for a “soft excess”, nicely described by a blackbody with a temperature of ∼0.2 keV, consistent with being produced by bulk Comptonization along the jet.

A simple framework for modelling the dependence of bulk Comptonization by turbulence on accretion disc parameters

Warm Comptonization models for the soft X-ray excess in AGN do not self-consistently explain the relationship between the Comptonizing medium and the underlying accretion disc. Because of this, they cannot directly connect the fitted Comptonization temperatures and optical depths to accretion disc parameters. Since bulk velocities exceed thermal velocities in highly radiation pressure dominated discs, in these systems bulk Comptonization by turbulence may provide a physical basis in the disc itself for warm Comptonization models. We model the dependence of bulk Comptonization on fundamental accretion disc parameters, such as mass, luminosity, radius, spin, inner boundary condition, and $\alpha$. In addition to constraining warm Comptonization models, our model can help distinguish contributions from bulk Comptonization to the soft X-ray excess from those due to other physical mechanisms, such as absorption and reflection. By linking the time variability of bulk Comptonization to fluctuations in the disc vertical structure due to magnetorotational instability (MRI) turbulence, our results show that observations of the soft X-ray excess can be used to study disc turbulence in the radiation pressure dominated regime. Because our model connects bulk Comptonization to one dimensional vertical structure temperature profiles in a physically intuitive way, it will be useful for understanding this effect in future simulations run in new regimes.

High energy power-law tail in X-ray binaries and bulk Comptonization due to an outflow from a disk

We study the high energy power-law tail emission of X-ray binaries (XRBs) by a bulk Comptonization process which usually observe in the very high soft VHS state of blackhole BH XRBs and the high soft HS state of neutron star (NS) and BH XRBs. Earlier, to generate the power-law tail in bulk Comptonization framework, a free-fall converging flow into BH or NS has been considered as a bulk region. In this work, for a bulk region we consider mainly an outflow geometry from the accretion disk which is bounded by a torus surrounding the compact object. We have a two choice for an outflow geometry i) collimated flow ii) conical flow of opening angle $\theta_b$ and the axis is perpendicular to the disk. We also consider an azimuthal velocity of the torus fluids as a bulk motion where the fluids are rotating around the compact object (a torus flow). We find that the power-law tail can be generated in a torus flow with having large optical depth and bulk speed ($>$ 0.75c), and in conical flow with $\theta_b$ $>$ $\sim$30 degree for a low value of Comptonizing medium temperature. Particularly, in conical flow the low opening angle is more favourable to generate the power-law tail in both state HS and VHS. We notice that when the outflow is collimated, then the emergent spectrum does not have power-law component for a low Comptonizing medium temperature.

Monte Carlo simulations of relativistic radiation-mediated shocks – I. Photon-rich regime

We explore the physics of relativistic radiation mediated shocks (RRMSs) in the regime where photon advection dominates over photon generation. For this purpose, a novel iterative method for deriving a self-consistent steady-state structure of RRMS is developed, based on a Monte-Carlo code that solves the transfer of photons subject to Compton scattering and pair production/annihilation. Systematic study is performed by imposing various upstream conditions which are characterized by the following three parameters: the photon-to-baryon inertia ratio $\xi_{u *}$, the photon-to-baryon number ratio $\tilde{n}$, and the shock Lorentz factor $\gamma_u$. We find that the properties of RRMSs vary considerably with these parameters. In particular, while a smooth decline in the velocity, accompanied by a gradual temperature increase is seen for $\xi_{u*} \gg 1$, an efficient bulk Comptonization, that leads to a heating precursor, is found for $\xi_{u*} \lesssim 1$. As a consequence, although particle acceleration is highly inefficient in these shocks, a broad non-thermal spectrum is produced in the latter case. The generation of high energy photons through bulk Comptonization leads, in certain cases, to a copious production of pairs that provide the dominant opacity for Compton scattering. We also find that for certain upstream conditions a weak subshock appears within the flow. For a choice of parameters suitable to gamma-ray bursts, the radiation spectrum within the shock is found to be compatible with that of the prompt emission, suggesting that subphotospheric shocks may give rise to the observed non-thermal features despite the absence of accelerated particles.

Bulk Comptonization: new hints from the luminous blazar 4C+25.05

Blazars are often characterized by a spectral break at soft X-rays, whose origin is still debated. While most sources show a flattening, some exhibit a blackbody-like soft excess with temperatures of the order of $\sim$0.1 keV, similar to low-luminosity, non-jetted Seyferts. Here we present the analysis of the simultaneous XMM-Newton and NuSTAR observation of the luminous FSRQ 4C+25.05 ($z=2.368$). The observed 0.3-30 keV spectrum is best described by the sum of a hard X-ray power law ($\Gamma = 1.38_{-0.03}^{+0.05}$) and a soft component, approximated by a blackbody with $kT_{\rm BB} = 0.66_{-0.04}^{+0.05}$ keV (rest frame). If the spectrum of 4C+25.05 is interpreted in the context of bulk Comptonization by cold electrons of broad-line region photons emitted in the direction of the jet, such an unusual temperature implies a bulk Lorentz factor of the jet of $\Gamma_{\rm bulk}\sim 11.7$. Bulk Comptonization is expected to be ubiquitous on physical grounds, yet no clear signature of it has been found so far, possibly due to its transient nature and the lack of high-quality, broad-band X-ray spectra.

Decade long RXTE monitoring observations of Be/X-ray binary pulsar EXO 2030+375

We present a comprehensive timing and spectral studies of Be/X-ray binary pulsar EXO 2030+375 using extensive Rossi X-ray Timing Explorer observations from 1995 till 2011, covering numerous Type I and 2006 Type II outbursts. Pulse profiles of the pulsar were found to be strongly luminosity dependent. At low luminosity, the pulse profile consisted of a main peak and a minor peak that evolved into a broad structure at high luminosity with a significant phase shift. A narrow and sharp absorption dip, also dependent on energy and luminosity, was detected in the pulse profile. Comparison of pulse profiles showed that the features at a particular luminosity are independent of type of X-ray outbursts. This indicates that the emission geometry is solely a function of mass accretion rate. The broadband energy spectrum was described with a partial covering high energy cutoff model as well as a physical model based on thermal and bulk Comptonization in accretion column. We did not find any signature of cyclotron resonance scattering feature in the spectra obtained from all the observations. A detailed analysis of spectral parameters showed that, depending on source luminosity, the power-law photon index was distributed in three distinct regions. It suggests the phases of spectral transition from sub-critical to super-critical regimes in the pulsar as proposed theoretically. A region with constant photon index was also observed in ~(2-4) x 10^37 erg/s range, indicating critical luminosity regime in EXO 2030+375.

The contribution of bulk Comptonization to the soft X-ray excess in AGN

Bulk velocities exceed thermal velocities for sufficiently radiation pressure dominated accretion flows. We model the contribution of bulk Comptonization to the soft X-ray excess in AGN. Bulk Comptonization is due to both turbulence and the background shear. We calculate spectra both taking into account and not taking into account bulk velocities using scaled data from radiation magnetohydrodynamic (MHD) shearing box simulations. We characterize our results with temperatures and optical depths to make contact with other warm Comptonization models of the soft excess. We chose our fiducial mass, $M = 2 \times 10^6 M_{\odot}$, and accretion rate, $L/L_{\rm Edd} = 2.5$, to correspond to those fit to the super-Eddington narrow line Seyfert 1 (NLS1) RE1034+396. The temperatures, optical depths, and Compton $y$ parameters we find broadly agree with those fit to RE1034+396. The effect of bulk Comptonization is to shift the Wien tail to higher energy and lower the gas temperature, broadening the spectrum. Observations of the soft excess in NLS1s can constrain the properties of disc turbulence if the bulk Comptonization contribution can be separated out from contributions from other physical effects, such as reflection and absorption.