Context. X-ray spectra of accretion-powered X-ray pulsars can often be described using a power-law continuum with a high-energy cutoff, which might be further modified by additional spectral components. The Be X-ray binary system 4U 0115+63 is well known for having one of the highest numbers of detected harmonics of its cyclotron resonant scattering features (CRSFs), a pronounced spectral component known as the "10 keV feature", and quasiperiodic oscillations (QPOs) with a period of about 500 s during outbursts. Aims. The changes in count rate by a factor of two during the similar to 500 s QPOs allow us to probe the variation in the spectral components with flux. We study the "10 keV feature" in emission, aiming to disentangle it from the broadband continuum and CRSFs and investigate its origin. Methods. We focus on the flux-dependent behavior of the CRSF and its harmonics, and particularly the contribution of the "10 keV feature", as seen in the flux-resolved analysis of two NuSTAR observations of the 2015 outburst. Results. Comparing the flux-resolved spectra of a given observation with the respective total dataset revealed a distinct change in overall spectral shape at the position of the "10 keV feature" but no comparable deviation at the energies of the harmonic CRSFs. The change associated with the "10 keV feature" does not seem to involve its centroid energy, which remains constant within a given observation. We find indications for an anticorrelation between the continuum flux and the ratio of the "10 keV feature" flux to the continuum flux within each observation. Conclusions. The analysis strengthens previous claims that the "10 keV feature" shows some independence from the remaining features. This result supports the interpretation that the "10 keV feature" has a different formation mechanism than the continuum emission, although its origin lies within the same physical environment.

X-ray pulsars are highly magnetized (B∼ 10^12 G) neutron stars accreting from a donor star. Their characteristic X-ray emission arises from accreted material decelerated from relativistic velocities near the magnetic poles of the neutron star. As our line of sight onto the magnetic poles changes with the rotation of the neutron star, the X-rays are periodically modulated, resulting in X-ray pulsations. The shape of the pulse profiles depends on the physics of the interaction between the bright X-rays from the magnetic poles with the infalling matter, the location of the magnetic poles on the neutron star with respect to its spin axis, and on the properties of the space-time around the neutron star. In this review we give a pedagogical introduction to the accretion mechanisms operating in the various types of accreting neutron star systems and the observational techniques used to characterize the pulse profiles. We summarize how the pulse profiles depend on X-ray luminosity and energy and discuss the attempts to connect theoretically these observables with the physical accretion mechanisms. We conclude with an outline of future observational needs and further developments for theoretical models of magnetic accretion.

We develop a new analytical model describing the radiative and dynamical structure of an accretion-powered X-ray pulsar, including relativistic effects and a detailed representation of the rotational and magnetic geometry of the neutron star and the two accretion columns. The model provides for the first time a simultaneous calculation of both the phase-averaged spectrum and the pulse profile for an accretion-powered X-ray pulsar. The X-ray continuum spectrum is calculated using the analytical model of Becker Wolff (2022), which assumes a conical accretion column geometry. The trajectory of the radiation escaping from the two columns is tracked through the curved spacetime using the Schwarzschild metric. The angular distribution of the radiation escaping from the surfaces of the columns (the beaming pattern) is represented using a set of "laser-like" emission directions, with associated amplitudes, called weight coefficients, that each contribute "sub-profiles" to the observed pulse profile. The sub-profiles provide basis functions that are used to fit the observed pulse profile. This yields a set of weight coefficients that determine the beaming pattern of the emission from the accretion column. We use the new model to analyze NuSTAR data for Her X-1, allowing the determination of the temperature, accretion rate, and magnetic field strength, as well as the rotational inclination angle and the latitudes of the two magnetic poles. The method also yields the beaming pattern of the emission, hence providing for the first time a self-consistent phenomenological description of the physical and radiative structures of the two accretion columns.

X-ray Fourier time lags detected from accreting black holes in active galactic nuclei (AGNs) provide important glimpses into the high-energy processes occurring near the event horizon. For many narrow-line Seyfert 1 (NLS1) galaxies, the lag-frequency distribution displays multiple sign changes, indicating several transitions between hard and soft time lags. We develop a new Compton reverberation model that can reproduce the observed time lag distributions for multiple NLS1 galaxies, based on the Compton reprocessing of iron K and L seed photons that are injected in two coupled bursts occurring at different radii in the disk. The variability is driven by transient high-energy emission generated by the Compton upscattering in the hot corona of soft thermal photons produced in the cool outer region of the accretion disk. The two bursts of K and L seed photons are linked by a pressure wave that propagates outward and deposits its energy near the standing shock at the outer boundary of the hot inner region, triggering the second burst. The new model is based on a Fourier-transformed, vertically averaged radiation transport equation. We use our new model to analyze and interpret the observational time lag data for the NLS1 galaxies 1H 0707-495, Ark 564, NGC 4051, and Mrk 766. We demonstrate that the incorporation of a second seed photon burst allows our model to accurately reproduce the time lag data for several AGNs that display complex time lag patterns, including multiple sign changes. We also discuss the physical scenario for connecting the two coupled bursts.

Aims. We aim to investigate the energy-resolved pulse profile changes of the accreting X-ray pulsar V 0332+53 focusing in the cyclotron line energy range, using the full set of available NuSTAR observations. Methods. We applied a tailored pipeline to study the energy dependence of the pulse profiles and to build the pulsed fraction spectra (PFS) for the different observations. We also studied the profile changes using cross-correlation and lag spectra. We re-analysed the energy spectra to search for links between the local features observed in the PFS and spectral emission components associated with the shape of the fundamental cyclotron line. Results. In the PFS data, with sufficiently high statistics, we observe a consistent behaviour around the cyclotron line energy. Specifically, two Gaussian-shaped features appear symmetrically on either side of the putative cyclotron line. These features exhibit minimal variation with source luminosity, and their peak positions consistently remain on the left and right of the cyclotron line energy. Associated with the cyclotron line-forming region, we interpret them as evidence for the resonant cyclotron absorption line wings, as predicted by theoretical models of how the cyclotron line profile should appear along the observer's line of sight. A phase-resolved analysis of the pulse in the energy bands surrounding these features enables us to determine both the spectral shape and the intensity of the photons responsible for these peaks in the PFS. Assuming these features correspond to a spectral component, we used their shapes as priors for the corresponding emission components, finding a statistically satisfactory description of the spectra. To explain these results, we propose that our line of sight is close to the direction of the spin axis, while the magnetic axis is likely orthogonal to it.

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.

Major outbursts of BeXRBs offer a unique laboratory for studying accretion onto magnetized neutron stars (NSs) over a large dynamic range. The accreting material is entrained from the accretion disk by the strong magnetic field, and then channeled onto the NS, forming a so-called accretion column (AC). Physical simulation of the AC requires consideration of various physical processes occurring in strongly magnetized plasma, including complex multi-dimensional radiative transfer and the presence of a radiation-dominated shock. Analytical models based on the Becker and Wolff (2007) model have proven successful at reproducing the observed AC spectra in super-critical sources in which radiation pressure plays the dominant role in controlling the dynamics of the accreting material. In this study, we will apply the model to obtain spectra observed during super-Eddington outbursts of BeXRBs in the Magellanic Clouds.

XTE J1829-098 is a transient X-ray pulsar with a period of similar to 7.8 s. It is a candidate Be star system, although the evidence for this is not yet definitive. We investigated the twenty-year-long X-ray light curve using the Rossi X-ray Timing Explorer Proportional Counter Array (PCA), Neil Gehrels Swift Observatory Burst Alert Telescope, and the Monitor of All-sky X-ray Image. We find that all three light curves are clearly modulated on the similar to 244 days orbital period previously reported from PCA monitoring observations, with outbursts confined to a narrow phase range. The light curves also show that XTE J1829-098 was in an inactive state between approximately 2008 December and 2018 April, and no strong outbursts occurred. Such behavior is typical of Be X-ray binary systems, with the absence of outbursts likely related to the dissipation of the Be star's decretion disk. The mean outburst shapes can be approximated with a triangular profile and, from a joint fit of this to all three light curves, we refine the orbital period to 243.95 +/- 0.04 days. The mean outburst profile does not show any asymmetry and has a total phase duration of 0.140 +/- 0.007. However, the PCA light curve shows that there is considerable cycle-to-cycle variability of the individual outbursts. We compare the properties of XTE J1829-098 with other sources that show short phase-duration outbursts, in particular GS 1843-02 (2S 1845-024), which has a very similar orbital period, but longer pulse period, and whose orbit is known to be highly eccentric.

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 $L_ X erg\ $. 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.

We model the spectral formation occurring in the binary X-ray pulsar (XRP) RX J0209.6−7427 during the 2019 super-Eddington outburst. Using a theoretical model previously developed by the authors, we are able to produce spectra that closely resemble the phase-averaged X-ray spectra observed using the Nuclear Spectroscopic Telescope Array and Insight-HXMT during low- and high-luminosity states of the outburst, respectively. The theoretical model simulates the accretion of fully ionized gas in a dipole magnetic field and includes a complete description of the radiation hydrodynamics, matter distribution, and spectral formation. Type II X-ray outbursts provide an opportunity to study accretion over a large range of luminosities for the same neutron star. The analysis performed here represents the first time both the outburst low and high states of an accretion-powered XRP are modeled using a physics-based model rather than standard phenomenological fitting with arbitrary mathematical functions. We find that the outer polar cap radius remains constant and the column is more fully filled with increasing luminosity, Comptonized bremsstrahlung dominates the formation of the phase-averaged X-ray spectrum, and a negative correlation exists between cyclotron centroid energy and luminosity, as expected. The super-Eddington nature of the outburst is rendered possible owing to the low scattering cross section for photons propagating parallel to the magnetic field. We also find that emission through the column top dominates in both the low and high states, implying that the pulse profiles should have a roughly sinusoidal shape, which agrees with observed properties of ultraluminous XRPs.

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.

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.

Due to the complexity of modeling the radiative transfer inside the accretion columns of neutron star binaries, their X-ray spectra are still commonly described with phenomenological models, for example, a cutoff power law. While the behavior of these models is well understood and they allow for a comparison of different sources and studying source behavior, the extent to which the underlying physics can be derived from the model parameters is very limited. During recent years, several physically motivated spectral models have been developed to overcome these limitations. Their application, however, is generally computationally much more expensive and they require a high number of parameters which are difficult to constrain. Previous works have presented an analytical solution to the radiative transfer equation inside the accretion column assuming a velocity profile that is linear in the optical depth. An implementation of this solution that is both fast and accurate enough to be fitted to observed spectra is available as a model in XSPEC. The main difficulty of this implementation is that some solutions violate energy conservation and therefore have to be rejected by the user. We propose a novel fitting strategy that ensures energy conservation during the $\chi^2$-minimization which simplifies the application of the model considerably. We demonstrate this approach as well a study of possible parameter degeneracies with a comprehensive Markov-chain Monte Carlo analysis of the complete parameter space for a combined NuSTAR and Swift/XRT dataset of Cen X-3. The derived accretion-flow structure features a small column radius of $\sim$63 m and a spectrum dominated by bulk-Comptonization of bremsstrahlung seed photons, in agreement with previous studies.

The multi-wavelength spectrum observed from M87 extends from radio wavelengths up to TeV gamma-ray energies. The radio through GeV components have been interpreted successfully using SSC models based on misaligned blazar jets, but the origin of the intense TeV emission detected during flares in 2004, 2005, and 2010 remains puzzling. It has been previously suggested that the TeV flares are produced when a relativistic proton jet originating in the core of M87 collides with a molecular cloud (or stellar atmosphere) located less than one parsec from the central black hole. We explore this scenario in detail here using a self-consistent model for the acceleration of relativistic protons in a shocked, two-fluid ADAF accretion disc. The relativistic protons accelerated in the disc escape to power the observed jet outflows. The distribution function for the jet protons is used to compute the TeV emission produced when the jet collides with a cloud or stellar atmosphere. The simulated broadband radiation spectrum includes radio, X-ray, and GeV components generated via synchrotron, as well as TeV emission generated via the production and decay of muons, positrons, and electrons. The self-consistency of the model is verified by computing the relativistic particle pressure using the distribution function, and comparing it with the relativistic particle pressure obtained from the hydrodynamical model. We demonstrate that the model is able to reproduce the multi-wavelength spectrum from M87 observed by VERITAS and HESS during the high-energy flares in 2004, 2005, and 2010.

Multiwavelength monitoring of the blazar 3C 279 observed a very bright, 12-hour, orphan gamma-ray flare on 20 Dec 2013 with a uniquely hard Fermi-LAT spectrum and high Compton dominance. We work with a one-zone, leptonic model with both first- and second-order Fermi acceleration, which now reproduces the unique flaring behavior. We present a simplified analytic electron energy distribution to provide intuition about how particle acceleration shapes multi-wavelength blazar jet emission spectra. The contributions of individual processes in relativistic jets is fundamental to understanding the particle energy budget in the formation and propagation of astrophysical jets. We show that first- and second-order Fermi acceleration are sufficient to explain the flare, and that magnetic reconnection is not needed. Our analysis suggests that the flare is initiated by an increase in the particle energies due to shock acceleration, which also increases the stochastic acceleration. The higher energy particle preferentially occupy the outer jet, along the sheath, which decreases the apparent magnetic field and synchrotron radiation, while increasing electron exposure to the broad line region photon fields, driving up the external Compton emission.

We present an analysis of X-ray spectra of the high mass X-ray binary 4U 0115+634 as observed with Suzaku and RXTE in 2011 July, during the fading phase of a giant X-ray outburst. We used a continuum model consisting of an absorbed cutoff power-law and an ad-hoc Gaussian emission feature centered around 8.5 keV, which we discuss to be due to cyclotron emission. Our results are consistent with a fundamental cyclotron absorption line centered at ${\sim}10.2$ keV for all observed flux ranges. At the same time we rule out significant influence of the 8.5 kev Gaussian on the CRSF parameters, which are not consistent with the cyclotron line energies and depths of previously reported flux-dependent descriptions. We also show that some continuum models can lead to artificial line-like residuals in the analyzed spectra, which are then misinterpreted as unphysically strong cyclotron lines. Specifically, our results do not support the existence of a previously claimed additional cyclotron feature at ${\sim}15$ keV. Apart from these features, we find for the first time evidence for a He-like Fe XXV emission line at ${\sim}6.7$ keV and weak H-like Fe XXVI emission close to ${\sim}7.0$ keV.