Peter A. Becker

We develop a new analytical model describing the radiative and dynamical structure of an accretion-powered X-ray pulsar (XRP), 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 XRP that can be used to analyze observational data. The X-ray continuum spectrum is calculated using the analytical model of P. A. Becker & M. T. Wolff, which assumes a conical accretion column geometry. The trajectory of the radiation is tracked through the curved spacetime surrounding the neutron star using the Schwarzschild metric. The angular distribution of the radiation escaping from the surface of a column (the beaming pattern) is represented using a set of “laser-like” emission directions, with associated amplitudes, called weight coefficients, that determine the contributions of the corresponding “subprofiles” to the observed pulse profile. The subprofiles provide basis functions that are used to fit the observed pulse profile. The resulting set of weight coefficients determine the beaming pattern of the emission from the accretion column. We use the new model to analyze NuSTAR data for Her X-1, which allows us to determine the temperature, accretion rate, and magnetic field strength, as well as the inclination angle of the neutron star's spin axis and the rotational latitudes of the two magnetic poles. The procedure 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.

Modeling the observed emission from highly magnetized accreting neutron stars is essential for interpreting their X-ray spectra and variability. This task is challenging due to the dynamic, multidimensional nature of the accretion columns and the strong gravitational field. Radiation propagation outside the column, within the neutron star's gravitational field, significantly shapes the observed emission and its variability with rotational phase. Geometry -- the location of the magnetic poles and the observer’s inclination -- is one of the key factors influencing the observables due to the anisotropy of the problem. In this work, we study how visibility effects in the gravitational field of the neutron star influence the direct emission from an accretion column, highlighting their importance when interpreting plasma parameters from observed spectra. Building on the physical model from the previous paper in this series, we investigate the directly observable X-ray flux from one and two columns with fan-beam wall emission, down-boosted by the bulk flow, focusing on the impact of geometry. We find that the observed flux strongly depends on the geometrical setup, which we illustrate across various observables. Particularly notable are special geometries in which a column on the far side of the neutron star aligns with the line of sight. In these cases, shadowing and strong light bending produce a narrow intense peak in pulse profiles at soft energies and a pronounced dip at higher energies (≳ 20, ). The combination of shadowing and height dependence of emission also leads to spectral softening. Flux-derived luminosities can be overestimated by up to a factor of 10. The fundamental cyclotron resonant scattering feature (CRSF) appears predominantly in emission across geometries, and we discuss possible causes. keV Our results demonstrate that geometry has a major impact on pulse profiles, phase-averaged spectra, phase–energy maps, and the anisotropy factor relevant for luminosity estimates. Future studies should include the reflected component in addition to the direct emission considered here, and account for a more accurate treatment of resonant redistribution in the CRSF-forming region.

Accretion-powered X-ray pulsars show complex spectral and timing behavior that reflects the extreme conditions near the neutron star. Modeling these observables remains challenging, particularly at high mass-accretion rates, dot M 17 , , ^ g s -1 , where the extended accretion column plays a role in shaping anisotropic emission seen by a remote observer. Here, we present a modular framework that links radiation processes inside the column to the emission observed at infinity. The framework combines existing models for continuum and cyclotron resonant scattering feature (CRSF) formation in sidewall column emission with ray tracing, thereby bridging the gap between the rest-frame emission and the observable flux. We model the radiation from the accretion column using continuum emission from the column walls, calculated in the regime of saturated Comptonization in the presence of a radiation-dominated shock. This emission then passes through a thin outer layer with a fast-moving bulk flow, where CRSFs, derived from Monte Carlo simulations, are imprinted. Finally, a geometry-independent ray-tracing code accounts for light bending in the Schwarzschild metric, incorporating the shape and location of the emitting regions and neutron star rotation to compute the observed phase- and energy-dependent flux. We present the height-dependent anisotropic emission in the column rest frame. For the chosen model, approximately 70% of the radiation is emitted within 1, of the base of the column, predominantly at large angles to the magnetic field. Relativistic boosting in the bulk flow affects the appearance of CRSFs in the spectra, leading to a strong dependence of the line locations on the angle relative to the magnetic field. The proposed theoretical framework allows a straightforward combination of internal emission models with ray tracing to study the observed flux. Here, we focus on the joint treatment of the two-dimensional column structure and CRSF formation in the neutron star rest frame. The observed phase and spectral variations of the flux are highly sensitive to the location of the emitting regions and the observer's viewing angle, which is explored in an accompanying paper.

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 ∼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.

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.

XTE J1829−098 is a transient X-ray pulsar with a period of ∼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 ∼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 ∼ × 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.

In 2021, the high-mass X-ray binary EXO 2030+375 underwent a giant X-ray outburst, the first since 2006, that reached a peak flux of ∼600 mCrab (3–50 keV). The goal of this work is to study the spectral evolution over the course of the outburst, search for possible cyclotron resonance scattering features (CRSFs), and to associate spectral components with the emission pattern of the accretion column. We used broadband spectra taken with the Nuclear Spectroscopic Telescope Array (NuSTAR), the Neutron Star Interior Composition Explorer (NICER), and Chandra near the peak and during the decline phase of the outburst. We describe the data with established empirical continuum models and perform pulse-phase-resolved spectroscopy. We compare the spectral evolution with pulse phase using a proposed geometrical emission model. We find a significant spectral hardening toward lower luminosity, a behavior that is expected for super-critical sources. The continuum shape and evolution cannot be described by a simple power-law model with exponential cutoff; it requires additional absorption or emission components. We can confirm the presence of a narrow absorption feature at ∼10 keV in both NuSTAR observations. The absence of harmonics puts into question the interpretation of this feature as a CRSF. The empirical spectral components cannot be directly associated with identified emission components from the accretion column.

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.