RX J1713 Research Articles

Evidence for a shock-compressed magnetic field in the northwestern rim of Vela Jr. from X-ray polarimetry

Synchrotron X-ray emission has been detected from nearly a dozen young supernova remnants (SNRs). X-rays of synchrotron origin exhibit linear polarization in a regular, non-randomly oriented magnetic field. The significant polarized X-ray emission from four such SNRs has already been reported on the basis of observations with the Imaging X-ray Polarimetry Explorer (IXPE). The magnetic-field structure as derived from IXPE observations is radial for Cassiopeia A, Tycho's SNR, and SN 1006, and tangential for RX J1713.7-3946. The latter together with the recent detection of a tangential magnetic field in SNR 1E 0102.2-7219 by the Australia Telescope Compact Array in the radio band shows that tangential magnetic fields can also be present in young SNRs. Thus, the dichotomy in polarization between young and middle-aged SNRs (radial magnetic fields in young SNRs, but tangential magnetic fields in middle-aged SNRs), previously noticed in the radio band, deserves additional attention. The present analysis of IXPE observations determines, for the first time, a magnetic-field structure in the northwestern rim of Vela Jr, also known as RX J0852.0$-$4622, and provides a new example of a young SNR with a tangential magnetic field.

Fragments of harmony amid apparent chaos: A closer look at the X-ray quasi-periodic eruptions of the galaxy RX J1301.9+2747

Quasi-periodic eruptions (QPEs) are an extreme X-ray variability phenomenon associated with low-mass ($M_ BH < 10^7 M_ odot $) supermassive black holes (SMBHs). First discovered in the nucleus of the galaxy GSN 069, they have been so far securely detected in five other galaxies, including RX J1301.9+2747. When detected, the out-of-QPE emission (quiescence) is consistent with the high-energy tail of thermal emission from an accretion disk. In this article we present the X-ray properties of RX J1301.9+2747, both in quiescence and during QPEs, and complement this information with radio observations. We analyze X-ray data taken during five XMM-Newton observations between 2000 and 2022. The last three observations were taken in coordination with radio observations with the Karl G. Jansky Very Large Array. We also made use of EXOSAT, ROSAT, and Chandra archival observations taken between 1983 and 2009. XMM-Newton detected 34 QPEs of which eight have significantly lower amplitudes than the others. No correlated radio/X-ray variability was observed during QPEs. In terms of timing properties, the QPEs in RX J1301.9+2747 do not exhibit the striking regularity observed in the discovery source GSN 069. In fact there is no clear repetition pattern between QPEs: the average time separation between their peaks is about four hours, but it can be as short as one, and as long as six hours. The QPE spectral properties of RX J1301.9+2747 as a function of energy are, however, very similar to those of GSN 069 and of other QPE sources. During their evolution, X-ray QPEs follow a hysteresis pattern in the temperature-luminosity plane, with a hotter rise than decay. The quiescent emission of RX J1301.9+2747 is more complex than that of GSN 069, as it requires a soft X-ray excess-like component in addition to the thermal emission from the accretion disk. Its long-term X-ray quiescent flux variations are of a low amplitude and not strictly monotonic, with a general decay over the course of $ years. We discuss our observational results in terms of some of the ideas and models that have been proposed so far for the physical origin of QPEs.

Probing Magnetic Fields in Young Supernova Remnants with IXPE

Synchrotron emission from the shocked regions in supernova remnants provides, through its polarization, crucial details about the magnetic field strength and orientation in these regions. This, in turn, provides information on particle acceleration in these shocks. Due to the rapid losses of the highest-energy relativistic electrons, X-ray polarization measurements allow for investigations of the magnetic field to be carried outvery close to the sites of particle acceleration. Measurements of both the geometry of the field and the levels of turbulence implied by the observed polarization degree thus provide unique insights into the conditions leading to efficient particle acceleration in fast shocks. The Imaging X-ray Polarimetry Explorer (IXPE) has carried out observations of multiple young SNRs, including Cas A, Tycho, SN 1006, and RX J1713.7−3946. In each, significant X-ray polarization detections provide measurements of magnetic field properties that show some common behavior but also considerable differences between these SNRs. Here, we provide a summary of results from IXPE studies of young SNRs, providing comparisons between the observed polarization and the physical properties of the remnants and their environments.

Probing the energy and luminosity-dependent spectro-timing properties of RX J0440.9+4431 with AstroSat

ABSTRACT The Be/X-ray binary pulsar RX J0440.9+4431 went through a giant outburst in December 2022 with a peak flux of $\sim$2.3 Crab in 15–50 keV. We studied the broad-band timing and spectral properties of RX J0440.9+4431 using four AstroSat observations, where the source transited between subcritical and supercritical accretion regimes. Pulsations were detected significantly above 100 keV. The pulse profiles were found to be highly luminosity- and energy-dependent. A significant evolution in the pulse profile shape near the peak of the outburst indicates a possible change in the accretion mode and beaming patterns of RX J0440.9+4431. The rms pulsed fraction was luminosity- and energy-dependent, with a concave-like feature around 20–30 keV. The depth of this feature varied with luminosity, indicating changes in the accretion column height and proportion of reflected photons. The broad-band continuum spectra were best fitted with a two-component Comptonization model with a blackbody component or a two-blackbody component model with a thermal Comptonization component. A quasi-periodic oscillation (QPO) at 60 mHz was detected at a luminosity of $2.6 \times 10^{37}$ erg s$^{-1}$, which evolved into 42 mHz at $1.5 \times 10^{37}$ erg s$^{-1}$. The QPO rms were found to be energy dependent with an overall increasing trend with energy. For the first time, we found the QPO frequency varying with photon energy in an X-ray pulsar, which poses a challenge in explaining the QPO with current models such as the Keplarian and beat frequency model. Hence, more physically motivated models are required to understand the physical mechanism behind the mHz QPOs.

NICER Timing of the X-Ray Thermal Isolated Neutron Star RX J0806.4–4123

The X-ray thermal isolated neutron star (XTINS) RX J0806.4–4123 shows interesting multiwavelength properties that seemingly deviate from those of similar neutron stars. An accurate determination of the spin frequency change over time can assist in interpreting RX J0806.4–4123's properties in comparison to those of other XTINSs and the wider pulsar population. From 2019 to 2023 we carried out a tailored X-ray timing campaign of RX J0806.4–4123 with the NICER instrument. We used statistical properties of the Fourier coefficients and the Z K 2 test for phase connecting separate observations and finding a timing solution for the entire data set. We also developed a simple and universal method for estimating the uncertainties of the frequency ν and its derivative ν̇ from the empirical dependencies of Z K 2 on trial values of these parameters, with account of all significant harmonics of the frequency. Applying this method, we determined a spin-down rate ν̇=−7.3(1.2)×10−17Hzs−1 . The resulting spin-down power Ė=2.6×1029 erg s−1 is the lowest among the XTINSs, and it is a factor of 60 lower than the X-ray luminosity of this neutron star. RX J0806.4–4123 is also among the pulsars with the lowest measured Ė in general.

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.

Application of hydrostatic local thermodynamic equilibrium atmosphere models to interpretations of supersoft X-ray source spectra

Supersoft X-ray sources (SSSs) are accreting white dwarfs (WDs) with stable or recurrent thermonuclear burning on their surfaces. High-resolution X-ray spectra of such objects are rather complex, often consist of several components, and are difficult to interpret accurately. The main emission source is the hot surface of the WD and the emergent radiation can potentially be described by hot WD model atmospheres. We present a new set of such model atmosphere spectra computed in the effective temperature range from 100 kK to 1000 kK, for eight values of surface gravity and three different chemical compositions. These compositions correspond to the solar one as well as to the Large and Small Magellanic Clouds, with decreased heavy element abundances, at one-half and one-tenth of the solar value. The presented model grid covers a broad range of physical parameters and, thus, it can be applied to a wide range of objects. It is also publicly available in XSPEC format. As an illustration, we applied it here for the interpretation of Chandra and XMM grating spectra of two classical SSSs, namely, CAL 83 (RX J0543.5–6823) and RX J0513.9–6951. The obtained effective temperatures and surface gravities of Teff ≈ 560 kK, log g ≈ 8.6–8.7, and Teff ≈ 630 kK, log g ≈ 8.5–8.6, respectively, are in a good agreement with previous estimations for both sources. The derived WD mass estimations are within 1.1–1.4 M⊙ for CAL 83 and 1.15–1.4 M⊙ for RX J0513.9–6951. The mass of the WD in CAL 83 is consistent with the mass predicted from the respective model of recurrent thermonuclear burning.

The “Magnificent Seven” X-Ray Isolated Neutron Stars Revisited. I. Improved Timing Solutions and Pulse Profile Analysis

We present the first systematic X-ray pulse timing analysis of the six members of the so-called “Magnificent Seven” nearby thermally emitting isolated neutron stars (XINS) with detected pulsations. Using the extensive collection of archival XMM-Newton, Chandra, and NICER observations spanning over two decades, we obtain the first firm measurement of the spin-down rate for RX J2143.0+0654, while for the rest we improve upon previously published spin ephemerides and extend them by up to an additional decade. Five of the XINS follow steady spin-down with no indication of major anomalies in their long-term timing behavior; the notable exception is RX J0720.4−3125, for which, in addition to confirming the previously identified glitch, we detect a second spin derivative. The high-quality folded X-ray pulse profiles produced with the updated timing solutions exhibit diverse and complex morphologies, as well as striking energy dependence. These peculiarities cannot be readily explained by blackbody-like isotropic emission and simple hot-spot configurations, hinting at the presence of complex multitemperature surface heat distributions and highly anisotropic radiation patterns, such as may arise from a strongly magnetized atmospheric layer.

Discovery of a Shock-compressed Magnetic Field in the Northwestern Rim of the Young Supernova Remnant RX J1713.7–3946 with X-Ray Polarimetry

Supernova remnants (SNRs) provide insights into cosmic-ray acceleration and magnetic field dynamics at shock fronts. Recent X-ray polarimetric measurements by the Imaging X-ray Polarimetry Explorer (IXPE) have revealed radial magnetic fields near particle acceleration sites in young SNRs, including Cassiopeia A, Tycho, and SN 1006. We present here the spatially resolved IXPE X-ray polarimetric observation of the northwestern rim of SNR RX J1713.7–3946. For the first time, our analysis shows that the magnetic field in the particle acceleration sites of this SNR is oriented tangentially with respect to the shock front. Because of the lack of precise Faraday rotation measurements in the radio band, this was not possible before. The average measured polarization degree (PD) of the synchrotron emission is 12.5% ± 3.3%, lower than the one measured by IXPE in SN 1006, comparable to the Tycho one, but notably higher than the one in Cassiopeia A. On subparsec scales, localized patches within RX J1713.7–3946 display a PD of up to 41.5% ± 9.5%. These results are compatible with a shock-compressed magnetic field. However, in order to explain the observed PD, either the presence of a radial net magnetic field upstream of the shock or partial reisotropization of the turbulence downstream by radial magnetohydrodynamical instabilities can be invoked. From comparison of PD and magnetic field distribution with γ-rays and 12CO data, our results provide new inputs in favor of a leptonic origin of the γ-ray emission.

First evidence of a connection between cluster-scale diffuse radio emission in cool-core galaxy clusters and sloshing features

Radio observations of a few cool-core galaxy clusters have revealed the presence of diffuse emission on cluster scales, similar to what was found in merging clusters in the form of radio halos. These sources might suggest that a minor merger, while not sufficiently energetic to disrupt the cool core, could still trigger particle acceleration in the intracluster medium on scales of hundreds of kiloparsecs. We aim to verify the occurrence of cluster-scale diffuse radio emission in cool-core clusters and test the minor merger scenario. With the LOw Frequency ARray (LOFAR) at 144 MHz, we observed a sample of twelve cool-core galaxy clusters presenting some level of dynamical disturbances, according to X-ray data. We also performed a systematic search of cold fronts in these clusters, re-analysing archival Chandra observations. The clusters PSZ1G139.61+24, A1068 (new detection), MS 1455.0+2232, and RX J1720.1+2638 present diffuse radio emission on a cluster scale ($r $). This emission is characterised by a double component: a central mini-halo confined by cold fronts and diffuse emission on larger scales, whose radio power at 144 MHz is comparable to that of radio halos detected in merging systems with the same cluster mass. The cold fronts in A1068 are a new detection. We also found a candidate plasma depletion layer in this cluster. No sloshing features are found in the other eight clusters. Two of them present a mini-halo, with diffuse radio emission confined to the cluster core. We also found a new candidate mini-halo. Whereas, for the remaining five clusters, we did not detect halo-like emission. For clusters without cluster-scale halos, we derived upper limits to the radio halo power. We found that cluster-scale diffuse radio emission is not present in all cool-core clusters when observed at a low frequency, but it is correlated to the presence of cold fronts. The coexistence of cluster-scale diffuse radio emission and cold fronts in cool-core clusters requires a specific configuration of the merger and so it puts some constraints on the turbulence, which deserves to be investigated in the future with theoretical works.

Broad-band noise and quasi-periodic oscillation characteristics of the X-ray pulsar RX J0440.9+4431

ABSTRACT We present a comprehensive timing analysis on the Be/X-ray binary pulsar RX J0440.9+4431 using observations from NICER and Insight-HXMT during the 2022–2023 outburst. The power density spectrum (PDS) of RX J0440.9+4431 exhibits typical aperiodic variability in X-ray flux across a wide frequency range. During a supercritical accretion state, we detect quasi-periodic oscillations (QPOs) at 0.2–0.5 Hz in the light curves of five pulses for RX J0440.9+4431. The observed QPOs manifest during flares, while the flares appear at the peaks of the pulse profiles on a time-scale of seconds and are primarily caused by an increase in hard photons. These flares can be explained by increased material ingestion in the accretion column at a fixed phase, primarily generating hard photons. Alternatively, an increase in accretion rate, independent of phase, may result in highly beamed hard photons within the accretion column, causing the flares. We argue the origin of QPOs to instabilities within the accretion flow. Additionally, we find that the break frequencies in the noise power spectra align well with $\propto L_{\mathrm{x}}^{3 / 7}$ across three orders of magnitude in the luminosity, which points to a relatively strong magnetic field in RX J0440.9+4431, estimated to be ~1013 G.

The Gamma-Ray Origin of RX J0852.0-4622 Quantifying the Hadronic and Leptonic Components: Further Evidence for the Cosmic-Ray Acceleration in Young Shell-type SNRs

Fukui et al. quantified the hadronic and leptonic gamma-rays in the young TeV gamma-ray shell-type supernova remnant (SNR) RX J1713.7-3946 (RX J1713), and demonstrated that gamma rays are a combination of hadronic and leptonic gamma-ray components with a ratio of ∼6: 4 in gamma-ray counts N g. This discovery, which adopted a new methodology of multi-linear gamma-ray decomposition, was the first quantification of the two gamma-ray components. In the present work, we applied the same methodology to another TeV gamma-ray shell-type SNR RX J0852.0-4622 (RXJ0852) in 3D space characterized by (the interstellar proton column density N p)-(the nonthermal X-ray count N x)-[N g], and quantified the hadronic and leptonic gamma-ray components as having a ratio of ∼5:5 in N g. The present work adopted the fitting of two/three flat planes in 3D space instead of a single flat plane, which allowed suppression of the fitting errors. This quantification indicates that hadronic and leptonic gamma-rays are of the same order of magnitude in these two core-collapse SNRs, verifying the significant hadronic gamma-ray components. We argue that the target interstellar protons, in particular their spatial distribution, are essential in any attempts to identify the type of particles responsible for gamma-ray emission. The present results confirm that cosmic-ray (CR) energy ≲100 TeV is compatible with a scheme in which SNRs are the dominant source of these Galactic CRs.

Discovery of spin-phase-dependent QPOs in the supercritical accretion regime from the X-ray pulsar RX J0440.9+4431

RX J0440.9+4431 is an accreting X-ray pulsar (XRP) that remained relatively unexplored until recently, when major X-ray outburst activity enabled more in-depth studies. Here, we report on the discovery of ~0.2 Hz quasi-periodic oscillations (QPOs) from this source observed with Fermi-GBM. The appearance of QPOs in RX J0440.9+4431 is triple transient, that is, QPOs appear only above a certain luminosity, only at certain pulse phases (namely corresponding to the peak of its sine-like pulse profile), and only for a few oscillations at time. We argue that this newly discovered phenomenon (with the appearance of triple transient QPOs – or ATTO) occurs if QPOs are fed through an accretion disk whose inner region viscosity is unstable when exposed to mass accretion rate and temperature variations. Such variations are triggered when the source switches to the supercritical accretion regime and the emission pattern changes. We also argue that the emission region configuration is likely responsible for the observed QPOs spin-phase dependence.

NuSTAR Hard X-Ray Monitoring of Gravitationally Lensed Quasar RX J1131–1231

The X-ray emission from active galactic nuclei is believed to come from a combination of inverse Compton scattering of photons from the accretion disk and reprocessing of the direct X-ray emission by reflection. We present hard (10–80 keV) and soft (0.5–8 keV) X-ray monitoring of a gravitationally lensed quasar RX J1131−1231 (hereafter RXJ1131) with NuSTAR, Swift, and XMM-Newton between 2016 June 10 and 2020 November 30. Comparing the amplitude of quasar microlensing variability at the hard and soft bands allows a size comparison, where larger sources lead to smaller microlensing variability. During the period between 2018 June 6 and 2020 November 30, where both the hard and soft light curves are available, the hard and soft bands varied by factors of 3.7 and 5.5, respectively, with rms variability of 0.40 ± 0.05 and 0.57 ± 0.02. Both the variability amplitude and rms are moderately smaller for the hard X-ray emission, indicating that the hard X-ray emission is moderately larger than the soft X-ray emission region. We found the reflection fraction from seven joint hard and soft X-ray monitoring epochs is effectively consistent with a constant with low significance variability. After decomposing the total X-ray flux into direct and reprocessed components, we find a smaller variability amplitude for the reprocessed flux compared to the direct emission. The power-law cutoff energy is constrained at keV, which positions the system in the allowable parameter space due to the pair production limit.

On the influence of shock–cloud interactions on the nonthermal X-ray emission from the supernova remnant RCW 86

Abstract The effect of the surrounding environment of supernova remnant shocks on nonthermal X-rays from accelerated electrons, with or without interacting dense material, is an open issue. We conduct spatially resolved X-ray spectroscopy of the shock–cloud interacting region of RCW 86 with XMM–Newton. It is found that bright soft X-ray filaments surround the dense cloud, observed with 12CO and H i emission lines. These filaments are brighter in thermal X-ray emission, and fainter and possibly softer in synchrotron X-rays, compared to those without interaction. Our results show that the shock decelerates due to the interaction with clouds, which results in an enhancement of thermal X-ray emission. This could possibly also explain the softer X-ray synchrotron component, because it implies that those shocks that move through a low-density environment, and therefore decelerate much less, can be more efficient accelerators. This is similar to SN 1006 and Tycho, and is in contrast to RX J1713.7−3946. This difference among remnants may be due to the clumpiness of dense material interacting with the shock, which should be examined in future observations.

Neutron stars with polytropic equation of state

In this work, the neutron star model is considered in the framework of general relativity with the polytropic equation of state p=ργ, where γ=1+1k and k is known as a polytropic index. The homotopy perturbation method is used to solve Tolman–Oppenheimer–Volkoff (TOV) equation which gives the mass of the stellar structure. The solution of Einstein’s field equations is obtained and stability, causality, and physical viability of the considered model are examined. Using the observational results of mass and radius of known stars 4U 1608-52 RX J185635-3754, SAX J1748.9-2021 and 4U 1728-34, the model parameters are estimated which led to the non-singular solutions satisfying the energy conditions.

Timing properties of the X-ray accreting pulsar RX J0440.9+4431 studied with Insight-HXMT and NICER

ABSTRACT RX J0440.9+4431, a Be/X-ray binary, had its brightest outburst in 2022 since its discovery, with a peak X-ray flux of 2.25 Crab (as recorded by Swift/BAT, 15–50 keV). We analyze the timing properties of this giant outburst using data from Insight-Hard X-ray Modulation Telescope and Neutron Star Interior Composition Exlporer, focusing on the evolution of the pulse profile and pulse fraction. We observe that when the luminosity reached around ~$3\times 10^{37}\ {\rm erg\ \rm s^{-1}}$, a transition from double-peaked to single-peaked pulse profiles occurred across the energy range, with the peak of the low-energy profile aligning gradually with the peak of the high-energy profile. This change indicates a transition from subcritical to supercritical accretion. Additionally, we found a concave in the pulse fraction as a function of energy around 20–30 keV throughout the entire outburst period. Compared to the low luminosity, the concave becomes weaker in high luminosities, and overall, the pulse fraction is higher. We propose that this concave could be caused by the scattering of high-energy photons by the atmosphere of a neutron star, leading to a dilution of the pulse fraction. As the accretion reaches the supercritical state, the accretion column height increases, resulting in a larger direct component of strongly beamed X-ray flux, and an elevated pulse fraction.

Probing spectral and timing properties of the X-ray pulsar RX J0440.9 + 4431 in the giant outburst of 2022–2023

ABSTRACT The X-ray pulsar RX J0440.9 + 4431 went through a giant outburst in 2022 and reached a record-high flux of 2.3 Crab, as observed by Swift/BAT. We study the evolution of different spectral and timing properties of the source using NICER observations. The pulse period is found to decrease from 208 s to 205 s, and the pulse profile evolves significantly with energy and luminosity. The hardness ratio and hardness intensity diagram (HID) show remarkable evolution during the outburst. The HID turns towards the diagonal branch from the horizontal branch above a transition (critical) luminosity, suggesting the presence of two accretion modes. Each NICER spectrum can be described using a cutoff power law with a blackbody component and a Gaussian at 6.4 keV. At higher luminosities, an additional Gaussian at 6.67 keV is used. The observed photon index shows negative and positive correlations with X-ray flux below and above the critical luminosity, respectively. The evolution of spectral and timing parameters suggests a possible change in the emission mechanism and beaming pattern of the pulsar depending on the spectral transition to sub- and supercritical accretion regimes. Based on the critical luminosity, the magnetic field of the neutron star can be estimated in the order of 1012 or 1013 G, assuming different theoretical models. Moreover, the observed iron emission line evolves from a narrow to a broad feature with luminosity. Two emission lines originating from neutral and highly ionized Fe atoms are evident in the spectra around 6.4 and 6.67 keV (later is seen only in higher luminosities).

RX J0440.9+4431: another supercritical X-ray pulsar

ABSTRACT In the beginning of 2023, the Be transient X-ray pulsar RX J0440.9+4431 underwent a first-ever giant outburst observed from the source peaking in the beginning of February and reaching peak luminosity of ≈4.3 × 1037 erg s−1. Here, we present the results of a detailed spectral and temporal study of the source based on NuSTAR, Swift, INTEGRAL, and NICER observations performed during this period and covering wide range of energies and luminosities. We find that both the pulse profile shape and spectral hardness change abruptly around ≈2.8 × 1037 erg s−1, which we associate with a transition to supercritical accretion regime and erection of the accretion column. The observed pulsed fraction decreases gradually with energy up to 20 keV (with a local minimum around fluorescence iron line), which is unusual for an X-ray pulsar, and then rises rapidly at higher energies with the pulsations significantly detected up to ≈120 keV. The broad-band energy spectra of RX J0440.9+4431 at different luminosity states can be approximated with a two-hump model with peaks at energies of about 10–20 and 50–70 keV previously suggested for other pulsars without additional features. In particular, an absorption feature around 30 keV previously reported and interpreted as a cyclotron line in the literature appears to be absent when using this model, so the question regarding the magnetic field strength of the neutron star remains open. Instead, we attempted to estimate field using several indirect methods and conclude that all of them point to a relatively strong field of around B ∼ 1013 G.

Quasi-periodic eruptions from impacts between the secondary and a rigidly precessing accretion disc in an extreme mass-ratio inspiral system

X-ray quasi-periodic eruptions (QPEs) represent a recently discovered example of extreme X-ray variability associated with supermassive black holes. These are high-amplitude bursts recurring every few hours that are detected in the soft X-ray band from the nuclei of nearby galaxies whose optical spectra lack the broad emission lines typically observed in unobscured active galaxies. The physical origin of this new X-ray variability phenomenon is still unknown and several theoretical models have been presented. However, no attempt has been made so far to account for the varying QPE recurrence time and luminosity in individual sources, nor for the diversity of the QPE phenomenology in the different known erupters. We present a semi-analytical model based on an extreme mass-ratio inspiral (EMRI) system where the secondary intersects, along its orbit, a rigidly precessing accretion disc surrounding the primary. We assume that QPEs result from emission from an adiabatically expanding, initially optically thick gas cloud expelled from the disc plane at each impact. We produced synthetic X-ray light curves, which we then compared with X-ray data from four QPE sources: GSN 069, eRO-QPE1, eRO-QPE2, and RX J1301.9+2747. Our model aptly reproduces the diversity of QPE properties between the considered objects and it is also able to naturally account for the varying QPE amplitudes and recurrence times in individual sources. Future implementations will enable us to refine the match with the data and to estimate the system parameters precisely, making additional use of multi-epoch QPE data. We briefly discuss the nature of the secondary object, as well as the possible implications of our findings for the EMRI population at large.