arXiv subjects

Alessandro Papitto

Publications and source records attributed to Alessandro Papitto.

At least 19 recordsLinked to original sources

arXiv2026

Searching for optical pulsations from spider millisecond pulsars with the fast photometer SiFAP2

Optical pulsations from millisecond pulsars (MSPs) have recently been discovered from a transitional MSP and an accreting MSP. Evidence for optical pulsations has also been found for a rotation-powered redback MSP. Observations suggest that optical pulsed emission is produced by different mechanisms depending on whether an accretion disk is present in the system or not. We explore a sample of rotation-powered MSPs in close binaries (P$_{orb}<1\,$day, redbacks and black widows), searching for optical periodic signals with the $SiFAP2$ photometer mounted on the $Telescopio\ Nazionale\ Galileo$ (TNG). We perform pulsation searches using the epoch folding method with the most updated (radio or gamma-ray) orbital solution for each system, employing already published solutions or recent observations with Nan\c{c}ay, the Giant Metrewave Radio Telescope, the Parkes Observatory, and $Fermi$-LAT. We update or confirm radio and gamma-ray ephemerides for five of the presented systems. No optical pulsations were detected with a significance exceeding a $3\sigma$ confidence level in any of our searches, despite often achieving sensitivities on the verge of the instrument's limit. This places correspondingly stringent upper limits on the systems' optical pulsed magnitude and conversion efficiency. Our upper limits are consistent with the pulsed optical luminosity of optical pulsations from the redback PSR J2339-0533. Compared to accreting and transitional MSPs, redback and black widow systems show much lower efficiency in converting their spin down power into pulsed optical emission, supporting the recently advanced idea that the accretion disk around the neutron star plays a role in accelerating the particles responsible for producing bright optical pulsed emission.

astro-ph.HE↗

arXiv2026

Peering through the dip: IXPE unveils the extended scattering environment of GX 13+1

Neutron star low-mass X-ray binaries feature complex accretion geometries, often including an accretion disk corona or disk winds. Here, a study of the highly inclined dipping source GX 13+1, using coordinated observations from the IXPE, NuSTAR, and Swift-XRT, is presented; this is the first time that such a campaign was conducted to monitor its periodic dip. Our analysis reveals significant variations in polarimetric properties tracking the dip. At the center of the dip, the polarization degree reaches a maximum of ${\sim}$9% (at more than $8\sigma$ confidence level). This is accompanied by a highly significant polarization angle rotation of roughly 60$^\circ$ when passing from the dip to the subsequent off-dip state. Furthermore, the dip state exhibits energy-dependent polarization. By modeling the polarization during the periodic dip, we constrain the geometry of the scattering medium. In the scenario of an oblate extended accretion disk corona (ADC), an equatorial radius at least 1.5 times its polar radius is needed with $\tau{\sim}0.3$. Alternatively, the results can be modeled as scattering in a disk wind with a most probable electron density of $1.3\times10^{14}$ cm$^{-3}$ and an opening angle near 40$^\circ$, corresponding to an optical depth of ${\sim}0.2$. The obtained results highlight the crucial role of X-ray polarimetric data to unveil the geometry of the extended scattering environment surrounding the accretion disks, advancing our understanding of neutron star low-mass X-ray binaries.

astro-ph.HE↗

arXiv2026

3D particle-in-cell simulations of pulsar wind-disk interaction: application to the transitional millisecond pulsar PSR J1023+0038

Transitional millisecond pulsars constitute a peculiar subclass of neutron stars in which the pulsar alternates between accretion-powered and rotation-powered states, depending on the variations in the mass accretion flow coming from a low-mass companion star. A third intermediate state, referred to as ``sub-luminous disk state'', has been identified. During this state, observations indicate the presence of a disk surrounding the pulsar, and the system exhibits intriguing features, such as broad optical and X-ray pulsations characterized by a high luminosity. To date, no ab initio model of a pulsar wind interacting with an accretion disk has been developed to address these observables. We perform three-dimensional particle-in-cell simulations of a pulsar magnetosphere surrounded by a perfectly conducting torus to model the interaction between the pulsar wind and the disk. We find that the presence of the disk induces a significant reconfiguration of the magnetosphere compared to the rotation-powered state, leading to enhanced plasma density at the inner disk boundary, increased magnetic field strength, and more efficient plasma isotropization and particle acceleration. As a result, the synchrotron radiation is substantially enhanced, and characterized by a strong continuous component and either one or two-peaked light curves, depending on the pulsar's magnetic obliquity. The polarization degree is reduced compared to isolated systems, and its energy dependence is explored. The rotation of the polarization angle can also be altered, depending on the observer's viewing angle. The model successfully reproduces some of the main features of the optical and X-ray pulsed emission originating from PSR J1023+0038, thereby corroborating the scenario in which these pulsations originate from synchrotron radiation generated as the pulsar wind interacts with the inner edge of the disk.

astro-ph.HE↗

arXiv2026

Pulse profile modelling of the 2024 outburst of the accreting millisecond pulsar SRGA J144459.2-604207

Pulse profile modelling via relativistic ray-tracing can constrain the system parameters of neutron stars, notably their mass and radius. Among these objects, accreting millisecond pulsars (AMPs) are promising targets, because they are bright in X-rays and their potentially polarized radiation can lead to complementary constraints on the emission geometry. We perform combined analysis of NICER and IXPE observations of the recently discovered the 448-Hz pulsar SRGA J144459.2-604207, with IXPE providing X-ray polarization information. NICER and IXPE jointly favour a large mass and radius for our best-fitting model, for which the neutron star has two independent hotspots. The primary hotspot is centered near the northern rotational pole, the secondary in the southern hemisphere, and the observer inclination is in the range 50-75 degrees. The primary hotspot is large (up to half the surface area) and contributes the majority of the non-pulsed X-rays, while the secondary is hotter and the major contributor to the overall pulse profile shape. However, many parameters are inferred to be near the prior bounds, which could indicate that the model does not adequately account for important physics. Furthermore, we tested several different methodologies for joint analysis of the two data sets: the results are sensitive to the method used, something that merits further study with synthetic data. In the future, we expect simultaneously recorded data will lead to improved parameter constraints, especially when multi-band and polarized data are combined.

astro-ph.HE↗

arXiv2026

Magnetic-field Order in the Southwestern Rim of RCW 86 Constrained Using X-Ray Polarimetry

RCW 86 is a supernova remnant whose origin has recently been linked to an off-center explosion within a cavity created by its progenitor star. In the southwestern region, the forward shock is thought to have reached the cavity wall, encountering diverse environmental conditions. We report on the spatially resolved X-ray polarimetric observation of RCW 86 with the Imaging X-ray Polarimetry Explorer (IXPE). In the 2--4.5 keV energy band we find no significant detection of polarization. Employing a dedicated background subtraction procedure and Bayesian spectropolarimetric fitting, we derive 99% upper limits on the polarization degree of the synchrotron component: 15% in higher-statistics regions and 30%--40% in lower-statistics regions. These upper limits on the polarization degree in several regions exclude the possibility of a strongly coherent magnetic field down to the subparsec scale, and that of a moderately coherent one on the scale of the synchrotron features as resolved by IXPE. The results indicate that the shocks in the southwestern rim of RCW 86 propagate more slowly than the unshocked ejecta at their locations, yet exceed the measured proper motion speeds. This behavior is consistent with reflected shocks occurring in tenuous regions of the shocked ejecta, distinct from regions that are radio-bright.

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arXiv2025

Super-Eddington Accretion Geometry: a Remarkable Stability of the Hidden Ultraluminous X-Ray Source Cygnus X-3

We report on the average and orbital phase-resolved polarization of Cyg X-3 in the hard state during the 2023 Imaging X-ray Polarimetry Explorer (IXPE) observational campaign. We find the polarization degree of $ 21.2 \pm 0.4 \% $ and polarization angle of $ 92.2 \pm 0.5^\circ $, well compatible with the first hard-state IXPE observation in 2022. As the observed polarization depends on both the accretion geometry and the X-ray emission mechanism, which we attribute to reflection from the optically thick envelope surrounding the central source, our result indicates that both are very stable on year-long timescale. We discuss time- and energy-dependent polarization properties and their implications for the geometry and stability of the accretion funnel.

astro-ph.HE↗

arXiv2025

A semi-coherent search for optical pulsations from Scorpius X-1

The emission of continuous gravitational waves (CWs) possibly explains why pulsars spinning with a period shorter than a millisecond have not been observed so far. Neutron stars accreting mass at the highest rates are the most promising targets for a search for CWs, because a strong emission of gravitational waves is required to balance the torque exerted by mass accretion onto the neutron star. Detecting coherent pulsations in the electromagnetic emission maximizes the search sensitivity, but has so far not been successful for most of the brightest accreting neutron stars. Here, we present the first search for pulsations in the optical band from the brightest accreting neutron star known, Sco X-1. To this end, we tailored semi-coherent search strategies to data obtained over four years, for a total of $\sim$$56$ ks, by the SiFAP2 fast photometer mounted at the Telescopio Nazionale Galileo (TNG). These searches are especially suited to analysing long observations of systems for which only limited knowledge on the orbital parameters is available, and involve joining coherent analyses on shorter segments without connecting the spin phase between them. The large count rates afforded by an optical telescope and the efficiency of the search strategy employed allowed us to set an upper limit of $9 \times 10^{-5}$ to the pulsed amplitude, which is lower by a factor of four with respect to previous searches in the X-ray band. We also show that the application of semi-coherent searches to SiFAP2 observations of the first detected optical millisecond pulsar, PSR J1023+0038, could have preceded its detection in the radio band. These results highlight the role played by high-time-resolution optical observations in performing deep searches of quickly rotating pulsars.

astro-ph.HE↗

arXiv2025

Polarization of reflected X-ray emission from the Sgr A molecular complex: multiple flares, multiple sources?

The extended X-ray emission observed in the direction of several molecular clouds in the central molecular zone of our Galaxy exhibits spectral and temporal properties consistent with the X-ray echo scenario. This concept postulates that the observed signal is a light-travel-time delayed reflection of a short ($\delta t<$1.5 yr) and bright ($L_{\rm X}>10^{39} {\rm erg s^{-1}}$) flare that was most probably produced a few hundred years ago by Sgr A*. This scenario predicts a distinct polarization signature for the reflected X-ray continuum, with the polarization vector being perpendicular to the direction toward the primary source and the polarization degree being determined by the scattering angle. We report the results of two deep observations of the currently brightest (in reflected emission) molecular complex Sgr A taken with the Imaging X-ray Polarimetry Explorer in 2022 and 2023. We confirm the previous polarization measurement for a large region encompassing the Sgr A complex with high significance. We reveal an inconsistent polarization pattern for the brightest reflection region in its center. The X-ray polarization from this region is almost perpendicular to the expected direction in the case of Sgr A* illumination and shows smaller degree of polarization compared to the large region. This could indicate the simultaneous propagation of several illumination fronts throughout the CMZ, with the origin of one of them not being Sgr A*. The primary source could be associated with the Arches stellar cluster or a currently unknown source located closer to the illuminated cloud, potentially lowering the required luminosity of the primary source. Although significantly deeper observations with IXPE would be required to unequivocally distinguish between the scenarios, a combination of high-resolution imaging and micro-calorimetric spectroscopy offers an additional promising path forward.

astro-ph.HE↗

arXiv2025

Detection of low-luminosity X-ray pulsations from the accreting millisecond pulsar IGR J17511-3057: An ever-thinning thread between bright accretion and sub-luminous states

After nearly a decade in quiescence, the accreting millisecond pulsar IGR J17511$-$3057 displayed a new outburst on 2025 February 11, its third since discovery, following previous activity in 2009 and 2015. We report on an XMM-Newton Target of Opportunity observation performed on 2025 March 4, more than twenty days after the outburst onset. From the X-ray spectrum - well described by an absorbed Comptonization model - we estimated an unabsorbed 0.5$-$10 keV luminosity of $L_X \sim 7 \times 10^{33} \, \mathrm{erg \, s^{-1}}$ (assuming a source distance equal to the upper limit of $6.9$ kpc). To place this in context, we analyzed an archival Chandra observation performed in 2019, which yielded a quiescent luminosity of $L_\mathrm{X,q} \sim 2 \times 10^{32} \, \mathrm{erg \, s^{-1}}$ in the same energy band. Although this comparison indicates that the source was still well above its quiescent level during the XMM-Newton observation, the estimated low luminosity during the late stage of the 2025 outburst would typically place the source in the propeller regime. Nevertheless, we unexpectedly detected coherent X-ray pulsations with an amplitude peaking at $\sim$42% in the 0.3$-$3 keV band. We also observed a spectral softening compared to the early stages of the outburst. Finally, we report a 3$\sigma$ upper limit of 60 $\mu$Jy beam$^{-1}$ on the source flux density at 5.5 GHz from ATCA observations acquired on 2025 April 12, following a decline of the accretion activity, as indicated by our analysis of NICER data from 2025 March 15, which revealed no significant X-ray pulsations at a luminosity level of $L_X \sim 1 \times 10^{34} \, \mathrm{erg \, s^{-1}}$. We discuss our findings in the context of other accreting millisecond pulsars and draw comparisons with transitional systems in the sub-luminous disk state.

astro-ph.HE↗

arXiv2025

Probing multi-band variability and mode switching in the candidate transitional millisecond pulsar 3FGL J1544.6-1125

We present the most extensive high-time resolution multi-band campaign to date on the candidate transitional millisecond pulsar (tMSP) 3FGL J1544.6-1125 in the sub-luminous disk state, with coordinated observations from the radio to the X-ray band. While XMM-Newton and NuSTAR X-ray light curves exhibit the characteristic high- and low-mode bimodality, the source faintness prevents firm evidence for similar bimodality in the ultraviolet and near-infrared light curves, presented here for the first time. A re-analysis of archival XMM-Newton/OM data reveals an optical flare without an X-ray counterpart, likely originating from the outer accretion disk or the companion star. During our observations, no radio emission was detected, with a 3$\sigma$ flux density upper limit of 8 $\mu$Jy at 6 GHz. While past works have already reported radio variability in the source, this limit is a factor of 3.5 below the average value measured in 2019 in similar conditions, underscoring significant radio variability despite the relatively stable X-ray flux. Simultaneous optical light curves in five filters with GTC/HiPERCAM revealed flickering and dipping activities that resemble the observed X-ray variability, along with a reddening trend at lower fluxes. The latter is consistent with discrete mass ejections that disrupt the inner flow and reduce both X-ray and optical fluxes, thereby driving the high-to-low-mode switches. This suggests a common origin for most optical and X-ray emission at the boundary region between the pulsar wind and the inner disk, as also supported by our modelling of the spectral energy distribution in the high mode. Overall, our findings reinforce the mini-pulsar nebula picture for tMSPs in the sub-luminous state and demonstrate how coordinated, high-time resolution, multi-wavelength campaigns are essential to probe the processes governing rapid mode switches in these systems.

astro-ph.HE↗

arXiv2025

A deep X-ray and UV look into the reflaring stage of the accreting millisecond pulsar SAX J1808.4-3658

We present an X-ray and UV high-time-resolution monitoring of the final flaring phase of the 2022 outburst of the AMSP SAX J1808.4-3658, based on simultaneous XMM-Newton and HST observations. The uninterrupted coverage provided by XMM-Newton enabled a detailed characterization of the spectral and temporal evolution of the source X-ray emission, as the flux varied by approximately 1 order of magnitude. We detected coherent X-ray pulsations during the whole X-ray observation, down to a 0.5-10 keV luminosity of $L_{X(low)0.5-10} \simeq 6.21^{+0.20}_{-0.15}\times 10^{34} d^2_{3.5}erg/s$, among the lowest ever observed in this source. At the lowest flux levels, we observed significant variations in pulse amplitude and phase. These variations were anticorrelated with the X-ray source flux. We found a sharp phase jump of $\sim 0.4$ cycles, accompanied by a doubling of the pulse amplitude and a softening of the X-ray emission. We interpreted changes in the X-ray pulse profiles as drifts of emission regions on the neutron-star surface, driven by an increase in the inner-disk radius when the mass-accretion rate decreased. The dependence of the pulse phase on the X-ray flux was consistent with a magnetospheric radius scaling as $R_{m} \propto \dot{M}^{\Lambda}$, with $\Lambda = -0.17(9)$, in broad agreement with theoretical predictions. Simultaneous HST observations confirmed the presence of significant UV pulsations at an X-ray luminosity approximately a factor of two lower than during the 2019 outburst, extending the range of mass accretion rates at which UV pulsations have been detected. The measured pulsed UV luminosity, $L_{pulsed}^{UV}=1.1(3) \times 10^{32}erg/s$, was consistent with that observed during the 2019 outburst. Such a UV luminosity exceeds the predictions of standard emission models, as further confirmed by the shape of the pulsed spectral energy distribution.

astro-ph.HE↗

arXiv2025

Observatory Science with eXTP

Scheduled for launch in 2030, the enhanced X-ray Timing and Polarization (eXTP) telescope is a Chinese space-based mission aimed at studying extreme conditions and phenomena in astrophysics. eXTP will feature three main payloads: Spectroscopy Focusing Arrays (SFAs), Polarimetry Focusing Arrays (PFAs), and a Wide-field Camera (W2C). This white paper outlines observatory science, incorporating key scientific advances and instrumental changes since the publication of the previous white paper [1]. We will discuss perspectives of eXTP on the research domains of flare stars, supernova remnants, pulsar wind nebulae, cataclysmic variables, X-ray binaries, ultraluminous X-ray sources, AGN, and pulsar-based positioning and timekeeping.

astro-ph.IM↗

arXiv2025

Dense Matter in Neutron Stars with eXTP

In this White Paper, we present the potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission to constrain the equation of state of dense matter in neutron stars, exploring regimes not directly accessible to terrestrial experiments. By observing a diverse population of neutron stars - including isolated objects, X-ray bursters, and accreting systems - eXTP's unique combination of timing, spectroscopy, and polarimetry enables high-precision measurements of compactness, spin, surface temperature, polarimetric signals, and timing irregularity. These multifaceted observations, combined with advances in theoretical modeling, pave the way toward a comprehensive description of the properties and phases of dense matter from the crust to the core of neutron stars. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is planned to be launched in early 2030.

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arXiv2025

X-ray Polarization Detection of the Pulsar Wind Nebula in G21.5-0.9 with IXPE

We present the X-ray polarization observation of G21.5-0.9, a young Galactic supernova remnant (SNR), conducted with the Imaging X-ray Polarimetry Explorer (IXPE) in October 2023, with a total livetime of approximately 837 ks. Using different analysis methods, such as a space-integrated study of the entire region of the PWN and a space-resolved polarization map, we detect significant polarization from the pulsar wind nebula (PWN) at the center of the SNR, with an average polarization degree of ~10% oriented at ~33{\deg} (north through east). No significant energy-dependent variation in polarization is observed across the IXPE band (2-8 keV). The polarization map, corrected for the effect of polarization leakage, reveals a consistent pattern in both degree and angle, with little change across the nebula. Our findings indicate the presence of a highly polarized central torus, suggesting low levels of turbulence at particle acceleration sites. Unlike Vela, but similar to the Crab Nebula, we observe substantial differences between radio and X-ray polarization maps. This suggests a clear separation in energy of the emitting particle populations and hints at an important, yet poorly understood, role of instabilities in the turbulence dynamics of PWNe.

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arXiv2025

A Multi-wavelength Characterization of the 2023 Outburst of MAXI J1807+132: Manifestations of Disk Instability and Jet Emission

Several phenomenological aspects of low-luminosity neutron star transients, such as atolls, remain poorly understood. One such source, MAXI J1807+132, entered its latest outburst in July 2023. To thoroughly characterize this outburst, we conducted an extensive observational campaign spanning radio to X-ray wavelengths. Here, we present the results of this campaign, which covered the period from before the outburst to the return to quiescence. We detected a delay between the X-ray and optical rise times, which is consistent with the predictions of the disk instability model with a truncated disk. The color evolution and optical/X-ray correlations, along with infrared and radio detections, support the presence of jet synchrotron emission during the gradual decay phase following the peak. We also report for the first time in an X-ray binary a near-orthogonal rotation of the optical polarization just before a small flare, after which the jet is thought to be quenched. The main outburst is followed by several high-amplitude, rapid reflares in the optical, ultraviolet, and X-ray bands, the origin of which remains difficult to constrain.

astro-ph.HE↗

arXiv2025

X-ray Polarization of the High-Synchrotron-Peak BL Lacertae Object 1ES 1959+650 during Intermediate and High X-ray Flux States

We report the Imaging X-ray Polarimetry Explorer (IXPE) polarimetric and simultaneous multiwavelength observations of the high-energy-peaked BL Lacertae (HBL) object 1ES 1959+650, performed in 2022 October and 2023 August. In 2022 October IXPE measured an average polarization degree $\Pi_{\rm X}=9.4\;\!\%\pm 1.6\;\!\%$ and an electric-vector position angle $\psi_{\rm X}=53^{\circ}\pm 5^{\circ}$. The polarized X-ray emission can be decomposed into a constant component, plus a rotating component, with rotation velocity $\omega_{\rm EVPA}=(-117\;\!\pm\;\!12)$ ${\rm deg}\;\!{\rm d}^{-1}$. In 2023 August, during a period of pronounced activity of the source, IXPE measured an average $\Pi_{\rm X}=12.4\;\!\%\pm0.7\;\!\%$ and $\psi_X=20^{\circ}\pm2^{\circ}$, with evidence ($\sim$0.4$\;\!\%$ chance probability) for a rapidly rotating component with $\omega_{\rm EVPA}=(1864\;\!\pm\;\!34)$ ${\rm deg}\;\!{\rm d}^{-1}$. These findings suggest the presence of a helical magnetic field in the jet of 1ES 1959+650 or stochastic processes governing the field in turbulent plasma. Our multiwavelength campaigns from radio to X-ray reveal variability in both polarization and flux from optical to X-rays. We interpret the results in terms of a relatively slowly varying component dominating the radio and optical emission, while rapidly variable polarized components dominate the X-ray and provide minor contribution at optical wavelengths. The radio and optical data indicate that on parsec scales the magnetic field is primarily orthogonal to the jet direction. On the contrary, X-ray measurements show a magnetic field almost aligned with the parsec jet direction. Confronting with other IXPE observations, we guess that the magnetic field of HBLs on sub-pc scale should be rather unstable, often changing its direction with respect to the VLBA jet.

astro-ph.HE↗

arXiv2025

Disk reflection and energetics from the accreting millisecond pulsar SRGA J144459.2-604207

Accreting millisecond pulsars (AMSPs) are excellent laboratories to study reflection spectra and their features from an accretion disk truncated by a rapidly rotating magnetosphere near the neutron star surface. These systems also exhibit thermonuclear (type-I) bursts that can provide insights on the accretion physics and fuel composition. We explore spectral properties of the AMSP SRGA J144459 observed during the outburst that recently led to its discovery in February 2024. We aim to characterize the spectral shape of the persistent emission and to analyze type-I bursts properties employing XMM + NuSTAR overlapping observations taken during the most recent outburst. We perform spectral analysis of the time-averaged persistent (i.e., non-bursting) emission. For this, we first employ a semi-phenomenological continuum model made of a dominant thermal Comptonization plus two thermal contributions. A separate fit has also been performed employing a physical reflection model. We also perform time-resolved spectral analysis of a type-I burst employing a blackbody model. We observe a broadened iron emission line, thus suggesting relativistic effects, supported by the physical model accounting for relativistically blurred reflection. The resulting accretion disk extends down to 6 gravitational radii, inclined at ~$53^{\circ}$, and only moderately ionized (log$\xi\simeq2.3$). We observe an absorption edge at ~9.7 keV that can be interpreted as an Fe XXVI edge blueshifted by an ultrafast ($\simeq0.04$c) outflow. Our broadband observations of type-I bursts do not find evidence of photospheric radius expansion. The burst recurrence time shows a dependence on the count rate with the steepest slope ever observed in these systems. We also observe a discrepancy of ~3 between the observed and expected burst recurrence time, which we discuss in the framework of fuel composition and high NS mass scenarios.

astro-ph.HE↗

arXiv2025

Modelling polarized X-ray pulses from accreting millisecond pulsars with X-PSI, using different hot spot locations and shapes

We present an analysis of polarized X-ray pulses based on simulated data for accreting millisecond pulsars (AMPs). We used the open-source X-ray Pulse Simulation and Inference code (previously applied to NICER observations), which we upgraded to allow polarization analysis. We provide estimates of how well neutron star (NS) parameters can be constrained for the Imaging X-ray Polarimetry Explorer (IXPE) and find that strong limits on the hot region geometries can be hard to obtain if the emitting hot region is large and the number of polarized photons relatively small. However, if the star is bright enough and the hot regions are small and located so that polarization degree is higher, the observer inclination and hot spot colatitude can be constrained to a precision of within a few degrees. We also found that the shape of the hot region, whether a circle or a ring, cannot be distinguished in our most optimistic scenario. Nevertheless, future X-ray polarization missions are expected to improve the constraints, and already the recent AMP polarization detections by IXPE should help to infer the NS mass and radius when combined with modelling of X-ray pulse data sets that do not contain polarization information.

astro-ph.HE↗