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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), that we upgraded to allow polarization analysis. We predicted neutron star parameter constraints for the Imaging X-ray Polarimetry Explorer (IXPE) and found 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 hotspot 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 neutron star mass and radius when combined with modelling of X-ray pulse data sets that do not contain polarization information., Comment: 8 pages, 3 figures, 1 table, submitted to MNRAS

We present the result from the April 2024 observation of the low-mass X-ray binary GX 13+1 with the Imaging X-ray Polarimetry Explorer (IXPE), together with NICER and Swift-XRT coordinated observations. Two light curve dips were observed; during them, the harder Comptonized spectral component was dominant and the polarization degree higher than in the softer, off-dip intervals. Through a joint analysis of the three IXPE observations, which also included the dip from the first observation, we demonstrate that the polarization properties varied in response to the intensity and spectral hardness changes associated with the dips. The polarization degree attained values up to ~4%. The polarization angle showed a swing of ~70{\deg} across the dip and off-dip states, comparable to the continuous rotation seen during the first IXPE observation. We discuss these results in the context of models for polarized emission from the accretion disk and the boundary/spreading layer on the neutron star surface. We also draw attention to the role that an extended accretion disk corona or disk wind can play in generating high polarization degrees and, possibly, swings of the polarization angle., Comment: Accepted on ApJL

We report the first simultaneous X-ray spectropolarimetric observation of the bright atoll neutron star low-mass X-ray binary GX 3+1, performed by the Imaging X-ray Polarimetry Explorer (IXPE) joint with NICER and NuSTAR. The source does not exhibit significant polarization in the 2-8 keV energy band, with an upper limit of 1.3% at a 99% confidence level on the polarization degree. The observed spectra can be well described by a combination of thermal disk emission, the hard Comptonization component, and reflected photons off the accretion disk. In particular, from the broad Fe K$\alpha$ line profile, we were able to determine the inclination of the system ($i \approx 36^\circ$), which is crucial for comparing the observed polarization with theoretical models. Both the spectral and polarization properties of GX 3+1 are consistent with those of other atoll sources observed by IXPE. Therefore, we may expect a similar geometrical configuration for the accreting system and the hot Comptonizing region. The low polarization is also consistent with the low inclination of the system., Comment: 7 pages, 6 figures, 4 tables. Accepted for publication in Astronomy & Astrophysics. arXiv admin note: text overlap with arXiv:2408.02309

We report the first detection of X-ray polarization in the horizontal branch for GX 340+0 as obtained by Imaging X-ray Polarimetry Explorer (IXPE). A polarization degree of 4.3%$\pm$0.3% is obtained. This value is in agreement with the previous polarization measurements of Z-sources in the horizontal branch. Spectro-polarimetric analysis, performed using a broad-band spectral model obtained by NICER and NuSTAR quasi-simultaneous observations, allowed us to constrain the polarization for the soft and hard spectral components typical to these sources. The polarization angle for the two components differs by ${\sim}40{\deg}$. This result could be explained by a misalignment of the NS rotations axis with respect to the accretion disk axis. We provide a comparison of the results with polarization expected in different models. Theoretical expectations for the polarization of the disk and the Comptonization components favor an orbital inclination for GX 340+0 higher than 60{\deg}, as expected for Cyg-like sources, in contrast with results we report for the reflection component using broad-band spectrum., Comment: A&A 691, A253 (2024)

Observations show that the X-ray emission of the accreting weakly magnetized neutron stars is polarized. Here, we develop a theoretical model, where we assume the emission of the accreting neutron star coming from the spreading layer, the extension of the boundary between the disk and the neutron star surface onto the surface. We then calculate the Stokes parameters of the emission accounting for relativistic aberration and gravitational light bending in the Schwarzschild metric. We show that regardless of the geometry, for the spreading layer, we cannot expect the polarization degree to be higher than 1.5%. Our results have implications with regard to the understanding of the X-ray polarization from weakly magnetized neutron stars observed with the Imaging X-ray Polarimetry Explorer and the future enhanced X-ray Timing and Polarimetry mission., Comment: 9 pages, 7 figures, submitted to A&A

Pulse profile modelling (PPM) is a technique for inferring mass, radius and hotspot properties of millisecond pulsars. PPM is now regularly used for analysis of rotation-powered millisecond pulsars (RMPs) with data from the Neutron Star Interior Composition ExploreR (NICER). Extending PPM to accreting millisecond pulsars (AMPs) is attractive, because they are a different source class featuring bright X-ray radiation from hotspots powered by accretion. In this paper, we present a modification of one of the PPM codes, X-PSI, so that it can be used for AMPs. In particular, we implement a model of an accretion disc and atmosphere model appropriate for the hotspots of AMPs, and improve the overall computational efficiency. We then test parameter recovery with synthetic NICER data in two scenarios with reasonable parameters for AMPs. We find in the first scenario, where the hotspot is large, that we are able to tightly and accurately constrain all parameters including mass and radius. In the second scenario, which is a high inclination system with a smaller hotspot, we find degeneracy between a subset of model parameters and a slight bias in the inferred mass and radius. This analysis of synthetic data lays the ground work for future analysis of AMPs with NICER data. Such an analysis could be complemented by future (joint) analysis of polarization data from the Imaging X-ray Polarimetry Explorer (IXPE)., Comment: 14 pages, 5 figures, 3 tables. Paper submitted to MNRAS

Low-mass X-ray binaries hosting weakly magnetized neutron stars (NS-LMXBs) are among the brightest sources in the X-ray sky. Since 2021, the Imaging X-ray Polarimetry Explorer (IXPE) has provided new measurements of the X-ray polarization of these sources. IXPE observations have revealed that most NS-LMXBs are significantly polarized in the X-rays, providing unprecedented insight into the geometry of their accretion flow. In this review paper, we summarize the first results obtained by IXPE on NS-LMXBs, the emerging trends within each class of sources (atoll/Z), and possible physical interpretations., Comment: 8 pages, 3 figures, invited review for the Special Issue X-ray Polarization: A New Era Begins

We present simultaneous X-ray polarimetric and spectral observations of the bright atoll source Ser~X-1 carried out with the Imaging X-ray Polarimetry Explorer (IXPE), NICER, and NuSTAR. We obtain an upper limit of 2% (99% confidence level) on the polarization degree in the 2--8 keV energy band. We detect four type-I X-ray bursts, two of which during the IXPE observation. This is the first time that has IXPE observed type-I X-ray bursts, and it allows us to place an upper limit on their polarization degree; however, due to the limited total number of counts in each burst, we obtain a relatively high upper limit (80%). We confirm the presence of reflection features in the X-ray spectrum, notably a broad iron line. Fitting the data with a relativistic reflection model, we derive a disk inclination of 25 deg. The spectral and polarization properties are comparable with other atolls observed by IXPE, suggesting a similar accretion geometry, and the relatively low polarization is consistent with the low inclination., Comment: Accepted by A&A

We report on the discovery of polarized X-ray emission from an accreting millisecond pulsar. During a 10-day-long coverage of the February 2024 outburst of SRGA J144459.2-604207, the Imaging X-ray Polarimetry Explorer (IXPE) detected an average polarization degree of the 2-8 keV emission of 2.3% +/- 0.4% at an angle of 59{\deg} +/- 6{\deg} (East of North; uncertainties quoted at the 1${\sigma}$ confidence level). The polarized signal shows a significant energy dependence with a degree of 4.0% +/- 0.5% between 3 and 6 keV and < 1.5% (90% c.l.) in the 2-3 keV range. We used NICER, XMM-Newton, and NuSTAR observations to obtain an accurate pulse timing solution and perform a phase-resolved polarimetric analysis of IXPE data. We did not detect any significant variability of the Stokes parameters Q and U with the spin and the orbital phases. We used the relativistic rotating vector model to show that a moderately fan-beam emission from two point-like spots at a small magnetic obliquity ($\simeq$ 10{\deg}) is compatible with the observed pulse profile and polarization properties. IXPE also detected 52 type-I X-ray bursts, with a recurrence time $\Delta t_{rec}$ increasing from 2 to 8 h as a function of the observed count rate $C$ as as $\Delta t_{rec} \simeq C^{-0.8}$ We stacked the emission observed during all the bursts and obtained an upper limit on the polarization degree of 8.5% (90% c.l.)., Comment: 10 pages, 10 figures, accepted for publication by A&A

Weakly magnetized neutron stars (WMNS) are complicated sources with challenging phenomenology. For decades, they have been studied via spectrometry and timing. It has been established that the spectrum of WMNSs consists of several components traditionally associated with the accretion disk, the boundary or spreading layer, and the wind and their interactions with each other. Since 2022, WMNSs have been actively observed with the Imaging X-ray Polarimetry Explorer (IXPE). Polarimetric studies provided new information about the behavior and geometry of these sources. One of the most enigmatic sources of the class, galactic X-ray burster GX 13+1 was first observed with IXPE in October 2023. A strongly variable polarization at the level 2-5$\%$ was detected with the source showing a rotation of the polarization angle (PA) that hinted towards the misalignment within the system. The second observation was performed in February 2024 with a complementary observation by Swift/XRT. IXPE measured an overall polarization degree (PD) of 2.5$\%$ and the PA of 24 degrees, and the Swift/XRT data helped us evaluate the galactic absorption and fit the continuum. Here we study the similarities and differences between the polarimetric properties of the source during the two observations. We confirm the expectation of the misalignment in the system and the assignment of the harder component to the boundary layer. We emphasize the importance of the wind in the system. We note the difference in the variation of polarimetric properties with energy and with time., Comment: 8 pages, 7 figures

Weakly magnetized neutron stars in X-ray binaries show complex phenomenology with several spectral components that can be associated with the accretion disk, boundary and/or spreading layer, a corona, and a wind. Spectroscopic information alone is, however, not enough to disentangle these components. Additional information about the nature of the spectral components and in particular the geometry of the emission region can be provided by X-ray polarimetry. One of the objects of the class, a bright, persistent, and rather peculiar galactic Type I X-ray burster was observed with the Imaging X-ray Polarimetry Explorer (IXPE) and the X-ray Multi-Mirror Mission Newton (XMM-Newton). Using the XMM-Newton data we estimated the current state of the source as well as detected strong absorption lines associated with the accretion disk wind. IXPE data showed the source to be significantly polarized in the 2-8 keV energy band with the overall polarization degree (PD) of 1.4% at a polarization angle (PA) of -2 degrees (errors at 68% confidence level). During the two-day long observation, we detected rotation of the PA by about 70 degrees with the corresponding changes in the PD from 2% to non-detectable and then up to 5%. These variations in polarization properties are not accompanied by visible changes in spectroscopic characteristics. The energy-resolved polarimetric analysis showed a significant change in polarization, from being strongly dependent on energy at the beginning of the observation to being almost constant with energy in the later parts of the observation. As a possible interpretation, we suggest the presence of a constant component of polarization, strong wind scattering, or different polarization of the two main spectral components with individually peculiar behavior. The rotation of the PA suggests a 30-degree misalignment of the neutron star spin from the orbital axis., Comment: 12 pages, 12 figures

We present the first X-ray polarimetric study of the dipping accreting neutron star 4U 1624$-$49 with the Imaging X-ray Polarimetry Explorer (IXPE). We report a detection of polarization in the non-dip time intervals with a confidence level of 99.99%. We find an average polarization degree (PD) of $3.1\pm0.7$% and a polarization angle of $81\pm6$ degrees east of north in the 2-8 keV band. We report an upper limit on the PD of 22% during the X-ray dips with 95% confidence. The PD increases with energy, reaching from $3.0\pm0.9$% in the 4-6 keV band to $6\pm2$% in the 6-8 keV band. This indicates the polarization likely arises from Comptonization. The high PD observed is unlikely to be produced by Comptonization in the boundary layer or spreading layer alone. It can be produced by the addition of an extended geometrically thin slab corona covering part of the accretion disk, as assumed in previous models of dippers, and/or a reflection component from the accretion disk.

The Imaging X-ray Polarimetry Explorer (IXPE) measured with high significance the X-ray polarization of the brightest Z-source Scorpius X-1, resulting in the nominal 2-8 keV energy band in a polarization degree of 1.0(0.2)% and a polarization angle of 8(6){\deg} at 90% of confidence level. This observation was strictly simultaneous with observations performed by NICER, NuSTAR, and Insight-HXMT, which allowed for a precise characterization of its broad-band spectrum from soft to hard X-rays. The source has been observed mainly in its soft state, with short periods of flaring. We also observed low-frequency quasi-periodic oscillations. From a spectro-polarimetric analysis, we associate a polarization to the accretion disk at <3.2% at 90% of confidence level, compatible with expectations for an electron-scattering dominated optically thick atmosphere at the Sco X-1 inclination of 44{\deg}; for the higher-energy Comptonized component, we obtain a polarization of 1.3(0.4)%, in agreement with expectations for a slab of Thomson optical depth of ~7 and an electron temperature of ~3 keV. A polarization rotation with respect to previous observations by OSO-8 and PolarLight, and also with respect to the radio-jet position angle, is observed. This result may indicate a variation of the polarization with the source state that can be related to relativistic precession or to a change in the corona geometry with the accretion flow.

Cir X-1 is a neutron star X-ray binary characterized by strong variations in flux during its eccentric $\sim$16.6 days orbit. There are also strong variations in the spectral state, and historically it has shown both atoll and Z state properties. We observed the source with the Imaging X-ray Polarimetry Explorer during two orbital segments, 6 days apart, for a total of 263~ks. We find an X-ray polarization degree in these segments of $1.6\%\pm0.3\%$ and $1.4\%\pm0.3\%$ at polarization angles of $37^\circ\pm5^\circ$ and $-12^\circ\pm7^\circ$, respectively. Thus we observed a rotation of the polarization angle by $49^\circ\pm8^\circ$ along the orbit. Because variations of accretion flow, and then of the hardness ratio, are expected during the orbit, we also studied the polarization binned in hardness ratio, and found the polarization angle differing by $67^\circ\pm11^\circ$ between the lowest and highest values of the hardness ratio. We discuss possible interpretations of this result that could indicate a possible misalignment between the symmetry axes of the accretion disk and the Comptonizing region caused by the misalignment of the neutron star's angular momentum with respect to the orbital one., Comment: 15 pages, 6 figures, Accepted for publication in ApJL

We report on the coordinated observations of the neutron star low-mass X-ray binary (NS-LMXB) \gx in X-rays (IXPE, NICER, Nustar and INTEGRAL), optical (REM and LCO), near-infrared (REM), mid-infrared (VLT VISIR), and radio (ATCA). This Z-source was observed by \IXPE twice in March-April 2023 (Obs. 1 and 2). In the radio band, the source was detected, but only upper-limits to the linear polarization were obtained at a $3\sigma$ level of $6.1\%$ at 5.5 GHz and $5.9\%$ at 9 GHz in Obs.~1 and $12.5\%$ at 5.5~GHz and $20\%$ at 9~GHz in Obs.~2. The mid-IR, near-IR and optical observations suggest the presence of a compact jet which peaks in the mid- or far-IR. The X-ray polarization degree was found to be $3.7\% \pm 0.4 \%$ (at $90\%$ confidence level) during Obs.~1 when the source was in the horizontal branch of the Z-track and $1.8\% \pm 0.4 \%$ during Obs.~2 when the source was in the normal-flaring branch. These results confirm the variation of polarization degree as a function of the position of the source in the color-color diagram as for previously observed Z-track sources (Cyg~X-2 and XTE~1701$-$462). Evidence for a variation of the polarization angle $\sim 20^\circ$ with energy is found in both observations, likely related to the different, non-orthogonal polarization angles of the disk and Comptonization components which peak at different energies., Comment: Submitted to Astronomy and Astrophysics on 06 July 2023. Accepted on 21 November 2023

Pulse profiles of accreting millisecond pulsars can be used to determine neutron star (NS) parameters, such as their masses and radii, and therefore provide constraints on the equation of state of cold dense matter. Information obtained by the Imaging X-ray Polarimetry Explorer (IXPE) can be used to decipher pulsar inclination and magnetic obliquity, providing ever tighter constraints on other parameters. In this paper, we develop a new emission model for accretion-powered millisecond pulsars based on thermal Comptonization in an accretion shock above the NS surface. The shock structure was approximated by an isothermal plane-parallel slab and the Stokes parameters of the emergent radiation were computed as a function of the zenith angle and energy for different values of the electron temperature, the Thomson optical depth of the slab, and the temperature of the seed blackbody photons. We show that our Compton scattering model leads to a significantly lower polarization degree of the emitted radiation compared to the previously used Thomson scattering model. We computed a large grid of shock models, which can be combined with pulse profile modeling techniques both with and without polarization included. In this work, we used the relativistic rotating vector model for the oblate NS in order to produce the observed Stokes parameters as a function of the pulsar phase. Furthermore, we simulated the data to be produced by IXPE and obtained constraints on model parameters using nested sampling. The developed methods can also be used in the analysis of the data from future satellites, such as the enhanced X-ray Timing and Polarimetry mission., Comment: Accepted to A&A on 11 August 2023

After about 16 years since its first outburst, the transient neutron star low-mass X-ray binary XTE J1701$-$462 turned on again in September 2022, allowing for the first study of its X-ray polarimetric characteristics by a dedicated observing program with the Imaging X-ray Polarimeter Explorer (IXPE). Polarimetric studies of XTE J1701$-$462 have been expected to improve our understanding of accreting weakly magnetized neutron stars, in particular, the physics and the geometry of the hot inner regions close to the compact object. The IXPE data of two triggered observations were analyzed using time-resolved spectroscopic and polarimetric techniques, following the source along its Z-track of the color-color diagram. During the first pointing on 2022 September 29, an average 2-8 keV polarization degree of 4.6$\pm$ 0.4\% was measured, the highest value found up to now for this class of sources. Conversely, only a $\sim$0.6\% average degree was obtained during the second pointing ten days later. The polarimetric signal appears to be strictly related to the higher energy blackbody component associated with the boundary layer (BL) emission and its reflection from the inner accretion disk, and it is as strong as 6.1\% and 1.2\% ($>95\%$ significant) above 3-4 keV for the two measurements, respectively. The variable polarimetric signal is apparently related to the spectral characteristics of XTE J1701$-$462, which is the strongest when the source was in the horizontal branch of its Z-track and the weakest in the normal branch. These IXPE results provide new important observational constraints on the physical models and geometry of the Z-sources. Here, we discuss the possible reasons for the presence of strong and variable polarization among these sources., Comment: 7 pages, 8 figures; published in A&A 674, L10 (2023)

This paper reports the first detection of polarization in the X-rays for atoll-source 4U 1820-303, obtained with the Imaging X-ray Polarimetry Explorer (IXPE) at 99.999% confidence level (CL). Simultaneous polarimetric measurements were also performed in the radio with the Australia Telescope Compact Array (ATCA). The IXPE observations of 4U 1820-303 were coordinated with Swift-XRT, NICER, and NuSTAR aiming to obtain an accurate X-ray spectral model covering a broad energy interval. The source shows a significant polarization above 4 keV, with a polarization degree of 2.0(0.5)% and a polarization angle of -55(7) deg in the 4-7 keV energy range, and a polarization degree of 10(2)% and a polarization angle of -67(7) deg in the 7-8 keV energy bin. This polarization also shows a clear energy trend with polarization degree increasing with energy and a hint for a position-angle change of about 90 deg at 96% CL around 4 keV. The spectro-polarimetric fit indicates that the accretion disk is polarized orthogonally to the hard spectral component, which is presumably produced in the boundary/spreading layer. We do not detect linear polarization from the radio counterpart, with a 99.97% upper limit of 50% at 7.25 GHz.

The recently standardized millimeter wave-based 3GPP New Radio technology is expected to become an enabler for both enhanced Mobile Broadband (eMBB) and ultra-reliable low latency communication (URLLC) services specified to future 5G systems. One of the first steps in mathematical modeling of such systems is the characterization of the session resource request probability mass function (pmf) as a function of the channel conditions, cell size, application demands, user location and system parameters including modulation and coding schemes employed at the air interface. Unfortunately, this pmf cannot be expressed via elementary functions. In this paper, we develop an accurate approximation of the sought pmf. First, we show that Normal distribution provides a fairly accurate approximation to the cumulative distribution function (CDF) of the signal-to-noise ratio for communication systems operating in the millimeter frequency band, further allowing evaluating the resource request pmf via error function. We also investigate the impact of shadow fading on the resource request pmf., Comment: The 19th International Conference on Next Generation Wired/Wireless Networks and Systems (New2An 2019)