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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 consider the identification of non-causal systems with arbitrary switching modes (NCS-ASM), a class of models essential for describing typical power load management and department store inventory dynamics. The simultaneous identification of causal-and-anticausal subsystems, along with the presence of possibly random switching sequences, however, make the overall identification problem particularly challenging. To this end, we develop an expectation-maximization (EM) based system identification technique, where the E-step proposes a modified Kalman filter (KF) to estimate the states and switching sequences of causal-and-anticausal subsystems, while the M-step consists in a switching least-squares algorithm to estimate the parameters of individual subsystems. We establish the main convergence features of the proposed identification procedure, also providing bounds on the parameter estimation errors under mild conditions. Finally, the effectiveness of our identification method is validated through two numerical simulations.

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 present a stability analysis of Physics-Informed Neural Networks (PINNs) coupled with random projections, for the numerical solution of (stiff) linear differential equations. For our analysis, we consider systems of linear ODEs, and linear parabolic PDEs. We prove that properly designed PINNs offer consistent and asymptotically stable numerical schemes, thus convergent schemes. In particular, we prove that multi-collocation random projection PINNs guarantee asymptotic stability for very high stiffness and that single-collocation PINNs are $A$-stable. To assess the performance of the PINNs in terms of both numerical approximation accuracy and computational cost, we compare it with other implicit schemes and in particular backward Euler, the midpoint, trapezoidal (Crank-Nikolson), the 2-stage Gauss scheme and the 2 and 3 stages Radau schemes. We show that the proposed PINNs outperform the above traditional schemes, in both numerical approximation accuracy and importantly computational cost, for a wide range of step sizes.

We present the first X-ray polarization measurements of GX 339-4. IXPE observed this source twice during its 2023-2024 outburst, once in the soft-intermediate state and again during a soft state. The observation taken during the intermediate state shows significant ($4\sigma$) polarization degree P = $1.3\% \pm 0.3\%$ and polarization angle $\theta$ = -74\degree $\pm$ 7\degree only in the 3 - 8 keV band. FORS2 at VLT observed the source simultaneously detecting optical polarization in the B, V, R, I bands (between $0.1%$ and $0.7\%$), all roughly aligned with the X-ray polarization. We also detect a discrete jet knot from radio observations taken later in time; this knot would have been ejected from the system around the same time as the hard-to-soft X-ray state transition and a bright radio flare occurred $\sim$3 months earlier. The proper motion of the jet knot provides a direct measurement of the jet orientation angle on the plane of the sky at the time of the ejection. We find that both the X-ray and optical polarization angles are aligned with the direction of the ballistic jet., Comment: Submitted to ApJ

We present a phase-dependent analysis of the polarized emission from the Crab pulsar based on three sets of observations by the Imaging X-ray Polarimetry Explorer (IXPE). We found that a phenomenological model involving a simple linear transformation of the Stokes parameters adequately describes the IXPE data. This model enables us to establish, for the first time, a connection between the polarization properties of the Crab pulsar in the optical and soft X-ray bands, suggesting a common underlying emission mechanism across these bands. In particular, the phase-dependent polarization degree in X-rays for pure pulsar emission shows similar features but is reduced by a factor $\approx (0.46-0.56)$ compared to the optical band, implying an energy-dependent polarized emission. In addition, using this model, we study the polarization angle swing in X-rays and identify a potentially variable phase-shift at the interpulse relative to the optical band, alongside a phase-shift marginally consistent with zero persisting at the main pulse. While the variability presents a new challenge for theoretical interpretation, our findings suggest that the emission mechanism for the main pulse is likely located far from the neutron star surface, perhaps near or beyond the light cylinder, rather than operating in the inner magnetosphere where vacuum birefringence is expected to be at work. Ignoring the phase-shifts would result in identical phase-dependent polarization angles between the optical and X-ray bands for pure pulsar emission., Comment: 16 pages, 11 figures, submitted to A&A

We present Crab X-ray polarization measurements using IXPE data with a total exposure of 300ks, three times more than the initial 2022 discovery paper. Polarization is detected in three times more pulsar phase bins, revealing an S-shaped $+40^\circ$ polarization angle sweep in the main pulse and ${>}1\sigma$ departures from the OPTIMA optical polarization in both pulses, suggesting different radiation mechanisms or sites for the polarized emission at the two wavebands. Our polarization map of the inner nebula reveals a toroidal magnetic field, as seen in prior IXPE analyses. Along the southern jet, the magnetic field orientation relative to the jet axis changes from perpendicular to parallel and the polarization degree decreases by ${\sim}6\%$. These observations may be explained by kink instabilities along the jet or a collision with a dense, jet-deflecting medium at the tip. Using spectropolarimetric analysis, we find asymmetric polarization in the four quadrants of the inner nebula, as expected for a toroidal field geometry, and a spatial correlation between polarization degree and photon index., Comment: 14 pages, 7 figures, 3 tables. Accepted by The Astrophysical Journal

We present multiwavelength polarization measurements of the luminous blazar Mrk~501 over a 14-month period. The 2--8 keV X-ray polarization was measured with the Imaging X-ray Polarimetry Explorer (IXPE) with six 100-ks observations spanning from 2022 March to 2023 April. Each IXPE observation was accompanied by simultaneous X-ray data from NuSTAR, Swift/XRT, and/or XMM-Newton. Complementary optical-infrared polarization measurements were also available in the B, V, R, I, and J bands, as were radio polarization measurements from 4.85 GHz to 225.5 GHz. Among the first five IXPE observations, we did not find significant variability in the X-ray polarization degree and angle with IXPE. However, the most recent sixth observation found an elevated polarization degree at $>3\sigma$ above the average of the other five observations. The optical and radio measurements show no apparent correlations with the X-ray polarization properties. Throughout the six IXPE observations, the X-ray polarization degree remained higher than, or similar to, the R-band optical polarization degree, which remained higher than the radio value. This is consistent with the energy-stratified shock scenario proposed to explain the first two IXPE observations, in which the polarized X-ray, optical, and radio emission arises from different regions., Comment: Accepted for publication in ApJ

The CUbesat Solar Polarimeter (CUSP) project is a future CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band, by means of a Compton scattering polarimeter. CUSP will allow us to study the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. The project is in the framework of the Italian Space Agency Alcor Program, which aims to develop new CubeSat missions. CUSP is approved for a Phase B study that will last for 12 months, starting in mid-2024. We report on the current status of the CUSP mission project as the outcome of the Phase A., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024. arXiv admin note: substantial text overlap with arXiv:2208.06211

X-ray polarimetry of solar flares is still a not well established field of observation of our star. Past polarimeters were not able to measure with a high significance the polarization in X-rays from solar flares. Moreover, they had no imaging capabilities and measured only the polarization by integrating on all the image of the source. We propose a mission concept based on a gas photoelectric polarimeter, coupled with multilayer lobster-eye optics, to perform imaging-spectro-polarimetry of solar flares while monitoring the entire solar disc., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

The CUbesat Solar Polarimeter (CUSP) project is a CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter. CUSP will allow the study of the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. CUSP is a project in the framework of the Alcor Program of the Italian Space Agency aimed at developing new CubeSat missions. It is approved for a Phase B study. In this work, we report on the characterization of the Avalanche Photodiodes (APDs) that will be used as readout sensors of the absorption stage of the Compton polarimeter. We assessed the APDs gain and energy resolution as a function of temperature by irradiating the sensor with a \textsuperscript{55}Fe radioactive source. Moreover, the APDs were also characterized as being coupled to a GAGG scintillator., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

The CUbesat Solar Polarimeter (CUSP) project aims to develop a constellation of two CubeSats orbiting the Earth to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter on board of each satellite. CUSP will allow to study the magnetic reconnection and particle acceleration in the flaring magnetic structures. CUSP is a project approved for a Phase B study by the Italian Space Agency in the framework of the Alcor program aimed to develop CubeSat technologies and missions. In this paper we describe the a method for a multi-physical simulation analysis while analyzing some possible design optimization of the payload design solutions adopted. In particular, we report the mechanical design for each structural component, the results of static and dynamic finite element analysis, the preliminary thermo-mechanical analysis for two specific thermal cases (hot and cold orbit) and a topological optimization of the interface between the platform and the payload., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

The CUbesat Solar Polarimeter (CUSP) project is a CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter. CUSP will allow to study the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. CUSP is a project in the framework of the Alcor Program of the Italian Space Agency aimed to develop new CubeSat missions. It is approved for a Phase B study. In this work, we report on the accurate simulation of the detector's response to evaluate the scientific performance. A GEANT4 Monte Carlo simulation is used to assess the physical interactions of the source photons with the detector and the passive materials. Using this approach, we implemented a detailed CUSP Mass Model. In this work, we report on the evaluation of the detector's effective area as a function of the beam energy., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

We present the first X-ray spectropolarimetric results for Cygnus X-1 in its soft state from a campaign of five IXPE observations conducted during 2023 May-June. Companion multiwavelength data during the campaign are likewise shown. The 2-8 keV X-rays exhibit a net polarization degree PD=1.99%+/-0.13% (68% confidence). The polarization signal is found to increase with energy across IXPE's 2-8 keV bandpass. The polarized X-rays exhibit an energy-independent polarization angle of PA=-25.7+/-1.8 deg. East of North (68% confidence). This is consistent with being aligned to Cyg X-1's AU-scale compact radio jet and its pc-scale radio lobes. In comparison to earlier hard-state observations, the soft state exhibits a factor of 2 lower polarization degree, but a similar trend with energy and a similar (also energy-independent) position angle. When scaling by the natural unit of the disk temperature, we find the appearance of a consistent trendline in the polarization degree between soft and hard states. Our favored polarimetric model indicates Cyg X-1's spin is likely high (a* above ~0.96). The substantial X-ray polarization in Cyg X-1's soft state is most readily explained as resulting from a large portion of X-rays emitted from the disk returning and reflecting off the disk surface, generating a high polarization degree and a polarization direction parallel to the black hole spin axis and radio jet. In IXPE's bandpass, the polarization signal is dominated by the returning reflection emission. This constitutes polarimetric evidence for strong gravitational lensing of X-rays close to the black hole., Comment: 20 pages, accepted for publication in ApJL

Recent observations of X-ray pulsars (XRPs) performed by the Imaging X-ray Polarimetry Explorer (IXPE) have made it possible to investigate the intricate details of these objects in a new way, thanks to the added value of X-ray polarimetry. Here we present the results of the IXPE observations of SMC X-1, a member of the small group of XRPs displaying super-orbital variability. SMC X-1 was observed by IXPE three separate times during the high state of its super-orbital period. The observed luminosity in the 2-8 keV energy band of $L=2\times10^{38}$ erg/s makes SMC X-1 the brightest XRP ever observed by IXPE. We detect significant polarization in all three observations, with values of the phase-averaged polarization degree (PD) and polarization angle (PA) of $3.2\pm0.8$% and $97\deg\pm8\deg$ for Observation 1, $3.0\pm0.9$% and $90\deg\pm8\deg$ for Observation 2, and $5.5\pm1.1$% and $80\deg\pm6\deg$ for Observation 3, for the spectro-polarimetric analysis. The observed PD shows an increase over time with decreasing luminosity, while the PA decreases in decrements of 10\deg. The phase-resolved spectro-polarimetric analysis reveals significant detection of polarization in three out of seven phase bins, with the PD ranging between 2% and 10%, and a corresponding range in the PA from $\sim$70\deg\ to $\sim$100\deg. The pulse-phase resolved PD displays an apparent anti-correlation with the flux. Using the rotating vector model, we obtain constraints on the pulsar's geometrical properties for the individual observations. The position angle of the pulsar displays an evolution over time supporting the idea that we observe changes related to different super-orbital phases. Scattering in the wind of the precessing accretion disk may be responsible for the behavior of the polarimetric properties observed during the high-state of SMC X-1's super-orbital period., Comment: 11 pages, 11 figures, submitted to A&A

Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, poses a barrier to achieving high numerical accuracy. Here, inpsired by DeepONets and to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections that learn linear and nonlinear operators. The implementation of RandONets involves: (a) incorporating random bases, thus enabling the use of shallow neural networks with a single hidden layer, where the only unknowns are the output weights of the network's weighted inner product; this reduces dramatically the dimensionality of the parameter space; and, based on this, (b) using established least-squares solvers (e.g., Tikhonov regularization and preconditioned QR decomposition) that offer superior numerical approximation properties compared to other optimization techniques used in deep-learning. In this work, we prove the universal approximation accuracy of RandONets for approximating nonlinear operators and demonstrate their efficiency in approximating linear nonlinear evolution operators (right-hand-sides (RHS)) with a focus on PDEs. We show, that for this particular task, RandONets outperform, both in terms of numerical approximation accuracy and computational cost, the ``vanilla" DeepOnets.

We report the X-ray polarization properties of the high-synchrotron-peaked (HSP) blazar PKS 2155$-$304 based on observations with the Imaging X-ray Polarimetry Explorer (IXPE). We observed the source between Oct 27 and Nov 7, 2023. We also conducted an extensive contemporaneous multiwavelength (MW) campaign. We find that during the first half ($T_1$) of the IXPE pointing, the source exhibited the highest X-ray polarization degree detected for an HSP blazar thus far, (30.7$\pm$2.0)%, which dropped to (15.3$\pm$2.1)% during the second half ($T_2$). The X-ray polarization angle remained stable during the IXPE pointing at 129.4$^\circ$$\pm$1.8$^\circ$ and 125.4$^\circ$$\pm$3.9$^\circ$ during $T_1$ and $T_2$, respectively. Meanwhile, the optical polarization degree remained stable during the IXPE pointing, with average host-galaxy-corrected values of (4.3$\pm$0.7)% and (3.8$\pm$0.9)% during the $T_1$ and $T_2$, respectively. During the IXPE pointing, the optical polarization angle changed achromatically from $\sim$140$^\circ$ to $\sim$90$^\circ$ and back to $\sim$130$^\circ$. Despite several attempts, we only detected (99.7% conf.) the radio polarization once (during $T_2$, at 225.5 GHz): with degree (1.7$\pm$0.4)% and angle 112.5$^\circ$$\pm$5.5$^\circ$. The direction of the broad pc-scale jet is rather ambiguous and has been found to point to the east and south at different epochs; however, on larger scales (> 1.5 pc) the jet points toward the southeast ($\sim$135$^\circ$), similar to all of the MW polarization angles. Moreover, the X-ray to optical polarization degree ratios of $\sim$7 and $\sim$4 during $T_1$ and $T_2$, respectively, are similar to previous IXPE results for several HSP blazars. These findings, combined with the lack of correlation of temporal variability between the MW polarization properties, agree with an energy-stratified shock-acceleration scenario in HSP blazars., Comment: 17 pages, 10 figures, 4 tables, Accepted for publication in A&A

Discovery of pulsations from a number of ultra-luminous X-ray (ULX) sources proved that accretion onto neutron stars can produce luminosities exceeding the Eddington limit by a couple of orders of magnitude. The conditions necessary to achieve such high luminosities as well as the exact geometry of the accretion flow in the neutron star vicinity are, however, a matter of debate. The pulse phase-resolved polarization measurements that became possible with the launch of the IXPE can be used to determine the pulsar geometry and its orientation relative to the orbital plane. They provide an avenue to test different theoretical models of ULX pulsars. In this paper we present the results of three IXPE observations of the first Galactic ULX pulsar Swift J0243.6+6124 during its 2023 outburst. We find strong variations of the polarization characteristics with the pulsar phase. The average polarization degree increases from about 5% to 15% as the flux dropped by a factor of three in the course of the outburst. The polarization angle (PA) as function of the pulsar phase shows two peaks in the first two observations, but changes to a characteristic sawtooth pattern in the remaining data set. This is not consistent with a simple rotating vector model. Assuming the existence of an additional constant polarized component, we were able to fit the three observations with a common rotating vector model and obtain constraints on the pulsar geometry. In particular, we find the pulsar angular momentum inclination with respect to the line-of-sight of 15-40 deg, the magnetic obliquity of 60-80 deg, and the pulsar spin position angle of -50 deg, which differs from the constant component PA of about 10 deg. Combining these X-ray measurements with the optical PA, we find evidence for a 30 deg misalignment between the pulsar spin and the binary orbital axis., Comment: 13 pages, 10 figures, submitted to A&A

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 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 synchtrotron emission is 12.5 {\pm} 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 sub-parsec scales, localized patches within RX J1713.7-3946 display PD up to 41.5 {\pm} 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 magneto-hydrodynamical instabilities, can be invoked. From comparison of PD and magnetic field distribution with {\gamma}-rays and 12 CO data, our results provide new inputs in favor of a leptonic origin of the {\gamma}-ray emission., Comment: 18 pages, 6 figures, 2 tables, published in ApJ Letters

We design a computational approach to find equilibria in a class of Nash games possessing a hierarchical structure. By using tools from mixed-integer programming and the characterization of variational equilibria in terms of the Karush--Kuhn--Tucker conditions, we propose a mixed-integer game formulation for solving such a challenging instance. Besides providing an equivalent reformulation, we build upon our previous work and design a proximal Gauss--Seidel method with global convergence guarantees for the case in which the game enjoys a potential structure. In addition to proving the convergence of the resulting scheme, we show its performance on a numerical instance of a ride-hail market problem., Comment: submitted as a conference proceeding

We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design. We propose a specific neural network (NN) architecture that yields a hybrid system with piecewise-affine dynamics that is differentiable with respect to the network's parameters, thereby enabling the use of derivative-based training procedures. We show that a careful choice of our NN's weights produces a hybrid system model with structural properties that are highly favourable when used as part of a finite horizon optimal control problem (OCP). Specifically, we show that optimal solutions with strong local optimality guarantees can be computed via nonlinear programming, in contrast to classical OCPs for general hybrid systems which typically require mixed-integer optimization. In addition to being well-suited for optimal control design, numerical simulations illustrate that our NN-based technique enjoys very similar performance to state-of-the-art system identification methodologies for hybrid systems and it is competitive on nonlinear benchmarks.

We used the Imaging X-ray Polarimetry Explorer (IXPE) satellite to measure, for the first time, the 2-8 keV polarization of NGC 1068. We pointed IXPE for a net exposure time of 1.15 Ms on the target, in addition to two ~ 10 ks each Chandra snapshots in order to account for the potential impact of several ultraluminous X-ray source (ULXs) within IXPE's field-of-view. We measured a 2 - 8 keV polarization degree of 12.4% +/- 3.6% and an electric vector polarization angle of 101{\deg} +/- 8{\deg} at 68% confidence level. If we exclude the spectral region containing the bright Fe K lines and other soft X-ray lines where depolarization occurs, the polarization fraction rises up to 21.3% +/- 6.7% in the 3.5 - 6.0 keV band, with a similar polarization angle. The observed polarization angle is found to be perpendicular to the parsec scale radio jet. Using a combined Chandra and IXPE analysis plus multi-wavelength constraints, we estimated that the circumnuclear "torus" may sustain a half-opening angle of 50{\deg} - 55{\deg} (from the vertical axis of the system). Thanks to IXPE, we have measured the X-ray polarization of NGC 1068 and found comparable results, both in terms of polarization angle orientation with respect to the radio-jet and torus half-opening angle, to the X-ray polarimetric measurement achieved for the other archetypal Compton-thick AGN : the Circinus galaxy. Probing the geometric arrangement of parsec-scale matter in extragalactic object is now feasible thanks to X-ray polarimetry., Comment: 9 pages, 5 figures, 2 tables, submited to A&A

We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a nonlinear state transformation map by solving a system of inhomogeneous functional equations. The performance of the proposed PINN approach is assessed via two illustrative case studies for which the observer linearizing transformation map can be derived analytically. We also perform an uncertainty quantification analysis for the proposed PINN scheme and we compare it with conventional power-series numerical implementations, which rely on the computation of a power series solution.

We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal weights and biases, offering computational efficiency. We demonstrate that there exists a choice of external weights, for any family of such RPNNs, with non-polynomial infinitely differentiable activation functions, that exhibit an exponential convergence rate when approximating any infinitely differentiable function. For illustration purposes, we test the proposed RPNN-based function approximation, with parsimoniously chosen basis functions, across five benchmark function approximation problems. Results show that RPNNs achieve comparable performance to established methods such as Legendre Polynomials, highlighting their potential for efficient and accurate function approximation., Comment: 21 pages, 5 figures

We report on X-ray polarization measurements of the extra-galactic Crab-like PSR B0540-69 and its Pulsar Wind Nebula (PWN) in the Large Magellanic Cloud (LMC), using a ~850 ks Imaging X-ray Polarimetry Explorer (IXPE) exposure. The PWN is unresolved by IXPE. No statistically significant polarization is detected for the image-averaged data, giving a 99% confidence polarization upper limit (MDP99) of 5.3% in 2-8 keV energy range. However, a phase-resolved analysis detects polarization for both the nebula and pulsar in the 4-6 keV energy range. For the PWN defined as the off-pulse phases, the polarization degree (PD) of (24.5 ${\pm}$ 5.3)% and polarization angle (PA) of (78.1 ${\pm}$ 6.2){\deg} is detected at 4.6${\sigma}$ significance level, consistent with the PA observed in the optical band. In a single on-pulse window, a hint of polarization is measured at 3.8${\sigma}$ with polarization degree of (50.0 ${\pm}$ 13.1)% and polarization angle of (6.2 ${\pm}$ 7.4){\deg}. A 'simultaneous' PSR/PWN analysis finds two bins at the edges of the pulse exceeding 3${\sigma}$ PD significance, with PD of (68 ${\pm}$ 20)% and (62 ${\pm}$ 20)%; intervening bins at 2-3${\sigma}$ significance have lower PD, hinting at additional polarization structure., Comment: 10 pages, 7 figures, 4 tables, author's version of the paper accepted for publication in ApJ

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

Observations of linear polarization in the 2-8 keV energy range with the Imaging X-ray Polarimetry Explorer (IXPE) explore the magnetic field geometry and dynamics of the regions generating non-thermal radiation in relativistic jets of blazars. These jets, particularly in blazars whose spectral energy distribution peaks at X-ray energies, emit X-rays via synchrotron radiation from high-energy particles within the jet. IXPE observations of the X-ray selected BL Lac-type blazar 1ES 1959+650 in 2022 May 3-4 showed a significant linear polarization degree of $\Pi_\mathrm{x} = 8.0\% \pm 2.3\%$ at an electric-vector position angle $\psi_\mathrm{x} = 123^\circ \pm 8^\circ$. However, in 2022 June 9-12, only an upper limit of $\Pi_\mathrm{x} \leq 5.1\%$ could be derived (at the 99% confidence level). The degree of optical polarization at that time $\Pi_\mathrm{O} \sim 5\%$ is comparable to the X-ray measurement. We investigate possible scenarios for these findings, including temporal and geometrical depolarization effects. Unlike some other X-ray selected BL Lac objects, there is no significant chromatic dependence of the measured polarization in 1ES 1959+650, and its low X-ray polarization may be attributed to turbulence in the jet flow with dynamical timescales shorter than 1 day., Comment: 16 pages, 4 figures, accepted for publication in The Astrophysical Journal

X-ray binary systems consist of a companion star and a compact object in close orbit. Thanks to their copious X-ray emission, these objects have been studied in detail using X-ray spectroscopy and timing. The inclination of these systems is a major uncertainty in the determination of the mass of the compact object using optical spectroscopic methods. In this paper, we present a new method to constrain the inclination of X-ray binaries, which is based on the modeling of the polarization of X-rays photons produced by a compact source and scattered off the companion star. We describe our method and explore the potential of this technique in the specific case of the low mass X-ray binary GS 1826-238 observed by the Imaging X-ray Polarimetry Explorer (IXPE) observatory., Comment: 9 pages, 8 figures, accepted for publication in ApJ

Thanks to IXPE , the X-ray spectro-polarimeter launched at the end of 2021, X-ray polarimetry has finally become an extraordinary tool in investigating the physics of accretion in low mass X-ray binaries. Similarly to what happened with gravitational waves, X-ray polarimetry would play a new complementary but at the same time fundamental role in the high-energy astrophysical domain. We summarize here the first 1.5 year results on accreting low-mass X-ray binaries obtained by a huge IXPE observation campaign coordinated with the principal X-ray and Gamma-ray telescopes. Then we compare these results with the theoretical prediction highlighting the unexpected results., Comment: Proceeding presented at the Fifth Zeldovich meeting, an international conference held in Yerevan, Armenia on June 12-16, 2023. To be published in Astronomy Report

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.

We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed $\zeta$-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the $\zeta$-core.

We report the discovery of X-ray polarization from the X-ray-bright filament. G0.13-0.11 in the Galactic center (GC) region. This filament features a bright, hard X-ray source that is most plausibly a pulsar wind nebula (PWN) and an extended and structured diffuse component. Combining the polarization signal from IXPE with the imaging/spectroscopic data from Chandra, we find that X-ray emission of G0.13-0.11 is highly polarized PD=$57(\pm18)$% in the 3-6 keV band, while the polarization angle is PA=$21^\circ(\pm9^\circ)$. This high degree of polarization proves the synchrotron origin of the X-ray emission from G0.13-0.11. In turn, the measured polarization angle implies that the X-ray emission is polarized approximately perpendicular to a sequence of nonthermal radio filaments that may be part of the GC Radio Arc. The magnetic field on the order of $100\,{\rm\mu G}$ appears to be preferentially ordered along the filaments. The above field strength is the fiducial value that makes our model self-consistent, while the other conclusions are largely model independent., Comment: Accepted for publication in A&A

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.

We report on an observational campaign on the bright black hole X-ray binary Swift J1727.8$-$1613 centered around five observations by the Imaging X-ray Polarimetry Explorer (IXPE). These observations track for the first time the evolution of the X-ray polarization of a black hole X-ray binary across a hard to soft state transition. The 2--8 keV polarization degree decreased from $\sim$4\% to $\sim$3\% across the five observations, but the polarization angle remained oriented in the North-South direction throughout. Based on observations with the Australia Telescope Compact Array (ATCA), we find that the intrinsic 7.25 GHz radio polarization aligns with the X-ray polarization. Assuming the radio polarization aligns with the jet direction (which can be tested in the future with higher spatial resolution images of the jet), our results imply that the X-ray corona is extended in the disk plane, rather than along the jet axis, for the entire hard intermediate state. This in turn implies that the long ($\gtrsim$10 ms) soft lags that we measure with the Neutron star Interior Composition ExploreR (NICER) are dominated by processes other than pure light-crossing delays. Moreover, we find that the evolution of the soft lag amplitude with spectral state does not follow the trend seen for other sources, implying that Swift J1727.8$-$1613 is a member of a hitherto under-sampled sub-population., Comment: Accepted for publication in ApJ. 21 pages, 8 figures

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

In an accreting X-ray pulsar, a neutron star accretes matter from a stellar companion through an accretion disk. The high magnetic field of the rotating neutron star disrupts the inner edge of the disc, funneling the gas to flow onto the magnetic poles on its surface. Hercules X-1 is in many ways the prototypical X-ray pulsar; it shows persistent X-ray emission and it resides with its companion HZ Her, a two-solar-mass star, at about 7~kpc from Earth. Its emission varies on three distinct timescales: the neutron star rotates every 1.2~seconds, it is eclipsed by its companion each 1.7~days, and the system exhibits a superorbital period of 35~days which has remained remarkably stable since its discovery. Several lines of evidence point to the source of this variation as the precession of the accretion disc, the precession of the neutron star or both. Despite the many hints over the past fifty years, the precession of the neutron star itself has yet not been confirmed or refuted. We here present X-ray polarization measurements with the Imaging X-ray Polarimetry Explorer (IXPE) which probe the spin geometry of the neutron star. These observations provide direct evidence that the 35-day-period is set by the free precession of the neutron star crust, which has the important implication that its crust is somewhat asymmetric fractionally by a few parts per ten million. Furthermore, we find indications that the basic spin geometry of the neutron star is altered by torques on timescale of a few hundred days., Comment: 37 pages

We report on IXPE, NICER and XMM-Newton observations of the magnetar 1E 2259+586. We find that the source is significantly polarized at about or above 20% for all phases except for the secondary peak where it is more weakly polarized. The polarization degree is strongest during the primary minimum which is also the phase where an absorption feature has been identified previously (Pizzocaro et al. 2019). The polarization angle of the photons are consistent with a rotating vector model with a mode switch between the primary minimum and the rest of the rotation of the neutron star. We propose a scenario in which the emission at the source is weakly polarized (as in a condensed surface) and, as the radiation passes through a plasma arch, resonant cyclotron scattering off of protons produces the observed polarized radiation. This confirms the magnetar nature of the source with a surface field greater than about 1015 G, Comment: 13 pages, 13 figures, 5 tables