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The lowest-order Neural Approximated Virtual Element Method on polygonal elements is proposed here. This method employs a neural network to locally approximate the Virtual Element basis functions, thereby eliminating issues concerning stabilization and projection operators, which are the key components of the standard Virtual Element Method. We propose different training strategies for the neural network training, each correlated by the theoretical justification and with a different level of accuracy. Several numerical experiments are proposed to validate our procedure on general polygonal meshes and demonstrate the advantages of the proposed method across different problem formulations, particularly in cases where the heavy usage of projection and stabilization terms may represent challenges for the standard version of the method. Particular attention is reserved to triangular meshes with hanging nodes which assume a central role in many virtual element applications.

We prove that the Hessian transformation of a plane projective cubic corresponds to a $3$-endomorphism of a model elliptic curve. By exploiting this result, we investigate a family of functional graphs -- called Hessian graphs -- defined by the Hessian transformation. We show that, over arbitrary fields of characteristics different from $2$ and $3$, the Hessian graphs inherit distinctive features from the arithmetic of the model curve. We then specialize our analysis to the finite-field case, proving several regularities of Hessian graphs.

The discovery of pulsations in (at least) six ultraluminous X-ray sources (ULXs) has shown that neutron stars can accrete at (highly) super-Eddington rates, challenging the standard accretion theories. M51 ULX-7, with a spin signal of $P\simeq2.8$ s, is the pulsating ULX (PULX) with the shortest known orbital period ($P_\mathrm{orb}\simeq2$ d) and has been observed multiple times by XMM-Newton, Chandra, and NuSTAR. We report on the timing and spectral analyses of three XMM-Newton observations of M51 ULX-7 performed between the end of 2021 and the beginning of 2022, together with a timing re-analysis of XMM-Newton, Chandra, and NuSTAR archival observations. We investigated the spin signal by applying accelerated search techniques and studied the power spectrum through the fast Fourier transform, looking for (a)periodic variability in the source flux. We analysed the energy spectra of the 2021-2022 observations and compared them to the older ones. We report the discovery of a recurrent, significant ($>$3$\sigma$) broad complex at mHz frequencies in the power spectra of M51 ULX-7. We did not detect the spin signal, setting a 3$\sigma$ upper limit on the pulsed fraction of $\lesssim10\%$ for the single observation. The complex is significantly detected also in five Chandra observations performed in 2012. M51 ULX-7 represents the second PULX for which we have a significant detection of mHz-QPOs at super-Eddington luminosities. These findings suggest that one should avoid using the observed QPO frequency to infer the mass of the accretor in a ULX. The absence of spin pulsations when the broad complex is detected suggests that the mechanism responsible for the aperiodic modulation also dampens the spin signal's pulsed fraction. If true, this represents an additional obstacle in the detection of new PULXs, suggesting an even larger occurrence of PULXs among ULXs., Comment: 14 pages (12 main text + Appendix), 5 figures. Accepted for publication on A&A

We report on the multi-year evolution of the population of X-ray sources in the nuclear region of NGC 3621 based on Chandra, XMM-Newton and Swift observations. Among these, two sources, X1 and X5, after their first detection in 2008, seem to have faded below the detectability threshold, a most interesting fact as X1 is associated with the AGN of the galaxy. Two other sources, X3 and X6 are presented for the first time, the former showing a peculiar short-term variability in the latest available dataset, suggesting an egress from eclipse, hence belonging to the handful of known eclipsing ultra-luminous X-ray sources. One source, X4, previously known for its "heart-beat", i.e. a characteristic modulation in its signal with a period of $\approx1$ h, shows a steady behaviour in the latest observation. Finally, the brightest X-ray source in NGC 3621, here labelled X2, shows steady levels of flux across all the available datasets but a change in its spectral shape, reminiscent of the behaviours of Galactic disk-fed X-ray binaries., Comment: 11 pages, 10 figures, 3 tables, 2 appendices available online. Accepted for publication on A&A

In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space, we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational-Physics-Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh., Comment: 24 pages, 65 figures, 1 table

We report on the orbit of the binary system powering the most extreme ultraluminous X-ray pulsar known to date: NGC 5907 ULX-1 (hereafter ULX1). ULX1 has been the target of a substantial multi-instrument campaign, mainly in the X-ray band, but no clear counterparts are known in other bands. Although ULX1 is highly variable and pulsations can be transient (regardless of the source flux), the timing data collected so far allow us to investigate the orbit of this system. We find an orbital period $P_{orb}=5.7^{+0.1}_{-0.6}\text{ d}$ and a projected semi-axis $A_1 =3.1^{+0.8}_{-0.9}\text{ lts}$. The most likely ephemeris is: $P_{orb}=5.6585(6)\text{ d}$, $A_1 = 3.1(4)\text{ lts}$, and the epoch of ascending nodes passage is: $T_{asc} = 57751.37(5)\text{ MJD}$. However, there are 6 similar solutions, acceptable within $3\,\sigma$. We find further indications that ULX1 is a high-mass X-ray binary. This implies that we are observing its orbit face-on, with an inclination $<5\text{ deg}$., Comment: 11 pages, 2 tables, 6 figures

The fourth-DR3 version (4FGL-DR3) of the Fermi/LAT catalogue of $\gamma$-ray sources contains $\sim$ 1000 objects at a galactic latitude |b| > 10$^{\circ}$ which are not identified with an optical counterpart (UGS). We performed a systematic study of these sources, focusing on 190 objects that have a unique X-ray counterpart in the available Swift/XRT observations. Optical counterparts are then selected, and for 33 sources optical spectra were found in the literature. We found that 21 can be classified as BL Lac objects. Among these we were able to provide the redshift for 8 of them while for 2 others we established a lower limit to the redshift by detecting intervening absorption. The other 12 objects display optical spectra with prominent emission lines (0.036

Ultraluminous X-ray sources (ULXs) represent an extreme class of accreting compact objects: from the identification of some of the accretors as neutron stars to the detection of powerful winds travelling at 0.1-0.2 c, the increasing evidence points towards ULXs harbouring stellar-mass compact objects undergoing highly super-Eddington accretion. Measuring their intrinsic properties, such as the accretion rate onto the compact object, the outflow rate, the masses of accretor/companion -- hence their progenitors, lifetimes, and future evolution -- is challenging due to ULXs being mostly extragalactic and in crowded fields. Yet ULXs represent our best opportunity to understand super-Eddington accretion physics and the paths through binary evolution to eventual double compact object binaries and gravitational wave sources. Through a combination of end-to-end and single-source simulations, we investigate the ability of HEX-P to study ULXs in the context of their host galaxies and compare it to XMM-Newton and NuSTAR, the current instruments with the most similar capabilities. HEX-P's higher sensitivity, which is driven by its narrow point-spread function and low background, allows it to detect pulsations and broad spectral features from ULXs better than XMM-Newton and NuSTAR. We describe the value of HEX-P in understanding ULXs and their associated key physics, through a combination of broadband sensitivity, timing resolution, and angular resolution, which make the mission ideal for pulsation detection and low-background, broadband spectral studies., Comment: 24 pages, 9 figures. Accepted for publication in Frontiers of Astronomy and Space Science. Minor corrections included

The detection of gravitational waves from a binary neutron star merger by Advanced LIGO and Advanced Virgo (GW170817), along with the discovery of the electromagnetic counterparts of this gravitational wave event, ushered in a new era of multimessenger astronomy, providing the first direct evidence that BNS mergers are progenitors of short gamma-ray bursts (GRBs). Such events may also produce very-high-energy (VHE, > 100GeV) photons which have yet to be detected in coincidence with a gravitational wave signal. The Cherenkov Telescope Array (CTA) is a next-generation VHE observatory which aims to be indispensable in this search, with an unparalleled sensitivity and ability to slew anywhere on the sky within a few tens of seconds. New observing modes and follow-up strategies are being developed for CTA to rapidly cover localization areas of gravitational wave events that are typically larger than the CTA field of view. This work will evaluate and provide estimations on the expected number of of gravitational wave events that will be observable with CTA, considering both on- and off-axis emission. In addition, we will present and discuss the prospects of potential follow-up strategies with CTA., Comment: Presented at the 38th International Cosmic Ray Conference (ICRC 2023), 2023 (arXiv:2309.08219)

X-ray photons from energetic sources such as gamma-ray bursts (GRBs) can be scattered on dust clouds in the Milky Way, creating a time-evolving halo around the GRB position. X-ray observations of such halos allow the measurement of dust clouds distances in the Galaxy on which the scattering occurs. We present the first systematic comparison of the distances to scattering regions derived from GRB halos with the 3D dust distribution derived from recently published optical-to-near infrared extinction maps. GRB halos were observed around 7 sources by the Swift XRT and the XMM-Newton EPIC instruments, namely GRB 031203, GRB 050713A, GRB 050724, GRB 061019, GRB 070129, GRB 160623A and GRB 221009A. We used four 3D extinction maps that exploit photometric data from different surveys and apply diverse algorithms for the 3D mapping of extinction, and compared the X-ray halo-derived distances with the local maxima in the 3D extinction density distribution. We found that in all GRBs we can find at least one local maximum in the 3D dust extinction map that is in agreement with the dust distance measured from X-ray rings. For GRBs with multiple X-ray rings, the dust distance measurements coincide with at least 3 maxima in the extinction map for GRB 160623A, and 5 maxima for GRB 221009A. The agreement of these independent distance measurements shows that the methods used to create dust extinction maps may potentially be optimized by the X-ray halo observations from GRBs., Comment: 15 pages, 10 figures, accepted for publication in MNRAS

Galaxy clusters are expected to be dark matter (DM) reservoirs and storage rooms for the cosmic-ray protons (CRp) that accumulate along the cluster's formation history. Accordingly, they are excellent targets to search for signals of DM annihilation and decay at gamma-ray energies and are predicted to be sources of large-scale gamma-ray emission due to hadronic interactions in the intracluster medium. We estimate the sensitivity of the Cherenkov Telescope Array (CTA) to detect diffuse gamma-ray emission from the Perseus galaxy cluster. We perform a detailed spatial and spectral modelling of the expected signal for the DM and the CRp components. For each, we compute the expected CTA sensitivity. The observing strategy of Perseus is also discussed. In the absence of a diffuse signal (non-detection), CTA should constrain the CRp to thermal energy ratio within the radius $R_{500}$ down to about $X_{500}<3\times 10^{-3}$, for a spatial CRp distribution that follows the thermal gas and a CRp spectral index $\alpha_{\rm CRp}=2.3$. Under the optimistic assumption of a pure hadronic origin of the Perseus radio mini-halo and depending on the assumed magnetic field profile, CTA should measure $\alpha_{\rm CRp}$ down to about $\Delta\alpha_{\rm CRp}\simeq 0.1$ and the CRp spatial distribution with 10% precision. Regarding DM, CTA should improve the current ground-based gamma-ray DM limits from clusters observations on the velocity-averaged annihilation cross-section by a factor of up to $\sim 5$, depending on the modelling of DM halo substructure. In the case of decay of DM particles, CTA will explore a new region of the parameter space, reaching models with $\tau_{\chi}>10^{27}$s for DM masses above 1 TeV. These constraints will provide unprecedented sensitivity to the physics of both CRp acceleration and transport at cluster scale and to TeV DM particle models, especially in the decay scenario., Comment: 93 pages (including author list, appendix and references), 143 figures. Submitted to JCAP

In this article, we present Gammapy, an open-source Python package for the analysis of astronomical $\gamma$-ray data, and illustrate the functionalities of its first long-term-support release, version 1.0. Built on the modern Python scientific ecosystem, Gammapy provides a uniform platform for reducing and modeling data from different $\gamma$-ray instruments for many analysis scenarios. Gammapy complies with several well-established data conventions in high-energy astrophysics, providing serialized data products that are interoperable with other software packages. Starting from event lists and instrument response functions, Gammapy provides functionalities to reduce these data by binning them in energy and sky coordinates. Several techniques for background estimation are implemented in the package to handle the residual hadronic background affecting $\gamma$-ray instruments. After the data are binned, the flux and morphology of one or more $\gamma$-ray sources can be estimated using Poisson maximum likelihood fitting and assuming a variety of spectral, temporal, and spatial models. Estimation of flux points, likelihood profiles, and light curves is also supported. After describing the structure of the package, we show, using publicly available $\gamma$-ray data, the capabilities of Gammapy in multiple traditional and novel $\gamma$-ray analysis scenarios, such as spectral and spectro-morphological modeling and estimations of a spectral energy distribution and a light curve. Its flexibility and power are displayed in a final multi-instrument example, where datasets from different instruments, at different stages of data reduction, are simultaneously fitted with an astrophysical flux model., Comment: 26 pages, 16 figures

Since its start in 2014, the lightweight open source Python library Gammapy has come a long way to become a popular data analysis package for high-energy astrophysics. Selected as the official CTAO Science Analysis tool, it is also an approved analysis software within the H.E.S.S. and MAGIC collaborations. The first long-term version, Gammapy v1.0 was released on late 2022. It is compliant with several well-established data conventions in high-energy astrophysics, and provides serialised data products that are interoperable with other software. Event lists and instrument response functions curated within the same format from various instruments can be reduced to data binned in energy, time or spatial coordinates. Thereafter, the flux and morphology of one or more gamma-ray sources can be estimated using Poisson maximum likelihood fitting and assuming a variety of spectral, temporal and spatial models. Flux points, likelihood profiles and light curves extractions are supported. Complex user defined likelihoods and models can also be implemented. In this contribution, we will highlight the main features of Gammapy v1.0, including data reduction and analysis examples from different space and ground-based instruments, applications of various background rejection techniques, and a simultaneous fitting across multiple instruments with astrophysical models. We will also present our plans for the future, showcasing new features such as the support of different event types, unbinned likelihood analysis, spectral unfolding and transient source detections. In addition to an improved API with distributed computing for scalable analysis, enhanced support for all-sky instruments like Fermi-LAT and HAWC is foreseen., Comment: Proceedings paper presented at the 38th International Cosmic Ray Conference (ICRC2023), held 26 July - 3 August, 2023, in Nagoya, Japan

The accretion flow / jet correlation in neutron star (NS) low-mass X-ray binaries (LMXBs) is far less understood when compared to black hole (BH) LMXBs. In this paper we will present the results of a dense multi-wavelength observational campaign on the NS LMXB 4U 1820-30, including X-ray (Nicer, NuSTAR and AstroSAT) and quasi-simultaneous radio (ATCA) observations in 2022. 4U 1820-30 shows a peculiar 170 day super-orbital accretion modulation, during which the system evolves between "modes" of high and low X-ray flux. During our monitoring, the source did not show any transition to a full hard state. X-ray spectra were well described using a disc blackbody, a Comptonisation spectrum along with a Fe K emission line at 6.6 keV. Our results show that the observed X-ray flux modulation is almost entirely produced by changes in the size of the region providing seed photons for the Comptonisation spectrum. This region is large (about 15 km) in the high mode and likely coincides with the whole boundary layer, while it shrinks significantly (<10 km) in low mode. The electron temperature of the corona and the observed RMS variability in the hard X-rays also exhibit a slight increase in low mode. As the source moves from high to low mode, the radio emission due to the jet becomes about 5 fainter. These radio changes appear not to be strongly connected to the hard-to-soft transitions as in BH systems, while they seem to be connected mostly to variations observed in the boundary layer., Comment: 12 pages, 6 figures. Accepted for publication by MNRAS

The transient X-ray source MAXI J1810-222 was discovered in 2018 and has been active ever since. A long combined radio and X-ray monitoring campaign was performed with ATCA and Swift respectively. It has been proposed that MAXI J1810-222 is a relatively distant black hole X-ray binary, albeit showing a very peculiar outburst behaviour. Here, we report on the spectral study of this source making use of a large sample of NICER observations performed between 2019 February and 2020 September. We detected a strong spectral absorption feature at $\sim$1 keV, which we have characterised with a physical photoionisation model. Via a deep scan of the parameters space, we obtained evidence for a spectral-state dependent outflow, with mildly relativistic speeds. In particular, the soft and intermediate states point to a hot plasma outflowing at 0.05-0.15 $c$. This speeds rule-out thermal winds and, hence, they suggest that such outflows could be radiation pressure or (most likely) magnetically-driven winds. Our results are crucial to test current theoretical models of wind formation in X-ray binaries., Comment: 6 pages, 10 figures, accepted for publication in MNRAS Letter

In this paper we introduce a multistep generalization of the guess-and-determine or hybrid strategy for solving a system of multivariate polynomial equations over a finite field. In particular, we propose performing the exhaustive evaluation of a subset of variables stepwise, that is, by incrementing the size of such subset each time that an evaluation leads to a polynomial system which is possibly unfeasible to solve. The decision about which evaluation to extend is based on a preprocessing consisting in computing an incomplete Grobner basis after the current evaluation, which possibly generates linear polynomials that are used to eliminate further variables. If the number of remaining variables in the system is deemed still too high, the evaluation is extended and the preprocessing is iterated. Otherwise, we solve the system by a complete Grobner basis computation. Having in mind cryptanalytic applications, we present an implementation of this strategy in an algorithm called MultiSolve which is designed for polynomial systems having at most one solution. We prove explicit formulas for its complexity which are based on probability distributions that can be easily estimated by performing the proposed preprocessing on a testset of evaluations for different subsets of variables. We prove that an optimal complexity of MultiSolve is achieved by using a full multistep strategy with a maximum number of steps and in turn the standard guess-and-determine strategy, which essentially is a strategy consisting of a single step, is the worst choice. Finally, we extensively study the behaviour of MultiSolve when performing an algebraic attack on the well-known stream cipher Trivium., Comment: 29 pages. To appear in Finite Fields and Their Applications

GRB 221009A is the brightest gamma-ray burst (GRB) ever detected and occurred at low Galactic latitude. Owing to this exceptional combination, its prompt X-ray emission could be detected for weeks in the form of expanding X-ray rings produced by scattering in Galactic dust clouds. We report on the analysis of 20 rings, generated by dust at distances ranging from 0.3 to 18.6 kpc, detected during two XMM-Newton observations performed about 2 and 5 days after the GRB. By fitting the spectra of the rings with different models for the dust composition and grain size distribution, we reconstructed the spectrum of the GRB prompt emission in the 0.7-4 keV energy range as an absorbed power law with photon index 1-1.4 and absorption in the host galaxy nHz=(4.1-5.3)E21 cm-2. Taking into account the systematic uncertainties on the column density of dust contained in the clouds producing the rings, the 0.5-5 keV fluence of GRB 221009A can be constrained between 1E-3 and 7E-3 erg cm-2., Comment: 14 pages, 7 figures, submitted to ApJL

In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed by adding penalization terms in the loss function and properly choosing the corresponding scaling coefficients; however, in practice, this requires an expensive tuning phase. We show through several numerical tests that modifying the output of the neural network to exactly match the prescribed values leads to more efficient and accurate solvers. The best results are achieved by exactly enforcing the Dirichlet boundary conditions by means of an approximate distance function. We also show that variationally imposing the Dirichlet boundary conditions via Nitsche's method leads to suboptimal solvers., Comment: 22 pages, 45 figures

The ASTRI Mini-Array (MA) is an INAF project to build and operate a facility to study astronomical sources emitting at very high-energy in the TeV spectral band. The ASTRI MA consists of a group of nine innovative Imaging Atmospheric Cherenkov telescopes. The telescopes will be installed at the Teide Astronomical Observatory of the Instituto de Astrofisica de Canarias (IAC) in Tenerife (Canary Islands, Spain) on the basis of a host agreement with INAF. Thanks to its expected overall performance, better than those of current Cherenkov telescopes' arrays for energies above \sim 5 TeV and up to 100 TeV and beyond, the ASTRI MA will represent an important instrument to perform deep observations of the Galactic and extra-Galactic sky at these energies., Comment: 19 pages, 22 figures

The ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana) Mini-Array will be composed of nine imaging atmospheric Cherenkov telescopes at the Observatorio del Teide site. The array will be best suited for astrophysical observations in the 0.3-200 TeV range with an angular resolution of few arc-minutes and an energy resolution of 10-15\%. A core-science programme in the first four years will be devoted to a limited number of key targets, addressing the most important open scientific questions in the very-high energy domain. At the same time, thanks to a wide field of view of about 10 degrees, ASTRI Mini-Array will observe many additional field sources, which will constitute the basis for the long-term observatory programme that will eventually cover all the accessible sky. In this paper, we review different astrophysical Galactic environments, e.g. pulsar wind nebulae, supernova remnants, and gamma-ray binaries, and show the results from a set of ASTRI Mini-Array simulations of some of these field sources made to highlight the expected performance of the array (even at large offset angles) and the important additional observatory science that will complement the core-science program., Comment: Accepted for publication in Journal of High-Energy Astrophysics

The ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana) Project led by the Italian National Institute for Astrophysics (INAF) is developing and will deploy at the Observatorio del Teide a mini-array (ASTRI Mini-Array) composed of nine telescopes similar to the small-size dual-mirror Schwarzschild-Couder telescope (ASTRI-Horn) currently operating on the slopes of Mt. Etna in Sicily. The ASTRI Mini-Array will surpass the current Cherenkov telescope array differential sensitivity above a few tera-electronvolt (TeV), extending the energy band well above hundreds of TeV. This will allow us to explore a new window of the electromagnetic spectrum, by convolving the sensitivity performance with excellent angular and energy resolution figures. In this paper we describe the Core Science that we will address during the first four years of operation, providing examples of the breakthrough results that we will obtain when dealing with current open questions, such as the acceleration of cosmic rays, cosmology and fundamental physics and the new window, for the TeV energy band, of the time-domain astrophysics., Comment: Published in Journal of High Energy Astrophysics. 46 Figures, 7 Tables

Despite two decades of studies, it is still not clear whether ULX spectral transitions are due to stochastic variability in the wind or variations in the accretion rate or in the source geometry. The compact object is also unknown for most ULXs. In order to place constraints onto such scenarios and on the structure of the accretion disc, we studied the temporal evolution of the spectral components of the variable source NGC 55 ULX-1. Using recent and archival data obtained with the XMM-Newton satellite, we modelled the spectra with two blackbody components which we interpret as thermal emission from the inner accretion flow and the regions around or beyond the spherization radius. The luminosity-temperature (L-T) relation of each spectral component agrees with the L proportional T^4 relationship expected from a thin disc model, which suggests that the accretion rate is close to the Eddington limit. However, there are some small deviations at the highest luminosities, possibly due to an expansion of the disc and a contribution from the wind at higher accretion rates. Assuming that such deviations are due to the crossing of the Eddington or supercritical accretion rate, we estimate a compact object mass of 6-14 Msun, favouring a stellar-mass black hole as the accretor., Comment: 12 pages, 9 figures, accepted for publication in MNRAS

Ultraluminous X-ray sources (ULXs) are a class of accreting compact objects with X-ray luminosities above 10$^{39}$ erg s$^{-1}$. The average number of ULXs per galaxy is still not well constrained, especially given the uncertainty on the fraction of ULX transients. Here, we report the identification of a new transient ULX in the galaxy NGC 55 (which we label as ULX-2), thanks to recent XMM-Newton and the Neil Gehrels Swift Observatory observations. This object was previously classified as a transient X-ray source with a luminosity around a few 10$^{38}$ erg s$^{-1}$ in a 2010 XMM-Newton observation. Thanks to new and deeper observations ($\sim$ 130 ks each), we show that the source reaches a luminosity peak $>1.6 \times 10^{39}$ erg s$^{-1}$. The X-ray spectrum of ULX-2 is much softer than in previous observations and fits in the class of soft ULXs. It can be well described using a model with two thermal components, as often found in ULXs. The time scales of the X-ray variability are of the order of a month and are likely driven by small changes in the accretion rate or due to super-orbital modulations, attributed to precession of the accretion disc, which is similar to other ULXs., Comment: 6 pages, including 4 figures and 2 tables, accepted for pubblication in MNRAS

We present results from radio and X-ray observations of the X-ray transient MAXI J1810-222. The nature of the accretor in this source has not been identified. In this paper, we show results from a quasi-simultaneous radio and X-ray monitoring campaign taken with the Australia Telescope Compact Array (ATCA), the Neil Gehrels Swift observatory X-ray telescope (XRT), and the Swift Burst Alert Telescope (BAT). We also analyse the X-ray temporal behaviour using observations from the Neutron star Interior Composition Explorer (NICER). Results show a seemingly peculiar X-ray spectral evolution of MAXI J1810-222 during this outburst, where the source was initially only detected in the soft X-ray band for the early part of the outburst. Then, ~200 days after MAXI J1810-222 was first detected the hard X-ray emission increased and the source transitioned to a long-lived (~1.5 years) bright, harder X-ray state. After this hard state, MAXI J1810-222 returned back to a softer state, before fading and transitioning again to a harder state and then appearing to follow a more typical outburst decay. From the X-ray spectral and timing properties, and the source's radio behaviour, we argue that the results from this study are most consistent with MAXI J1810-222 being a relatively distant ($\gtrsim$6 kpc) black hole X-ray binary. A sufficiently large distance to source can simply explain the seemingly odd outburst evolution that was observed, where only the brightest portion of the outburst was detectable by the all-sky X-ray telescopes., Comment: 15 pages, 8 figures, 5 tables, accepted for publication in MNRAS

We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a posteriori error estimator, made of a residual-type term, a loss-function term, and data oscillation terms. We prove that the estimator is both reliable and efficient in controlling the energy norm of the error between the exact and VPINN solutions. Numerical results are in excellent agreement with the theoretical predictions., Comment: 14 pages, 3 figures

ZTF J213056.71+442046.5 is the prototype of a small class of recently discovered compact binaries composed of a white dwarf and a hot subdwarf that fills its Roche-lobe. Its orbital period of only 39 min is the shortest known for the objects in this class. Evidence for a high orbital inclination (i=86 deg) and for the presence of an accretion disk has been inferred from a detailed modeling of its optical photometric and spectroscopic data. We report the results of an XMM-Newton observation carried out on 2021 January 7. ZTF J213056.71+442046.5 was clearly detected by the Optical Monitor, which showed a periodic variability in the UV band (200-400 nm), with a light curve similar to that seen at longer wavelengths. Despite accretion on the white dwarf at an estimated rate of the order of 10^{-9} M_sun/yr, no X-rays were detected with the EPIC instrument, with a limit of ~10^{30} erg/s on the 0.2-12 keV luminosity. We discuss possible explanations for the lack of a strong X-ray emission from this system., Comment: Accepted for publication on The Astrophysical Journal

Variability is a powerful tool to investigate properties of X-ray binaries (XRB), in particular for Ultraluminous X-ray sources (ULXs) that are mainly detected in the X-ray band. For most ULXs the nature of the accretor is unknown, although a few ULXs have been confirmed to be accreting at super-Eddington rates onto a neutron star (NS). Monitoring these sources is particularly useful both to detect transients and to derive periodicities, linked to orbital and super-orbital modulations. Here we present the results of our monitoring campaign of the galaxy NGC 925, performed with the Neil Gehrels Swift Observatory. We also include archival and literature data obtained with Chandra, XMM-Newton and NuSTAR. We have studied spectra, light-curves and variability properties on days to months time-scales. All the three ULXs detected in this galaxy show flux variability. ULX-1 is one of the most luminous ULXs known, since only 10% of the ULXs exceed a luminosity of $\sim$5$\times$10$^{40}$ erg s$^{-1}$, but despite its high flux variability we found only weak spectral variability. We classify it as in a hard ultraluminous regime of super-Eddington accretion. ULX-2 and ULX-3 are less luminous but also variable in flux and possibly also in spectral shape. We classify them as in between the hard and the soft ultraluminous regimes. ULX-3 is a transient source: by applying a Lomb-Scargle algorithm we derive a periodicity of $\sim$ 126 d, which could be associated with an orbital or super-orbital origin., Comment: 14 pages, 7 figures, Accepted for publication in MNRAS

We have studied the unusual time variability of an ultraluminous X-ray source in M 101, 4XMM J140314.2$+$541806 (henceforth, J1403), using Chandra and XMM-Newton data. Over the last two decades, J1403 has shown short-duration outbursts with an X-ray luminosity $\sim1-3 \times 10^{39}$ erg s$^{-1}$, and longer intervals at luminosities $\sim0.5-1 \times 10^{38}$ erg s$^{-1}$. The bimodal behaviour and fast outburst evolution (sometimes only a few days) are more consistent with an accretor/propeller scenario for a neutron star than with the canonical outburst cycles of stellar-mass black holes. If this scenario is correct, the luminosities in the accretor and propeller states suggest a fast spin ($P \approx$ 5 ms) and a low surface magnetic field ($B \sim 10^{10}$ G), despite our identification of J1403 as a high-mass X-ray binary. The most striking property of J1403 is the presence of strong $\sim$600-s quasi periodic oscillations (QPOs), mostly around frequencies of $\approx 1.3-1.8$ mHz, found at several epochs during the ultraluminous regime. We illustrate the properties of such QPOs, in particular their frequency and amplitude changes between and within observations, with a variety of techniques (Fast Fourier Transforms, Lomb-Scargle periodograms, weighted wavelet Z-transform analysis). The QPO frequency range $<$10 mHz is an almost unexplored regime in X-ray binaries and ultraluminous X-ray sources. We compare our findings with the (few) examples of very low frequency variability found in other accreting sources, and discuss possible explanations (Lense-Thirring precession of the inner flow or outflow; radiation pressure limit-cycle instability; marginally stable He burning on the neutron star surface)., Comment: 23 pages, 29 figures, 5 tables. Accepted for publication in MNRAS

We model the multiwavelength properties of binaries accreting at super-critical rates with the aim to better understand the observational properties of Ultra-luminous X-ray Sources (ULXs). We calculate an extended grid of binary systems which evolve through Roche Lobe Overflow and undergo case A mass transfer from massive donors (up to 25 Msol) onto massive Black Holes (BH) (up to 100 Msol). Angular momentum loss with the ejection of mass through an outflow is incorporated. We apply our super-Eddington accretion model to these systems, computing their evolutionary tracks on the color-magnitude diagram (CMD) for the Johnson and HST photometric systems. We found that the tracks occupy specific positions on the CMD depending on the evolutionary stage of the donor and of the binary. Moreover, their shapes are similar, regardless the BH mass. More massive BHs lead to more luminous tracks. We additionally compute their optical-through-X-ray Spectral Energy Distribution (SED) considering the effects of a Comptonizing corona which surrounds the innermost regions of the disc. We apply our model to four ULXs: NGC4559 X-7, NGC 5204 X-1, Holmberg II X-1 and NGC 5907 ULX-2. We found that accretion onto BHs with mass in the range 35-55 Msol is consistent with to the observational properties of these sources. We finally explore and discuss the possibility to extend our model also to ULXs powered by accreting Pulsars (PULXs)., Comment: 20 pages, 14 figures, Accepted for publication in MNRAS

In this work we analyze how quadrature rules of different precisions and piecewise polynomial test functions of different degrees affect the convergence rate of Variational Physics Informed Neural Networks (VPINN) with respect to mesh refinement, while solving elliptic boundary-value problems. Using a Petrov-Galerkin framework relying on an inf-sup condition, we derive an a priori error estimate in the energy norm between the exact solution and a suitable high-order piecewise interpolant of a computed neural network. Numerical experiments confirm the theoretical predictions and highlight the importance of the inf-sup condition. Our results suggest, somehow counterintuitively, that for smooth solutions the best strategy to achieve a high decay rate of the error consists in choosing test functions of the lowest polynomial degree, while using quadrature formulas of suitably high precision., Comment: 20 pages, 22 figures