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HESS J1832−093 is a member of the rare class of gamma-ray binaries, as recently confirmed by the detection of orbitally modulated X-ray and gamma-ray emission with a period of ∼86 d. The spectral type of the massive companion star has been difficult to retrieve as there is no optical counterpart, but the system is coincident with a near-infrared source. Previous results have shown that the infrared counterpart is consistent with an O or B-type star, but a clear classification is still lacking. We observed the counterpart twice, in 2019 and 2021, with the X-Shooter spectrograph operating on the Very Large Telescope (VLT). The obtained spectra classify the counterpart as an O6 V-type star. We estimate a distance to the source of 6.7 ± 0.5 kpc, although this estimate can be severely affected by the high extinction towards the source. This new O6 V classification for the companion star in HESS J1832−093 provides further support to an apparent grouping around a given spectral type for all discovered gamma-ray binaries that contain an O-type star. This may be due to the interplay between the initial mass function and the wind momentum–luminosity relation.

We present the first 3D fully coupled magneto-thermal simulations of neutron stars (including the most realistic background structure and microphysical ingredients so far) applied to a very complex initial magnetic field topology in the crust, similar to what recently obtained by proto-neutron star dynamo simulations. In such configurations, most of the energy is stored in the toroidal field, while the dipolar component is a few percent of the mean magnetic field. This initial feature is maintained during the long-term evolution (∼106 yr), since the Hall term favours a direct cascade (compensating for Ohmic dissipation) rather than a strong inverse cascade, for such an initial field topology. The surface dipolar component, responsible for the dominant electromagnetic spin-down torque, does not show any increase in time, when starting from this complex initial topology. This is at contrast with the timing properties of young pulsars and magnetars which point to higher values of the surface dipolar fields. A possibility is that the deep-seated magnetic field (currents in the core) is able to self-organize in large scales (during the collapse or in the early life of a neutron star). Alternatively, the dipolar field might be lower than is usually thought, with magnetosphere substantially contributing to the observed high spin-down, via e.g., strong winds or strong coronal magnetic loops, which can also provide a natural explanation to the tiny surface hotspots inferred from X-ray data.

Serving as the progenitors of electromagnetic and gravitational-wave transients, massive stars have received renewed interest in recent years. However, many aspects of their birth and evolution remain opaque, particularly in the context of binary interactions. The centre of our Galaxy hosts a rich cohort of very massive stars, which appear to play a prominent role in the ecology of the region. In this paper, we investigate the binary properties of the Arches cluster, which is thought to host a large number of very massive stars. A combination of multi-epoch near-IR spectroscopy and photometry was utilized to identify binaries. 13 from 36 cluster members meet our criteria to be classed as RV variable. Combining the spectroscopic data with archival radio and X-ray observations – to detect colliding wind systems – provides a lower limit to the binary fraction of ∼43 per cent; increasing to ≳50 per cent for the O-type hypergiants and WNLha. Dynamical and evolutionary masses reveal the primaries to be uniformly massive (⁠≳50M⊙⁠). Where available, orbital analysis reveals a number of short period, highly eccentric binaries, which appear to be pre-interaction systems. Such systems are X-ray luminous, with 80 per cent above an empirical bound of (Lx/Lbol) ∼ 10−7 and their orbital configurations suggest formation and evolution via a single-star channel; however, we cannot exclude a binary formation channel for a subset. Qualitative comparison to surveys of lower mass OB-type stars confirms that the trend to an extreme binary fraction (≥60 per cent) extends to the most massive stars currently forming in the local Universe.

Using Physics-Informed Neural Networks (PINNs) to solve a specific boundary value problem is becoming more popular as an alternative to traditional methods. However, depending on the specific problem, they could be computationally expensive and potentially less accurate. The functionality of PINNs for real-world physical problems can significantly improve if they become more flexible and adaptable. To address this, our work explores the idea of training a PINN for general boundary conditions and source terms expressed through a limited number of coefficients, introduced as additional inputs in the network. Although this process increases the dimensionality and is computationally costly, using the trained network to evaluate new general solutions is much faster. Our results indicate that PINN solutions are relatively accurate, reliable, and well-behaved. We applied this idea to the astrophysical scenario of the magnetic field evolution in the interior of a neutron star connected to a force-free magnetosphere. Solving this problem through a global simulation in the entire domain is expensive due to the elliptic solver’s needs for the exterior solution. The computational cost with a PINN was more than an order of magnitude lower than the similar case solved with a finite difference scheme, arguably at the cost of accuracy. These results pave the way for the future extension to 3D of this (or a similar) problem, where generalised boundary conditions are very costly to implement.

We carefully develop the framework required to model the dynamical tidal response of a spinning neutron star in an inspiralling binary system, in the context of Newtonian gravity, making sure to include all relevant details and connections to the existing literature. The tidal perturbation is decomposed in terms of the normal oscillation modes, used to derive an expression for the effective Love number which is valid for any rotation rate. In contrast to previous work on the problem, our analysis highlights subtle issues relating to the orthogonality condition required for the mode-sum representation of the dynamical tide and shows how the prograde and retrograde modes combine to provide the overall tidal response. Utilising a slow-rotation expansion, we show that the dynamical tide (the effective Love number) is corrected at first order in rotation, whereas in the case of the static tide (the static Love number) the rotational corrections do not enter until second order.

In this study, Physics-Informed Neural Networks (PINNs) are skilfully applied to explore a diverse range of pulsar magnetospheric models, specifically focusing on axisymmetric cases. The study successfully reproduced various axisymmetric models found in the literature, including those with non-dipolar configurations, while effectively characterizing current sheet features. Energy losses in all studied models were found to exhibit reasonable similarity, differing by no more than a factor of three from the classical dipole case. This research lays the groundwork for a reliable elliptic Partial Differential Equation solver tailored for astrophysical problems. Based on these findings, we foresee that the utilization of PINNs will become the most efficient approach in modelling three-dimensional magnetospheres. This methodology shows significant potential and facilitates an effortless generalization, contributing to the advancement of our understanding of pulsar magnetospheres.

WEAVE, the new wide-field, massively multiplexed spectroscopic survey facility for the William Herschel Telescope, will see first light in late 2022. WEAVE comprises a new 2-degree field-of-view prime-focus corrector system, a nearly 1000-multiplex fibre positioner, 20 individually deployable ‘mini’ integral field units (IFUs), and a single large IFU. These fibre systems feed a dual-beam spectrograph covering the wavelength range 366−959 nm at R ∼ 5000, or two shorter ranges at R ∼ 20 000. After summarising the design and implementation of WEAVE and its data systems, we present the organisation, science drivers and design of a five- to seven-year programme of eight individual surveys to: (i) study our Galaxy’s origins by completing Gaia’s phase-space information, providing metallicities to its limiting magnitude for ∼3 million stars and detailed abundances for ∼1.5 million brighter field and open-cluster stars; (ii) survey ∼0.4 million Galactic-plane OBA stars, young stellar objects and nearby gas to understand the evolution of young stars and their environments; (iii) perform an extensive spectral survey of white dwarfs; (iv) survey ∼400 neutral-hydrogen-selected galaxies with the IFUs; (v) study properties and kinematics of stellar populations and ionised gas in z < 0.5 cluster galaxies; (vi) survey stellar populations and kinematics in ∼25 000 field galaxies at 0.3 ≲ z ≲ 0.7; (vii) study the cosmic evolution of accretion and star formation using >1 million spectra of LOFAR-selected radio sources; (viii) trace structures using intergalactic/circumgalactic gas at z > 2. Finally, we describe the WEAVE Operational Rehearsals using the WEAVE Simulator.

Neutron stars cool down during their lifetime through the combination of neutrino emission from the interior and photon cooling from the surface. Strongly magnetised neutron stars, called magnetars, are no exception, but the effect of their strong fields adds further complexities to the cooling theory. Besides other factors, modelling the outermost hundred meters (the envelope) plays a crucial role in predicting their surface temperatures. In this letter, we revisit the influence of envelopes on the cooling properties of neutron stars, with special focus on the critical effects of the magnetic field. We explore how our understanding of the relation between the internal and surface temperatures has evolved over the past two decades, and how different assumptions about the neutron star envelope and field topology lead to radically different conclusions on the surface temperature and its cooling with age. In particular, we find that relatively old magnetars with core-threading magnetic fields are actually much cooler than arotation-powered pulsar of the same age. This is at variance with what is typically observed in crustal-confined models. Our results have important implications for the estimates of the X-ray luminosities of aged magnetars, and the subsequent population study of the different neutron star classes.

We aim to identify and characterise binary systems containing red supergiant (RSG) stars in the Small Magellanic Cloud (SMC) using a newly available ultraviolet (UV) point source catalogue obtained using the Ultraviolet Imaging Telescope (UVIT) on board AstroSat. We select a sample of 560 SMC RSGs based on photometric and spectroscopic observations at optical wavelengths and cross-match this with the far-UV point source catalogue using the UVIT F172M filter, finding 88 matches down to mF172M = 20.3 ABmag, which we interpret as hot companions to the RSGs. Stellar parameters (luminosities, effective temperatures and masses) for both components in all 88 binary systems are determined and we find mass distributions in the ranges 6.1 < M/M⊙ < 22.3 for RSGs and 3.7

The long-term evolution of the internal, strong magnetic fields of neutron stars needs a specific numerical modeling. The diversity of the observed phenomenology of neutron stars indicates that their magnetic topology is rather complex and three-dimensional simulations are required, for example, to explain the observed bursting mechanisms and the creation of surface hotspots. We present MATINS, a new three dimensions numerical code for magneto-thermal evolution in neutron stars, based on a finite-volume scheme that employs the cubed-sphere system of coordinates. In this first work, we focus on the crustal magnetic evolution, with the inclusion of realistic calculations for the neutron star structure, composition and electrical conductivity assuming a simple temperature evolution profile. MATINS follows the evolution of strong fields (1014 − 1015 Gauss) with complex non-axisymmetric topologies and dominant Hall-drift terms, and it is suitable for handling sharp current sheets. After introducing the technical description of our approach and some tests, we present long-term simulations of the non-linear field evolution in realistic neutron star crusts. The results show how the non-axisymmetric Hall cascade redistributes the energy over different spatial scales. Following the exploration of different initial topologies, we conclude that during a few tens of kyr, an equipartition of energy between the poloidal and toroidal components happens at small-scales. However, the magnetic field keeps a strong memory of the initial large-scales, which are much harder to be restructured or created. This indicates that large-scale configuration attained during the neutron star formation is crucial to determine the field topology at any evolution stage.

Magnetars exhibit a variety of transient high-energy phenomena in the form of bursts, outbursts, and giant flares. It is a common belief that these events originate in the sudden release of magnetic energy due to the rearrangement of a twisted magnetic field. We present global models of a 3D force-free (FF) non-linear twisted magnetar magnetosphere. We solve the FF equations following the Grad–Rubin approach in a compactified spherical domain. Appropriate boundary conditions are imposed at the surface of the star for the current distribution and the magnetic field. Our implementation is tested by reproducing various known analytical as well as axisymmetric numerical results. We then proceed to study general 3D models with non-axisymmetric current distributions, such as fields with localized twists that resemble hotspots at the surface of the star, and we examine characteristic quantities such as energy, helicity, and twist. Finally, we discuss implications on the available energy budget, the surface temperature, and the diffusion time-scale, which can be associated with observations.

After 15 yr, in late 2018, the magnetar XTE J1810−197 underwent a second recorded X-ray outburst event and reactivated as a radio pulsar. We initiated an X-ray monitoring campaign to follow the timing and spectral evolution of the magnetar as its flux decays using Swift, XMM–Newton, NuSTAR, and NICER observations. During the year-long campaign, the magnetar reproduced similar behaviour to that found for the first outburst, with a factor of 2 change in its spin-down rate from ∼7.2 × 10−12 to ∼1.5 × 10−11 s s−1 after two months. Unique to this outburst, we confirm the peculiar energy-dependent phase shift of the pulse profile. Following the initial outburst, the spectrum of XTE J1810−197 is well modelled by multiple blackbody components corresponding to a pair of non-concentric, hot thermal caps surrounded by a cooler one, superposed to the colder star surface. We model the energy-dependent pulse profile to constrain the viewing and surface emission geometry and find that the overall geometry of XTE J1810−197 has likely evolved relative to that found for the 2003 event.

The characterization of multiplicity of high-mass stars is of fundamental importance to understand their evolution, the diversity of observed core-collapse supernovae and the formation of gravitational wave progenitor systems. Despite that, until recently, one of the final phases of massive star evolution – the cool supergiant phase – has received comparatively little attention. In this study, we aim to explore the multiplicity among the cool supergiant (CSG) population in the Large and Small Magellanic Clouds (LMC and SMC, respectively). To do this we compile extensive archival radial velocity (RV) measurements for over 1000 CSGs from the LMC and SMC, spanning a baseline of over 40 yr. By statistically correcting the RV measurements of each stellar catalogue to the Gaia DR2 reference frame we are able to effectively compare these diverse observations. We identify 45 CSGs where RV variations cannot be explained through intrinsic variability, and are hence considered binary systems. We obtain a minimum binary fraction of 15±4 per cent for the SMC and of 14±5 per cent for the LMC, restricting our sample to objects with at least 6 and 5 observational epochs, respectively. Combining these results, we determine a minimum binary fraction of 15±3 per cent for CSGs. These results are in good agreement with previous results which apply a correction to account for observational biases. These results add strength to the hypothesis that the binary fraction of CSGs is significantly lower than their main-sequence counterparts. Going forward, we stress the need for long-baseline multi-epoch spectroscopic surveys to cover the full parameter space of CSG binary systems.

Obscuration and confusion conspire to limit our knowledge of the inner Milky Way. Even at moderate distances, the identification of stellar systems becomes compounded by the extremely high density of background sources. Here we provide a very revealing example of these complications by unveiling a large, massive, young cluster in the Sagittarius arm that has escaped detection until now despite containing more than 30 stars brighter than G = 13. By combining Gaia DR2 astrometry, Gaia and 2MASS photometry and optical spectroscopy, we find that the new cluster, which we name Valparaiso 1, located at ∼2.3 kpc, is about 75 Ma old and includes a large complement of evolved stars, among which we highlight the 4 d classical Cepheid CM Sct and an M-type giant that probably represents the first detection of an AGB star in a Galactic young open cluster. Although strong differential reddening renders accurate parameter determination unfeasible with the current dataset, direct comparison to clusters of similar age suggests that Valparaiso 1 was born as one of the most massive clusters in the Solar Neighbourhood, with an initial mass close to 104 M⊙.

The presence of massive stars (MSs) in the region close to the Galactic Centre (GC) poses several questions about their origin. The harsh environment of the GC favours specific formation scenarios, each of which should imprint characteristic kinematic features on the MSs. We present a 2D kinematic analysis of MSs in a GC region surrounding Sgr A* based on high-precision proper motions obtained with the Hubble Space Telescope. Thanks to a careful data reduction, well-measured bright stars in our proper-motion catalogues have errors better than 0.5 mas yr−1. We discuss the absolute motion of the MSs in the field and their motion relative to Sgr A*, the Arches, and the Quintuplet. For the majority of the MSs, we rule out any distance further than 3–4 kpc from Sgr A* using only kinematic arguments. If their membership to the GC is confirmed, most of the isolated MSs are likely not associated with either the Arches or Quintuplet clusters or Sgr A*. Only a few MSs have proper motions, suggesting that they are likely members of the Arches cluster, in agreement with previous spectroscopic results. Line-of-sight radial velocities and distances are required to shed further light on the origin of most of these massive objects. We also present an analysis of other fast-moving objects in the GC region, finding no clear excess of high-velocity escaping stars. We make our astro-photometric catalogues publicly available.

MEGARA is an optical integral field and multi-object fibre-based spectrograph for the 10.4 m Gran Telescopio CANARIAS that offers medium-to-high spectral resolutions (FWHM) of R ≃ 6000, 12 000, 20 000. Commissioned at the telescope in 2017, it started operation as a common-user instrument in 2018. We are creating an instrument-oriented empirical spectral library from MEGARA-GTC stars observations, MEGASTAR, crucial for the correct interpretation of MEGARA data. This piece of work describes the content of the first release of MEGASTAR, formed by the spectra of 414 stars observed with R ≃ 20 000 in the spectral intervals 6420–6790 Å and 8370–8885 Å, and obtained with a continuum average signal-to-noise ratio around 260. We describe the release sample, the observations, the data reduction procedure and the MEGASTAR data base. Additionally, we include in Appendix A an atlas with the complete set of 838 spectra of this first release of the MEGASTAR catalogue.

Classical Cepheids represent the first step of the distance scale ladder. Claims of tension between the locally calculated Hubble constant and the values deduced from Planck’s results have sparked new interest in these distance calibrators. Cluster membership provides an independent distance measurement, as well as astrophysical context for studies of their stellar properties. Here, we report the discovery of a young open cluster in the vicinity of SV Vul, one of the most luminous Cepheids known in the Milky Way. Gaia DR2 data show that SV Vul is a clear astrometric and photometric member of the new cluster, which we name Alicante 13. Although dispersed, Alicante 13 is moderately well populated, and contains three other luminous stars, one early-A bright giant and two low-luminosity red supergiants. The cluster is about 30 Ma old at a nominal distance of 2.5 kpc. With this age, SV Vul should have a mass around 10 M⊙, in good accordance with its luminosity, close to the highest luminosity for Cepheids allowed by recent stellar models.

We present 3D force-free electrodynamics simulations of magnetar magnetospheres that demonstrate the instability of certain degenerate, high energy equilibrium solutions of the Grad–Shafranov equation. This result indicates the existence of an unstable branch of twisted magnetospheric solutions and allows us to formulate an instability criterion. The rearrangement of magnetic field lines as a consequence of this instability triggers the dissipation of up to 30 per cent of the magnetospheric energy on a thin layer above the magnetar surface. During this process, we predict an increase of the mechanical stresses on to the stellar crust, which can potentially result in a global mechanical failure of a significant fraction of it. We find that the estimated energy release and the emission properties are compatible with the observed giant flare events. The newly identified instability is a candidate for recurrent energy dissipation, which could explain part of the phenomenology observed in magnetars.

In this letter, we present the first 3D force-free general relativity simulations of the magnetosphere dynamics related to the magnetar outburst/flare phenomenology. Starting from an initial dipole configuration, we adiabatically increase the helicity by twisting the footprints of a spot on the stellar surface and follow the succession of quasi-equilibrium states until a critical twist is reached. Twisting beyond that point triggers instabilities that results in the rapid expansion of magnetic field lines, followed by reconnection, as observed in previous axi-symmetric simulations. If the injection of magnetic helicity goes on, the process is recurrent, periodically releasing a similar amount of energy, of the order of a few per cent of the total magnetic energy. From our current distribution, we estimate the local temperature assuming that dissipation occurs mainly in the highly resistive outermost layer of the neutron star. We find that the temperature smoothly increases with injected twist, being larger for spots located in the tropical regions than in polar regions, and rather independent of their sizes. After the injection of helicity ceases, the magnetosphere relaxes to a new stable state, in which the persistent currents maintain the footprints area slightly hotter than before the onset of the instability.

After two major outbursts in 2006 and 2011, on 2017 May 16 the magnetar CXOU J164710.2−455216, hosted within the massive star cluster Westerlund I, emitted a short (∼20 ms) burst, which marked the onset of a new active phase. We started a long-term monitoring campaign with Swift (45 observations), Chandra (five observations), and NuSTAR (four observations) from the activation until 2018 April. During the campaign, Swift Burst Alert Telescope (BAT) registered the occurrence of multiple bursts, accompanied by two other enhancements of the X-ray persistent flux. The long time span covered by our observations allowed us to study the spectral and the timing evolution of the source. After ∼11 months since the 2017 May outburst onset, the observed flux was ∼15 times higher than its historical minimum level and a factor of ∼3 higher than the level reached after the 2006 outburst. This suggests that the crust has not fully relaxed to the quiescent level, or that the source quiescent level has changed following the multiple outburst activities in the past 10 yr or so. This is another case of multiple outbursts from the same source on a yearly time-scale, a somehow recently discovered behaviour in magnetars.

We study the coupling of the force-free magnetosphere to the long-term internal evolution of a magnetar. We allow the relation between the poloidal and toroidal stream functions – that characterizes the magnetosphere – to evolve freely without constraining its particular form. We find that, on time-scales of the order of kyr, the energy stored in the magnetosphere gradually increases, as the toroidal region grows and the field lines expand outwards. This continues until a critical point is reached beyond which force-free solutions for the magnetosphere can no longer be constructed, likely leading to some large-scale magnetospheric reorganization. The energy budget available for such events can be as high as several 1045 erg for fields of 1014 G. Subsequently, starting from the new initial conditions, the evolution proceeds in a similar manner. The time-scale to reach the critical point scales inversely with the magnetic field amplitude. Allowing currents to pass through the last few metres below the surface, where the magnetic diffusivity is orders of magnitude larger than in the crust, should give rise to a considerable amount of energy deposition through Joule heating. We estimate that the effective surface temperature could increase locally from ∼0.1 keV to ∼0.3-0.6 keV, in good agreement with observations. Similarly, the power input from the interior into the magnetosphere could be as high as 1035-1036 erg s−1, which is consistent with peak luminosities observed during magnetar outbursts. Therefore, a detailed treatment of currents flowing through the envelope may be needed to explain the thermal properties of magnetars.

As part of a wider investigation of evolved massive stars in Galactic open clusters, we have spectroscopically identified three candidate classical Cepheids in the little-studied clusters Berkeley 51, Berkeley 55, and NGC 6603. Using new multi-epoch photometry, we confirm that Be 51 #162 and Be 55 #107 are bona fide Cepheids, with pulsation periods of 9.83±0.01 d and 5.850±0.005 d respectively, while NGC 6603 star W2249 does not show significant photometric variability. Using the period–luminosity relationship for Cepheid variables, we determine a distance to Be 51 of 5.3+1.0−0.8 kpc and an age of 44+9−8 Myr, placing it in a sparsely attested region of the Perseus arm. For Be 55, we find a distance of 2.2±0.3 kpc and age of 63+12−11 Myr, locating the cluster in the Local arm. Taken together with our recent discovery of a long-period Cepheid in the starburst cluster VdBH222, these represent an important increase in the number of young, massive Cepheids known in Galactic open clusters.We also consider new Gaia (data release 2) parallaxes and proper motions for members of Be 51 and Be 55; the uncertainties on the parallaxes do not allow us to refine our distance estimates to these clusters, but the well-constrained proper motion measurements furnish further confirmation of cluster membership. However, future final Gaia parallaxes for such objects should provide valuable independent distance measurements, improving the calibration of the period–luminosity relationship, with implications for the distance ladder out to cosmological scales.

We present the results of the systematic study of all magnetar outbursts observed to date, through a reanalysis of data acquired in about 1100 X-ray observations. We track the temporal evolution of the outbursts’ soft X-ray spectral properties and the luminosities of the single spectral components as well as of the total emission. We model empirically all outburst light curves, and estimate the characteristic decay time-scales as well as the energetics involved. We investigate the link between different parameters (e.g. the luminosity at the peak of the outburst and in quiescence, the maximum luminosity increase, the decay time-scale and energy of the outburst, the neutron star surface dipolar magnetic field and characteristic age, etc.), and unveil several correlations among these quantities. We discuss our results in the context of the internal crustal heating and twisted bundle models for magnetar outbursts. This study is complemented by the Magnetar Outburst Online Catalogue (http://magnetars.ice.csic.es), an interactive data base where the user can plot any combination of the parameters derived in this work, and download all data.

We extend our previous study of equilibrium solutions of non-rotating force-free magnetospheres of neutron stars. We show that multiple solutions exist for the same sets of parameters, implying that the solutions are degenerate. We are able to obtain configurations with disconnected field lines, however, in nearly all cases these correspond to degenerate higher energy solutions. We carry out a wide parametric search in order to understand the properties of the solutions. We confirm our previous results that the lower energy solutions have up to ∼ 25 per cent more energy than the vacuum case, helicity of the order of ∼5 (in some defined units), maximum twist of ∼1.5 rad and a dipole strength that is up to ∼ 40 per cent larger than the vacuum dipole. Including the degenerate higher energy solutions allows for larger theoretical limits of up to ∼ 80 per cent more energy with respect to the vacuum case, helicity of the order of ∼8 and a dipole strength that can now be up to four times that of the vacuum dipole, while the twist can be significantly larger and even diverge for configurations with disconnected domains. The higher energy solutions are probably unstable, therefore, it is unlikely that such magnetospheres exist under normal conditions in magnetars and high magnetic field pulsars.

Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the protoneutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS–shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation spectrum of the PNS, obtained through linear perturbation analysis in general relativity of a background physical system, with information from the gravitational-wave spectrum of the corresponding non-linear, core-collapse simulation. Using results from the simulation of the collapse of a 35 M⊙ pre-supernova progenitor we show that both types of spectra are indeed related and we are able to identify the modes of oscillation of the PNS, namely g-modes, p-modes, hybrid modes, and standing accretion shock instability (SASI) modes, obtaining a remarkably close correspondence with the time–frequency distribution of the gravitational-wave modes. The analysis presented in this paper provides a proof of concept that asteroseismology is indeed possible in the core-collapse scenario, and it may serve as a basis for future work on PNS parameter inference based on gravitational-wave observations.

We study the long-term quasi-steady evolution of the force-free magnetosphere of a magnetar coupled to its internal magnetic field. We find that magnetospheric currents can be maintained on long time-scales of the order of thousands of years. Meanwhile, the energy, helicity and twist stored in the magnetosphere all gradually increase over the course of this evolution, until a critical point is reached, beyond which a force-free magnetosphere cannot be constructed. At this point, some large-scale magnetospheric rearrangement, possibly resulting in an outburst or a flare, must occur, releasing a large fraction of the stored energy, helicity and twist. After that, the quasi-steady evolution should continue in a similar manner from the new initial conditions. The time-scale for reaching this critical point depends on the overall magnetic field strength and on the relative fraction of the toroidal field. The energy stored in the force-free magnetosphere is found to be up to ∼30 per cent larger than the corresponding vacuum energy. This implies that for a 1014 G field at the pole, the energy budget available for fast magnetospheric events is of the order of a few 1044 erg. The spin-down rate is estimated to increase by up to ∼60 per cent, since the dipole content in the magnetosphere is enhanced by the currents present there. A rough estimate of the braking index n reveals that it is systematically n < 3 for the most part of the evolution, consistent with actual measurements for pulsars and early estimates for several magnetars.

We report on 3.5 yr of Chandra monitoring of the Galactic Centre magnetar SGR J1745−2900 since its outburst onset in 2013 April. The magnetar spin-down has shown at least two episodes of period derivative increases so far, and it has slowed down regularly in the past year or so. We observed a slightly increasing trend in the time evolution of the pulsed fraction, up to ∼55 per cent in the most recent observations. SGR J1745−2900 has not reached the quiescent level yet, and so far the overall outburst evolution can be interpreted in terms of a cooling hot region on the star surface. We discuss possible scenarios, showing in particular how the presence of a shrinking hotspot in this source is hardly reconcilable with internal crustal cooling and favours the untwisting bundle model for this outburst. Moreover, we also show how the emission from a single uniform hotspot is incompatible with the observed pulsed fraction evolution for any pair of viewing angles, suggesting an anisotropic emission pattern.

We revisit the various approximations employed to study the long-term evolution of the magnetic field in neutron star cores and discuss their limitations and possible improvements. A recent controversy on the correct form of the induction equation and the relevant evolution time-scale in superconducting neutron star cores is addressed and clarified. We show that this ambiguity in the estimation of time-scales arises as a consequence of nominally large terms that appear in the induction equation, but which are, in fact, mostly irrotational. This subtlety leads to a discrepancy by many orders of magnitude when velocity fields are absent or ignored. Even when internal velocity fields are accounted for, only the solenoidal part of the electric field contributes to the induction equation, which can be substantially smaller than the irrotational part. We also argue that stationary velocity fields must be incorporated in the slow evolution of the magnetic field as the next level of approximation.

We study the torsional magneto-elastic oscillations of relativistic superfluid magnetars and explore the effects of a phase transition in the crust–core interface (nuclear pasta) which results in a weaker elastic response. Exploring various models with different extension of nuclear pasta phases, we find that the differences in the oscillation spectrum present in purely elastic modes (weak magnetic field) are smeared out with increasing strength of the magnetic field. For magnetar conditions, the main characteristic and features of models without nuclear pasta are preserved. We find, in general, two classes of magneto-elastic oscillations which exhibit a different oscillation pattern. For Bp < 4 × 1014 G, the spectrum is characterized by the turning points and edges of the continuum which are mostly confined into the star's core, and have no constant phase. Increasing the magnetic field, we find, in addition, several magneto-elastic oscillations which reach the surface and have an angular structure similar to crustal modes. These global magneto-elastic oscillations show a constant phase and become dominant when Bp > 5 × 1014 G. We do not find any evidence of fundamental pure crustal modes in the low-frequency range (below 200 Hz) for Bp ≥ 1014 G.

We report on the discovery of a new member of the magnetar class, SGR J1935+2154, and on its timing and spectral properties measured by an extensive observational campaign carried out between 2014 July and 2015 March with Chandra and XMM–Newton (11 pointings). We discovered the spin period of SGR J1935+2154 through the detection of coherent pulsations at a period of about 3.24 s. The magnetar is slowing down at a rate of P˙=1.43(1)×10−11 s s−1 and with a decreasing trend due to a negative P¨ of −3.5(7) × 10−19 s s−2. This implies a surface dipolar magnetic field strength of ∼2.2 × 1014 G, a characteristic age of about 3.6 kyr and a spin-down luminosity Lsd ∼1.7 × 1034 erg s−1. The source spectrum is well modelled by a blackbody with temperature of about 500 eV plus a power-law component with photon index of about 2. The source showed a moderate long-term variability, with a flux decay of about 25 per cent during the first four months since its discovery, and a re-brightening of the same amount during the second four months. The X-ray data were also used to study the source environment. In particular, we discovered a diffuse emission extending on spatial scales from about 1 arcsec up to at least 1 arcmin around SGR J1935+2154 both in Chandra and XMM–Newton data. This component is constant in flux (at least within uncertainties) and its spectrum is well modelled by a power-law spectrum steeper than that of the pulsar. Though a scattering halo origin seems to be more probable we cannot exclude that part, or all, of the diffuse emission is due to a pulsar wind nebula.

The observation of several neutron stars in the centre of supernova remnants and with significantly lower values of the dipolar magnetic field than the average radio-pulsar population has motivated a lively debate about their formation and origin, with controversial interpretations. A possible explanation requires the slow rotation of the protoneutron star at birth, which is unable to amplify its magnetic field to typical pulsar levels. An alternative possibility, the hidden magnetic field scenario, considers the accretion of the fallback of the supernova debris on to the neutron star as responsible for the submergence (or screening) of the field and its apparently low value. In this paper, we study under which conditions the magnetic field of a neutron star can be buried into the crust due to an accreting, conducting fluid. For this purpose, we consider a spherically symmetric calculation in general relativity to estimate the balance between the incoming accretion flow and the magnetosphere. Our study analyses several models with different specific entropy, composition, and neutron star masses. The main conclusion of our work is that typical magnetic fields of a few times 1012 G can be buried by accreting only 10−3–10−2 M⊙, a relatively modest amount of mass. In view of this result, the central compact object scenario should not be considered unusual, and we predict that anomalously weak magnetic fields should be common in very young (< few kyr) neutron stars.

We study the timing and spectral properties of the low-magnetic field, transient magnetar SWIFT J1822.3−1606 as it approached quiescence. We coherently phase-connect the observations over a time-span of ∼500 d since the discovery of SWIFT J1822.3−1606 following the Swift-Burst Alert Telescope (BAT) trigger on 2011 July 14, and carried out a detailed pulse phase spectroscopy along the outburst decay. We follow the spectral evolution of different pulse phase intervals and find a phase and energy-variable spectral feature, which we interpret as proton cyclotron resonant scattering of soft photon from currents circulating in a strong (≳1014 G) small-scale component of the magnetic field near the neutron star surface, superimposed to the much weaker (∼3 × 1013 G) magnetic field. We discuss also the implications of the pulse-resolved spectral analysis for the emission regions on the surface of the cooling magnetar.

The study of long-term evolution of neutron star (NS) magnetic fields is key to understanding the rich diversity of NS observations, and to unifying their nature despite the different emission mechanisms and observed properties. Such studies in principle permit a deeper understanding of the most important parameters driving their apparent variety, e.g. radio pulsars, magnetars, X-ray dim isolated NSs, gamma-ray pulsars. We describe, for the first time, the results from self-consistent magnetothermal simulations considering not only the effects of the Hall-driven field dissipation in the crust, but also adding a complete set of proposed driving forces in a superconducting core. We emphasize how each of these core-field processes drive magnetic evolution and affect observables, and show that when all forces are considered together in vectorial form, the net expulsion of core magnetic flux is negligible, and will have no observable effect in the crust (consequently in the observed surface emission) on megayear time-scales. Our new simulations suggest that strong magnetic fields in NS cores (and the signatures on the NS surface) will persist long after the crustal magnetic field has evolved and decayed, due to the weak combined effects of dissipation and expulsion in the stellar core.

Population synthesis studies constitute a powerful method to reconstruct the birth distribution of periods and magnetic fields of the pulsar population. When this method is applied to populations in different wavelengths, it can break the degeneracy in the inferred properties of initial distributions that arises from single-band studies. In this context, we extend previous works to include X-ray thermal emitting pulsars within the same evolutionary model as radio-pulsars. We find that the cumulative distribution of the number of X-ray pulsars can be well reproduced by several models that, simultaneously, reproduce the characteristics of the radio-pulsar distribution. However, even considering the most favourable magneto-thermal evolution models with fast field decay, lognormal distributions of the initial magnetic field overpredict the number of visible sources with periods longer than 12 s. We then show that the problem can be solved with different distributions of magnetic field, such as a truncated lognormal distribution, or a binormal distribution with two distinct populations. We use the observational lack of isolated neutron stars (NSs) with spin periods P > 12 s to establish an upper limit to the fraction of magnetars born with B > 1015 G (less than 1 per cent). As future detections keep increasing the magnetar and high-B pulsar statistics, our approach can be used to establish a severe constraint on the maximum magnetic field at birth of NSs.

The thermal X-ray spectra of several isolated neutron stars display deviations from a pure blackbody. The accurate physical interpretation of these spectral features bears profound implications for our understanding of the atmospheric composition, magnetic field strength and topology, and equation of state of dense matter. With specific details varying from source to source, common explanations for the features have ranged from atomic transitions in the magnetized atmospheres or condensed surface, to cyclotron lines generated in a hot ionized layer near the surface. Here, we quantitatively evaluate the X-ray spectral distortions induced by inhomogeneous temperature distributions of the neutron star surface. To this aim, we explore several surface temperature distributions, we simulate their corresponding general relativistic X-ray spectra (assuming an isotropic, blackbody emission), and fit the latter with a single blackbody model. We find that, in some cases, the presence of a spurious ‘spectral line’ is required at a high significance level in order to obtain statistically acceptable fits, with central energy and equivalent width similar to the values typically observed. We also perform a fit to a specific object, RX J0806.4−4123, finding several surface temperature distributions able to model the observed spectrum. The explored effect is unlikely to work in all sources with detected lines, but in some cases it can indeed be responsible for the appearance of such lines. Our results enforce the idea that surface temperature anisotropy can be an important factor that should be considered and explored also in combination with more sophisticated emission models like atmospheres.

We present a long-term phase-coherent timing analysis and pulse-phase resolved spectroscopy for the two outbursts observed from the transient anomalous X-ray pulsar CXOU J164710.2−455216. For the first outburst we used 11 Chandra and XMM–Newton observations between 2006 September and 2009 August, the longest baseline yet for this source. We obtain a coherent timing solution with P = 10.61065583(4) s, Ṗ = 9.72(1) × 10−13 s s−1 and P̈ = –1.05(5) × 10−20 s s−2. Under the standard assumptions this implies a surface dipolar magnetic field of ∼1014 G, confirming this source as a standard B magnetar. We also study the evolution of the pulse profile (shape, intensity and pulsed fraction) as a function of time and energy. Using the phase-coherent timing solution we perform a phase-resolved spectroscopy analysis, following the spectral evolution of pulse-phase features, which hints at the physical processes taking place on the star. The results are discussed from the perspective of magnetothermal evolution models and the untwisting magnetosphere model. Finally, we present similar analysis for the second, less intense, 2011 outburst. For the timing analysis we used Swift data together with 2 XMM–Newton and Chandra pointings. The results inferred for both outbursts are compared and briefly discussed in a more general framework.