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Paolo Esposito

Publications and source records attributed to Paolo Esposito.

At least 19 recordsLinked to original sources

Stellar flare detection in XMM-Newton with gradient boosted trees

The EXTraS project, based on data collected with the XMM-Newton observatory, provided us with a vast amount of light curves for X-ray sources. For each light curve, EXTraS also provided us with a set of features (https://extras.inaf.it). We extract from the EXTraS database a tabular dataset of 31,832 variable sources by 108 features. Of these, 13,851 sources were manually labeled as stellar flares or non-flares based on direct visual inspection. We employ a supervised learning approach to produce a catalog of stellar flares based on our dataset, releasing it to the community. We leverage explainable AI tools and interpretable features to better understand our classifier. We train a gradient boosting classifier on 80\% of the data for which labels are available. We compute permutation feature importance scores, visualize feature space using UMAP, and analyze some false positive and false negative data points with the help of Shapley additive explanations -- an AI explainability technique used to measure the importance of each feature in determining the classifier's prediction for each instance. On the test set made up of the remainder 20\% of our labeled data, we obtain an accuracy of 97.1\%, with a precision of 82.4\% and a recall of 73.3\%. Our classifier outperforms a simple criterion based on fitting the light curve with a flare template and significantly surpasses a gradient-boosted classifier trained only on model-independent features. False positives appear related to flaring light curves that are not associated with a stellar counterpart, while false negatives often correspond to multiple flares or otherwise peculiar or noisy curves. We apply our trained classifier to currently unlabeled sources, releasing the largest catalog of X-ray stellar flares to date. [abridged]

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Classification of Unidentified Extended LHAASO Sources based on their Gamma-Ray Morphology: Prospects for Future IACTs

While Supernova Remnants (SNRs) are widely considered the primary accelerators of cosmic rays (CRs) up to hundreds of TeV, they struggle to account for the CR flux at PeV energies, suggesting the existence of additional PeVatrons. Observations from LHAASO (Large High Altitude Air Shower Observatory) have identified several PeVatron candidates, including some SNRs, pulsar wind nebulae, TeV halos and young massive star clusters (YMSCs). These objects accelerate particles that interact with the surrounding interstellar medium and radiation fields, producing very-high-energy gamma rays (>100 TeV), a key signature of both leptonic and hadronic PeVatrons. We simulate and model the emission of TeV halos and YMSCs, adopting radial emission profiles derived from observational data. Given the current angular resolution of gamma-ray instruments, these profiles often appear similar, making it challenging to distinguish between source classes. We explore how next-generation Imaging Atmospheric Cherenkov Telescopes (IACTs), namely the CTAO (Cherenkov Telescope Array Observatory) and the ASTRI Mini-Array (Astrofisica con Specchi a Tecnologia Replicante Italiana), can classify these sources based on their morphology. We test our classification methods, derived from the profile features of known sources, on simulated CTAO and ASTRI Mini-Array observations of unidentified extended sources from the first LHAASO catalog. We present the results of our analysis to highlight the potential of future IACT observations in identifying the nature of extended gamma-ray sources, refining PeVatron candidate classifications, and improving our understanding of cosmic-ray accelerators.

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Morphology of Young Massive Stellar Clusters with Next-Generation IACTs

The term PeVatron designates astrophysical objects capable of accelerating particles to PeV energies. Their nature and particle acceleration mechanisms are uncertain, but ultra-high-energy gamma rays are produced when particles accelerated by either leptonic or hadronic PeVatrons interact with the surrounding medium or radiation fields. The atmospheric air shower observatory LHAASO detected photons with energies above 100 TeV from 43 sources in the Galactic Plane, proving the existence of PeVatrons within the Milky Way. In particular, one of the detections was a 1.4 PeV photon in spatial correspondence with Cygnus OB2, providing a strong hint that young massive stellar clusters (YMSCs) can act as PeVatrons. The next-generation Cherenkov telescopes will have unprecedented energy and angular resolution. Therefore, they will be able to resolve spatially YMSCs better than LHAASO. We focused on a sample of 5 YMSCs and their environments visible from either hemisphere with the CTAO or ASTRI Mini-Array. We modeled the gamma-ray emission above 1 TeV. We devised methods for classifying YMSCs that could be detected as unidentified extended TeV sources and estimated the observational time needed to distinguish the morphology of different classes of sources. We study the morphology of the sources in our sample in order to identify the main features. We simulated observations of all sources with the instrument response function (IRF) of CTAO or ASTRI Mini-Array. We compare their emission distribution to the one of the TeV halos observed by HAWC. We parametrize their radial profiles in order to develop methodologies to classify them and to distinguish YMSCs from TeV halos based on their morphology. We expect some feature, such as the emission peak, to be key in differentiating between the two classes of objects. We then test them on a sample of sources of the first LHAASO catalog.

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IXPE detection of highly polarized X-rays from the magnetar 1E 1841-045

The Imaging X-ray Polarimetry Explorer (IXPE) observed for the first time highly polarized X-ray emission from the magnetar 1E 1841-045, targeted after a burst-active phase in August 2024. To date, IXPE has observed four other magnetars during quiescent periods, highlighting substantially different polarization properties. 1E 1841-045 exhibits a high, energy-dependent polarization degree, which increases monotonically from ~15% at 2-3 keV up to ~55% at 5.5-8 keV, while the polarization angle, aligned with the celestial North, remains fairly constant. The broadband spectrum (2-79 keV) obtained by combining simultaneous IXPE and NuSTAR data is well modeled by a blackbody and two power-law components. The unabsorbed 2-8 keV flux (~2E-11 erg/cm2/s) is about 10% higher than that obtained from archival XMM-Newton and NuSTAR observations. The polarization of the soft, thermal component does not exceed ~25%, and may be produced by a condensed surface or a bombarded atmosphere. The intermediate power law is polarized at around 30%, consistent with predictions for resonant Compton scattering in the star magnetosphere; while, the hard power law exhibits a polarization degree exceeding 65%, pointing to a synchrotron/curvature origin.

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Long-term study of the 2020 magnetar-like outburst of the young pulsar PSRJ1846-0258 in Kes 75

Magnetar-like activity has been observed in a large variety of neutron stars. PSR J1846-0258 is a young 327 ms radio-quiet pulsar with a large rotational power ($\sim 8 \times 10^{36}$ erg s$^{-1}$), and resides at the center of the supernova remnant Kes 75. It is one of the rare examples of a high magnetic field pulsar showing characteristics both of magnetars and radio pulsars, and can thus provide important clues on the differences in the emission mechanisms between these two classes. In 2006, PSR J1846-0258 was detected to undergo an outburst for the first time, accompanied by a large flux increase, millisecond X-ray bursts, significant spectral changes and a large timing glitch. In the period between May-June 2020, after fourteen years of quiescent stable emission, the source underwent a second magnetar-like outburst, which was followed up with several observations by NICER, XMM-Newton, NuSTAR and Swift. In this work, we report on the long-term timing and X-ray spectral properties of the source following the 2020 outburst, and place upper limits on any source activity at radio wavelengths. We demonstrate that the pulsed flux increased by a factor $> 6$ during the outburst, followed by non-trivial variability in the spin-down rate. Our timing analysis shows that the spin frequency and its derivative are clearly affected by magnetospheric activity due to the outburst. We find hints for an oscillation in the frequency derivative with a timescale of 50-60 days, recovering later on to stable quiescence.

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Skipping a beat: discovery of persistent quasi-periodic oscillations associated with pulsed fraction drop of the spin signal in M51 ULX-7

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 ($>$3$σ$) broad complex at mHz frequencies in the power spectra of M51 ULX-7. We did not detect the spin signal, setting a 3$σ$ 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.

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The Orbit of NGC 5907 ULX-1

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 $3\,σ$. 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 $<5\text{ deg}$.

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A magnetar giant flare in the nearby starburst galaxy M82

Giant flares, short explosive events releasing up to 10$^{47}$ erg of energy in the gamma-ray band in less than one second, are the most spectacular manifestation of magnetars, young neutron stars powered by a very strong magnetic field, 10$^{14-15}$ G in the magnetosphere and possibly higher in the star interior. The rate of occurrence of these rare flares is poorly constrained, as only three have been seen from three different magnetars in the Milky Way and in the Large Magellanic Cloud in about 50 years since the beginning of gamma-ray astronomy. This sample can be enlarged by the discovery of extragalactic events, since for a fraction of a second giant flares reach peak luminosities above 10$^{46}$ erg/s, which makes them visible by current instruments up to a few tens of Mpc. However, at these distances they appear similar to, and difficult to distinguish from, regular short gamma-ray bursts (GRBs). The latter are much more energetic events, 10$^{50-53}$ erg, produced by compact binary mergers and originating at much larger distances. Indeed, only a few short GRBs have been proposed, with different levels of confidence, as magnetar giant flare candidates in nearby galaxies. Here we report the discovery of a short GRB positionally coincident with the central region of the starburst galaxy M82. Its spectral and timing properties, together with the limits on its X-ray and optical counterparts obtained a few hours after the event and the lack of an associated gravitational wave signal, qualify with high confidence this event as a giant flare from a magnetar in M82.

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Isolated Neutron Stars

Non-accreting neutron stars display diverse characteristics, leading us to classify them into several groups. This chapter is an observational driven review in which we survey the properties of the different classes of isolated neutron stars: from the 'normal' rotation-powered pulsars, to magnetars, the most magnetic neutron stars in the Universe we know of; from central compact objects (sometimes called also anti-magnetars) in supernova remnants, to the X-ray dim isolated neutron stars. We also highlight a few sources that have exhibited features straddling those of different sub-groups, blurring the apparent diversity of the neutron star zoo and pointing to a gran unification.

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The Luminosity Phase Space of Galactic and Extragalactic X-ray Transients Out to Intermediate Redshifts

We present a detailed compilation and analysis of the X-ray phase space of low- to intermediate-redshift ($ 0\le z \le 1$) transients that consolidates observed light curves (and theory where necessary) for a large variety of classes of transient/variable phenomena in the 0.3--10 keV energy band. We include gamma-ray burst afterglows, supernovae, supernova shock breakouts and shocks interacting with the environment, tidal disruption events and active galactic nuclei, fast blue optical transients, cataclysmic variables, magnetar flares/outbursts and fast radio bursts, cool stellar flares, X-ray binary outbursts, and ultraluminous X-ray sources. Our overarching goal is to offer a comprehensive resource for the examination of these ephemeral events, extending the X-ray duration-luminosity phase space (DLPS) to show luminosity evolution. We use existing observations (both targeted and serendipitous) to characterize the behavior of various transient/variable populations. Contextualizing transient signals in the larger DLPS serves two primary purposes: to identify areas of interest (i.e., regions in the parameter space where one would expect detections, but in which observations have historically been lacking) and to provide initial qualitative guidance in classifying newly discovered transient signals. We find that while the most luminous (largely extragalactic) and least luminous (largely Galactic) part of the phase space is well-populated at $t > 0.1$ days, intermediate luminosity phenomena (L$_x = 10^{34} - 10^{42}$ erg s$^{-1}$) represent a gap in the phase space. We thus identify L$_x = 10^{34} - 10^{42}$ erg s$^{-1}$ and $t = 10^{-4} - 0.1$ days as a key discovery phase space in transient X-ray astronomy.

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The power of the rings: the GRB 221009A soft X-ray emission from its dust-scattering halo

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.

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Capturing the lowest luminosity state of the Supergiant Fast X-ray Transient XTE J1739-302

We report here on the results of the analysis of Chandra, XMM-Newton and NuSTAR recent observations of the Supergiant Fast X-ray Transient XTEJ1739-302. The source was caught in a low X-ray luminosity state, from a few $10^{31}$ to $10^{34}$ erg/s (0.5-10 keV). In particular, a very low X-ray luminosity was captured during an XMM-Newton observation performed in October 2022, at a few $10^{31}$ erg/s (0.5-10 keV), never observed before in XTEJ1739-302. The XMM-Newton spectrum could be well fitted either by an absorbed, steep power law model (photon index of 3.5) or by a collisionally-ionized diffuse gas with a temperature of 0.7 keV, very likely produced by shocks in the supergiant donor wind. These observations covered different orbital phases, but all appear compatible with the low luminosity level expected from the orbital INTEGRAL light curve. The absorbing column density is variable in the range $10^{22}-10^{23}$ cm$^{-2}$. A broad-band X-ray spectrum could be investigated at $10^{34}$ erg/s (0.5-30 keV) for the first time in XTEJ1739-302 with not simultaneous (but at similar orbital phases) Chandra and NuSTAR data, showing a power law spectral shape with a photon index of about 2.2 and an absorbing column density of $\sim$$10^{23}$ cm$^{-2}$. Remarkably, owing to the XMM-Newton observation, the amplitude of the X-ray variability has increased to five orders of magnitude, making XTEJ1739-302 one of the most extreme SFXTs.

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Timing six energetic rotation-powered X-ray pulsars, including the fast-spinning young PSR J0058-7218 and Big Glitcher PSR J0537-6910

Measuring a pulsar's rotational evolution is crucial to understanding the nature of the pulsar. Here we provide updated timing models for the rotational evolution of six pulsars, five of which are rotation phase-connected using primarily NICER X-ray data. For the newly-discovered fast energetic young pulsar, PSR J0058-7218, we increase the baseline of its timing model from 1.4 days to 8 months and not only measure more precisely its spin-down rate nudot = (-6.2324+/-0.0001)x10^-11 Hz s^-1 but also for the first time the second time derivative of spin rate nuddot = (4.2+/-0.2)x10^-21 Hz s^-2. For the fastest and most energetic young pulsar, PSR J0537-6910 (with 16 ms spin period), we detect 4 more glitches, for a total of 15 glitches over 4.5 years of NICER monitoring, and show that its spin-down behavior continues to set this pulsar apart from all others, including a long-term braking index n = -1.234+/-0.009 and interglitch braking indices that asymptote to <~ 7 for long times after a glitch. For PSR J1101-6101, we measure a much more accurate spin-down rate that agrees with a previous value measured without phase-connection. For PSR J1412+7922 (also known as Calvera), we extend the baseline of its timing model from our previous 1-year model to 4.4 years, and for PSR J1849-0001, we extend the baseline from 1.5 years to 4.7 years. We also present a long-term timing model of the energetic pulsar, PSR J1813-1749, by fitting previous radio and X-ray spin frequencies from 2009-2019 and new ones measured here using 2018 NuSTAR and 2021 Chandra data.

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The first 7 months of the 2020 X-ray outburst of the magnetar SGR J1935+2154

The magnetar SGR J1935+2154 underwent a new active episode on 2020 April 27-28, when a forest of hundreds of X-ray bursts and a large enhancement of the persistent flux were detected. For the first time, a radio burst with properties similar to those of fast radio bursts and with a X-ray counterpart was observed from this source, showing that magnetars can power at least a group of fast radio bursts. In this paper, we report on the X-ray spectral and timing properties of SGR J1935+2154 based on a long-term monitoring campaign with Chandra, XMM-Newton, NuSTAR, Swift and NICER covering a time span of ~7 months since the outburst onset. The broadband spectrum exhibited a non-thermal power-law component (photon index~1.2) extending up to ~20-25 keV throughout the campaign and a blackbody component with temperature decreasing from ~1.5 keV at the outburst peak to ~0.45 keV in the following months. We found that the luminosity decay is well described by the sum of two exponential functions, reflecting the fast decay (~1 d) at the early stage of the outburst followed by a slower decrease (~30 d). The source reached quiescence about ~80 days after the outburst onset, releasing an energy of ~6e40 erg during the outburst. We detected X-ray pulsations in the XMM-Newton data sets and derived an average spin-down rate of ~3.5e-11 s/s using the spin period measurements derived in this work and three values reported previously during the same active period. Moreover, we report on simultaneous radio observations performed with the Sardinia Radio Telescope. No evidence for periodic or single-pulse radio emission was found.

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Quasi periodic whispers from a transient ULX in M\,101: signatures of a fast-spinning neutron star?

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).

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Analysis of the unconcentrated background of the EPIC-pn camera on board XMM-Newton

Our understanding of the background of the EPIC/pn camera onboard XMM-Newton is incomplete. This affects the study of extended sources and can influence the predictions of the background of future X-ray missions. We provide new results based on the analysis of the largest data set ever used. We focus on the unconcentrated component of the EPIC/pn background - supposedly related to cosmic rays interacting with the telescope. We find that the out-field of view region of the pn detector is actually exposed to the sky. After cleaning from the sky contamination, the unconcentrated background does not show significant spatial variations and its time behaviour is anti-correlated with the solar cycle. We find a very tight, linear correlation between unconcentrated backgrounds detected in the EPIC/pn and MOS2 cameras: this permits the correct evaluation of the pn unconcentrated background of each exposure on the basis of MOS2 data, avoiding the use (as usual) of the contaminated pn regions. We find a tight, linear correlation between the pn unconcentrated background and the proton flux in the 630-970 MeV energy band measured by SOHO/EPHIN. Through this relationship we quantify the contribution of cosmic ray interactions to the pn unconcentrated background and we find a second source which contributes to the pn unconcentrated background for a significant fraction (30%-70%), that does not vary with time and is roughly isotropic. Hard X-ray photons of the CXB satisfy all the known properties of this new component. Our findings provide an important observational confirmation of simulation results on ATHENA.

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The long-term enhanced brightness of the magnetar 1E 1547.0-5408

We present the evolution of the X-ray emission properties of the magnetar 1E 1547.0-5408 since February 2004 over a time period covering three outbursts. We analyzed new and archival observations taken with the Swift, NuSTAR, Chandra and XMM-Newton X-ray satellites. The source has been observed at a relatively steady soft X-ray flux of $\approx$ 10$^{-11}$ erg cm$^{-2}$ s$^{-1}$ (0.3-10 keV) over the last 9 years, which is about an order of magnitude fainter than the flux at the peak of the last outburst in 2009, but a factor of $\sim$ 30 larger than the level in 2006. The broad-band spectrum extracted from two recent NuSTAR observations in April 2016 and February 2019 showed a faint hard X-ray emission up to $\sim$ 70 keV. Its spectrum is adequately described by a flat power law component, and its flux is $\sim$ $7 \times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$ (10-70 keV), that is a factor of $\sim$ 20 smaller than at the peak of the 2009 outburst. The hard X-ray spectral shape has flattened significantly in time, which is at variance with the overall cooling trend of the soft X-ray component. The pulse profile extracted from these NuSTAR pointings displays variability in shape and amplitude with energy (up to $\approx$ 25 keV). Our analysis shows that the flux of 1E 1547.0-5408 is not yet decaying to the 2006 level and that the source has been lingering in a stable, high-intensity state for several years. This might suggest that magnetars can hop among distinct persistent states that are probably connected to outburst episodes and that their persistent thermal emission can be almost entirely powered by the dissipation of currents in the corona.

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Diffuse X-ray emission around an ultraluminous X-ray pulsar

Ultraluminous X-ray sources (ULXs) are extragalactic X-ray emitters located off-center of their host galaxy and with a luminosity in excess of a few ${10^{39}\text{ erg s}^{-1}}$, if emitted isotropically. The discovery of periodic modulation revealed that in some ULXs the accreting compact object is a neutron star, indicating luminosities substantially above their Eddington limit. The most extreme object in this respect is ${NGC 5907~ULX-1}$ (ULX1), with a peak luminosity that is 500 times its Eddington limit. During a Chandra observation to probe a low state of ULX1, we detected diffuse X-ray emission at the position of ULX1. Its diameter is $2.7 \pm 1.0$ arcsec and contains 25 photons, none below 0.8 keV. We interpret this extended structure as an expanding nebula powered by the wind of ULX1. Its diameter of about ${200\text{ pc}}$, characteristic energy of ${\sim 1.9\text{ keV}}$, and luminosity of ${\sim 2\times10^{38}\text{ erg s}^{-1}}$ imply a mechanical power of ${1.3\times10^{41}\text{ erg s}^{-1}}$ and an age ${\sim 7 \times 10^{4}\text{ yr}}$. This interpretation suggests that a genuinely super-Eddington regime can be sustained for time scales much longer than the spin-up time of the neutron star powering the system. As the mechanical power from a single ULX nebula can rival the injection rate of cosmic rays of an entire galaxy, ULX nebulae could be important cosmic ray accelerators.

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