A new code for the Hall-driven magnetic evolution of neutron stars

Over the past decade, the numerical modeling of the magnetic field evolution in astrophysical scenarios has become an increasingly important field. In the crystallized crust of neutron stars the evolution of the magnetic field is governed by the Hall induction equation. In this equation the relative contribution of the two terms (Hall term and Ohmic dissipation) varies depending on the local conditions of temperature and magnetic field strength. This results in the transition from the purely parabolic character of the equations to the hyperbolic regime as the magnetic Reynolds number increases, which presents severe numerical problems. Up to now, most attempts to study this problem were based on spectral methods, but they failed in representing the transition to large magnetic Reynolds numbers. We present a new code based on upwind finite differences techniques that can handle situations with arbitrary low magnetic diffusivity and it is suitable for studying the formation of sharp current sheets during the evolution. The code is thoroughly tested in different limits and used to illustrate the evolution of the crustal magnetic field in a neutron star in some representative cases. Our code, coupled to cooling codes, can be used to perform long-term simulations of the magneto-thermal evolution of neutron stars.

Unifying the observational diversity of isolated neutron stars via magneto-thermal evolution models

Observations of magnetars and some of the high magnetic field pulsars have shown that their thermal luminosity is systematically higher than that of classical radio-pulsars, thus confirming the idea that magnetic fields are involved in their X-ray emission. Here we present the results of 2D simulations of the fully coupled evolution of temperature and magnetic field in neutron stars, including the state-of-the-art kinetic coefficients and, for the first time, the important effect of the Hall term. After gathering and thoroughly re-analysing in a consistent way all the best available data on isolated, thermally emitting neutron stars, we compare our theoretical models to a data sample of 40 sources. We find that our evolutionary models can explain the phenomenological diversity of magnetars, high-B radio-pulsars, and isolated nearby neutron stars by only varying their initial magnetic field, mass and envelope composition. Nearly all sources appear to follow the expectations of the standard theoretical models. Finally, we discuss the expected outburst rates and the evolutionary links between different classes. Our results constitute a major step towards the grand unification of the isolated neutron star zoo.

The imprint of the crustal magnetic field on the thermal spectra and pulse profiles of isolated neutron stars

Isolated neutron stars (NSs) show a bewildering variety of astrophysical manifestations, presumably shaped by the magnetic field strength and topology at birth. Here, using state-of-the-art calculations of the coupled magnetic and thermal evolution of NSs, we compute the thermal spectra and pulse profiles expected for a variety of initial magnetic field configurations. In particular, we contrast models with purely poloidal magnetic fields to models dominated by a strong internal toroidal component. We find that, while the former displays double-peaked profiles and very low pulsed fractions, in the latter, the anisotropy in the surface temperature produced by the toroidal field often results in a single pulse profile, with pulsed fractions that can exceed the 50–60 per cent level even for perfectly isotropic local emission. We further use our theoretical results to generate simulated ‘observed’ spectra, and show that blackbody (BB) fits result in inferred radii that can be significantly smaller than the actual NS radius, even as low as ∼1–2 km for old NSs with strong internal toroidal fields and a high absorption column density along their line of sight. We compute the size of the inferred BB radius for a few representative magnetic field configurations, NS ages and magnitudes of the column density. Our theoretical results are of direct relevance to the interpretation of X-ray observations of isolated NSs, as well as to the constraints on the equation of state of dense matter through radius measurements.

The circumstellar environment and evolutionary status of the supergiant B[e] star Wd1-9

Context. Historically, supergiant (sg)B[e] stars have been difficult to include in theoretical schemes for the evolution of massive OB stars. Aims. The location of Wd1-9 within the coeval starburst cluster Westerlund 1 means that it may be placed into a proper evolutionary context and we therefore aim to utilise a comprehensive multiwavelength dataset to determine its physical properties and consequently its relation to other sgB[e] stars and the global population of massive evolved stars within Wd1. Methods. Multi-epoch R- and I-band VLT/UVES and VLT/FORS2 spectra are used to constrain the properties of the circumstellar gas, while an ISO-SWS spectrum covering 2.45−45μm is used to investigate the distribution, geometry and composition of the dust via a semi-analytic irradiated disk model. Radio emission enables a long term mass-loss history to be determined, while X-ray observations reveal the physical nature of high energy processes within the system. Results. Wd1-9 exhibits the rich optical emission line spectrum that is characteristic of sgB[e] stars. Likewise its mid-IR spectrum resembles those of the LMC sgB[e] stars R66 and 126, revealing the presence of equatorially concentrated silicate dust, with a mass of ~10−4M⊙. Extreme historical and ongoing mass loss (≳ 10−4M⊙yr−1) is inferred from the radio observations. The X-ray properties of Wd1-9 imply the presence of high temperature plasma within the system and are directly comparable to a number of confirmed short-period colliding wind binaries within Wd1. Conclusions. The most complete explanation for the observational properties of Wd1-9 is that it is a massive interacting binary currently undergoing, or recently exited from, rapid Roche-lobe overflow, supporting the hypothesis that binarity mediates the formation of (a subset of) sgB[e] stars. The mass loss rate of Wd1-9 is consistent with such an assertion, while viable progenitor and descendent systems are present within Wd1 and comparable sgB[e] binaries have been identified in the Galaxy. Moreover, the rarity of sgB[e] stars - only two examples are identified from a census of ~ 68 young massive Galactic clusters and associations containing ~ 600 post-Main Sequence stars - is explicable given the rapidity (~ 104yr) expected for this phase of massive binary evolution.

GRO J1008−57: an (almost) predictable transient X-ray binary

A study of archival RXTE, Swift, and Suzaku pointed observations of the transient high-mass X-ray binary GRO J1008−57 is presented. A new orbital ephemeris based on pulse arrival-timing shows the times of maximum luminosities during outbursts of GRO J1008−57 to be close to periastron at orbital phase − 0.03. This makes the source one of a few for which outburst dates can be predicted with very high precision. Spectra of the source in 2005, 2007, and 2011 can be well described by a simple power law with high-energy cutoff and an additional black body at lower energies. The photon index of the power law and the black-body flux only depend on the 15–50 keV source flux. No apparent hysteresis effects are seen. These correlations allow us to predict the evolution of the pulsar’s X-ray spectral shape over all outbursts as a function of just one parameter, the source’s flux. If modified by an additional soft component, this prediction even holds during GRO J1008−57’s 2012 type II outburst.

No anticorrelation between cyclotron line energy and X-ray flux in 4U 0115+634

We report on an outburst of the high mass X-ray binary 4U 0115+634 with a pulse period of 3.6 s in 2008 March/April as observed with RXTE and INTEGRAL. During the outburst the neutron star’s luminosity varied by a factor of 10 in the 3–50 keV band. In agreement with earlier work we find evidence of five cyclotron resonance scattering features at ~10.7, 21.8, 35.5, 46.7, and 59.7 keV. Previous work had found an anticorrelation between the fundamental cyclotron line energy and the X-ray flux. We show that this apparent anticorrelation is probably due to the unphysical interplay of parameters of the cyclotron line with the continuum models used previously, e.g., the negative and positive exponent power law (NPEX). For this model, we show that cyclotron line modeling erroneously leads to describing part of the exponential cutoff and the continuum variability, and not the cyclotron lines. When the X-ray continuum is modeled with a simple exponentially cutoff power law modified by a Gaussian emission feature around 10 keV, the correlation between the line energy and the flux vanishes, and the line parameters remain virtually constant over the outburst. We therefore conclude that the previously reported anticorrelation is an artifact of the assumptions adopted in the modeling of the continuum.

Accreting magnetars: a new type of high-mass X-ray binaries?

The discovery of very slow pulsations (Pspin =5560 s) has solved the long-standing question of the nature of the compact object in the high-mass X-ray binary 4U 2206+54 but has posed new ones. According to spin evolutionary models in close binary systems, such slow pulsations require a neutron star magnetic field strength larger than the quantum critical value of 4.4 × 1013 G, suggesting the presence of a magnetar. We present the first XMM–Newton observations of 4U 2206+54 and investigate its spin evolution. We find that the observed spin-down rate agrees with the magnetar scenario. We analyse Integral Spacecraft Gamma-Ray Imager (ISGRI)/INTErnational Gamma-RAy Laboratory (INTEGRAL) observations of 4U 2206+54 to search for the previously suggested cyclotron resonance scattering feature at ∼30 keV. We do not find a clear indication of the presence of the line, although certain spectra display shallow dips, not always at 30 keV. The association of these dips with a cyclotron line is very dubious because of its apparent transient nature. We also investigate the energy spectrum of 4U 2206+54 in the energy range 0.3–10 keV with unprecedented detail and report for the first time the detection of very weak 6.5 keV fluorescence iron lines. The photoelectric absorption is consistent with the interstellar value, indicating very small amount of local matter, which would explain the weakness of the florescence lines. The lack of matter locally to the source may be the consequence of the relatively large orbital separation of the two components of the binary. The wind would be too tenuous in the vicinity of the neutron star.

Fast X-ray transients towards the Galactic bulge with the Rossi X-ray Timing Explorer

In X-ray binaries, rapid variability in X-ray flux of greater than an order of magnitude on time-scales of a day or less appears to be a signature of wind accretion from a supergiant companion. When the variability takes the form of rare, brief, bright outbursts with only faint emission between them, the systems are called supergiant fast X-ray transients (SFXTs). We present data from twice-weekly scans of the Galactic bulge by the Rossi X-ray Timing Explorer that allow us to compare the behaviour of known SFXTs and possible SFXT candidates with the persistently bright supergiant X-ray binary 4U 1700−377. We independently confirm the orbital periods reported by other groups for SFXTs SAX J1818.6−1703 and IGR J17544−2619. The new data do not independently reproduce the orbital period reported for XTE J1739−302, but slightly improve the significance of the original result when the data are combined. The bulge source XTE J1743−363 shows a combination of fast variability and a long-term decline in activity, the latter behaviour not being characteristic of supergiant X-ray binaries. A far-red spectrum of the companion suggests that it is a symbiotic neutron star binary rather than a high-mass binary, and the reddest known of this class: the spectral type is approximately M8 III.

A Be-type star with a black-hole companion

Stellar-mass black holes have all been discovered through X-ray emission, which arises from the accretion of gas from their binary companions (this gas is either stripped from low-mass stars or supplied as winds from massive ones). Binary evolution models also predict the existence of black holes accreting from the equatorial envelope of rapidly spinning Be-type stars1, 2, 3 (stars of the Be type are hot blue irregular variables showing characteristic spectral emission lines of hydrogen). Of the approximately 80 Be X-ray binaries known in the Galaxy, however, only pulsating neutron stars have been found as companions2, 3, 4. A black hole was formally allowed as a solution for the companion to the Be star MWC 656 (ref. 5; also known as HD 215227), although that conclusion was based on a single radial velocity curve of the Be star, a mistaken spectral classification6 and rough estimates of the inclination angle. Here we report observations of an accretion disk line mirroring the orbit of MWC 656. This, together with an improved radial velocity curve of the Be star through fitting sharp Fe ii profiles from the equatorial disk, and a refined Be classification (to that of a B1.5–B2 III star), indicates that a black hole of 3.8 to 6.9 solar masses orbits MWC 656, the candidate counterpart of the γ-ray source AGL J2241+4454 (refs 5, 6). The black hole is X-ray quiescent and fed by a radiatively inefficient accretion flow giving a luminosity less than 1.6 × 10−7 times the Eddington luminosity. This implies that Be binaries with black-hole companions are difficult to detect in conventional X-ray surveys.

Astrophysical parameters of the peculiar X-ray transient IGR J11215−5952

Context. The current generation of X-ray satellites has discovered many new X-ray sources that are difficult to classify within the well-described subclasses. The hard X-ray source IGR J11215−5952 is a peculiar transient, displaying very short X-ray outbursts every 165 days. Aims. To characterise the source, we obtained high-resolution spectra of the optical counterpart, HD 306414, at different epochs, spanning a total of three months, before and around the 2007 February outburst with the combined aims of deriving its astrophysical parameters and searching for orbital modulation. Methods. We fit model atmospheres generated with the fastwind code to the spectrum, and used the interstellar lines in the spectrum to estimate its distance. We also cross-correlated each individual spectrum to the best-fit model to derive radial velocities. Results. From its spectral features, we classify HD 306414 as B0.5 Ia. From the model fit, we find Teff ≈ 24 700 K and log g ≈ 2.7, in good agreement with the morphological classification. Using the interstellar lines in its spectrum, we estimate a distance to HD 306414 d ≳ 7 kpc. Assuming this distance, we derive R∗ ≈ 40 R⊙ and Mspect ≈ 30 M⊙ (consistent, within errors, with Mevol ≈ 38 M⊙, and in good agreement with calibrations for the spectral type). Analysis of the radial velocity curve reveals that radial velocity changes are not dominated by the orbital motion, and provide an upper limit on the semi-amplitude for the optical component Kopt ≲ 11 ± 6 km   s-1. Large variations in the depth and shape of photospheric lines suggest the presence of strong pulsations, which may be the main cause of the radial velocity changes. Very significant variations, uncorrelated with those of the photospheric lines are seen in the shape and position of the Hα emission feature around the time of the X-ray outburst, but large excursions are also observed at other times. Conclusions. HD 306414 is a normal B0.5 Ia supergiant. Its radial velocity curve is dominated by an effect that is different from binary motion, and is most likely stellar pulsations. The data available suggest that the X-ray outbursts are caused by the close passage of the neutron star in a very eccentric orbit, perhaps leading to localised mass outflow.

Astrophysical parameters and orbital solution of the peculiar X-ray transient IGR J00370+6122

Context. BD + 60° 73 is the optical counterpart of the X-ray source IGR J00370+6122, a probable accretion-powered X-ray pulsar. The X-ray light curve of this binary system shows clear periodicity at 15.7 d, which has been interpreted as repeated outbursts around the periastron of an eccentric orbit. Aims. We aim to characterise the binary system IGR J00370+6122 by deriving its orbital and physical parameters. Methods. We obtained high-resolution spectra of BD + 60° 73 at different epochs. We used the fastwind code to generate a stellar atmosphere model to fit the observed spectrum and obtain physical magnitudes. The synthetic spectrum was used as a template for cross-correlation with the observed spectra to measure radial velocities. The radial velocity curve provided an orbital solution for the system. We also analysed the RXTE/ASM and Swift/BAT light curves to confirm the stability of the periodicity. Results. BD + 60° 73 is a BN0.7 Ib low-luminosity supergiant located at a distance ~3.1 kpc, in the Cas OB4 association. We derive Teff = 24 000 K and log gc = 3.0, and chemical abundances consistent with a moderately high level of evolution. The spectroscopic and evolutionary masses are consistent at the 1-σ level with a mass M∗ ≈ 15 M⊙. The recurrence time of the X-ray flares is the orbital period of the system. The neutron star is in a high-eccentricity (e = 0.56 ± 0.07) orbit, and the X-ray emission is strongly peaked around orbital phase φ = 0.2, though the observations are consistent with some level of X-ray activity happening at all orbital phases. Conclusions. The X-ray behaviour of IGR J00370+6122 is reminiscent of “intermediate” supergiant X-ray transients, though its peak luminosity is rather low. The orbit is somewhat wider than those of classical persistent supergiant X-ray binaries, which when combined with the low luminosity of the mass donor, explains the low X-ray luminosity. IGR J00370+6122 will very likely evolve towards a persistent supergiant system, highlighting the evolutionary connection between different classes of wind-accreting X-ray sources.

Spectral features in isolated neutron stars induced by inhomogeneous surface temperatures

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.

Population synthesis of isolated neutron stars with magneto-rotational evolution

We revisit the population synthesis of isolated radio-pulsars incorporating recent advances on the evolution of the magnetic field and the angle between the magnetic and rotational axes from new simulations of the magneto-thermal evolution and magnetosphere models, respectively. An interesting novelty in our approach is that we do not assume the existence of a death line. We discuss regions in parameter space that are more consistent with the observational data. In particular, we find that any broad distribution of birth spin periods with P0 ≲ 0.5 s can fit the data, and that if the alignment angle is allowed to vary consistently with the torque model, realistic magnetospheric models are favoured compared to models with classical magneto-dipolar radiation losses. Assuming that the initial magnetic field is given by a lognormal distribution, our optimal model has mean strength 〈log B0[G]〉 ≈ 13.0–13.2 with width σ(log B0) = 0.6–0.7. However, there are strong correlations between parameters. This degeneracy in the parameter space can be broken by an independent estimate of the pulsar birth rate or by future studies correlating this information with the population in other observational bands (X-rays and γ-rays).

The many lives of magnetized neutron stars

The magnetic field strength at birth is arguably one of the most important properties to determine the evolutionary path of a neutron star. Objects with very high fields, collectively known as magnetars, are characterized by high X-ray quiescent luminosities, occurrence of outbursts, and, for some of them, sporadic giant flares. While the magnetic field strength is believed to drive their collective behaviour, however, the diversity of their properties, and, especially, the observation of magnetar-like bursts from “low-field” pulsars, has been a theoretical puzzle. In this review, we discuss results of long-term simulations following the coupled evolution of the X-ray luminosity and the timing properties for a large, homogeneous sample of X-ray emitting isolated neutron stars, accounting for a range of initial magnetic field strengths, envelope compositions, and neutron star masses. In addition, by following the evolution of magnetic stresses within the neutron star crust, we can also relate the observed magnetar phenomenology to the physical properties of neutron stars, and in particular to their age and magnetic field strength and topology. The dichotomy of “high-B” field pulsars versus magnetars is naturally explained, and occasional outbursts from old, low B-field neutron stars are predicted. We conclude by speculating on the fate of old magnetars, and by presenting observational diagnostics of the neutron star crustal field topology.

Mapping Binary Liquid-Vapor or Liquid-Liquid-Vapor Equilibria Regions, including the Different Azeotropic Behaviours, as a Function of the NRTL Binary Parameters

13th Mediterranean Congress of Chemical Engineering (Sociedad Española de Química Industrial e Ingeniería Química, Fira Barcelona, Expoquimia), Barcelona, September 30-October 3, 2014