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.

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).

Population synthesis of isolated neutron stars with magneto-rotational evolution – II. From radio-pulsars to magnetars

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.

Ballistic spin-valves with Ni nanocontacts

Poster presented in TNT 2005 "Trends in Nanotechnology", Oviedo, Spain, 29 August-02 September, 2005.

Electronic structure and transport properties of atomic NiO spinvalves

Ab initio quantum transport calculations show that short NiO chains suspended in Ni nanocontacts present a very strong spin-polarization of the conductance.The generalized gradient approximation we use here predicts a similar polarization of the conductance as the one previously computed with non-local exchange, confirming the robustness of the result. Their use as nanoscopic spinvalves is proposed.

Force-free twisted magnetospheres of neutron stars

Context. The X-ray spectra observed in the persistent emission of magnetars are evidence for the existence of a magnetosphere. The high-energy part of the spectra is explained by resonant cyclotron upscattering of soft thermal photons in a twisted magnetosphere, which has motivated an increasing number of efforts to improve and generalize existing magnetosphere models. Aims. We want to build more general configurations of twisted, force-free magnetospheres as a first step to understanding the role played by the magnetic field geometry in the observed spectra. Methods. First we reviewed and extended previous analytical works to assess the viability and limitations of semi-analytical approaches. Second, we built a numerical code able to relax an initial configuration of a nonrotating magnetosphere to a force-free geometry, provided any arbitrary form of the magnetic field at the star surface. The numerical code is based on a finite-difference time-domain, divergence-free, and conservative scheme, based of the magneto-frictional method used in other scenarios. Results. We obtain new numerical configurations of twisted magnetospheres, with distributions of twist and currents that differ from previous analytical solutions. The range of global twist of the new family of solutions is similar to the existing semi-analytical models (up to some radians), but the achieved geometry may be quite different. Conclusions. The geometry of twisted, force-free magnetospheres shows a wider variety of possibilities than previously considered. This has implications for the observed spectra and opens the possibility of implementing alternative models in simulations of radiative transfer aiming at providing spectra to be compared with observations.

Pulsar timing irregularities and the imprint of magnetic field evolution

Context. The rotational evolution of isolated neutron stars is dominated by the magnetic field anchored to the solid crust of the star. Assuming that the core field evolves on much longer timescales, the crustal field evolves mainly though Ohmic dissipation and the Hall drift, and it may be subject to relatively rapid changes with remarkable effects on the observed timing properties. Aims. We investigate whether changes of the magnetic field structure and strength during the star evolution may have observable consequences in the braking index n. This is the most sensitive quantity to reflect small variations of the timing properties that are caused by magnetic field rearrangements. Methods. We performed axisymmetric, long-term simulations of the magneto-thermal evolution of neutron stars with state-of-the-art microphysical inputs to calculate the evolution of the braking index. Relatively rapid magnetic field modifications can be expected only in the crust of neutron stars, where we focus our study. Results. We find that the effect of the magnetic field evolution on the braking index can be divided into three qualitatively different stages depending on the age and the internal temperature: a first stage that may be different for standard pulsars (with n ~ 3) or low field neutron stars that accreted fallback matter during the supernova explosion (systematically n < 3); in a second stage, the evolution is governed by almost pure Ohmic field decay, and a braking index n > 3 is expected; in the third stage, at late times, when the interior temperature has dropped to very low values, Hall oscillatory modes in the neutron star crust result in braking indices of a high absolute value and both positive and negative signs. Conclusions. Current magneto-thermal evolution models predict a large contribution to the timing noise and, in particular, to the braking index, from temporal variations of the magnetic field. Models with strong (≳ 1014 G) multipolar or toroidal components, even with a weak (~1012 G) dipolar field are consistent with the observed trend of the timing properties.

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.

The outburst decay of the low magnetic field magnetar SGR 0418+5729

We report on the long-term X-ray monitoring of the outburst decay of the low magnetic field magnetar SGR 0418+5729 using all the available X-ray data obtained with RXTE, Swift, Chandra, and XMM-Newton observations from the discovery of the source in 2009 June up to 2012 August. The timing analysis allowed us to obtain the first measurement of the period derivative of SGR 0418+5729: ˙ P = 4(1) × 10−15 s s−1, significant at a ∼3.5σ confidence level. This leads to a surface dipolar magnetic field of Bdip 6 × 1012 G. This measurement confirms SGR 0418+5729 as the lowest magnetic field magnetar. Following the flux and spectral evolution from the beginning of the outburst up to ∼1200 days, we observe a gradual cooling of the tiny hot spot responsible for the X-ray emission, from a temperature of ∼0.9 to 0.3 keV. Simultaneously, the X-ray flux decreased by about three orders of magnitude: from about 1.4 × 10−11 to 1.2 × 10−14 erg s−1 cm−2. Deep radio, millimeter, optical, and gamma-ray observations did not detect the source counterpart, implying stringent limits on its multi-band emission, as well as constraints on the presence of a fossil disk. By modeling the magneto-thermal secular evolution of SGR 0418+5729, we infer a realistic age of ∼550 kyr, and a dipolar magnetic field at birth of ∼1014 G. The outburst characteristics suggest the presence of a thin twisted bundle with a small heated spot at its base. The bundle untwisted in the first few months following the outburst, while the hot spot decreases in temperature and size. We estimate the outburst rate of low magnetic field magnetars to be about one per year per galaxy, and we briefly discuss the consequences of such a result in several other astrophysical contexts.

Is SGR 0418+5729 indeed a waning magnetar?

SGR 0418+5729 is a transient soft gamma-ray repeater which underwent a major outburst in 2009 June, during which the emission of short bursts was observed. Its properties appeared quite typical of other sources of the same class until long-term X-ray monitoring failed to detect any period derivative. The present upper limit on P implies that the surface dipole field is Bp lsim 7.5 × 1012 G, well below those measured in other soft gamma-ray repeaters (SGRs) and in the Anomalous X-ray Pulsars (AXPs), a group of similar sources. Both SGRs and AXPs are currently believed to be powered by ultra-magnetized neutron stars (magnetars, Bp ≈ 1014-1015 G). SGR 0418+5729 hardly seems to fit in such a picture. We show that the magneto-rotational properties of SGR 0418+5729 can be reproduced if this is an aged magnetar, ≈1 Myr old, which experienced substantial field decay. The large initial toroidal component of the internal field required to match the observed properties of SGR 0418+5729 ensures that crustal fractures, and hence bursting activity, can still occur at the present time. The thermal spectrum observed during the outburst decay is compatible with the predictions of a resonant Compton scattering model (as in other SGRs/AXPs) if the field is low and the magnetospheric twist is moderate.

3XMM J185246.6+003317: another low magnetic field magnetar

We study the outburst of the newly discovered X-ray transient 3XMMJ185246.6+003317, re-analyzing all available XMM-Newton observations of the source to perform a phase-coherent timing analysis, and derive updated values of the period and period derivative. We find the source rotating at P = 11.55871346(6) s (90% confidence level; at epoch MJD 54728.7) but no evidence for a period derivative in the seven months of outburst decay spanned by the observations. This translates to a 3σ upper limit for the period derivative of ˙ P <1.4×10−13 s s−1, which, assuming the classical magneto-dipolar braking model, gives a limit on the dipolar magnetic field of Bdip < 4.1×1013 G. The X-ray outburst and spectral characteristics of 3XMM J185246.6+003317 confirm its identification as a magnetar, but the magnetic field upper limit we derive defines it as the third “low-B” magnetar discovered in the past 3 yr, after SGR 0418+5729 and Swift J1822.3−1606. We have also obtained an upper limit to the quiescent luminosity (<4×1033 erg s−1), in line with the expectations for an old magnetar. The discovery of this new low field magnetar reaffirms the prediction of about one outburst per year from the hidden population of aged magnetars.