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.

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.

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 influence of magnetic field geometry on magnetars X-ray spectra

Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering (RCS) in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions [14] in a previously developed MC code [9] to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.

Central compact objects and the hidden magnetic field scenario

Central compact objects (CCOs) are X-ray sources lying close to the centre of supernova remnants, with inferred values of the surface magnetic fields significantly lower (≲1011 G) than those of standard pulsars. In this paper, we revise the hidden magnetic field scenario, presenting the first 2D simulations of the submergence and re-emergence of the magnetic field in the crust of a neutron star. A post-supernova accretion stage of about 10−4–10−3 M⊙ over a vast region of the surface is required to bury the magnetic field into the inner crust. When accretion stops, the field re-emerges on a typical time-scale of 1–100 kyr, depending on the submergence conditions. After this stage, the surface magnetic field is restored close to its birth values. A possible observable consequence of the hidden magnetic field is the anisotropy of the surface temperature distribution, in agreement with observations of several of these sources. We conclude that the hidden magnetic field model is viable as an alternative to the antimagnetar scenario, and it could provide the missing link between CCOs and the other classes of isolated neutron stars.

A new low magnetic field magnetar: the 2011 outburst of Swift J1822.3–1606

We report on the long-term X-ray monitoring with Swift, RXTE, Suzaku, Chandra, and XMM-Newton of the outburst of the newly discovered magnetar Swift J1822.3–1606 (SGR 1822–1606), from the first observations soon after the detection of the short X-ray bursts which led to its discovery, through the first stages of its outburst decay (covering the time span from 2011 July until the end of 2012 April). We also report on archival ROSAT observations which detected the source during its likely quiescent state, and on upper limits on Swift J1822.3–1606's radio-pulsed and optical emission during outburst, with the Green Bank Telescope and the Gran Telescopio Canarias, respectively. Our X-ray timing analysis finds the source rotating with a period of P = 8.43772016(2) s and a period derivative P = 8.3(2)×10−14 s s−1, which implies an inferred dipolar surface magnetic field of B sime 2.7 × 1013 G at the equator. This measurement makes Swift J1822.3–1606 the second lowest magnetic field magnetar (after SGR 0418+5729). Following the flux and spectral evolution from the beginning of the outburst, we find that the flux decreased by about an order of magnitude, with a subtle softening of the spectrum, both typical of the outburst decay of magnetars. By modeling the secular thermal evolution of Swift J1822.3–1606, we find that the observed timing properties of the source, as well as its quiescent X-ray luminosity, can be reproduced if it was born with a poloidal and crustal toroidal fields of Bp ~ 1.5 × 1014 G and B tor ~ 7 × 1014 G, respectively, and if its current age is ~550 kyr.

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.

Modelling of the surface emission of the low magnetic field magnetar SGR 0418+5729

We perform a detailed modelling of the post-outburst surface emission of the low magnetic field magnetar SGR 0418+5729. The dipolar magnetic field of this source, B=6×1012G estimated from its spin-down rate, is in the observed range of magnetic fields for normal pulsars. The source is further characterized by a high pulse fraction and a single-peak profile. Using synthetic temperature distribution profiles, and fully accounting for the general-relativistic effects of light deflection and gravitational redshift, we generate synthetic X-ray spectra and pulse profiles that we fit to the observations. We find that asymmetric and symmetric surface temperature distributions can reproduce equally well the observed pulse profiles and spectra of SGR 0418. None the less, the modelling allows us to place constraints on the system geometry (i.e. the angles ψ and ξ that the rotation axis makes with the line of sight and the dipolar axis, respectively), as well as on the spot size and temperature contrast on the neutron star surface. After performing an analysis iterating between the pulse profile and spectra, as done in similar previous works, we further employed, for the first time in this context, a Markov-Chain Monte Carlo approach to extract constraints on the model parameters from the pulse profiles and spectra, simultaneously. We find that, to reproduce the observed spectrum and flux modulation: (a) the angles must be restricted to 65° ≲ ψ + ξ ≲ 125° or 235° ≲ ψ + ξ ≲ 295°; (b) the temperature contrast between the poles and the equator must be at least a factor of ∼6, and (c) the size of the hottest region ranges between 0.2 and 0.7 km (including uncertainties on the source distance). Lastly, we interpret our findings within the context of internal and external heating models.

Simulated magnetic field expulsion in neutron star cores

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.

The outburst decay of the low magnetic field magnetar SWIFT J1822.3−1606: phase-resolved analysis and evidence for a variable cyclotron feature

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.

Are pulsars born with a hidden magnetic field?

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.

Measurement of the magnetic field of small magnets with a smartphone: a very economical laboratory practice for introductory physics courses

In this work, we propose an inexpensive laboratory practice for an introductory physics course laboratory for any grade of science and engineering study. This practice was very well received by our students, where a smartphone (iOS, Android, or Windows) is used together with mini magnets (similar to those used on refrigerator doors), a 20 cm long school rule, a paper, and a free application (app) that needs to be downloaded and installed that measures magnetic fields using the smartphone's magnetic field sensor or magnetometer. The apps we have used are: Magnetometer (iOS), Magnetometer Metal Detector, and Physics Toolbox Magnetometer (Android). Nothing else is needed. Cost of this practice: free. The main purpose of the practice is that students determine the dependence of the component x of the magnetic field produced by different magnets (including ring magnets and sphere magnets). We obtained that the dependency of the magnetic field with the distance is of the form x-3, in total agreement with the theoretical analysis. The secondary objective is to apply the technique of least squares fit to obtain this exponent and the magnetic moment of the magnets, with the corresponding absolute error.

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.

Intrinsic spin noise in MgO magnetic tunnel junctions

We consider two intrinsic sources of noise in ultra-sensitive magnetic field sensors based on MgO magnetic tunnel junctions, coming both from 25 Mg nuclear spins (I = 5/2, 10% natural abundance) and S = 1 Mg-vacancies. While nuclear spins induce noise peaked in the MHz frequency range, the vacancies noise peaks in the GHz range. We find that the nuclear noise in submicron devices has a similar magnitude than the 1/f noise, while the vacancy-induced noise dominates in the GHz range. Interestingly, the noise spectrum under a finite magnetic field gradient may provide spatial information about the spins in the MgO layer.

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.