Unveiling the thermal and magnetic map of neutron star surfaces though their X-ray emission: method and light-curve analysis

Recent Chandra and XMM–Newton observations of a number of X-ray 'dim' pulsating neutron stars have revealed quite unexpected features in the emission from these sources. Their soft thermal spectrum, believed to originate directly from the star surface, shows evidence for a phase-varying absorption line at some hundred eVs. The pulse modulation is relatively large (pulsed fractions in the range ∼12–35 per cent), the pulse shape is often non-sinusoidal, and the hard X-ray colour appears to be anticorrelated in phase with the total emission. Moreover, the prototype of this class, RX J0720.4−3125, has been found to undergo rather sensible changes in both its spectral and timing properties over a time-scale of a few years. All these new findings seem difficult to reconcile with the standard picture of a cooling neutron star endowed with a purely dipolar magnetic field, at least if surface emission is produced in an atmosphere on top of the crust. In this paper we explore how a dipolar+quadrupolar star-centred field influences the properties of the observed light curves. The phase-resolved spectrum has been evaluated accounting for both radiative transfer in a magnetized atmosphere and general relativistic ray-bending. We computed over 78 000 light curves, varying the quadrupolar components and the viewing geometry. A comparison of the data with our model indicates that higher-order multipoles are required to reproduce the observations.     

The magnificent seven: magnetic fields and surface temperature distributions

Presently seven nearby radio-quiet isolated neutron stars discovered in ROSAT data and characterized by thermal X-ray spectra are known. They exhibit very similar properties and despite intensive searches their number remained constant since 2001 which led to their name “The Magnificent Seven”. Five of the stars exhibit pulsations in their X-ray flux with periods in the range of 3.4 s to 11.4 s. XMM-Newton observations revealed broad absorption lines in the X-ray spectra which are interpreted as cyclotron resonance absorption lines by protons or heavy ions and/or atomic transitions shifted to X-ray energies by strong magnetic fields of the order of 10¹³ G. New XMM-Newton observations indicate more complex X-ray spectra with multiple absorption lines. Pulse-phase spectroscopy of the best studied pulsars RX J0720.4-3125 and RBS 1223 reveals variations in derived emission temperature and absorption line depth with pulse phase. Moreover, RX J0720.4-3125 shows long-term spectral changes which are interpreted as due to free precession of the neutron star. Modeling of the pulse profiles of RX J0720.4-3125 and RBS 1223 provides information about the surface temperature distribution of the neutron stars indicating hot polar caps which have different temperatures, different sizes and are probably not located in antipodal positions.     

What is the nature of RX J0720.4–3125?

RX J0720.4–3125 has recently been identified as a pulsating soft X-ray source in the ROSAT all-sky survey with a period of 8.391 s. Its spectrum is well characterized by a blackbody with a temperature of 8 × 10⁵ K. We propose that the radiation from this object is thermal emission from a cooling neutron star. For this blackbody temperature we can obtain a robust estimate of the object's age of ∼ 3 × 10⁵ yr, yielding a polar field ∼ 10¹⁴ G for magnetic dipole spin-down and a value of P compatible with current observations.     

Isolated neutron stars: magnetic fields, distances,and spectra

We present timing measurements, astrometry, and high-resolution spectra of a number of nearby, thermally emitting, isolated neutron stars. We use these to infer magnetic field strengths and distances, but also encounter a number of puzzles. We discuss three specific ones in detail: (i) For RX J0720.4-3125 and RX J1308.6+2127, the characteristic ages are in excess of 1 Myr, while their temperatures and kinematic ages indicate that they are much younger; (ii) For RX J1856.5-3754, the brightness temperature for the optical emission is in excess of that measured at X-ray wavelengths for reasonable neutron-star radii; (iii) For RX J0720.4-3125, the spectrum changed from an initially featureless state to one with an absorption feature, yet there was only a relatively small change in T _eff. Furthermore, we attempt to see whether the spectra of all seven sources, in six of which absorption features have now been found, can be understood in the context of strongly magnetised hydrogen atmospheres. We find that the energies of the absorption features can be reproduced, but that it remains puzzling that, for J0720.4-3125 specifically, the spectrum was featureless in one state, and that, generally, the spectra do not have high-energy tails that are harder than the Wien-like ones obseved.      

Towards self-consistent models of isolated neutron stars

We propose a self–consistent model to explain all observational properties reported so far on the isolated neutron star (INS) RX J0720-3125 with the aim of giving a step forward towards our understanding of INSs. For a given magnetic field structure, which is mostly confined to the crust and outer layers, we obtain theoretical models and spectra which account for the broadband spectral energy distribution (including the apparent optical excess), the X-ray pulsations, and for the spectral feature seen in the soft X-ray spectrum of RX J0720-3125 around 0.3 keV. By fitting our models to existing archival X-ray data from 6 different XMM–Newton observations and available optical data, we show that the observed properties are fully consistent with a normal neutron star, with a proper radius of about 12 km, a temperature at the magnetic pole of about 100 eV, and a magnetic field strength of 2–3×10¹³ G. Moreover, we are able to reproduce the observed long–term spectral evolution in terms of free precession which induces changes in the orientation angles of about 40 degrees with a periodicity of 7 years. In addition to the evidence of internal toroidal components, we also find strong evidence of non–dipolar magnetic fields, since all spectral properties are better reproduced with models with strong quadrupolar components.      

Tkachenko waves, glitches and precession in neutron stars

Here I discuss possible relations between free precession of neutron stars, Tkachenko waves inside them and glitches. I note that the proposed precession period of the isolated neutron star RX J0720.4-3125 (Haberl et al. 2006) is consistent with the period of Tkachenko waves for the spin period 8.4 s. Based on a possible observation of a glitch in RX J0720.4-3125 (van Kerkwijk et al. 2007), I propose a simple model, in which long period precession is powered by Tkachenko waves generated by a glitch. The period of free precession, determined by a NS oblateness, should be equal to the standing Tkachenko wave period for effective energy transfer from the standing wave to the precession motion. A similar scenario can be applicable also in the case of the PSR B1828-11.     

Resonant cyclotron scattering in pulsar magnetospheres and its application to isolated neutron stars

Resonant cyclotron scattering(RCS)in pulsar magnetospheres is considered.The photon diffusion equation(Kompaneets equation)for RCS is derived.The photon system is modeled three dimensionally.Numerical calculations show that there exist not only up scattering but also down scattering of RCS,depending on the parameter space.RCS's possible applications to spectral energy distributions of magnetar candidates and radio quiet isolated neutron stars(INSs)are pointed out.The optical/UV excess of INSs may be caused by the down scattering of RCS.The calculations for RX J1856.5-3754 and RX J0720.4-3125 are presented and compared with their observational data.In our model,the INSs are proposed to be normal neutron stars,although the quark star hypothesis is still possible.The low pulsation amplitude of INSs is a natural consequence in the RCS model.     

New photometry and astrometry of the isolated neutron star RX J0720.4–3125 using recent VLT/FORS observations

Since the first optical detection of RX J0720.4–3125 various observations have been performed to determine astrometric and photometric data. We present the first detection of the isolated neutron star in the V Bessel filter to study the spectral energy distribution and derive a new astrometric position. At ESO Paranal we obtained very deep images with FORS 1 (three hours exposure time) of RX J0720.4–3125 in the V Bessel filter in January 2008. We derive the visual magnitude by standard star aperture photometry. Using sophisticated resampling software we correct the images for field distortions. Then we derive an updated position and proper motion value by comparing its position with FORS 1 observations of December 2000. We calculate a visual magnitude of V = 26.81 ± 0.09 mag, which is seven times in excess of what is expected from X‐ray data, but consistent with the extant U, B, and R data. Over about a seven year epoch difference we measured a proper motion of μ = 105.1 ± 7.4 mas yr^–1 towards θ = 296.951° ± 0.0063° (NW), consistent with previous data (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The optical counterparts to Be/X-ray binaries in the Magellanic Clouds

The fields of eight X-ray sources in the Magellanic Clouds believed to be Be/X-ray binaries have been searched for possible Be-star counterparts. BVR _c and H α CCD imaging was employed to identify early-type emission stars through colour indices and H α fluxes. Spectroscopy of five sources confirms the presence of H α emission in each case. Based on the positional coincidence of emission-line objects with the X-ray sources, we identify Be-star counterparts to the ROSAT sources RX J0032.9-7348, RX J0049.1-7250, RX J0054.9-7226 and RX J0101.0-7206, and to the recently discovered ASCA source AX J0051-722. We confirm the Be star nature of the counterpart to the HEAO1 source H0544-66. In the field of the ROSAT source RX J0051.8-7231 we find that there are three possible counterparts, each showing evidence for H α emission. We find a close double in the error circle of the EXOSAT source EXO 0531.1-6609, each component of which could be a Be star associated with the X-ray source.     

RX J1856.5-3754 as a possible strange star candidate

RX J1856.5-3754 has been proposed as a strange star candidate due to its very small apparent radius measured from its X-ray thermal spectrum. However, its optical emission requires a much larger radius and thus most of the stellar surface must be cold and undetectable in X-rays. In the case the star is a neutron star such a surface temperature distribution can be explained by the presence of a strong toroidal field in the crust (Pérez-Azorín et al.: Astron. Astrophys. 451, 1009 (2006); Geppert et al.: Astron. Astrophys. 457, 937 (2006)) We consider a similar scenario for a strange star with a thin baryonic crust to determine if such a magnetic field induced effect is still possible. This work was partially supported by PAPIIT, UNAM, grant IN119306. J.A.H. studies at UNAM and travel to London are covered by fellowships from UNAM’s Dirección General de Estudios de Posgrado.     

Cooling of neutron stars with strong toroidal magnetic fields

We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the surface in a large part of the crust. As a result, the neutron star surface presents two warm regions surrounded by extended cold regions and has a thermal luminosity much lower than in the case the magnetic field is purely poloidal. We apply these models to calculate the thermal evolution of such neutron stars and show that the lowered photon luminosity naturally extends their life-time as detectable thermal X-ray sources. Work partially supported by UNAM-DGAPA grant #IN119306.     

Detection of the optical counterpart of the proposed double degenerate polar RX J1914+24

We have detected the optical counterpart of the proposed double degenerate polar RX J1914+24. The I -band light curve is modulated on the 9.5-min period seen in X-rays. There is no evidence for any other periods. No significant modulation is seen in J . The infrared colours of RX J1914+24 are not consistent with a main-sequence dwarf secondary star. Our ASCA spectrum of RX J1914+24 is typical of a heavily absorbed polar and our ASCA light curve also shows only the 9.5-min period. We find that the folded I band and X-ray light curves are out of phase. We attribute the I -band flux to the irradiated face of the donor star. The long-term X-ray light curve shows a variation in the observed flux of up to an order of magnitude. These observations strengthen the view that RX J1914+24 is indeed the first double degenerate polar to be detected. In this light, we discuss the synchronizing mechanisms in such a close binary and other system parameters.     

Nature of the soft x-ray excess in the spectrum of RX J1037.5-5647

The source responsible for the soft x-ray excess in the emission spectrum of the pulsar RX J1037.5-5647 is associated with a hot spot on the surface of the neutron star near the base of an accretion column. The intensity of the emission from this source, however, only undergoes small (on the order of 15%) variations, while the intensity of the hard component varies substantially with the rotation period of the neutron star. We show that this situation can occur if the angle between the axis of rotation and the magnetic axis of the neutron star is no more than 8°. The variation in the intensity of the hard component of the radiation in this case is interpreted in terms of an anisotropy in the directional diagram. In this scenario, the angle of inclination of the orbit of the binary system is close to 10°.     

A cocoon model for thermal X-ray sources and ‘Oscillars’

A gas cocoon surrounding a neutron star can be heated to a high temperature by the low frequency radiation emitted by the neutron star whose rotation axis is inclined to its magnetic axis. This heated gas can emit X-rays and may be identified with thermal X-ray sources. If the neutron star emission shows periodicities larger than the cooling time of the gas, these will be reflected in the emission of X-ray; the recently observed X-ray sources which show oscillations and quasiperiodicities (Oscillars) may be such sources.     

Discovery of the high-field polar RX J1724.0+4114

We report the discovery of a new AM Herculis binary (polar) as the optical counterpart of the soft X-ray source RX J1724.0+4114 detected during the ROSAT all-sky survey. The magnetic nature of this V  ∼ 17 mag object is confirmed by low-resolution spectroscopy showing strong Balmer and He  II emission lines superimposed on a blue continuum, which is deeply modulated by cyclotron humps. The inferred magnetic field strength is 50 ± 4 MG (or possibly even ≈ 70 MG). Photometric observations spanning ∼ 3 yr reveal a period of 119.9 min, directly below the period gap. The morphology of the optical and X-ray light curves, which do not show eclipses by the secondary star, suggests a self-eclipsing geometry. We derive a lower limit on the distance of d  ≳ 250 pc.     

Cooling of quark stars in the colour superconductive phase: effect of photons from glueball decay

The cooling history of a quark star in the colour superconductive phase is investigated. Here we specifically focus on the two-flavour colour (2SC) phase where the novel process of photon generation via glueball (GLB) decay has already been investigated. The picture we present here can, in principle, be generalized to quark stars entering a superconductive phase where similar photon generation mechanisms are at play. As much as 10⁴⁵–10⁴⁷ erg of energy is provided by the GLB decay in the 2SC phase. The generated photons slowly diffuse out of the quark star, keeping it hot and radiating as a blackbody (with possibly a Wien spectrum in gamma-rays) for millions of years. We discuss hot radio-quiet isolated neutron stars in our picture (such as RX J185635–3754 and RX J0720.4–3125) and argue that their nearly blackbody spectra (with a few broad features) and their remarkably tiny hydrogen atmosphere are indications that these might be quark stars in the colour superconductive phase where some sort of photon generation mechanism (reminiscent of the GLB decay) has taken place. Fits to observed data of cooling compact stars favour models with superconductive gaps of  Δ_2SC∼ 15–35 MeV  and densities  ρ_2SC= (2.5–3.0) ×ρ_N  (ρ_N being the nuclear matter saturation density) for quark matter in the 2SC phase. If correct, our model combined with more observations of isolated compact stars could provide vital information to studies of quark matter and its exotic phases.     

Heat blanketing envelopes and thermal radiation of strongly magnetized neutron stars

Strong (B?10⁹ G) and superstrong (B?10¹⁴ G) magnetic fields profoundly affect many thermodynamic and kinetic characteristics of dense plasmas in neutron star envelopes. In particular, they produce strongly anisotropic thermal conductivity in the neutron star crust and modify the equation of state and radiative opacities in the atmosphere, which are major ingredients of the cooling theory and spectral atmosphere models. As a result, both the radiation spectrum and the thermal luminosity of a neutron star can be affected by the magnetic field. We briefly review these effects and demonstrate the influence of magnetic field strength on the thermal structure of an isolated neutron star, putting emphasis on the differences brought about by the superstrong fields and high temperatures of magnetars. For the latter objects, it is important to take proper account of a combined effect of the magnetic field on thermal conduction and neutrino emission at densities ρ?10¹⁰ g?cm^?3. We show that the neutrino emission puts a B-dependent upper limit on the effective surface temperature of a cooling neutron star.     

Two X-ray sources model of Cyg X-3

A model of Cyg X-3, as a binary cocooned star system with two sources of X-rays, one above the polar caps of the neutron star — the usual pulsar radiation — and the other around the equatorial plane of the magneto-bounding surface formed due to the interaction of the infalling plasma and the magnetic field of the neutron star, is made. The X-ray, -ray, and IR radiation light curves are considered from the shadow effect. An upper limit on the mass of the neutron star is estimated from the consideration of periodic derivative purely due to mass loss. A comparison is made with the results of Elsneret al. (1980) and Ghoshet al. (1981), which they derived from the consideration of period derivative purely from apsidal motion.     

Constraining the geometry of the neutron star RX J1856.5−3754

RX J1856.5−3754 is one of the brightest, nearby isolated neutron stars (NSs), and considerable observational resources have been devoted to its study. In previous work, we found that our latest models of a magnetic, hydrogen atmosphere match well the entire spectrum, from X-rays to optical (with best-fitting NS radius   R ≈ 14  km, gravitational redshift   z _g∼ 0.2  , and magnetic field   B ≈ 4 × 10¹²  G). A remaining puzzle is the non-detection of rotational modulation of the X-ray emission, despite extensive searches. The situation changed recently with XMM–Newton observations that uncovered 7-s pulsations at the     level. By comparing the predictions of our model (which includes simple dipolar-like surface distributions of magnetic field and temperature) with the observed brightness variations, we are able to constrain the geometry of RX J1856.5−3754, with one angle <6° and the other angle     , though the solutions are not definitive, given the observational and model uncertainties. These angles indicate a close alignment between the rotation and the magnetic axes or between the rotation axis and the observer. We discuss our results in the context of RX J1856.5−3754 being a normal radio pulsar and a candidate for observation by future X-ray polarization missions such as Constellation-X or XEUS .