Neutron stars harbor extremely strong magnetic fields within their solid outer crust. The topology of this field strongly influences the surface temperature distribution and, hence, the star's ...observational properties. In this work, we present the first realistic simulations of the coupled crustal magnetothermal evolution of isolated neutron stars in three dimensions accounting for neutrino emission, obtained with the pseudo-spectral code parody. We investigate both the secular evolution, especially in connection with the onset of instabilities during the Hall phase, and the short-term evolution following episodes of localized energy injection. Simulations show that a resistive tearing instability develops in about a Hall time if the initial toroidal field exceeds G. This leads to crustal failures because of the huge magnetic stresses coupled with the local temperature enhancement produced by dissipation. Localized heat deposition in the crust results in the appearance of hot spots on the star surface, which can exhibit a variety of patterns. Because the transport properties are strongly influenced by the magnetic field, the hot regions tend to drift away and get deformed following the magnetic field lines while cooling. The shapes obtained with our simulations are reminiscent of those recently derived from NICER X-ray observations of the millisecond pulsar PSR J0030+0451.
The launch of the IXPE telescope in late 2021 finally made polarization measurements in the 2–8keV band a reality, more than 40 years after the pioneering observations of the OSO-8 satellite. In the ...first two years of operations, IXPE targeted more than 60 sources, including four magnetars, neutron stars with magnetic fields in the petaGauss range. In this paper we summarize the IXPE main findings and discuss their implications for the physics of ultra-magnetized neutron stars. Polarimetric observations confirmed theoretical predictions, according to which X-ray radiation from magnetar sources is highly polarized, up to ≈80%, the highest value detected so far. This provides an independent confirmation that magnetars are indeed endowed with a super-strong magnetic field and that the twisted magnetosphere scenario is the most likely explanation for their soft X-ray emission. Polarization measurements allowed us to probe the physical conditions of the star’s outermost layers, showing that the cooler surface regions are in a condensed state, with no atmosphere on top. Although no smoking-gun of vacuum QED effects was found, the phase-dependent behavior of the polarization angle strongly hints that vacuum birefringence is indeed at work in magnetar magnetospheres.
Abstract
X-ray emission from the surface of isolated neutron stars (NSs) has been now observed in a variety of sources. The ubiquitous presence of pulsations clearly indicates that thermal photons ...either come from a limited area, possibly heated by some external mechanism, or from the entire (cooling) surface but with an inhomogeneous temperature distribution. In an NS the thermal map is shaped by the magnetic field topology since heat flows in the crust mostly along the magnetic field lines. Self-consistent surface thermal maps can hence be produced by simulating the coupled magnetic and thermal evolution of the star. We compute the evolution of the NS crust in three dimensions for different initial configurations of the magnetic field and use the ensuing thermal surface maps to derive the spectrum and the pulse profile as seen by an observer at infinity, accounting for general-relativistic effects. In particular, we compare cases with a high degree of symmetry with inherently 3D ones, obtained by adding a quadrupole to the initial dipolar field. Axially symmetric fields result in rather small pulsed fractions (≲5%), while more complex configurations produce higher pulsed fractions, up to ∼25%. We find that the spectral properties of our axisymmetric model are close to those of the bright isolated NS RX J1856.5-3754 at an evolutionary time comparable with the inferred dynamical age of the source.
We present the results of an XMM-Newton observation of the slowly rotating (P = 3.4 s), highly magnetized (B ≈ 3 × 1013 G) radio pulsar PSR J0726–2612. A previous X-ray observation with the Chandra ...satellite showed that some of the properties of PSR J0726–2612 are similar to those of the X-ray-dim isolated neutron stars (XDINSs), a small class of nearby slow pulsars characterized by purely thermal X-ray spectra and undetected in the radio band. We confirm the thermal nature of the X-ray emission of PSR J0726–2612, which can be fitted by the sum of two blackbodies with temperatures k T 1 = 0 . 074 − 0.011 + 0.006 $ kT_1 = 0.074_{-0.011}^{+0.006} $ kT1=0.074+0.006-0.011 keV and k T 2 = 0 . 14 − 0.02 + 0.04 $ kT_2=0.14_{-0.02}^{+0.04} $ kT2=0.14+0.004-0.002 keV and emitting radii R 1 = 10 . 4 − 2.8 + 10.8 $ R_1=10.4_{-2.8}^{+10.8} $ R1=10.4+10.8-2.8 km and R 2 = 0 . 5 − 0.3 + 0.9 $ R_2=0.5_{-0.3}^{+0.9} $ R2=0.5+0.9-0.3 km, respectively (assuming a distance of 1 kpc). A broad absorption line modeled with a Gaussian profile centered at 0 . 39 − 0.03 + 0.02 $ 0.39_{-0.03}^{+0.02} $ 0.39+0.02-0.03 keV is required in the fit. The pulse profile of PSR J0726–2612 is characterized by two peaks with similar intensity separated by two unequal minima, a shape and pulsed fraction that cannot be reproduced without invoking magnetic beaming of the X-ray emission. The presence of a single radio pulse suggests that in PSR J0726–2612 the angles that the dipole axis and the line of sight make with the rotation axis, ξ and χ, respectively, are similar. This geometry differs from that of the two radio-silent XDINSs with double-peaked pulse profiles similar to that of PSR J0726–2612, for which ξ ∼ 90° and χ ∼ 45° have recently been estimated. These results strengthen the similarity between PSR J0726–2612 and the XDINSs and support the possibility that the lack of radio emission from the latter might simply be due to an unfavorable viewing geometry.
Bursts and flares are among the distinctive observational manifestations of magnetars, isolated neutron stars endowed with an ultra-strong magnetic field ( B ≈ 10 14 – 10 15 G). It is believed that ...these events arise in a hot electron-positron plasma, injected in the magnetosphere, due to a magnetic field instability, which remains trapped within the closed magnetic field lines (the “trapped-fireball” model). We have developed a simple radiative transfer model to simulate magnetar flare emission in the case of a steady trapped fireball. After dividing the fireball surface in a number of plane-parallel slabs, the local spectral and polarization properties are obtained integrating the radiative transfer equations for the two normal modes. We assume that magnetic Thomson scattering is the dominant source of opacity, and neglect contributions from second-order radiative processes, although the presence of double-Compton scattering is accounted for in establishing local thermal equilibrium in the fireball atmospheric layers. The spectra we obtained in the 1–100 keV energy range are in broad agreement with those of available observations. The large degree of polarization (≳80%) predicted by our model should be easily detectable by new-generation X-ray polarimeters, like IXPE, XIPE and eXTP, allowing one to confirm the model predictions.
Abstract
Photon–axion mixing can create observable signatures in the thermal spectra of isolated, cooling neutron stars. Their shape depends on the polarization properties of the radiation, which, in ...turn, are determined by the structure of the stellar outermost layers. Here we investigate the effect of mixing on the spectrum and polarimetric observables, polarization fraction and polarization angle, using realistic models of surface emission. We focus on RX J1856.5–3754, the only source among the X-ray-dim isolated neutron stars for which polarimetric measurements in the optical band were performed. Our results show that in the case of a condensed surface in both fixed and free-ion limits, the mixing can significantly limit the geometric configurations that reproduce the observed linear polarization fraction of 16.43%. In the case of an atmosphere, the mixing does not create any noticeable signatures. Complementing our approach with the data from upcoming soft X-ray polarimetry missions will allow one to obtain constraints on
g
γ
a
∼ 10
−11
GeV
−1
and
m
a
≲ 10
−6
eV, improving the present experimental and astrophysical limits.
Context.
Phase-resolved spectral and spectropolarimetric X-ray observations of magnetars present us with the opportunity to test models of the origin of the X-ray emission from these objects, and to ...constrain the properties of the neutron star surface and atmosphere.
Aims.
Our first aim is to use archival
XMM-Newton
observations of the magnetar 1RXS J170849.0−400910 to ascertain how well four emission models describe the phase-resolved
XMM-Newton
energy spectra. Our second aim is to evaluate the scientific potential of future spectropolarimetric observations of 1RXS J170849.0−400910 with the Imaging X-ray Polarimetry Explorer (IXPE) scheduled for launch in late 2021. The most salient questions are whether IXPE is able to distinguish between the different emission models, and whether IXPE can unambiguously detect the signatures of quantum electrodynamics (QED) effects in strong magnetic fields.
Methods.
We used numerical radiation transport calculations for a large number of different system parameters to predict the X-ray flux and polarization energy spectra of the source 1RXS J170849.0−400910. Based on the numerical results, we developed a new model to fit phase-resolved and phase-averaged X-ray spectral (i.e.,
XMM-Newton
and IXPE) and spectropolarimetric (IXPE) data. In order to test the sensitivity of IXPE to strong-field QED effects, we fit a simulated IXPE observation with two versions of the model, i.e., with and without QED effects accounted for.
Results.
The fixed-ions condensed surface model gives the best description of the phase-resolved
XMM-Newton
spectra, followed by the blackbody and free-ions condensed surface models. The magnetized atmosphere model gives a poor description of the data and seems to be largely excluded. Simulations show that the IXPE observations of sources such as 1RXS J170849.0−400910 will allow us to cleanly distinguish between high-polarization (blackbody, magnetized atmosphere) and low-polarization (condensed surface) models. If the blackbody or magnetized atmosphere models apply, IXPE can easily prove QED effects based on ∼200 ksec observations as studied here; longer IXPE observation times will be needed for a clear detection in the case of the condensed surface models.
Conclusions.
The
XMM-Newton
data have such a good signal-to-noise ratio that they reveal some limitations of the theoretical models. Notwithstanding this caveat, the fits clearly favor the fixed-ions condensed surface and blackbody models over the free-ions condensed surface and magnetized atmosphere models. The IXPE polarization information will greatly help us to figure out how to improve the models. The first detection of strong-field QED effects in the signal from astrophysical sources seems possible if an adequate amount of time is dedicated to the observations.
ABSTRACT
We report the results of new XMM-Newton observations of the middle-aged (τc = 1.1 × 105 yr) radio pulsar PSR J1740+1000 carried out in 2017–2018. These long pointings (∼530 ks) show that the ...non-thermal emission, well described by a power-law spectrum with photon index Γ = 1.80 ± 0.17, is pulsed with a ∼30 per cent pulsed fraction above 2 keV. The thermal emission can be well-fit with the sum of two blackbodies of temperatures kT1 = 70 ± 4 eV and kT2 = 137 ± 7 eV, and emitting radii $R_1=5.4_{-0.9}^{+1.3}$ km and $R_2=0.70_{-0.13}^{+0.15}$ km (for a distance of 1.2 kpc). We found no evidence for absorption lines as those observed in the shorter XMM-Newton observations (∼67 ks) of this pulsar carried out in 2006. The X-ray thermal and non-thermal components peak in antiphase and none of them is seen to coincide in phase with the radio pulse. This, coupled with the small difference in the emission radii of the two thermal components, disfavours an interpretation in which the dipolar polar cap is heated by magnetospheric backward-accelerated particles. Comparison with the other thermally emitting isolated neutron stars with spectra well described by the sum of two components at different temperatures shows that the ratios T2/T1 and R2/R1 are similar for objects of different classes. The observed values cannot be reproduced with simple temperature distributions, such as those caused by a dipolar field, indicating the presence of more complicated thermal maps.
ABSTRACT
Magnetars, the most strongly magnetized neutron stars, are among the most promising targets for X-ray polarimetry. Imaging X-ray Polarimetry Explorer (IXPE), the first satellite devoted to ...exploring the sky in polarized X-rays, has observed four magnetars to date. A proper interpretation of IXPE results requires the development of new atmospheric models that can take into proper account the effects of the magnetized vacuum on par with those of the plasma. Here we investigate the effects of mode conversion at the vacuum resonance on the polarization properties of magnetar emission by computing plane-parallel atmospheric models under varying conditions of magnetic field strength/orientation, effective temperature, and allowing for either complete or partial adiabatic mode conversion. Complete mode conversion results in a switch of the dominant polarization mode, from the extraordinary (X) to the ordinary (O) one, below an energy that decreases with increasing magnetic field strength, occurring at $\approx 0.5\, \mathrm{keV}$ for a magnetic field strength of $B=10^{14}\, \mathrm{G}$. Partial adiabatic mode conversion results in a reduced polarization degree when compared with a standard plasma atmosphere. No dominant mode switch occurs for $B=10^{14}\, \mathrm{G}$, while there are two switches for lower fields of $B=3\times 10^{13}\, \mathrm{G}$. Finally, by incorporating our models in a ray-tracing code, we computed the expected polarization signal at infinity for different emitting regions on the star surface and for different viewing geometries. The observability of quantum electrodynamics signatures with IXPE and with future soft X-ray polarimeters as Rocket Experiment Demonstration of a Soft X-ray Polarimeter is discussed.
PSR B0943+10 is a mode-switching radio pulsar characterized by two emission modes with different radio and X-ray properties. Previous studies, based on simple combinations of blackbody and power-law ...models, showed that its X-ray flux can be decomposed in a pulsed thermal plus an unpulsed nonthermal components. However, if PSR B0943+10 is a nearly aligned rotator seen pole-on, as suggested by the radio data, it is difficult to reproduce the high observed pulsed fraction unless magnetic beaming is included. In this work, we reanalyze all of the available X-ray observations of PSR B0943+10 with simultaneous radio coverage, modeling its thermal emission with polar caps covered by a magnetized hydrogen atmosphere or with a condensed iron surface. The condensed surface model provides good fits to the spectra of both pulsar modes, but, similarly to the blackbody, it cannot reproduce the observed pulse profiles, unless an additional power law with an ad hoc modulation is added. Instead, the pulse profiles and phase-resolved spectra are well described using the hydrogen atmosphere model to describe the polar cap emission plus an unpulsed power law. For the X-ray brighter state (Q-mode) we obtain a best fit with a temperature , an emitting radius m, a magnetic field consistent with the value of the dipole field of 4 × 1012 G inferred from the timing parameters, and a small angle between the magnetic and spin axis, = 5 The corresponding parameters for the X-ray fainter state (B-mode) are and R ∼ 170 m.
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