Heating and cooling of magnetars with accreted envelopes

We study the thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in an internal layer. We focus on the effect of magnetized (   B ≳ 10¹⁴  G) non-accreted and accreted outermost envelopes composed of different elements, from iron to hydrogen or helium. We discuss a combined effect of thermal conduction and neutrino emission in the outer neutron star crust and calculate the cooling of magnetars with a dipole magnetic field for various locations of the heat layer, heat rates and magnetic field strengths. Combined effects of strong magnetic fields and light-element composition simplify the interpretation of magnetars in our model: these effects allow one to interpret observations assuming less extreme (therefore, more realistic) heating. Massive magnetars, with fast neutrino cooling in their cores, can have higher thermal surface luminosity.     

Transport properties of the degenerate electron gas of neutron stars along the quantizing magnetic field

The expressions are derived for thermal and electric conductivities as well as thermopower of a degenerate relativistic electron gas in the surface layers of neutron stars along the magnetic fieldB=4×10¹¹–10¹⁴G for two scattering mechanisms of electrons, namely, for Coulomb scattering on ions in the ion-liquid regime and on high-temperature phonons in the solid regime. The results may be of use to study neutron star cooling rates, nuclear burning of the matter in the surface layers, diffusion of the magnetic field, etc.     

On the differential rotation of the polar caps of neutron stars

The model of a magnetized rotating neutron star with an electric current in the region of its fluid polar magnetic caps is considered. The presence of an electric current leads to differential rotation of the magnetic caps. The rotation structure is determined by the electric current density distribution over the surface. In the simplest axisymmetric configuration, the current flows in one direction near the polar cap center and in the opposite direction in the outer ring (the total current is zero for the neutron star charge conservation). In this case, two rings with opposite directions of rotation appear on the neutron star surface, with the inner ring always lagging behind the star’s main rotation. The differential rotation velocity is directly proportional to the electric current density gradient along the polar cap radius. At a width of the region of change in the electric current from 1 to 10² cm and a period ～1 s and a magnetic field B ～ 10¹² G typical of radio pulsars, the linear differential rotation velocity is ～10^?2–10^?4 cm s^?1 (corresponding to a revolution time of ～0.1–10 yr).     

Relativistic plasma diffusion: a possible source for neutron star magnetic fields

Plasma density gradient which is inherent to degenerate neutron star matter is shown to lead to large scale plasma diffusion and subsequent charge separation. The surface (internal) fields generated by the spinning separated charges are found to be dipolar with intensities of ≃ 10¹⁴ G (for the surface fields) very early in the life-time of a typical neutron star. The internal fields, on the other hand, are relatively much weaker. These fields, which in this case are also shown to be temperature dependent, decay as a result of neutrino and photon emissions. The decay law derived from equations of standard cooling calculations and the equation connecting the magnetic field and temperature is indicated to have two distinct modes, each corresponding to the two branches of a typical neutron star cooling curve. We have found that results derived from the decay law are consistent with observational findings. Based on the theory behind our new model, we have also argued to show that isolated millisecond and sub-millisecond pulsars might be very rare objects. This revised version was published online in July 2006 with corrections to the Cover Date.     

A young cooling neutron star in the remnant of Supernova 1987A

We describe the cooling theory for isolated neutron stars that are several tens of years old. Their cooling differs greatly from the cooling of older stars that has been well studied in the literature. It is sensitive to the physics of the inner stellar crust and even to the thermal conductivity of the stellar core, which is never important at later cooling stages. The absence of observational evidence for the formation of a neutron star during the explosion of Supernova 1987A is consistent with the fact that the star was actually born there. It may still be hidden in the dense center of the supernova remnant. If, however, the star is not hidden, then it should have a low thermal luminosity (below ～10³⁴ erg s^?1) and a short internal thermal relaxation time (shorter than 13 yr). This requires that the star undergo intense neutrino cooling (e.g., via the direct Urca process) and have a thin crust with strong superfluidity of free neutrons and/or an anomalously high thermal conductivity.     

Magnetic field decay of magnetars in supernova remnants

In this paper, we modify our previous research carefully, and derive a new expression of electron energy density in superhigh magnetic fields. Based on our improved model, we re-compute the electron capture rates and the magnetic fields’ evolutionary timescales t of magnetars. According to the calculated results, the superhigh magnetic fields may evolve on timescales ～(10⁶?10⁷) yrs for common magnetars, and the maximum timescale of the field decay, t≈2.9507×10⁶ yrs, corresponding to an initial internal magnetic field B ₀=3.0×10¹⁵ G and an initial inner temperature T ₀=2.6×10⁸ K. Motivated by the results of the neutron star-supernova remnant (SNR) association of Zhang and Xie (2011), we calculate the maximum B ₀ of magnetar progenitors, B _max～(2.0×10¹⁴?2.93×10¹⁵) G when T ₀=2.6×10⁸ K. When T ₀～2.75×10⁸?1.75×10⁸ K, the maximum B ₀ will also be in the range of ～10¹⁴?10¹⁵ G, not exceeding the upper limit of magnetic field of a magnetar under our magnetar model. We also investigate the relationship between the spin-down ages of magnetars and the ages of their SNRs, and explain why all AXPs associated with SNRs look older than their real ages, whereas all SGRs associated with SNRs appear younger than they are.     

Neutrino energy loss on nuclides 56Fe, 56Co, 56Ni, 56Mn, 56Cr, and 56V by electron capture in magnetars

Based on the theory of relativity, the assumption of a superstrong magnetic field (SMF), and the shell model, the neutrino energy loss (NEL) rates of nuclides ⁵⁶Fe, ⁵⁶Co, ⁵⁶Ni, ⁵⁶Mn, ⁵⁶Cr, and ⁵⁶V by electron capture are investigated in the range of magnetic fields from 10¹³ G to 10¹⁸ G in magnetars. We also discuss the rates of change of the electron fraction (RCEF) in SMF and compare our results in SMF with those of FFN and Nabi, which is for the case without SMF. The results show that the NEL rates are increased greatly and even exceed by eight orders of magnitude in SMF. The RCEF are decreased largely and even exceed by seven orders of magnitude in SMF. On the other hand, our calculated NEL rates with SMF are larger by seven orders of magnitude than FFN’s at B=10¹⁸ G, and even by eight orders of magnitude compared to Nabi’s.     

Magnetar corona

Persistent high-energy emission of magnetars is produced by a plasma corona around the neutron star, with total energy output of ～10³⁶ erg/s. The corona forms as a result of sporadic starquakes that twist the external magnetic field of the star and induce electric currents in the closed magnetosphere. Once twisted, the magnetosphere cannot untwist immediately because of its self-induction. The self-induction electric field lifts particles from the stellar surface, accelerates them, and initiates avalanches of pair creation in the magnetosphere. The created plasma corona maintains the electric current demanded by curl B and regulates the self-induction e.m.f. by screening. This corona persists in dynamic equilibrium: it is continually lost to the stellar surface on the light-crossing time ～10^?4 s and replenished with new particles. In essence, the twisted magnetosphere acts as an accelerator that converts the toroidal field energy to particle kinetic energy. The voltage along the magnetic field lines is maintained near threshold for ignition of pair production, in the regime of self-organized criticality. The voltage is found to be about ～1 GeV which is in agreement with the observed dissipation rate ～10³⁶ erg/s. The coronal particles impact the solid crust, knock out protons, and regulate the column density of the hydrostatic atmosphere of the star. The transition layer between the atmosphere and the corona is the likely source of the observed 100 keV emission. The corona also emits curvature radiation up to 10¹⁴ Hz and can supply the observed IR-optical luminosity.     

Dynamics of the flows accreting onto a magnetized neutron star

We investigate the unsteady column accretion of material at a rate \(10^{15} g s^{ - 1} \leqslant \dot M \leqslant 10^{16} g s^{ - 1}\) onto the surface of a magnetized neutron star using a modified first-order Godunov method with splitting. We study the dynamics of the formation and evolution of a shock in an accretion column near the surface of a star with a magnetic field 5×10¹¹≤B≤10¹³ G. An effective transformation of the accretion flow energy into cyclotron radiation is shown to be possible for unsteady accretion with a collisionless shock whose front executes damped oscillations. The collisionless deceleration of the accreting material admits the conservation of a fraction of the heavy nuclei that have not been destroyed in spallation reactions. The fraction of the CNO nuclei that reach the stellar atmosphere is shown to depend on the magnetic field strength of the star.     

Exotic ion H 3 ++ in strong magnetic fields

1. The exotic system H ₃ ⁺⁺ (which does not exist without magnetic field) exists in strong magnetic fields:
   1. In triangular configuration for B≈10⁸–10¹¹?G (under specific external conditions)
   2. In linear configuration for B>10¹⁰?G
2. In the linear configuration the positive z-parity states 1σ _g , 1π _u , 1δ _g are bound states
3. In the linear configuration the negative z-parity states 1σ _u , 1π _g , 1δ _u are repulsive states
4. The H ₃ ⁺⁺ molecular ion is the most bound one-electron system made from protons at B>3×10¹³?G

Possible application: The H ₃ ⁺⁺ molecular ion may appear as a component of a neutron star atmosphere under a strong surface magnetic field B=10¹²–10¹³?G.     

Relativistic Correction of Neutrino Emission in Neutron Stars

By the relativistic mean field theory and relevant weak-interactional cooling theory, the relativistic cooling properties in the conventional and hyperonic neutron star matter are studied. Also a comparison between the relativistic and non-relativistic results after taking consideration of the gravity correction is performed. The results show that the relativistic effect of neutrino emission reduces the neutrino emissivity, luminosity, and the cooling rate of stellar objects, in comparison with the non-relativistic case. In the neutron star matter without hyperon, the amplitude of the cooling rate reduction caused by the relativistic effect is maximal after taking the gravity correction into consideration, it attains 56% for a 2 M_⊙ neutron star composed of conventional neutron star matter, and in the hyperonic matter the amplitude of reduction is minimal, about 38%.     

NuSTAR observations of the X-ray pulsar LMC X-4: A constraint on the magnetic field and tomography of the system in the fluorescent iron line

We present the results of the spectral and timing analysis of the X-ray pulsar LMC X-4 based on data from the NuSTAR observatory in the broad X-ray energy range 3–79 keV. Along with a detailed analysis of the source’s averaged spectrum, high-precision spectra corresponding to different phases of the neutron star spin cycle have been obtained for the first time. The Comptonization model is shown to describe best the source’s spectrum, and the evolution of its parameters as a function of the pulse phase has been traced. For all spectra (the averaged and phase-resolved ones) in the energy range 5–55 keV we have searched for the cyclotron absorption line. The derived upper limit on the optical depth of the cyclotron line τ ~ 0.15 (3σ) points to the absence of this feature in the given energy range, which provides a constraint on the magnetic field of the neutron star: B <3 × 10¹¹ or >6.5 × 10¹² G. The latter constraint is consistent with the magnetic field estimate obtained by analyzing the pulsar’s power spectrum, B ? 3 × 10¹³ G. Based on our analysis of the phase-resolved spectra, we have determined the delay between the emission peaks and the equivalent width of the fluorescent iron line. This delay depends on the orbital phase and is apparently associated with the travel time of photons between the emitting regions in the vicinity of the neutron star and the region where the flux is reflected (presumably in the inflowing stream or at the place of interaction between the stream and the outer edge of the accretion disk).     

Oscillations of optical emission from flare stars and coronal loop diagnostics

Based on an analogy between stellar and solar flares, we investigate the ten-second oscillations detected in the U and B bands on the star EV Lac. The emission pulsations are associated with fast magnetoacoustic oscillations in coronal loops. We have estimated the magnetic field, B ≈ 320 G; the temperature, T ≈ 3.7 × 10⁷ K; and the plasma density, n ≈ 1.6 × 10¹¹ cm^?3, in the region of energy release. We provide evidence suggesting that the optical emission source is localized at the loop footpoints.     

Tunnel effect in molecules in strong magnetic fields of neutron stars

It is shown that, in the strong magnetic field of the neutron starB=10¹²–10¹³ G, the probability of the tunnel effect in the molecules increases significantly. It is quite probable that this effect can catalyze nuclear reactions at the neutron star surface.     

Cosmic gamma-ray burst spectroscopy

A review is given of the gamma-ray burst energy spectrum measurements on Venera 11 and Venera 12 space probes. The gamma burst continuum approximates in shape thermal brems-strahlung emission of a hot plasma. The radiation temperature varies over a broad range, 50–1000 keV, for different events. Spectra of many bursts contain cyclotron absorption and/or redshifted annihilation lines. Strong variability is typically observed in both continuum and line spectra. These spectral data provide convincing evidence for the gamma-ray bursts being generated by neutron stars with superstrong magnetic fields 10¹²–10¹³ G.     

Influence of a strong magnetic field on the neutrino heating of a supernova shock

Based on the magnetorotational model of a supernova explosion with core collapse, we investigate the significant processes of neutrino heating of the supernova shock. These processes should be taken into account in self-consistent modeling, since the neutrino heating mechanism is capable of increasing the explosion efficiency. We show that, even in the presence of a strong magnetic field (B ～ 10¹⁵ G) in the shock formation region, the heating rate is determined with good accuracy by the absorption and emission of neutrinos in direct URCA processes. Moreover, the influence on them of a magnetic field is reduced to insignificant corrections.     

Hydrogen molecular ion in the magnetic field of a neutron star

A two-dimensional potential energy surface of an H ₂ ⁺ molecular ion is calculated for the case of the strong magnetic field of the neutron starB=10¹¹–10¹³ G. It is shown that the dependence of the potential energy from the angle between the magnetic field direction and the internuclear axis becomes very sharp as the magnetic field increases. The obtained potential energy surfaces can be used for studying the vibrational-rotational structure of the H ₂ ⁺ spectrum in a strong magnetic field and the development of the observational methods for the determination of the magnetic field of a neutron star.     

The nature of radio emission from pulsars

It is shown that radio emission from pulsars is unlikely to be of coherent synchrotron origin if the surface magnetic field of the central neutron star is greater than 10⁸ G.     

Neutrino synchrotron radiation

The neutrino luminosity of several models of neutron stars has been computed according to the photon-neutrino coupling theory and compared with that of the current-current coupling theory. It is shown that the NSR process alone should have cooled the core of the neutron star created in a supernova explosion in 1954 A.D. to a temperature around 2×10⁹ K according to the photon-neutrino coupling theory.The emission power of the star is greater than the emission power of the X-ray source discovered in the Crab Nebula; so the source may be interpreted as the thermal radiation of the star according to the photon-neutrino coupling theory.     

Thermal Evolution of Neutron Stars

We present results from simulations of protoneutron star thermal evolution using neutrino opacities that are consistently calculated with the equation of state. When hyperons are allowed to appear in the system, we obtain metastable configurations that after the deleptonization stage become unstable. Concerning the evolution of old neutron stars, we present the results of our investigation on the effect of the Joule heating due to magnetic field dissipation. We conclude that this mechanism can be efficient in maintaining the surface temperature of the star above 3 × 10⁴ - 10⁵ K during a very long time (≥ 100 Myr), comparable with the decay time of the magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.