The effects of ultra-strong magnetic fields on electron capture rates for iron group nuclei in the outer crust of magnetars

Based on the work of Wang et al. (Chin. Phys. Lett. 29:049701, 2012), we re-investigated electron capture on iron group nuclei in the outer crust of magnetars and studied magnetar evolution. Effects of ultra-strong magnetic field on electron capture rates for ⁵⁷Co have been analyzed in the nuclear shell model and under the Landau-level-quantization approximation, and the electron capture rates and the neutrino energy loss rates on iron group nuclei in the outer crust of magnetar have been calculated. The results show that electron capture rates on ⁵⁷Co are increase greatly in the ultra-strong magnetic field, and above 3 orders of magnitude generally; and the neutrino energy loss rates by electron capture on iron group nuclei increase above 3 orders of magnitude in the range from B=4.414×10¹³ G to B=4.414×10¹⁵ G. These conclusions play an important role in future studying the evolution of magnetar. Furthermore, we modify the expressions of the electron chemical potential (Fermi energy) and phase space factor by introducing Dirac δ-function, and select appropriate parameters of temperature T, magnetic field B and matter density ρ in the our crust, thus our results will be reliable than those of Wang et al.     

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.     

Evolution of superhigh magnetic fields of magnetars

In this paper, we consider the effect of Landau levels on the decay of superhigh magnetic fields of magnetars. Applying ³ P ₂ anisotropic neutron superfluid theory yield a second-order differential equation for a superhigh magnetic field B and its evolutionary timescale t. The superhigh magnetic fields may evolve on timescales ∼(10⁶–10⁷) yrs for common magnetars. According to our model, the activity of a magnetar may originate from instability caused by the high electron Fermi energy.     

Two-photon positron–electron annihilation in a strong magnetic field

We consider the two-photon positron and electron annihilation in flight, it means the annihilating particles exhibit the middly relativistic momenta in a super strong magnetic field. Such particles are present in the corona of pulsars and magnetars. The paper presents how the total emission rate for the two-photon process is affected not only by magnetic field but also by the relativistic momentum of the annihilating particles. We found that the momenta influence significantly the total emission rate and the directions of the emitted photons. Additionally, the total emission for the two-photon process is comparable to that for the one-photon process at the momentum of annihilating particles of about m₀, where m₀ is the electron mass, and the magnetic field close to the critical Schwinger value of 4.41 × 10¹³ G. The latter is reported as a main annihilation channel in a super strong magnetic field. We calculated also the energetic spectra of annihilating photons emitted, which are also affected by the magnetic field and the momenta of the annihilating particles.     

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.     

Lower bound on the magnetic field strength of a magnetar from analysis of SGR giant flares

Based on the magnetar model, we have studied in detail the processes of neutrino cooling of an electron-positron plasma generating an SGR giant flare and the influence of the magnetar magnetic field on these processes. Electron-positron pair annihilation and synchrotron neutrino emission are shown to make a dominant contribution to the neutrino emissivity of such a plasma. We have calculated the neutrino energy losses from a plasma-filled region at the long tail stage of the SGR 0526-66, SGR 1806–20, and SGR 1900+14 giant flares. This plasma can emit the energy observed in an SGR giant flare only in the presence of a strongmagnetic field suppressing its neutrino energy losses. We have obtained a lower bound on the magnetic field strength and showed this value to be higher than the upper limit following from an estimate of the magnetic dipole losses for the magnetars being analyzed in a wide range of magnetar model parameters. Thus, it is problematic to explain the observed energy release at the long tail stage of an SGR giant flare in terms of the magnetarmodel.     

On the mechanism of X-ray emission from radio pulsars

We discuss the correlations between the luminosities of radio pulsars in various frequency ranges and the magnetic fields on the light cylinder. These correlations suggest that the observed emission is generated in outer layers of the pulsar magnetospheres by the synchrotron mechanism. To calculate the distribution functions of the relativistic particles in the generation region, we use a model of quasilinear interactions between the waves excited by cyclotron instability and particles of the primary beam and the secondary electron—positron plasma. We derive a formula for calculating the X-ray luminosity L _x of radio pulsars. A strong correlation was found between L _x and the parameter \(\dot P_{ - 15} /P^{3.5}\), where P is the neutron-star rotation period, in close agreement with this formula. The latter makes it possible to predict the detection of X-ray emission from more than a hundred (114) known radio pulsars. We show that the Lorentz factors of the secondary particles are small (γ _p = 1.5–8.5), implying that the magnetic field near the neutron-star surface in these objects is multipolar. It follows from our model that almost all of the millisecond pulsars must emit X-ray synchrotron radiation. This conclusion differs from predictions of other models and can be used to test the theory under consideration. The list of potential X-ray radiators presented here can be used to search for X-ray sources with existing instruments.     

An accreting low magnetic field magnetar for the ultraluminous X-ray source in M82

One ultraluminous X-ray source in M82 has recently been identified as an accreting neutron star(named Nu STAR J095551+6940.8).It has a super-Eddington luminosity and is spinning up.An aged magnetar is more likely to be a low magnetic field magnetar.An accreting low magnetic field magnetar may explain both the superEddington luminosity and the rotational behavior of this source.Considering the effect of beaming,the spin-up rate is understandable using the traditional form of accretion torque.The transient nature and spectral properties of M82 X-2 are discussed.The theoretical range of periods for accreting magnetars is provided.Three observational appearances of accreting magnetars are summarized.     

Effect of rapid evolution of magnetic tilt angle on a newborn magnetar's dipole radiation

We study the electromagnetic radiation from a newborn magnetar whose magnetic tilt angle decreases rapidly. We calculate the evolution of the angular spin frequency, the perpendicular component of the surface magnetic field strength, and the energy loss rate through magnetic dipole radiation. We show that the spin-down of the magnetar experiences two stages characterized by two different timescales. The apparent magnetic field decreases with the decrease of the tilt angle. We further show that the energy loss rate of the magnetar is very different from that in the case of a fixed tilt angle. The evolution of the energy loss rate is consistent with the overall light curves of gamma-ray bursts which show a plateau structure in their afterglow stage. Our model supports the idea that some gamma-ray bursts with a plateau phase in their afterglow stage may originate from newborn millisecond magnetars.     

Newborn magnetars as sources of gravitational radiation: constraints from high energy observations of magnetar candidates

Two classes of high-energy sources, the Soft Gamma Repeaters and the Anomalous X-ray Pulsars are believed to contain slowly spinning “magnetars,” i.e. neutron stars the emission of which derives from the release of energy from their extremely strong magnetic fields (>10¹⁵ G). The enormous energy liberated in the 2004 December 27 giant flare from SGR 1806-20 (～5×10⁴⁶ erg), together with the likely recurrence time of such events, points to an internal magnetic field strength of ≥10¹⁶ G. Such strong fields are expected to be generated by a coherent α?Ω dynamo in the early seconds after the Neutron Star (NS) formation, if its spin period is of a few milliseconds at most. A substantial deformation of the NS is caused by such fields and, provided the deformation axis is offset from the spin axis, a newborn millisecond-spinning magnetar would thus radiate for a few days a strong gravitational wave signal the frequency of which (～0.5–2 kHz range) decreases in time. This signal could be detected with Advanced LIGO-class detectors up to the distance of the Virgo cluster, where ≥1 yr^?1 magnetars are expected to form. Recent X-ray observations revealed that SNRs around magnetar candidates do not appear to have received a larger energy input than in standard SNRs (see Vink and Kuiper, Mon. Not. Roy. Astron. Soc. 319, L14 (2006)). This is at variance with what would be expected if the spin energy of the young, millisecond NS were radiated away as electromagnetic radiation and/or relativistic particle winds. In fact, such energy would be transferred quickly and efficiently to the expanding gas shell. This may thus suggest that magnetars did not form with the expected very fast initial spin. We show here that these findings can be reconciled with the idea of magnetars being formed with fast spins, if most of their initial spin energy is radiated through GWs. In particular, we find that this occurs for essentially the same parameter range that would make such objects detectable by Advanced LIGO-class detectors up to the Virgo Cluster. If our argument holds for at least a fraction of newly formed magnetars, then these objects constitute a promising new class of gravitational wave emitters.     

A self-consistent model of the magnetosphere with centrifugal wind,II

In order to construct an axisymmetric model of magnetospheres with centrifugal wind, especially of the type II magnetosphere in Paper I (Shibata and Kaburaki, 1984), we present a numerical iterative scheme, in which a tenuous plasma with conspicuous trans-field motion are treated self-consistently with the electromagnetic field. Since the characteristic equations of the flow are solved, we are free from numerical diffusion terms obscuring the cause of the trans-field motion. The obtained properties of type II magnetosphere are as follows. (1) Plasma particles in fact flow out across the closed magnetic field lines. (2) The centrifugal force is exerted powerfully on the positive particles to form a disk-like structure, and the strong electric force makes the negative particles drift to the disk. (3) There appears the electric field parallel to the magnetic field,E , which is shown to be necessary for the steady wind to exist. Within the range of the model-parameters selected in this study we find two reasons for the appearance ofE : (1) plasma density decreases owing to the centrifugal acceleration, and it becomes insufficient to shieldE ; (2) the plasma with large inertia moves so as to reduce the charge separation, which would be necessary to shieldE .The notation and definitions are the same as in Paper I.     

Energization of charged particles in planetary magnetospheres

A model is presented to describe the energization of charged particles in planetary magnetospheres. The model is based on the stochastic acceleration produced by a random electric field that is induced by the magnetic field fluctuations measured within the magnetospheres. The stochastic behavior of the electric field is simulated through a Monte Carlo method. We solve the equation of motion for a single charged particle—which comprises the stochastic acceleration due to the stochastic electric field, the Lorentz acceleration (containing the local magnetic field and the corotational electric field) and the gravitational planetary acceleration of the particle—under several initial conditions. The initial conditions include the ion species and the velocity distribution of the particles which depends on the sources they come from (solar wind, ionospheres, rings and satellites). We applied this model to Saturn’s inner magnetosphere using a sample of particles (H⁺, H₂O⁺, N⁺, O⁺ and OH⁺) initially located on Saturn’s north pole, above the C-Ring, on the south pole of Enceladus, in the north pole of Dione and above the E-Ring. The results show that the particles tend to increase the value of their energy with time reaching several eV in a few seconds and the large energization is observed far from the planet. We can distinguish three main energization regions within Saturn’s inner magnetosphere: minimum (Saturn’s ionosphere), intermediate (Dione) and high-energy (Enceladus and the E-ring). The resulting energy spectrum follows a power-law distribution (>1 keV), a logistic, an exponential decay or an asymmetric sigmoidal (<1 keV).     

A note on the puzzling spindown behavior of the Galactic center magnetar SGR J1745-2900

SGR J1745-2900 is a magnetar near the Galactic center. X-ray observations of this source found a decreasing X-ray luminosity accompanied by an enhanced spindown rate. This negative correlation between X-ray luminosity and spindown rate is hard to understand. The wind braking model of magnetars is employed to explain this puzzling spindown behavior. During the release of magnetic energy of magnetars,a system of particles may be generated. Some of these particles remain trapped in the magnetosphere and may contribute to the X-ray luminosity. The rest of the particles can flow out and take away the rotational energy of the central neutron star. A smaller polar cap angle will cause the decrease of X-ray luminosity and enhanced spindown rate of SGR J1745-2900. This magnetar is shortly expected to have a maximum spindown rate.     

Topology of magnetars external field – I. Axially symmetric fields

There is an increasing theoretical and observational evidence that the external magnetic field of magnetars may contain a toroidal component, likely of the same order of the poloidal one. Such 'twisted magnetospheres' are threaded by currents flowing along the closed field lines which can efficiently interact with soft thermal photons via resonant cyclotron scatterings (RCS). Actually, RCS spectral models proved quite successful in explaining the persistent ∼1–10 keV emission from the magnetar candidates, the soft γ-ray repeaters (SGRs) and the anomalous X-ray pulsars (AXPs). Moreover, it has been proposed that, in the presence of highly relativistic electrons, the same process can give rise to the observed hard X-ray spectral tails extending up to  ∼200 keV  . Spectral calculations have been restricted up to now to the case of a globally twisted dipolar magnetosphere, although there are indications that the twist may be confined only to a portion of the magnetosphere, and/or that the large-scale field is more complex than a simple dipole. In this paper, we investigate multipolar, force–free magnetospheres of ultramagnetized neutron stars. We first discuss a general method to generate multipolar solutions of the Grad-Schlüter-Shafranov (GSS) equation, and analyse in detail dipolar, quadrupolar and octupolar fields. The spectra and lightcurves for these multipolar, globally twisted fields are then computed using a Monte Carlo code and compared with those of a purely dipolar configuration. Finally, the phase-resolved spectra and energy-dependent lightcurves obtained with a simple model of a locally sheared field are confronted with the International Gamma-Ray Astrophysics Laboratory ( INTEGRAL ) observations of the AXPs 1RXS J1708−4009 and 4U 0142+61. Results support a picture in which the field in these two sources is not globally twisted.     

Non-stationary pair plasma in a pulsar magnetosphere and the two-stream Instability

We test a new emission mechanism in pulsar magnetospheres, eventually responsible in part for the high level of observed radio radiation. This is carried out by comparing the efficiency of the two-stream instability of Langmuir waves in a pulsar emission region, where the stationary and non-stationary characters of pair plasma outflows produced in the gap region are characterized by two different time-scales. On the shorter time-scale, the Ruderman &38; Sutherland 'sparking' phenomenon leads to the creation of pair plasma clouds, in motion along magnetic field lines, that contain particles with a large spectrum of momenta. The overlapping of particles with different energies produced in successive clouds results in an efficient 'two stream'-like instability. This effect is a consequence of the non-stationary character of the pair plasma produced in the gap region, just above the magnetic poles of the neutron star. On a long time-scale, resulting pair plasma outflows in pulsar magnetospheres can be treated as stationary. In this case, the instability which results from interaction between existing primary beam particles and the pair plasma is negligible, whereas the instability owing to interaction between electrons and positrons of the pair plasma itself, and more precisely to their relative drift motion along curved magnetic field lines, is effective. We derive characteristic features of the triggered instability, using specific distribution functions to describe either particles in the assembly of clouds or relative drifting of electrons and positrons in these same plasma clouds. Although linear and local, our treatment suggests that non-stationary effects may compete with, or even dominate over, drifting effects in parts of pulsar emission regions.     

Electron capture of nuclei in the region surrounding magnetar

Effects of ultra-strong magnetic field on electron capture rates for ⁵⁷Fe, ⁵⁸Co and ⁵⁹Ni have been analyzed in the nuclear shell model and under the Landau energy levels quantized approximation in the ultra-strong magnetic field, the result increase about 3 orders magnitude. The rate of change of electron abundance, $\dot{Y}_{e}$ , for every nuclide and total $\dot{Y}_{e}$ in the condition without magnetic field and B=4.414×10¹⁵ G have been calculated, and exceed about 6 orders of magnitude generally. These conclusions play an important role in future studying the evolution of magnetar.     

X-ray plateaus followed by sharp drops in GRBs 060413, 060522, 060607A and 080330： Further evidences for central engine afterglow from gamma-ray bursts

The X-ray afterglows of GRBs 060413, 060522, 060607A and 080330 are characterized by a plateau followed by a very sharp drop. The plateau could be explained within the framework of the external forward shock model but the sharp drop can not.We interpret the plateau as the afterglows of magnetized central engines, plausibly magnetars. In this model, the X-ray afterglows are powered by the internal magnetic energy dissipation and the sudden drop is caused by the collapse of the magnetar. Accordingly,the X-ray plateau photons should have a high linear polarization, which can be tested by future X-ray polarimetry.     

Soft X-ray polarization in thermal magnetar emission

Emission spectra from magnetars in the soft X-ray band likely contain a thermal component emerging directly from the neutron star (NS) surface. However, the lack of observed absorption-like features in quiescent spectra makes it difficult to directly constrain physical properties of the atmosphere. We argue that future X-ray polarization measurements represent a promising technique for directly constraining the magnetar magnetic field strength and geometry. We construct models of the observed polarization signal from a finite surface hotspot, using the latest NS atmosphere models for magnetic fields   B = 4 × 10¹³–5 × 10¹⁴ G  . Our calculations are strongly dependent on the NS magnetic field strength and geometry, and are more weakly dependent on the NS equation of state and atmosphere composition. We discuss how the complementary dependencies of phase-resolved spectroscopy and polarimetry might resolve degeneracies that currently hamper the determination of magnetar physical parameters using thermal models.     

Limiting polarization effect—a key link in investigating the mean profiles of radio pulsars

Using a well-known method for calculating the propagation of waves in an inhomogeneous medium, we have managed to reduce the problem of wave propagation in pulsar magnetospheres to a system of two ordinary differential equations that allow the polarization characteristics of the radio emission to be quantitatively described for any magnetic field structure and an arbitrary density profile of the outflowing plasma. We confirm that for ordinary pulsars (period P ∼ 1 s, magnetic field B ₀ ∼ 10¹² G, particle production multiplicity parameter λ ∼ 10⁴), the polarization is formed inside the light cylinder at a distance of the order of a thousand neutron star radii. For reasonable magnetic field strengths and plasma densities on the emission propagation path, the degree of circular polarization is found to be ∼5–20%, in good agreement with observations.     

The cosmogonic shadow effect

We consider the Alfvén-Arrhenius fall-down mechanism and describe an approximate model for the infall, capture and distribution of dust particles on a given magnetic field line and their possible neutralization at the ‘2’/3 points, the points at which the field aligned compnents of the gravitational and centrifugal forces are equal and opposite. We find that a small fraction (<10%) of an incoming particle distribution will actually contribute to the above ‘2’/3 fall-down process. We also show that if at the 2/3 points, the ratio of dust to plasma density is $$\frac{{n_D \left( {\tfrac{2}{3}} \right)}}{{n_p \left( {\tfrac{2}{3}} \right)}} > \frac{{10^{ - 3} }}{{r_{g_\mu } T_{eV} }}$$ . (r _gμ=radius of a grain in microns,T=plasma temperature in eV), then the dust particles will lose their charge, decouple from the field line and follow Keplerian orbits in accordance with the Alfvén-Arrhenius mechanism. We then determine the limits on the plasma parameters in order that rotation of a quasi-neutral plasma in thermal equilibrium be possible in the gravitational and dipole field of a rotating central body. The constraints imposed by the above conditions are rather weak, and the plasma parameters can have a wide range of values. For a plasma corotating with an angular velocity Ω～10^?4s^?1, we show that the plasma temperature and density must satisfy $$10^{ - 1}<< T_{(eV)}<< 10^2 ,10T_{eV}^2<< n^p \left( {cm^3 } \right)<< 10^6 $$ .