New Approaches of Theoretical Astrophysics for Application to Some Astronomical Objects: I. An Application of Non-Classical Equation Mathematical Physics to the Magneto-Hydrodynamic Equilibrium (in Case of Mixed Magnetic Field) of Magnetic Stars

In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the necessary concepts about the equation of non-classical mathematical physics and the possibility of their applicability to astrophysical problems. The conditions of magneto-hydrodynamic equilibrium are determinate, and self-consistence provides the means to derive the corresponding partial differential equations describing this equilibrium in a magnetosphere magnetic star. Namely, this process is to the non-classical equations of mathematical physics in cases of types. Keldysh-Tricomi, a common case equation of non-classical type, is at first introduced by the author. Using the two main physical efficiencies of MHD. A mathematical model of a poloidal-toroidal mixed magnetic field for magnetic stars is constructed, and this model is classified with respect to degenerating case equations. According to Hopf’s theorem, Maxwell’s equation and the magnetic force balance equation constructed equilibrium conditions of the poloidal-toroidal of the magnetic field for a magnetic star. At the same time, the taken example, which is the self-consistency of this model by observation dates, is investigated. At first, in an application, the method of straight lines for recurrent formulas of calculation of magnetic flux and stream functions is used. The physical means, the corresponding singular point of the sonic line, cutoff, and resonance phenomena are considered. In this case, a general solution equation is found, which is interpreted by this phenomenon as a cutoff, resonance. Finally, this obtained solution gives the conditions of magneto-hydrodynamic equilibrium on the magnetosphere of magnetic stars. Methodology and obtained equations are new approaches that are at first considered.

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffu- sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 tr level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 MG, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.

A Study of Neutron Star Structure in Strong Magnetic Fields that includes Anomalous Magnetic Moments

We study the effect of strong magnetic fields on the structure of neutron star. We find that if the interior field is on the same order as the surface field currently observed, then the influences of the field on the star's mass and radius are negligible; if the field is as large as that estimated from the scalar virial theorem, then considerable effects will be induced. The maximum mass of the star will be increased substantially while the central density is greatly reduced. The radius of a magnetic star can be larger by about 10% ~ 20% than a nonmagnetic star of the same mass.

The effects of strong magnetic fields on neutron star structure:lowest order constrained variational calculations

We investigate the effects of strong magnetic fields upon the large-scale properties of neutron and protoneutron stars. In our calculations, the neutron star mat- ter was approximated by pure neutron matter. Using the lowest order constrained vari- ational approach at zero and finite temperatures, and employing AV18 potential, we present the effects of strong magnetic fields on the gravitational mass, radius, and gravitational redshift of neutron and protoneutron stars. It is found that the equation of state for a neutron star becomes stiffer with an increase of magnetic field and tem- perature. This leads to larger values of the maximum mass and radius for the neutron stars.

Amplifying magnetic fields of a newly born neutron star by stochastic angular momentum accretion in core collapse supernovae

I present a novel mechanism to boost magnetic field amplification of newly born neutron stars in core collapse supernovae.In this mechanism,that operates in the jittering jets explosion mechanism and comes on top of the regular magnetic field amplification by turbulence,the accretion of stochastic angular momentum in core collapse supernovae forms a neutron star with strong initial magnetic fields but with a slow rotation.The varying angular momentum of the accreted gas,which is unique to the jittering jets explosion mechanism,exerts a varying azimuthal shear on the magnetic fields of the accreted mass near the surface of the neutron star.This,I argue,can form an amplifying effect which I term the stochastic omega(Sω) effect.In the common αω dynamo the rotation has constant direction and value,and hence supplies a constant azimuthal shear,while the convection has a stochastic behavior.In the Sω dynamo the stochastic angular momentum is different from turbulence in that it operates on a large scale,and it is different from a regular rotational shear in being stochastic.The basic assumption is that because of the varying direction of the angular momentum axis from one accretion episode to the next,the rotational flow of an accretion episode stretches the magnetic fields that were amplified in the previous episode.I estimate the amplification factor of the Sω dynamo alone to be ≈ 10.I speculate that the Sω effect accounts for a recent finding that many neutron stars are born with strong magnetic fields.

Magnetic Field of a Compact Spherical Star under f(R,T) Gravity

We present the interior solutions of distributions of magnetized fluid inside a sphere in f（R, T） gravity. Tile magnetized sphere is embedded in an exterior Reissner NordstrOm metric. We assume that all physical quantities are in static equilibrium. The perfect fluid matter is studied under a particular form of the Lagrangian density f（R, T）. The magnetic field profile in modified gravity is calculated. Observational data of neutron stars are used to plot suitable models of magnetized compact objects. We reveal the effect of f（R, T） gravity on the magnetic field profile, with application to neutron stars, especially highly magnetized neutron stars found in x-ray pulsar systems. Finally, the effective potential Veff and innermost stable circular orbits, arising out of the motion of a test particle of negligible mass influenced by attraction or repulsion from the massive center, are discussed.

Thermal evolution of neutron stars with decaying magnetic fields

Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field （10^8 G） could have a lower temper- ature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature, except millisecond pulsar J0437-4715.

Quark stars with strong magnetic fields: considering different magnetic field geometries

We calculate the mass-radius relationship of quark stars with the magnetized density- dependent quark mass model in this work, considering two magnetic field geometries： a statistically isotropic, tangled field and a force-free configuration. In both cases, magnetic field production decreases in the case of maximum quark star mass. Furthermore, a tangled, isotropic magnetic field has a relatively smaller impact on the mass and radius, compared to the force-free configuration, which implies that the geometry of the interior magnetic field is at least as important as the field strength itself when the influ- ence of the strong magnetic field on the mass and radius is assessed.

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.

Determination of the magnetic fields of Magellanic X-ray pulsars

The 80 high-mass X-ray binary （HMXB） pulsars that are known to reside in the Magellanic Clouds （MCs） have been observed by the XMM-Newton and Chandra X-ray telescopes on a regular basis for 15 years, and the XMM-Newton and Chandra archives contain nearly complete information about the duty cycles of the sources with spin periods Ps 〈 100 s. We have reprocessed the archival data from both observatories and we combined the output products with all the published observations of 31 MC pulsars with Ps 〈 100 s in an attempt to investigate the faintest X-ray emission states of these objects that occur when accretion to the polar caps proceeds at the smallest possible rates. These states determine the so-called propeller lines of the accreting pulsars and yield information about the magnitudes of their surface magnetic fields. We have found that the faintest states of the pulsars segregate into five discrete groups which obey to a high degree of accuracy the theoretical relation between spin period and X-ray luminosity. So the entire population of these pulsars can be described by just five propeller lines and the five corresponding magnetic moments （0.29, 0.53, 1.2, 2.9 and 7.3, in units of 1030 G cma）.

A magnetic model for low/hard state of black hole binaries

A magnetic model for the low/hard state （LHS） of two black hole X-ray binaries （BHXBs）, H1743-322 and GX 339-4, is proposed based on transport of the magnetic field from a companion into an accretion disk around a black hole （BH）. This model consists of a truncated thin disk with an inner advection-dominated accretion flow （ADAF）. The spectral profiles of the sources are fitted in agreement with the data observed at four different dates corresponding to the rising phase of the LHS. In addition, the association of the LHS with a quasi-steady jet is modeled based on transport of magnetic field, where the Blandford-Znajek （BZ） and Blandford-Payne （BP） processes are invoked to drive the jets from BH and inner ADAE It turns out that the steep radio/X-ray correlations observed in H 1743-322 and GX 339-4 can be interpreted based on our model.

Research on the Magnetic Field of NGC 7793 P13 and Other Confirmed Pulsating Ultraluminous X-Ray Sources

A pulsating ultraluminous X-ray source(PULX)is a new kind of pulsar(PSR)whose characteristics are different from all known neutron stars.The magnetic field of PULX is suspected to be the main reason to support its supper Eddington luminosity of PULX.NGC 7793 P13,which is the second confirmed PULX,can be easily studied due to its nearby position and isolation from other sources in its host galaxy.In this paper,we calculate its magnetic field to be∼1.0×10^(12) G based on the continued observations from 2016 to 2020.The magnetic field evolution of NGC 7793 P13 is analyzed,which shows that the source has spent about 10^(4) yr for the field decaying from the simulated initial strength 4.0×10^(14) G to the present value.In case of an assumed constant accretion and the limitation of the companion mass,it will be a recycled PSR whose magnetic field is ∼10^(9) G and spin period is a few hundred milliseconds.We estimate the field strength of the other confirmed PULXs and find main range is 10^(13)-10^(14) G.Their positions of the magnetic field and spin period are around or below the magnetars.This is because these PULXs are in the binary systems and are with the spin-up rate that are 2-3 orders higher than the normal binary pulsars.We suggest that PULXs are the accreting magnetars whose multi-pole strong magnetic field can support the supper Eddington luminosity.They would be helpful for studying the evolution of the magnetars,the formation of the binary PSRs above the Eddington spin-up line,and the millisecond PSRs with the magnetic field stronger than ∼10^(9) G.

Anisotropic stellar structure equations for magnetized strange stars

The fact that a fermion system in an external magnetic field breaks the spherical symmetry suggests that its intrinsic geometry is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presence of a magnetic field, in the structure equations of a magnetized quark star.We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a strange star can sustain, closely related to the violation of the virial relations.

A Study of Magnetized White Dwarf+Helium Star Binary Evolution to Type Ia Supernovae

The white dwarf(WD)+helium(He)star binary channel plays an important role in the single degenerate scenario for the progenitors of type Ia supernovae(SNe Ia).Previous studies on the WD+main sequence star evolution have shown that the magnetic fields of WDs may significantly influence their accretion and nuclear burning processes.In this work we focus on the evolution of magnetized WD+He star binaries with detailed stellar evolution and binary population synthesis(BPS)calculations.In the case of magnetized WDs,the magnetic fields may disrupt the inner regions of the accretion disk,funnel the accretion flow onto the polar caps and even confine helium burning within the caps.We find that,for WDs with sufficiently strong magnetic fields,the parameter space of the potential SN Ia progenitor systems shrinks toward shorter orbital periods and lower donor masses compared with that in the non-magnetized WD case.The reason is that the magnetic confinement usually works with relatively high mass transfer rates,which can trigger strong wind mass loss from the WD,thus limiting the He-rich mass accumulation efficiency.The surviving companion stars are likely of low-mass at the moment of the SN explosions,which can be regarded as a possible explanation for the non-detection of surviving companions after the SNe or inside the SN remnants.However,the corresponding birthrate of Galactic SNe Ia in our high-magnetic models is estimated to be~(0.08–0.13)×10^(-3)yr^(-1)(~0.17–0.28×10^(-3)yr^(-1)for the non-magnetic models),significantly lower than the observed Galactic SN Ia birthrate.

Hardening of Thermal Photons Through Inverse Compton Scattering in Strong Magnetic Fields

A new spectrum function is obtained by use of the Compton scattering cross section in the laboratory frame derived earlier. This spectrum function, besides some modifications in the coefficients of the resonant term, contains also a non-resonant term which is inversely proportional to the square of the magnetic field. Based on this spectrum function, the hardening of thermal photons through inverse Compton scattering by relativistic electron beams on the surface of a strongly magnetized neutron star is investigated. Two new features are found. First, there is a maximum scattered photon energy for a given resonant scattering, beyond which resonance disappears. This maximum depends on the electron energy and the magnetic field, but is independent of the incident photon energy. Second, beyond each resonant scattering, there is a high-energy tail, resulting from non-resonant scattering. It is also found that all the tails have a common upper limit which is the highest scattered photon energy for the given incident photon and electron energies. These two new features are absent in the Monte Carlo simulations and therefore, may have physical implications for y-ray emissions.

Flaring activity from quiescent states in neutron-star X-ray binaries

We examine systematically the observed X-ray luminosity jumps(or flares) from quiescent states in millisecond binary pulsars(MSBPs) and high-mass X-ray binary pulsars(HMXBPs). We rely on the published X-ray light curves of seven pulsars: four HMXBPs, two MSBPs and the ultraluminous X-ray pulsar M82 X-2. We discuss the physics of their flaring activities or lack thereof, paying special attention to their emission properties when they are found on the propeller line, inside the Corbet gap or near the light-cylinder barrier. We provide guiding principles for future interpretations of faint X-ray observations, as well as a method of constraining the propeller lines and the dipolar surface magnetic fields of pulsars using a variety of quiescent states. In the process, we clarify some disturbing inaccuracies that have made their way into the published literature.

Short-living Supermassive Magnetar Model for the Early X-ray Flares Following Short GRBs

We suggest a short-lived supermassive magnetar model to account for the X-ray flares following short γ-ray bursts. In this model the central engine of the short γ-ray bursts is a supermassive millisecond magnetar, formed in coalescence of double neutron stars. The X-ray flares are powered by the dipole radiation of the magnetar. When the magnetar has lost a significant part of its angular momentum, it collapses to a black hole and the X-ray flares cease abruptly.

Kinematics and activity of M dwarfs in LAMOST DR1

We report on the first investigation into kinematics and chromospheric activity of M dwarfs from the Guo Shou Jing Telescope （also called the Large Sky Area Multi-Object Fiber Spectroscopic Telescope - LAMOST） data release one （DR1）. The sample comprises 71 304 M dwarfs. Their fundamental parameters such as spectral types, radial velocities, important molecular band indices and magnetic activities are measured. Their distances are determined by a spectroscopic parallax relation. Space motion （U, V, W） and Galactocentric cylindrical coordinates （R, θ, Z） for the M dwarfs are also computed. We examine velocity dispersion as a function of height from the Galactic plane and find that all three components of velocity dispersion in- crease with height as measured with respect to the Galactic plane. The investigation into chromospheric activities along the height from the Galactic plane confirms that M dwarfs closer to the Galactic plane are more likely to be active. We take a pure kinematical approach to select thin disk stars and thick disk stars from our sample, then to investigate the differences in properties between these two populations. Our analysis is in excellent agreement with previous studies and leads to a better understanding of the structure of the Galactic disk.

A Non-axisymmetric Spherical α~2-Dynamo

Using the Chebyshev-tau method, the generation of oscillatory nonaxisymmetric stellar magnetic fields by the α^2-dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert ＆ Zhang, the spherical α^2-dynamo consists of a fully convective spherical shell with inner radius ri and outer radius ro. A comparison of the critical dynamo numbers of axisymmetric and φ-dependent modes for different thicknesses of the convective shell and different α- profiles leads to the following qualitative results： （i） when the angular factor of α- profile is sin^n θ cosθ （n= 1, 2, 4） the solutions of the α^2dynamo are oscillatory and non-axisymmetric, （ii） the thinner the convective shell, the more easily is the nonaxisymmetric mode excited and the higher is the latitudinal wave number, （iii） the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.

A striking confluence between theory and observations of high-mass X-ray binary pulsars

We analyze the most powerful X-ray outbursts from neutron stars in eleven Magellanic high-mass X-ray binaries and three pulsating ultraluminous X-ray sources. Most of the outbursts rise to Lmax which is about the level of the Eddington luminosity, while the remaining more powerful outbursts also appear to recognize that limit when their emissions are assumed to be anisotropic and beamed toward our direction. We use the measurements of pulsar spin periods Ps and their derivatives Ps to calculate the X-ray luminosities Lp in their faintest accreting （＂propeller-line＂） states. In five cases with unknown Ps, we use the lowest observed X-ray luminosities, which only adds to the heterogeneity of the sample. Then we calculate the ratios Lp/Lmax and we obtain an outstanding confluence of theory and observations from which we conclude that work done on both fronts is accurate and the results are trustworthy： sources known to reside on the lowest Magellanic propeller line are all located on/near that line, whereas other sources jump higher and reach higher-lying propeller lines. These jumps can be interpreted in only one way, higher-lying pulsars have stronger surface magnetic fields in agreement with previous empirical results in which Ps and Lp values were not used.