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The inclination angle $\chi$ between magnetic and rotation axes of pulsars is an important parameter in pulsar physics. The changes in the inclination angle of a pulsar would lead to observable effects, such as changes in the pulse beam width and braking index of the star. In this paper, we perform a short review on the evolution of pulsar's magnetic inclination angle, as well as the latest research progress. Using an alignment rotator model in vacuum, we investigate the magnetic inclination angle change rates for 12 high-braking index pulsars without glitch, whose timing observations are obtained using the Nanshan 25-m Radio Telescope at Xinjiang Astronomical Observatory. For our purpose, three representative pulsars J0157+6212, J1743-3150 and J1857+0526 are chosen and their rotation and inclination angle evolutions are further investigated. In the future, radio and X-ray polarimetric observations will provide more information about the inclination angles of pulsars, which could help us understand the origin of the variations in $\chi$ of pulsars and shed light on the range of possibilities of pulsar magnetic field configuration. A continuous study of the pulsar inclination angle will provide an important window into additional physical processes at work in the young and highly magnetized pulsars., Comment: 9 pages, 4 figures, published in AN

The pulsar magnetic inclination angle is a key parameter for pulsar physics. It influences the observable properties of pulsars, such as the pulse beam width, braking index, polarisation, and emission geometry. In this study, we give a brief overview of the current state of knowledge and research on this parameter and its implications for the internal physics of pulsars. We use the observed pulsar data of magnetic inclination angle and braking index to constrain the star's number of precession cycles, $\xi$, which reflects the interaction between superfluid neutrons and other particles inside a neutron star\,(NS). We apply the method proposed by Cheng et al. (2019) to analyse the data of PSR J2013+3845 and obtain the constraints for $\xi$ ranging from $2.393\times 10^{5}$ to $1.268\times10^{6}$. And further analysis suggests that the internal magnetic field structure of PSR J2013+3845 is likely dominated by toroidal component. This study may help us understand the process of internal viscous dissipation and the related evolution of the inclination angles of pulsars, and may have important implications for the study of continuous gravitational wave emissions from NS., Comment: 7 pages, 2 figures, published in AN

The prompt emission mechanism of gamma-ray bursts (GRBs) is still unclear, and the time-resolved spectral analysis of GRBs is a powerful tool for studying their underlying physical processes. We performed a detailed time-resolved spectral analysis of 78 bright long GRB samples detected by Fermi/Gamma-ray Burst Monitor (GBM). A total of 1490 spectra were obtained and their properties were studied using a typical Band-shape model. Firstly, the parameter distribution of the time-resolved spectrum given as follows: the low-energy spectral index $\alpha \sim -0.72$, high-energy spectral index $\beta \sim -2.42$, the peak energy $E_{\rm p} \sim 221.69 \,\rm{keV}$, and the energy flux $F \sim 7.49\times 10^{-6} \rm{\, erg\,cm^{-2}\,s^{-1}}$. More than 80\% of the bursts exhibit the hardest low-energy spectral index $\alpha_{\rm max}$ exceeding the synchrotron limit (-2/3). Secondly, the evolution patterns of $\alpha$ and $E_{\rm p}$ were statistically analyzed. The results show that for multi-pulse GRBs the intensity-tracking pattern is more common than the hard-to-soft pattern in the evolution of both $E_{\rm p}$ and $\alpha$. The hard-to-soft pattern is generally shown in single-pulse GRBs or in the initial pulse of multi-pulse GRBs. Finally, we found a significant positive correlation between $F$ and $E_{\rm p}$, with half of the samples exhibiting a positive correlation between $F$ and $\alpha$. We discussed the spectral evolution of different radiation models. The diversity of spectral evolution patterns indicates that there may be more than one radiation mechanism occurring in the gamma-ray burst radiation process, including photospheric radiation and synchrotron radiation. However, it may also involve only one radiation mechanism, but more complicated physical details need to be considered., Comment: 19 pages, 7 figures, 4 tables, accepted and published in RAA

PSR J1012+5307 is a millisecond pulsar with an extremely low-mass (ELM) white dwarf (WD) companion in an orbit of 14.5 hours. Magnetic braking (MB) plays an important role in influencing the orbital evolution of binary systems with a low-mass ($\lt 1-2~M_{\odot}$) donor star. At present, there exist several different MB descriptions. In this paper, we investigate the formation of PSR J1012+5307 as a probe to test the plausible MB model. Employing a detailed stellar evolution model by the MESA code, we find that the Convection And Rotation Boosted MB and the 'Intermediate' MB models can reproduce the WD mass, WD radius, WD surface gravity, neutron-star mass, and orbital period observed in PSR J1012+5307. However, our simulated WD has higher effective temperature than the observation. Other three MB mechanisms including the standard MB model are too weak to account for the observed orbital period in a Hubble time. A long cooling timescale caused by H-shell flashes of the WD may alleviate the discrepancy between the simulated effective temperature and the observed value., Comment: 12 pages, 4 figures, 1 table; ApJ in press

Magnetic braking (MB) likely plays a vital role in the evolution of low-mass X-ray binaries (LMXBs). However, it is still uncertain about the physics of MB, and there are various proposed scenarios for MB in the literature. To examine and discriminate the efficiency of MB, we investigate the LMXB evolution with five proposed MB laws. Combining detailed binary evolution calculation with binary population synthesis, we obtain the expected properties of LMXBs and their descendants binary millisecond pulsars. We then discuss the strength and weakness of each MB law by comparing the calculated results with observations. We conclude that the $\tau$-boosted MB law seems to best match the observational characteristics., Comment: 30 pages, 9 figures, 3 tables, accepted for publication in ApJ

Magnetars are a kind of pulsars powered mainly by superhigh magnetic fields. They are popular sources with many unsolved issues in themselves, but also linked to various high energy phenomena, such as QPOs, giant flares, fast radio bursts and super-luminous supernovae. In this work, we first review our recent works on the dissipation of toroidal magnetic fields in magnetars and rotationally powered pulsars, then review the spin-down evolution of young and strongly magnetized pulsars, especially of magnetars. We present an interesting and important relation between the magnetization parameter, and magnetic field in the magnetar crust. Finally, we introduce our two works in progress: to explain the magnetar "anti-gltich" events in the thermal plastic flow model and to revisit the expression of braking index $n$, which is independent of the second derivative of spin frequency of a pulsar and give some proposals for our future work., Comment: 11pages,3figures

PSR J1640+2224 is a binary millisecond pulsar (BMSP) with a white dwarf (WD) companion. Recent observations indicate that the WD is very likely to be a $\sim 0.7\,M_{\odot}$ CO WD. Thus the BMSP should have evolved from an intermediate-mass X-ray binary (IMXB). However, previous investigations on IMXB evolution predict that the orbital periods of the resultant BMSPs are generally $<40$ days, in contrast with the 175 day orbital period of PSR J1640+2224. In this paper, we explore the influence of the mass of the neutron star (NS) and the chemical compositions of the companion star on the formation of BMSPs. Our results show that, the final orbital period becomes longer with increasing NS mass, and the WD mass becomes larger with decreasing metallicity. In particular, to reproduce the properties of PSR J1640+2224, the NS was likely born massive ($>2.0\,M_{\odot}$)., Comment: 24 pages, 5 figures, accepted for publication in ApJ

According to the recycling model, neutron stars in low-mass X-ray binaries were spun up to millisecond pulsars (MSPs), which indicates that all MSPs in the Galactic plane ought to be harbored in binaries. However, about $20\%$ Galactic field MSPs are found to be solitary. To interpret this problem, we assume that the accreting neutron star in binaries may collapse and become a strange star when it reaches some critical mass limit. Mass loss and a weak kick induced by asymmetric collapse during the phase transition (PT) from neutron star to strange star can result in isolated MSPs. In this work, we use a population-synthesis code to examine the PT model. The simulated results show that a kick velocity of $\sim60~{\rm km~s}^{-1}$ can produce $\sim6\times10^3$ isolated MSPs and birth rate of $\sim6.6\times10^{-7} {\rm ~yr}^{-1}$ in the Galaxy, which is approximately in agreement with predictions from observations. For the purpose of comparisons with future observation, we also give the mass distributions of radio and X-ray binary MSPs, along with the delay time distribution., Comment: 9 pages, 11 figures, accepted to publish on A&A

In this work, we interpreted the high braking index of PSR J1640$-$4631 with a combination of the magneto-dipole radiation and dipole magnetic field decay models. By introducing a mean rotation energy conversion coefficient $\overline{\zeta}$, the ratio of the total high-energy photon energy to the total rotation energy loss in the whole life of the pulsar, and combining the pulsar's high-energy and timing observations with reliable nuclear equation of state, we estimate the pulsar's initial spin period, $P_{0}\sim (17-44)$ ms, corresponding to the moment of inertia $I\sim (0.8-2.1)\times 10^{45}$ g cm$^{2}$. Assuming that PSR J1640$-$4631 has experienced a long-term exponential decay of the dipole magnetic field, we calculate the true age $t_{\rm age}$, the effective magnetic field decay timescale $\tau_{D}$, and the initial surface dipole magnetic field at the pole $B_{p}(0)$ of the pulsar to be $(2900-3100)$ yrs, $1.07(2)\times10^{5}$ yrs, and $(1.84-4.20)\times10^{13}$ G, respectively. The measured braking index of $n=3.15(3)$ for PSR J1640$-$4631 is attributed to its long-term dipole magnetic field decay and a low magnetic field decay rate, $dB_{\rm p}/dt\sim -(1.66-3.85)\times10^{8}$ G yr$^{-1}$. Our model can be applied to both the high braking index ($n>3$) and low braking index ($n<3$) pulsars, tested by the future polarization, timing, and high-energy observations of PSR J1640$-$4631., Comment: Correspoding to the publication version: 2017, ApJ, 849, 19 (12pp)

In this work, we reinvestigate the electron fraction $Y_{e}$ and electron Fermi energy $E_{F}(e)$ of neutron stars, based on our previous work of Li et al.(2016), in which we firstly deduced a special solution to $E_{F}(e)$, and then obtained several useful analytical formulae for $Y_{\rm e}$ and matter density $\rho$ within classical models and the relativistic mean field(RMF) theory using numerically fitting. The advantages of this work include the following aspects:(1) The linear functions are substituted for the nonlinear exponential functions used in the previous work. This method may be more simple, and closer to realistic equation of state\,(EoS) of a neutron star(NS), because there are linear or quasi-linear relationships between number fractions of leptons and matter density, which can be seen by solving NS EoS; (2)we introduce a dimensionless variable $\varrho$\,($\varrho=\rho/\rho_0$, $\rho_{0}$ is the standard saturated nuclear density), which greatly reduces the scope of the fitting coefficients;(3)we present numerical errors including absolute and relative deviations between the data and fit. By numerically simulating, we have obtained several analytical formulae for $Y_{e}$ and $\rho$ for both APR98 and RMF models. Combining these analytical formulae with the special solution, we can calculate the value of $E_{\rm F}(e)$ for any given matter density. Since $Y_e$ and $E_{ F}(e)$ are important in assessing cooling rate of a NS and the possibility of kaon/pion condensation in the NS interior, this study could be useful in the future study on the thermal evolution of a NS., Comment: 3 figures, 3 tables , and We welcome any comment you might have about the content, To be published in Astron. Nachr

In this paper we discuss in detail the quantization of Landau energy levels of a strongly magnetized and completely degenerate relativistic electron gas in neutron stars. In particular, we focus on the Fermi energy dependence of the magnetic field for a relativistic electron gas in the superstrong magnetic field of magnetars. We would like to point out that some of the results concerning the microscopic number density of states of a strongly magnetized electron gas given by well-known statistical physics text books are incorrect. The repeated use of these results in the last five decades probably seriously affects the physics of neutron stars and magnetars. The quantization of Landau energy levels is accurately delineated in terms of the Dirac (delta) function. Relatively simple calculation shows that the Fermi energy of relativistic electron gas in magnetars with superstrong magnetic fields( B > Bcr , here Bcr is the Landau critical magnetic field) increases with magnetic fieldstrength as B**(1/4). On the basis of this simple but importantnew result we are leading naturally to propose a new mechanism for the production of high X-ray luminosity from magnetars., Comment: 7 pages, three figures

Based on the basic definition of Fermi energy of degenerate and relativistic electrons, we obtain a special solution to electron Fermi energy, $E_{\rm F}(e)$, and express $E_{\rm F}(e)$ as a function of electron fraction, $Y_{e}$, and matter density, $\rho$. Several useful analytical formulae for $Y_{e}$ and $\rho$ within classical models and the work of Dutra et al. 2014 (Type-2) in relativistic mean field theory are obtained using numerically fitting. When describing the mean-field Lagrangian, density, we adopt the TMA parameter set, which is remarkably consistent with with the updated astrophysical observations of neutron stars. Due to the importance of the density dependence of the symmetry energy, $S$, in nuclear astrophysics, a brief discussion on the symmetry parameters $S_v$ and $L$ (the slope of $S$) is presented. Combining these fit formulae with boundary conditions for different density regions, we can evaluate the value of $E_{\rm F}(e)$ in any given matter density, and obtain a schematic diagram of $E_{\rm F}(e)$ as a continuous function of $\rho$. Compared with previous study on the electron Fermi energy in other models, our methods of calculating $E_{\rm F}(e)$ are more simple and convenient, and can be universally suitable for the relativistic electron regions in the circumstances of common neutron stars. We have deduced a general expression of $E_{\rm F}(e)$ and $n_{e}$, which could be used to indirectly test whether one EoS of a NS is correct in our future studies on neutron star matter properties. Since URCA reactions are expected in the center of a massive star due to high-value electron Fermi energy and electron fraction, this study could be useful in the future studies on the NS thermal evolution., Comment: 30 pages, 14 figures

Based on our previous work, we deduce a general formula for pressure of degenerate and relativistic electrons,Pe, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynam-ic(QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows:Pe is related to the magnetic field B, matter density ?, and electron fraction Ye ; the stronger the magnetic field, the higher the electron pressure becomes; the high electron pressure could be caused by high Fermi energy of electrons in a superhigh magnetic field; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron star due to the anisotropic total pressure; and an increase in the maximum mass of a magnetar is expected because of the positive contribution of the magnetic field energy to the EOS of the star., Comment: 26 Papers, 5 Figures, Published in Modern Physics Letters A ., Vol.28, No.36, p.1350138 (2013)

In order to depict the quantization of Landau levels, we introduce Dirac $\delta$ function, and gain a concise expression for the electron Fermi energy, $E_{F}(e) \propto B^{1/4}$. The high soft X-ray luminosities of magnetars may be naturally explained by our theory., Comment: 3 pages, 1 figure, submitted to OMEG11 Proceeding (Tokyo, Japan. Nov.14-18, 2011)