This paper uses population synthesis to investigate the possible origin of isolated millisecond pulsars as born from the coalescence of a neutron star and a white dwarf. Results show that the galactic birth rate of isolated millisecond pulsars is likely to lie between 5.8×10−5 yr−1 and 2.0×10−4 yr−1, depending on critical variables, such as the stability of mass transfer via the Roche lobe and the value of kick velocity. In addition to this, this paper estimates that the solar mass of isolated millisecond pulsars can range from 1.5 and 2.0 Mʘ, making them more massive than other ‘normal’ pulsars. Finally, the majority of isolated millisecond pulsars in our simulations have spin periods ranging from several to 20 ms, which is consistent with previous observations.

A summary is given of the present state of our knowledge of High-Mass X-ray Binaries (HMXBs), their formation and expected future evolution. Among the HMXB-systems that contain neutron stars, only those that have orbital periods upwards of one year will survive the Common-Envelope (CE) evolution that follows the HMXB phase. These systems may produce close double neutron stars with eccentric orbits. The HMXBs that contain black holes do not necessarily evolve into a CE phase. Systems with relatively short orbital periods will evolve by stable Roche-lobe overflow to short-period Wolf-Rayet (WR) X-ray binaries containing a black hole. Two other ways for the formation of WR X-ray binaries with black holes are identified: CE-evolution of wide HMXBs and homogeneous evolution of very close systems. In all three cases, the final product of the WR X-ray binary will be a double black hole or a black hole neutron star binary.

The standard engine behind core-collapse supernovae is continuously evolving with increasingly detailed models. At this time, most simulations focus on an engine invoking turbulence above the proto-neutron star, sometimes termed the “convection-enhanced” engine. Here we review this engine and why it has become the standard for normal supernovae, focusing on a wide set of observations that provide insight into the supernova engine.

The gravitational wave radiation will release the energy momentum, which will dissipate the rotation of neutron star while in the accretion process. If the deformation of star is known, then we can estimate the maximum spin frequency of pulsar, based on which we can interpret why the spin periods of all millisecond pulsars cannot be less than one millisecond.

From the extreme position of disk motion, we infer the neutron star (NS) surface magnetic field strength (B0) of Z-source GX 17+2 and Cyg X-2. The inferred B0 of GX 17+2 and Cyg X-2 are ~(1–5)×108 G and ~(1–3)×108 G, respectively, which are not inferior to that of millisecond X-ray pulsars or atoll sources. It is likely that the NS magnetic axis of Z sources is parallel to the axis of rotation, which could result in the lack of pulsations in these sources.

We have collected the parameter of 38 neutron stars (NSs) in binary systems with spin periods and measured masses. By adopting the Boot-strap method, we reproduced the procedure of mass calculated for each system separately, to determine the truly mass distribution of the NS that obtained from observation. We also applied the Monte-Carlo simulation and introduce the characteristic spin period 20 ms, in order to distinguish between millisecond pulsars (MSPs) and less recycled pulsars. The mass distributions of MSPs and the less recycled pulsars could be fitted by a Gaussian function as 1.45±0.42 M⊙ and 1.31±0.17 M⊙ (with 1σ) respectively. As such, the MSP masses are heavier than those in less recycled systems by factor of ~ 0.13M⊙, since the accretion effect during the recycling process.

According to the theoretical study, a deformation object (e.g., a spinning non-axisymmetric pulsar star) will radiate a gravitational wave (GW) signal during an accelaration motion process by LIGO science project. These types of disturbance sources with a large bump or dimple on the equator would survive and be identifiable as GW sources. In this work, we aim to provide a method for exploring GW radiation from isolated neutron stars (NSs) with deformation state using some observational results, which can be confirmed by the next LIGO project. Combination with the properties in observation results (e.g., PSR J1748-2446, PSR 1828-11 and Cygnus X-1), based on a binary population synthesis (BPS) approach we give a numerical GW radiation under the assumption that NS should have non-axisymmetric and give the results of energy spectrum. We find that the GW luminosity of LGW can be changed from about 1040 erg/s – 1055 erg/s.

Using RXTE observations, we investigate the evolution of inner disk radius (Rin) of Cir X-1 during two cycles and find obvious orbital modulation. We argue that the modulation is attributed to its high orbital eccentricity. The disk luminosity is inversely with the inner disk temperature (kTin), which is ascribed to the slow increase of kTin and, however, the rapid decrease of Rin during the passage for the neutron star to depart from the companion star.

About 0.2 solar mass is absorbed by the millisecond pulsar (MSP) at the binary accretion phase, while the polar magnetic field of MSP is diluted to a magnitude of order 108.5 Gauss, which is proportionally related to the mass accretion rate. It is found that the minimum magnetic field of MSP can be as low as 107 Gauss if the accretion rate of the binary system reaches its the minimum value of 1015 g/s. This bottom field has nothing to do with the MSP initial field. Some questions on MPSs are proposed and answered.

The kilohertz quasi-periodic oscillations (kHz QPOs) have been found in neutron star low mass X-ray binaries (NS-LMXBs), which present the millisecond timing phenomena close to the surface of the compact objects. We briefly summarize the following contents: (1). The correlations and distributions of twin kHz QPOs; (2). The relations of high-low frequency QPOs; (3). The QPO properties of NS Atoll and Z sources; (4). No clear direct correlations between NS spins and QPOs; (5). The mechanisms of kHz QPOs; (6). The implications of kHZ QPOs, e.g., NS mass and radius, disk thickness and magnetic field of Atoll and Z source.

I model changes in cyclotron line energy with luminosity, considering the effect of polar cap dimensions and changes in beam pattern as well as shock height. Cyclotron lines are calculated by a superposition of a large number of cyclotron lines formed in different heights of an accretion column. Cyclotron line energy has been observed to change with luminosity in a number of accreting X-ray pulsars. In X0115+63 and V0332+53, the fundamental cyclotron line energy has been observed to decrease with increasing luminosity. This phenomenon has been interpreted as a change in shock height with luminosity. However, the rate of the change seems to be very different, in which the line energy in V0332+53 seems to vary slowly with luminosity compared with that in X0115+63. I found that the changes in the cyclotron line energies with luminosity can be explained by changes in beam pattern and the size of a polar cap rather than a shock height.

We carried out relativistic force free simulations and Particle In Cell (PIC) simulations of twist injection into the magnetic arcades emerging on the surface of a magnetar. As the magnetic energy is accumulated in the arcades, they expand self-similarly. In the arcades, a current sheet is formed and magnetic reconnection takes place. We also carried out 2-dimensional PIC simulations for the study of particle acceleration through magnetic reconnection. As a result, the energy spectrum of particles can be fitted by a power-law.