Usually we think a X-ray source may be a compact(neutron) binary star on which the X-ray radiation might be generated by gravitational acceleration for the particles coming from the primary and going along magnetic field lines of the compact star to the poles. But, in the past, people don't consider well the problem of particle acceleration. It seems to be simplified for the situation only to consider the gravitation effect, because some electric-magnetic effect in a strong magnetic field could not be neglected. However, it is unreasonable to neglect the plasma turbulent waves in an electric-magnetic field, because strong enough turbulent waves such as Alfven waves, whistlers generated nearby the surface of neutron stars probably contribute energy to accelerate particles, which may be more important than gravitation sometimes. For a binary system with a neutron star if ion number density N > 1017 /cm3 in its surface atmosphere, the turbulent wavess will be stimulated that will accelerate the particles reaching a speed over 108cm/s. they strike the atmosphere of the compact star in the system, so that a shock wave is formed which turns part of kinetic energy to heat to form hot spots of about 108K to emit X-ray.

High quality spectra of Japanese X-ray satellite TENMA permit us detailed studies of X-ray burst on color temperature vs. luminosity diagram. Using this diagram, Sugimoto Ebisuzaki and Hanawa (1984) divided bursts from MXB1636-536 into two classes: bright class and faint class. In the decay phase of bright class bursts, surface of neutron star should be covered with pure helium matter processed on the surface of neutron star because hydrogen-rich matter is completely lost due to mass loss. On the other hand, surface of neutron star should be covered by hydrogen-rich matter in the case of faint class bursts because any mass loss is not driven in the faint class bursts. I constructed color temperature vs. luminosity diagrams of X-ray burst sources MXB1636-536 and MXB1608-522 using data of Japanese X-ray satellite TENMA and found systematic deviations between evolutional paths of the bright class and faint class bursts on these diagrams. The deviations are successfully accounted for by the difference in chemical composition between bright class and faint class bursts: evolutional paths of bright class and faint class are respectively in good agreement with theoretical curves for pure helium and hydrogen-rich matter. This is a direct evidence of ejection of hydrogen-rich envelope in the bright class bursts.

Self consistent neutron star atmospheric models have been constructed which include the effects of Comptonization, free-free and bound-free absorption. It has been demonstrated that for parameters relevant to x-ray bursting neutron stars the atmosphere does not radiate like a blackbody during any phase of an x-ray burst. In particular, during the initial rise and final decline of the burst the temperature structure of the atmosphere is affected by backwarming associated with the high opacity due to free-free processes at low frequencies to an extent that the radiation spectrum is shifted to higher energies than a blackbody of the same effective temperature. On the other hand, near the peak of the burst, the opacity is more gray-like as the electron scattering opacity dominates; however, in this case thermalizaton of the radiation field occurs at such large optical depths (τ ∼ 5) that the spectral temperature is higher than the effective temperature. This result is found despite the importance of Comptonization in the thermalization process. Thus, the super Eddington fluxes implied by the spectral data alone are misleading and result from the improper use of the spectral temperature for the effective temperature. For neutron stars characterized by a soft equation of state and radiating near the Eddington effective temperature, fluxes obtained in this way could be overestimated by a factor of about 5.

Presupernova models of massive stars are discussed and their explosion by either the “core bounce” or neutrino energy transport mechanism briefly reviewed. Special consideration is given to those attributes of the stellar evolution and explosion that might influence the properties of the neutron star remnant: its mass, rotation rate, magnetic field, and “kick” velocity.

Theory and numerical experiments on neutron star formation are critically reviewed. Several new numerical experiments are summarized, and the importance of advection is discussed.

The presupernova evolution of stars that form semi-degenerate or strongly degenerate O+Ne+Mg cores is discussed. For the 10–13 M⊙ stars, behavior of off-center neon flashes is crucial. The 8–10 M⊙ stars do not ignite neon and eventually collapse due to electron captures. Properties of supernova explosions and neutron stars expected from these low mass progenitors are compared with the Crab nebula. We also examine the conditions for which neutron stars form from accretion-induced collapse of white dwarfs in close binary systems.

It was just after the discovery of neutrons in 1932, Landau suggested the possibility of compact stars composed of neutrons. In 1934 Baade and Zwicky proposed the idea of neutron stars independently and suggested that neutron stars would be formed in supernova explosions.

The properties of the rapid, persistent quasi-periodic oscillations (QPO) discovered with EXOSAT in the X-ray flux of at least 7 bright low-mass X-ray binaries are described. Particular attention is given to the various relations observed between QPO frequency and X-ray intensity, the link between QPO and the low-frequency noise in the X-ray intensity and the bimodal properties of in particular Sco X-1, GX 5-1 and Cyg X-2. The merits of the hypothesis that the QPO indicate the presence of a neutron star with a magnetosphere are considered.

EXOSAT observations of Cyg X-2 reveal two types of QPO's (quasi-periodic oscillations) which are associated with different spectral behaviour. QPO's in the range 18–55 Hz with a hard spectrum are found in all observations where the source is on the ‘horizontal branch’ in an hardness-versus-intensity diagram. On the ‘vertical branch’, however, QPO's with a soft spectrum are found at a stable frequency of 5.6 Hz. A multitude of QPO frequency-intensity relations, found in different ‘horizontal branch’ observations, coalesce to an almost unique relation when the QPO frequency is correlated with spectral hardness. A cross-correlation analysis of the rapid variability reveals a time-lag of hard photons by 1.5–3.8 ms; the lag being smaller when the QPO frequency is larger. All results are consistent with a model where QPO's represent the Kepler frequency at the edge of the neutron star magnetosphere. In particular the data do not require the assumption of a beat frequency. The derived surface magnetic field strength is of the order of 1010G.

We have to date reports of Quasi-Periodic-Oscillation (QPO) observations in some twelve X-ray source, of which at least seven are low mass X-ray binaries (van der Klis 1987). They constitute a formidable zoo of phenomenae with so much variety that they, at times, do not at all even seem amenable to a single model. Some of the other QPO talks in these proceedings will try and present observations in the context of various models. My task is to talk about the Beat Frequency Model which, it seems to me, is by far the prime model for at least some of the QPOs.

The salient features of quasi-periodic oscillations (QPO) observed in type 2 bursts and in the persistent emission from the Rapid Burster are discussed. In addition, a brief review is given of the models that have recently been proposed to explain high-frequency QPO observed in several bright low-mass X-ray binaries. We do not yet know the mechanism(s) of the QPO, not even whether they are magnetospheric in origin. However, some of the proposed ideas could well be relevant to the various rather complex aspects of the QPO. It is likely that more than one mechanism is at work.

It is known that fluid object that it magnetized with a purely poloidal field is unstable to perturbations that overturn the field lines in one hemisphere relative to those in the other. We have shown that this instability occurs even when the entire object is encased by a solid crust, as conjectured by Flowers and Ruderman (FR) nearly a decade ago. We have derived the exact dispersion relation that displays this instability for an infinite, cylindrical geometry, which will be published elsewhere. The timescale for the instability is roughly the ohmic dissipation timescale of the crust.

In this paper, the author studied the evolution of magnetic inclination with age for several pulsars. According to the results obtained by the author (1981), the formula for this evolution is given below The evolutionary curves of magnetic inclination, calculated from this formula, for three pulsars — PSR 0525+21, PSR 0329+54 and PSR 1133+16 — are presented in Fig. 1.

It is generally agreed that the magnetic fields of pulsars decay with the time. The previous estimates for the decay timescale range from 2Myr to < 10Myr based on the evolutionary tracks in the (P,P) diagram and the kinematics of pulsars. We make a new estimate, by using the ‘measured fields’ themselves, to be about 20Myr and show that the z-distribution of pulsars is consistent with the new estimate if the known dependence of velocities of pulsars on the magnetic moment is taken into account.

Using the axisymmetric tortion tensor given by J. Nitsh in U4 gravitational gauge theory. Applying G. S. Yang and L. F. Luo's magnetic field model of neutron stars, i.e. magnetic field is originated from long-arranged neutron spin. Precession of spin coupled with tortion has been studied, indicating an influence on the magnetic field. The results show that the initial magnetic filed B made of long-arranged spin magnetic moment is at an angle of α with rotating axis, if radians, B makes a so small angle to the rotating axis at time 108 sec. that no pulses could be radiated from the neutron stars. Only when radians, the pulse radiation could be done. Based on the assumption that the orientation of the initial magnetic fields is isotropic, we can get then that only about ten percent of the rotating neutron stars radiate pulses.

The Galaxy contains a large number of neutron stars in gravitation-ally bound binary systems. Among the most fruitful of these to study have been the binary radio pulsars, of which seven are now known. Unlike the “accretion-powered” neutron stars located in mass-exchanging X-ray binary systems, the “rotation-powered” binary radio pulsars are found in dynamically simple, clean systems in which both stellar components have already completed their nuclear evolution, thereby shedding their atmospheres and most of their mass. In such circumstances the orbital parameters of the system and the rotational parameters of the pulsar can be determined with high precision from analysis of pulse timing data. These measurements constrain the component masses and yield an estimate of the pulsar's magnetic dipole moment, which turns out to be an essential parameter in understanding the evolution of the systems. In this paper I review the known facts concerning binary pulsars, and then briefly discuss some implications for our understanding of the place of neutron stars in stellar evolution.

The evolutionary history of binary radio pulsars, including the two millisecond binary pulsars, is reviewed. There are two groups of binary pulsars, the PSR 1913+16-group, which descended from massive X-ray binaries, and the PSR 1953+29-group, which descended from fairly wide low-mass X-ray binaries. The neutron stars in the second group probably formed by the accretion-induced collapse of a massive white dwarf. The companion stars in both groups of systems are expected to be dead stars, i.e. white dwarfs or neutron stars.

The large total number of millisecond binary pulsars in the galaxy (∼ 104), indicates that magnetic fields of neutron stars do not decay below a value of order 109 G. Possible explanations for this phenomenon are discussed.

Coalescence with a close degenerate companion provides a viable model for the formation of the single millisecond pulsar.

We report the discovery of white dwarf secondaries in 0655+64 and 0820+02 systems. In the 2303+46 system, we do not find any optical counterpart suggesting that the companion is another neutron star. The existence of a cool and therefore old white dwarf in the 0655+64 system implies that the surface magnetic field of neutron stars stops decaying beyond some value(s) of field strength.

The formation of neutron stars in binary systems is often used to explain the nature of specific radio pulsars and characteristics of the pulsar population as a whole. We have investigated the extent to which such scenarios provide a self-consistent description of the pulsar population. Using a computer simulation, we modeled the evolution of the main sequence stellar population and compared the predicted neutron star population to the observed radio pulsar population, focusing our attention on the pulsar velocity distribution and the incidence of binary pulsars. These characteristics relate very directly to the binary nature of pulsar progenitors, and are not strongly dependent on models of pulsar magentic field and luminosity evolution.

The need to reproduce both the high velocities typical of pulsars and the low incidence of binary pulsars strongly constrains the formation of pulsars in binary systems. Unless one assumes that virtually all pulsars originate in close binary systems, the observed velocity distribution cannot result from the disruption of binary systems by symmetric supernova explosions; some additional acceleration process (e.g. asymmetric supernova mass ejection or asymmetries in pulsar radiation) must act during or soon after a pulsar's formation. It is possible to reproduce the velocity distribution by assuming that all pulsars are born in binary systems with initial orbital periods less than about 30 years. However, the predicted incidence of binaries is then too large by more than an order of magnitude, unless one also assumes that the process of mass transfer from the primary to the secondary is almost always non-conservative, or that the minimum mass necessary for a stripped helium core to explode as a supernova is larger (over 4 M⊙) than currently believed. Further analyses of the radio pulsar population, the X-ray binary population and the abundances of elements ejected in supernovae should help determine which of these alternatives is most reasonble. Additional studies of the main sequence stellar population, accounting more accurately for evolutionary and observational selection effects, will reduce the uncertainties in modeling the formation of the neutron star population.

It has also been suggested that the observed correlation between pulsar velocities and magnetic moments (see Cordes, these Proceedings) is induced by the differing evolutionary paths by which stars in binary systems form radio pulsars. Our simulation does not reproduce this correlation, and we do not find any paths likely to produce low velocity, low magnetic field neutron stars not in binary systems.

We are submitting a full description of our model and results to The Astrophysical Journal.

Numerical computations were carried out to simulate the evolution of the recently discovered radio pulsar binary PSR 1831-00 with a very low mass function (Porb = 1.81 days, Dewey et al. 1986). These show that the minimum value of the initial mass of the progenitor of the mass-losing secondary is about 1 M⊙. All computed systems with a final period equal to the observed one, and an initial progenitor mass of 1 M⊙ have an age of the order of the Hubble time (∼ 1.3 × 1010years). For a 1.5 M⊙ progenitor of the mass-losing secondary we find that the final (= presently observed) orbital period sets strong constraints to the possible initial system configuration: the binary period should have been such that the 1.5 M⊙ star was just at the onset of the over-all contraction phase (Porb = 0.74 days, XC = 0.05) when it began to fill its Roche-lobe, and the initial mass or the compact mass-accreting star must have been < 0.85 M⊙. (This star was then presumably a white dwarf, which later collapsed due to the accretion). For example, the final period and remnant secondary mass for a system with an initial configuration of 1.5 + 0.8 M⊙ are 1.83 days and 0.20 M⊙, respectively.

If one would start out from a more evolved initial state of the 1.5 M⊙ secondary than the end of the overall-contraction phase, the maximum initial mass of the compact object will become drastically smaller and the final remnant mass of the secondary becomes larger than 0.20 M⊙ in all cases.

Calculations for a 2.0 M⊙ progenitor of the secondary suggest that if such a progenitor can produce the present system, the initial mass of the accreting primary was at maximum 1.30 M⊙.

All the calculations were performed with the inclusion of magnetic braking in so far as the extent of the convective envelope allowed this (see Pylyser & Savonije 1986, in preparation). The effects of the explosion effects due to the accretion induced collapse of the white dwarf were not taken into account.