Pulsed optical emission has been observed from the Crab and Vela pulsars (Manchester and Taylor 1977). The pulse profile of the Crab pulsar has a main pulse and a strong interpulse separated by about 40% of the pulsar period; the peak of the main pulse is just resolved at 20 μs resolution; the spectrum is peaked at about 1014.8 Hz; the pulse profile is constant over long time intervals; both the main pulse and the interpulse are strongly linearly polarized with position angle varying smoothly through each profile and with a minimum of polarization near each peak; the pulses are not significantly circularly polarized. A number of models have been proposed to explain the optical emission from the Crab pulsar but none is completely satisfactory. The spectral peak is too low for incoherent synchrotron emission, the pulse profile is too constant for inverse Compton scattering of radio emission and the similarity with the low-energy X-ray emission argues against coherent curvature emission.

Measurements of pulsars in the energy domain above ~ 1 keV have provided in the last few years new and interesting results. This paper presents a review of the observational features of PSR 0531+21 and PSR 0833–45 (the Crab and Vela pulsars). Searches for pulsed emission from old radio pulsars in the same energy domain are also reviewed and results assessed. The comparison of the observed features with each other and with the corresponding features observed at lower energies reveals similarities and differences capable to constrain theoretical models with special regard to the geometry of the emission mechanisms.

We present here the results from observations of pulsed gamma ray emission from the Crab and Vela pulsars for energies above 100 GeV using the atmospheric Cerenkov technique. The results suggest a very steep energy spectrum for gamma rays emitted from pulsars at high energies. Our observations over the last 4 years suggest also that the flux is highly variable with time.

In this report we shall discuss the origin of radiation from the neutron star component of X-ray binary systems whose spectra contain cyclotron lines (Her X-1 and 4U0115+63). A relevant model of the polar region of a neutron star is presented in Figure 1. According to this model the observed X-rays (continuum + cyclotron lines) are generated in the dense plasma atmosphere of a star (in its hot spot heated by accreting matter). The problem of heating the neutron star atmosphere due to accretion has been earlier investigated by Zeldovich and Shakura (1969). Cyclotron lines are formed similarly to the Fraunhofer spectrum of ordinary stars and are absorption lines. For objects such as Her X-1 and 4U0115+63 the cyclotron emission and absorption in the extended accreting column with an inhomogeneous magnetic field should be unessential. Otherwise the accreting column will produce an X-ray continuum devoid of any line type features.

The spectrum of Hercules X-1 reveals line features at 58 keV and probably at 110 keV, which have been interpreted as first and second cyclotron harmonics originating in the radiation from the hot polar cap region of a magnetic neutron star. The inferred magnetic field strength is ~ 5.3 × 1012 Gauss (Trümper et al. 1978). Other noteworthy spectral characteristics of this source are the very ‘flat’ intensity continuum in the frequency range 2 – 20 keV followed by a rather sharp spectral break near 25 keV and an intensity minimum near 40 keV. This spectrum is certainly not reminiscent of typical black-body emission. How can one understand these diverse characteristics?

The most recent review of pulsar timing observations (and pulsar astronomy generally) is contained in the monographs by Manchester and Taylor (1977) and Smith (1977). This paper reviews developments in radio timing observations since the time of writing these monographs (~ 1976). In Section 2 results based on the secular variation of pulsar period are reviewed and timing irregularities are discussed in Section 3. Results for binary pulsars, three of which are now known, are reviewed by Taylor (1981).

Eleven years of arrival time data for PSR 0833–45 collected at Goldstone, CA were analysed by fitting a simple model of the pulse period to the data in a least-squares sense. Four large jumps δP in period P of δP/P ~ −2 × 10−6 have occurred in which P increases up to 2% of its pre-jump value. Then P decays nearly exponentially with a time scale of 40 to 80 days to (1.2471 ±5) x 10−13 ss−1, regardless of the size of the jump. Q values for the jumps are about 6.5%. Further decay of P is at the constant rate (within an interjump era) of −5 × 10−24 < P < −9 × 10−24 ss−2. The observable effects of random fluctuations in P or P are an order of magnitude smaller than the systematic effects evident in P.

The implementation of pulse timing analysis as a probe of neutron star structure is reviewed for both pulsars and X-ray pulsators. Current results are particularly significant for the Crab pulsar.

It is shown that under certain assumptions the response of a neutron star to a perturbation in its temperature will be an increase in pulse repetition rate. Detailed models are presented which show behavior indistinguishable from the Vela pulsar period jumps. There appears to be no theoretical difficulty in arranging these events to recur every few years.

In the neutron star crust, the neutron superfluid coexists with a lattice of nuclei. There are two different local densities of superfluid neutrons, inside and outside the nuclei, with a corresponding difference in the values of the superfluid gap and condensation energy.

This paper reviews the information on neutron stars that has been obtained from radio and X-ray observations, with emphasis on recent results from timing studies. Included are summaries of the current theoretical picture of neutron stars, and the most recent evidence concerning stellar masses, radii, inertial moments, and magnetic fields. Also included are discussions of large frequency jumps (“macroglitches”), small-scale timing irregularities (“microglitches”), the characterization of the latter phenomenon in terms of random noise processes, and the use of both as probes of the internal structure and dynamics of neutron stars. Finally, some of the most promising directions for future work are briefly noted.

The current state of neutron star structure calculations is reviewed. Uncertainties in the equation of state for matter at and above nuclear density remain. The role of the delta resonance, pion condensates, and quark matter is reviewed. Despite uncertainties, we find that recent models yield stable neutron star masses which are consistent with observational estimates.

The problem of neutron star thermodynamics has become a rather hot issue during the last one to two years, mainly because the enormous technological improvements brought by the Einstein Observatory (HEAO-B) and the exciting data which have become available to us through this satellite have given us a better hope of testing some of neutron star theories, which may eventually give us invaluable insight into various fields of physics. A somewhat extensive review of the pre-Einstein (Observatory) days was given in Tsuruta (1979a). Since then, many papers, both observational and theoretical, have come out. Most of the observational papers are reports from the Einstein Observatory. Stimulated by such progress on the observational side, various authors of recent theoretical papers attempted to reinvestigate and (or) improve the cooling and heating theories. Dave Helfand (1981) has already given a comprehensive summary of the most recent developments in heating theories. Therefore, in our present report, we shall restrict ourselves to the most recent developments in cooling theories and the comparison with the latest observations. The reader is referred to the earlier reviews (e.g. Tsuruta 1979a, b, 1980a) for the earlier work and the details.

Most of the neutron star cooling calculations with the only exception of Malone's (1974) have assumed an isothermal stellar core. Here we report on a neutron star cooling calculation which makes full use of the stellar evolution code and the recent thermal conductivity calculations by Flowers and Itoh (1976, 1979).

The radio emission from pulsars is energetically insignificant, yet its distinctive character led to their discovery and subsequent identification with rotating magnetized neutron stars. In the intervening thirteen years, a wealth of radio data have been accumulated from which we have learned something of the magnetospheric properties, stellar structure, and evolutionary history of these objects. Yet we still do not know how pulsars pulse, what the neutron star interior is like or, with certainty, how and where pulsars are formed. And, we have not yet ‘seen’ a radio pulsar, in the sense that we see other stars, i.e., by detecting thermal photons from its surface. The Einstein Observatory soft X-ray telescope offers a new opportunity to attempt such an observation. We report herein the preliminary results of several programs aimed at the detection of thermal X-ray emission from isolated neutron stars.

The masses of 6 neutron stars have now been established through studies of binary X-ray and radio pulsars. All of the masses are found to be consistent with, but not necessarily constrained to, the range 1.2–1.6 M⊙. In this talk we discuss the methods and assumptions used in determining the masses of neutron stars in binary X-ray pulsar systems. For other recent reviews of this subject, the reader is referred to Bahcall (1978), Rappaport and Joss (1981), and references therein. Neutron-star parameters may also be obtained from studies of X-ray bursts that result from thermonuclear flashes near the surface of an accreting neutron star (see Joss 1980 and references therein), which we will not discuss here.

Pulsing X-ray sources are believed to be the progenitors of binary and runaway pulsars. Thus, their observed properties and predicted fates furnish information about the initial properties and evolution of these pulsars. Evidence is discussed which suggests that many binary and runaway pulsars are born with periods ~ seconds and dipole magnetic fields ~ 1011 – 1013 G, and that the turnoff of at least some is not due to decay of their dipole magnetic fields.

There are now three radio frequency pulsars known to be in binary systems: PSRs 1913+16, 0820+02, and 0655+64. The first of these, discovered in 1974, moves in a tight, highly eccentric orbit with a period of approximately 7h 45m. Its companion has not yet been identified with certainty, but must be a compact object of mass comparable to that of the pulsar. PSRs 0820+02 and 0655+64, recognized as binaries during the past fifteen months, have nearly circular orbits with periods of over three years and about one day, respectively. All three objects are of great interest for the opportunity they provide to measure the masses of neutron stars. In addition, the first has proven to be a useful probe of gravitational theories, and the study of all of them should yield important information concerning the evolution of binary systems and the formation of neutron stars.

The nature, dynamics and evolution of the three known radio pulsar binaries are discussed. The system containing 1913+16 appears to comprise two ~1.4 M⊙ components, and to undergo orbital decay as predicted by general relativity. It is proposed that 1913+16 has a neutron star companion and that 0655+64 and 0820+02 have white dwarf companions which should be observable optically.

The various ways in which compact objects (neutron stars and black holes) can be formed in interacting binary systems are outlined. It is argued that most of the remnants of massive stars (M1 ≳ 10 M⊙) will be runaway pulsars, with space velocities ≳ 100 km/s, i.e.:

1. (i) semi-conservatively evolving massive close binaries (~ 1/3 of all massive stars) after the first SN explosion consist of a massive star and a neutron star; subsequently, after a stage of common-envelope evolution and spiral-in most of these systems are disrupted in the second SN, producing two runaway pulsars, one young and one old.

2. (ii) highly non-conservatively evolving systems (with initial mass ratio q0 ≲ 0.5 and binary periods up to several decades; ≳ 1/3 of all massive stars) will spiral-in during the first phase of mass transfer and are disrupted in the first SN explosion, producing one young runaway pulsar, together with a runaway star of low or moderate mass.