Dr. Feldman described the optical variability which has been seen over the years in a region near the nucleus of NGC 4254 (M99) and he suggested that it might be a pulsar.

The low expansion velocity of the Crab Nebula proves conclusively that the supernova of + 1054 was not type I. Only five supernova remnants found in radio surveys are connected with ancient novae, +185, +1006, +1054, +1572, +1604. This corresponds to reasonable expectation. Most of the objects in historical records were comets, the remainder mostly ordinary novae. Most radio remnants are too old, some too heavily obscured to be found in historical records.

Observations of the radio emission from supernova remnants are reviewed with emphasis on the dissimilarity between the Crab Nebula and the other remnants. From this we conclude that there may be several non-thermal sources in the Galaxy with the same centrally filled structure as the Crab. These are, however, more evolved, and clearly there is no other source of the same age and type as the Crab Nebula.

Proper motion observations show that the explosion of the Cas A supernova took place in AD 1667 ± 8 (me). Individual moving knots have lifetimes ~ 10 yr. In these fast-moving knots oxygen and argon are overabundant by a factor of at least seventy with respect to hydrogen and nitrogen. Nitrogen is found to be overabundant in quasi-stationary flocculi. This suggests that these flocculi were formed from material that was ejected from the outer layers of the pre-supernova before its explosion in AD 1667.

Continuous injection models for the secular behavior of the radio and X-ray emission from supernova remnants are examined and compared with the observations. Among other things, it is concluded that (1) continuous injection probably occurs for at least 10 yr in every case and about 1000 yr in most supernova remnants, in which case the supernova remnants 3C392, W28, Pup A and IC443 should produce 1–10 keV X-ray fluxes ≈ 10-10 ergs/cm2-sec, and (2) the X-ray sources in the Crab Nebula, Cas A and Tycho can be explained in terms of a model wherein continuous injection occurs for 300 yr for the Crab Nebula, much less than 250 yr for Cas A and much longer than 400 yr for Tycho. Finally, it is shown that if Tycho and Cas A contain an X-ray star such as NP 0532, it is quite possible that the X-ray emission from those sources is predominantly due to the X-ray star.

It is first considered what must happen if pulsars (i.e. neutron stars) are formed in close binary systems (CBS), and whether the resulting orbital motion and mass transfer should be observable. As this set of alternatives seems unlikely, there follow suggestions of how one might prevent the formation of neutron stars in close binaries. Finally, it is shown that ‘runaway’ pulsars with velocities larger than about 15 km/sec cannot be produced by isotropic supernova explosions within close binaries, and an alternative explanation is suggested for the observed correlation of periods of pulsars with their distances from the galactic plane.

Alfvén waves can be carried by the thermal plasma in the Crab Nebula. Each such wave perturbs the relativistic plasma present, in particular it strongly affects those particles which are in resonance with it. For a wave travelling parallel to the magnetic field the resonances are quite simple, but a wave travelling obliquely can give rise to multiple resonances, and can therefore couple together particles with quite different energies.

It is shown that the interaction with the relativistic plasma leads to an amplification of the Alfvén waves when the mean velocity of relativistic plasma relative to the thermal plasma exceeds the Alfvén speed. The rise time for the instability is quite short, and the waves, once excited, are highly effective in redistributing the directions of motion of the relativistic particles. The relativistic plasma therefore cannot stream freely through the thermal plasma. On the other hand the disturbances will never quite die out in the Crab Nebula as long as the Crab pulsar keeps injecting fresh plasma, and thus keeps producing new inhomogeneities in the relativistic plasma density.

Optical and radio measurements of polarization can be combined to find the configuration of the magnetic field throughout the Crab Nebula. The component in the line of sight is found from the radio rotation measure.

New measurements of polarisation at 11 cm with a resolution of 7′ x 14′ are combined with previous results to show that the rotation measure is fairly uniform and near −25 rad m−2 near the centre, but that it becomes irregular near the edges. It rises to 300 rad m−2 in the filaments, possibly indicating a concentration of electrons about 10–100 cm−3.

Observed enhanced activity in the central region of the Crab Nebula following the spin-up of the pulsar is discussed from the point of view of the transfer of energy to relativistic electrons. It is argued that a rapid deposition of energy associated with the spin-up of the pulsar causes a radial energy flux which becomes a flux in hydromagnetic activity at about the regions where enhanced synchrotron emission is observed. It is shown that such hydromagnetic activity is rapidly damped by the relativistic electrons with energy being transferred to the relativistic electrons. This acceleration can account for the short synchrotron halflifetimes observed. The model predicts highly enhanced X-ray emission from the central region of the Nebula following a spin-up.

We have attempted to explain the observed excitation conditions in the filamentary system of the Crab Nebula in terms of ionization and heating by high frequency radiation. It was found that it is possible to reasonably fit most of the observed lines by assuming either (1) an ultraviolet continuum which smoothly joins the optical and X-ray data and a gas composition in which the number densities of hydrogen and helium are equal, (2) a spectrum which drops off about as steeply as v-2 and therefore does not smoothly fit the X-ray spectrum, or (3) an ultraviolet continuum which smoothly joins the optical and X-ray data plus strong emission-line features near 20 eV. A UV continuum which is much larger than in these models results in too much ionization in the filaments. The calculations suggest that most of the filaments consist of outer ionized regions with cores of neutral gas, so that the mass of the filamentary shell may be considerably larger than the 1.45 M⊙ required to explain the emission line intensities.

We suggest that if there exist within the Crab Nebula localised condensations of material containing high magnetic fields, (≫ 1 G), the rapidly evolving synchrotron radiation power spectrum emitted by a single electron can give a radiation continuum with a spectral index having a unique value similar to that observed in the optical and low-energy X-ray regions. One implication of this result is that a simple comparison between the observed fluxes of optical and gamma radiation emitted by the Nebula is no longer meaningful, so that one cannot draw any immediate conclusion regarding the fundamental mechanism of electron and gamma ray production.

Some characteristics of neutron star models are described. These include: the physics of the crystalline crust, the superfluid properties of the neutrons and protons, and the presence of rotational vortices in these superfluids. The possible relationship of some of these properties to the behavior of the Crab Nebula pulsar is described.

Except in cosmology, astrophysicists are used to thinking of general relativistic effects as small (e.g., light bending, perihelion advance, red shift) and have generally left such problems to general relativists. However, the discovery of pulsars (Hewish et al., 1968) may have changed this. Not only is general relativity necessary to treat rotating neutron stars, but relativity was also partly responsible for the elimination of pulsating white dwarfs as pulsar models.

The Nemeth-Sprung equation of state is modified and used to obtain neutron star models. Contrary to the results of some authors it is found that neutron stars with central densities ≲ 1014 g cm-3 are dynamically stable. It is suggested that some pulsars may belong to this category of stars.

We describe a numerical method of integration of Einstein's equations coupled with the hydrodynamic equations for a perfect fluid. We give, also, some preliminary results.

We point out that the analogous problem was considered by Ostriker and Mark (1968) in the Newtonian case; by Thorne (1969) in General Relativity, in the weak angular velocity approximation; by Barden and Wagoner (1969) for disk configurations in the pressure vanishing case.

The original models of neutron stars must be improved by including effects of nuclear interaction. This paper compares the models reached by various groups, and presents an improved model by the Kyoto group. The maximum mass varies between 0.2 M⊙ and 3 M⊙ in the various models. The Vγ model is recommended for use in the absence of further information on the equation of state at high densities.

The conditions for superfluidity or ferromagnetism in neutron stars are presented and discussed (but not derived). It is suggested that present estimates relating to these are in error and that the predictions made contradict at least one of three sets of nuclear physics data cited in the text. This is due to neglecting the action of the exclusion principle.

A comparatively simple method for calculating the strength of nuclear forces in the presence of many-body effects is outlined. Some preliminary results are presented together with projected future developments.

The diagnosis of pulsar-like symptoms in the quasar 3C 345 has renewed interest in differentially rotating supermassive stars (SMS). Quasi-periodic behavior follows from differential rotation. In reviewing early work on this quasar model it is found that SMS models with rotational periods of the order of a few hundred days and with pulsation periods approximately one-quarter as long can supply thermal and magnetic dipole radiation of the order of 1048 erg sec-1 for somewhat more than 106 yr. The surface field required for the magnetic dipole radiation is approximately 103 G. The SMS mass taken as typical in the calculations is 3 × 109M⊙.

Fragmentation in the collapse of a supernova core, followed by energy loss in neutron star formation, is shown to lead to disruption of the resulting system. The elements of the system, some of which should be pulsars, can attain velocities of the order of 103 km/sec if currently quoted parameters are correct.

Dr. Ruffini gave a brief survey of the present experimental evidence for the existence of gravitational waves, and discussed the possibility that the shapes of neutron stars might depart from rotational symmetry, leading to the emission of gravitational waves.