In principle the formation rate can be obtained on the basis of a knowledge of a spatial densities and lifetimes. Extreme care is needed, however because of the incompleteness of the available sample because of luminosity effects. Since luminosity and age are correlated it is essential that densities and lifetimes be evaluated for the same sample. Incompleteness affects the very faint pulsars most strongly, but because of their long lifetime the effect on the formation rate is comparatively small. We shall assume that the lifetime of a pulsar in our sample is on the average equal to twice its age. Further we estimate distances (r) from dispersion measures on the basis of a mean electron density ne of 0.05 cm−3 near the Sun. The fluctuations in ne again may cause systematic errors, but no information is available for an estimate of the magnitude of these.

There are 5 pulsars known with r cosb (b galactic latitude) less than 100 pc. For three of these ages are available from which a harmonic mean life time T of 2.5 × 107 yr is found. Of 19 pulsars with r cos b < 300 pc, eight have ages from which T= 1.1 × 107 yr. Samples with larger r cos b appear to be too incomplete for our purpose. Taking the Galaxy to be a uniform disk with a radius of 14 kpc, we obtain from both samples a formation rate of about one pulsar per 250 yr. It should be stressed that this is the rate for ‘visible’ pulsars. If beaming effects cause only a fraction η to be in principle observable, the formation rate is to be multiplied by η−1.

The basic idea that pulsars may be the origin of cosmic rays arises when one realizes that they meet some of the criteria, perhaps not all as yet, for an origin theory of cosmic rays. Those criteria are: (1) there must be some possible mechanism that one can recognize for the acceleration of particles; and the pulsars have given us a very clear hint that particles are accelerated to at least the medium range of energies of cosmic rays - 1013 eV. (2) The objects that are thought responsible for cosmic rays must have enough total energy available to them to produce the entire cosmic ray beam in the Galaxy. I will come back to that, but it is clear that the total number of pulsars that one might expect in the Galaxy can indeed produce an adequate supply and even a good margin above that, if one makes the estimate on the basis of one plausible set of assumptions. (3) One would like of course that the mechanism proposed should generate the right spectrum; but there we as yet know too little. We do not understand what the energy spectrum of particles accelerated in pulsars should be, and we cannot as yet make any conclusive statement as to whether this spectrum can or cannot match the observed cosmic ray spectrum in the Galaxy. There is no reason for thinking otherwise, but there is no positive evidence in favor at the moment.

Then we have (4) the problem that the process selected must generate the correct composition. There we have the problem that we have just discussed, which is certainly a difficult one; I don’t know that it is completely clear what type of particles you must expect to come from pulsars; how much of the material accelerated in the vicinity of the pulsar is material that is being cycled into it at the time and going out again; and how much is material which is preferentially sucked out of the surface, perhaps by reason of a high charge-to-mass ratio.

One of the major questions which has been raised with the rotating neutron star model of pulsars, is whether cosmic rays can be produced by the pulsar phenomenon through the acceleration of the surface material of neutron stars. It is therefore very instructive to review the calculations which have been made on the surface structure and cooling histories of neutron stars.

Figure 1 shows a diagram of the interior of a neutron star, one of a sequence of models calculated by Cohen et al. (1970). In this diagram the radii of the various parts of the model are to scale. The total radius of the model is 13.7 km. Over a fairly large range of distance downwards from the surface, ions and electrons also put in an appearance, and below that there is a still narrower strip where protons coexist with the ions, electrons, and neutrons. Below this the ions disappear, and at still greater depths mu mesons put in an appearance. Finally, near the center of the star, the calculations indicated that other hyperons probably appear.

The region containing the ions can be expected to form a crystalline solid, except in the outer fringes of the atmosphere, where thermal effects and the relatively small pressure will vaporize any crystals.

This discussion is concerned with the production of cosmic rays in supernova explosions. In particular, we are discussing the role of pulsars (which we all believe to be neutron stars) in this process. I should like first to recall that (so far as I am aware) the idea that neutron stars form in supernova explosions, and that this phenomenon is relevant to cosmic rays, was first proposed by Baade and Zwicky in 1934. The argument was originally based on energy considerations, and further estimates indicated that supernovae could indeed be the main source of cosmic rays (ter Haar, 1950). When radioastronomical data later showed that supernova remnants definitely contained large numbers of relativistic electrons, there could be no doubt that they were sources of cosmic rays as well (and it became quite probable that they were indeed the major source of such particles). The growth of these ideas can be studied in historical perspective in Rosen’s (1969) compilation of papers on cosmic ray origin theories. As is so often the case, this subject has developed in a cyclic and repetitious fashion. I wish to make this point because I feel that my own contribution to these theories has sometimes been overestimated - though I hope I cannot myself be blamed for this.

It would not be appropriate to consider cosmic ray origins in detail during this discussion. I have in my case given my present views elsewhere (Ginzburg, 1969, 1970). The following remarks will deal specifically with the role of pulsars.

The ‘Galactic’ cosmic rays impinging on the Earth come from afar over tortuous paths, traveling for millions of years. These particles are the only known samples of matter that reach us from regions of space beyond the solar system. Their chemical and isotopic composition and their energy spectra provide clues to the nature of cosmic-ray sources, the properties of interstellar space, and the dynamics of the Galaxy. Various processes in high-energy astrophysics could be illuminated by a more complete understanding of the arriving cosmic rays, including the electrons and gamma rays.

En route, some of the primordial cosmic-ray nuclei have been transformed by collision with interstellar matter, and the composition is substantially modified by these collisions. A dramatic consequence of the transformations is the presence in the arriving ‘beam’ of considerable fluxes of purely secondary elements (Li, Be, B), i.e., species that are, in all probability, essentially absent at the sources. We shall here discuss mainly the composition of the arriving ‘heavy’ nuclei -those heavier than helium - and what they teach us about the source composition, the galactic confinement of the particles, their path lengths, and their transit times.

Diffuse background radiation has been detected over 16 decades of frequency - from a few MHz up to ~3 × 1016 MHz (100 MeV) - and there are upper limits over an even wider range. Generally an important contribution comes from the galactic disc, but in some wavebands it has proved possible to isolate a truly cosmic isotropic component originating beyond our own Galaxy. A simple Olbers-type argument shows that the bulk of any extragalactic radiation field originates at cosmological distances. This is true whether the radiation is emitted by discrete sources, or comes from extragalactic (or pregalactic) space. Thus studies of the isotropie background radiation, or even upper limits to its intensity, yield data that are vital for cosmology, as well as telling us something about the properties of diffuse intergalactic matter, and about intrinsically faint extragalactic objects which cannot be observed individually.

In this talk I shall not attempt a systematic review of this extensive subject, but will merely discuss a few recent developments. I shall give special attention to the microwave and X-ray regions of the spectrum, as these are the two bands in which the cosmic background is so strong that it swamps the emission from the Galaxy.

The absolute magnitudes of pulsating variable stars, both RR Lyrae stars and Cepheid variables, may be assessed from observation in three ways: by the classical method of statistical parallaxes, by their occurrence in star clusters whose distance is otherwise known, particularly by ascertaining the position of the main sequence in the HR diagram, and by the Baade-Wesselink method of determining stellar diameters.

As regards the first of these, the method of statistical parallaxes, the RR Lyrae stars lend themselves to this better than do the Cepheid variables, because the velocities relative to the Sun are so much larger. RR Lyrae radial velocities are frequently as high as 200 km/sec or even 300 km/sec, and as many of the stars lie at distances between 1000 and 1500 pc the proper motions of the transverse velocities may be expected to be as high as 0”.050 per annum. And, indeed, many investigations have been made recently, among which one may mention those by Plaut, by van Herk, and by the Royal Greenwich Observatory.

In discussing the absolute magnitudes of RR Lyrae stars, I concur in the importance of the question but I would, at the outset, like to insert a word of caution: It seems to me most likely that the Mb of RR Lyrae stars is not an immutable constant but depends on the original composition of the star. I will come back to this point later.

The principal point of view which I shall emphasize is rather different from that of most observers. The observer is usually interested in using the RR Lyrae stars as a means to calibrate distances and thereby looks out from the star to the Galaxy and then to the Cosmos. In contrast, the interests of the theorist look inward and he views the RR Lyrae stars as convenient fixed points for the comparison of theory with observation.

At present, the theory of stellar structure is tied to fitting the Sun. We all know the difficulties in the solar neutrino experiment which casts some doubt on whether we even understand the Sun. But we have few if any cases of evolved stars where we know M, L, R, to check our stellar evolution calculations.

We are now in desperate need of new fixed points where we can compare observation and the theory of stellar structure and evolution. The RR Lyrae or Cepheid type variables provide excellent examples for this comparison of observation and calculation. They are in late stages of evolution where tests are needed, they are readily identifiable, and well observed, and already the knowledge of the period provides a very precise mass-radius relationship so that a complete determination of the model will be provided by only a few additional measures.

The data on which my work on the secular parallaxes of RR Lyrae stars is based (Bull. Astron. Inst. Neth.18) were in many respects so incomplete that I have tried to interest astronomers to get a more complete set of data. The number of stars for which I had a proper motion was only 168, and for which a radial velocity was known, was 180, with an overlap of only 138 stars. The accuracy of the proper motions was certainly unsatisfactory for 43% of the total. The greatest trouble in dealing with such insufficient numbers arises when one wants to subdivide the material into groups which are homogeneous from a physical point of view. Many subdivisions, in making up my paper, were not tried at all, simply because the material was inadequate.

In recent years plenty of work has been done by various investigators, of which I will at this point only mention the work on proper motions done at the Leander McCormick Observatory, and the great number of radial velocities determined by Dr. Clube and his associates. I do not, however, believe we are yet in a position to consider the whole subject as finished. Discussions about space motions, as given by Professor Oort in the book Stellar Structures, Volume V, will, at this time, be hardly improved upon. I still feel we should increase the number of stars substantially in order to get a better statistical discussion possible. This means we have to go to fainter stars. Plenty of these stars will be found on the plates which have served to make the Charts of the Carte du Ciel, which means we have at least one old position available for proper motions. At Leiden we are now engaged in the determination or redetermination of the proper motions of 430 RR Lyrae stars.

My remarks concern the kinematics of a-type RR Lyrae variables with large ∆s(≥5), supposedly halo members, which have relatively well determined proper motions (μ) and radial velocities (ϱ) as well as accurate photoelectric photometry (m). The number of variables fulfilling these criteria is about 60. Using procedures which need not be discussed in detail here, it is possible to determine the statistical kinematic properties of these stars - that is, their solar motion (υ) and velocity dispersion (σ) - in two different ways:

It is the purpose of this note to reveal the nature and progress of a long term astrometric program at the Lick Observatory (see references by S. Vasilevskis in Trans. Int. Astron. Union, XI B, 404, 1962). One of its many goals is the measurement of absolute proper motions of RR Lyrae stars with respect to faint galaxies. The first-epoch photographs, obtained in 1947-54 by Shane and Wirtanen for the sky north of declination – 23°, were supplemented later by plates of poorer quality down to –33° with the 20-in. astrograph. This means that first-epoch plates are now on hand which cover three-fourths of the sky and on which stars of 9-17 mag. may be measured for proper motions. Since these photographs represent the largest and most homogeneous set that will be available in the foreseeable future, we shall try to estimate the number of RR Lyrae stars which may be measured on them.

As a guide we take the 1968 edition of the Russian Variable Star Catalogue, which contains a little over 4400 RR Lyrae stars. For the sky north of —33° nearly 2000 of these stars are brighter than average magnitude 17.0, 1000 brighter than 15.0, and about 350 brighter than 12.0. Experience with the Lick program shows that 80% of these stars should be measurable, after account is made for losses due to plate defects, blended images, and other factors.

An important limitation to the usefulness of the measured motions is imposed by the size of the mean errors, which amount to 0.”7/century for an epoch difference of 20 yr. This mean error is the same size as the proper motion of a typical RR Lyrae star of 13.0 mag. But for an epoch difference of 50 yr the mean error drops to 0.”3/century, which is comparable to the motion of an RR Lyrae star of 15.0 mag. Useful results for the fainter RR Lyrae stars will not be possible until after a third epoch about the year 2000.