by Vladimir LIPUNOV, Cand. Sc. (Phys. & Math.), P. K. Sternberg State Institute of Astronomy of Moscow State University

All the way back in 1932 the Soviet physicist Lev Landau (Nobel prize, 1962) postulated the existence of superdense stars, or giant atomic nuclei commensurate with the sun in mass. Landau had published his work just before the discovery of the neutron. And a year later, with the neutron already discovered, the American astronomers W. Baade and F. Zwicky hypothesized that the bursts of supernovas resulted from the disastrous compression (collapse) of a normal star into a superdense state. Superdense stars embody the final stage in the lifetime of ordinary stars with the initial mass of their nucleus above 1.4 M_Θ (M_Θ denoting solar mass). With the pool of its nuclear fuel exhausted, a star collapses: its outer layers blow off on a supernova explosion at an immense velocity of about 10,000 km/s, and the inner ones plunge toward the core under the effect of the gravitational pull (drag), for there is no longer the counteracting gas pressure force to prevent that. Within split seconds the star's inner layers contract to a 100,000th part of the original mass, and its volume shrinks ~10¹⁵fold. The mean density increases as much over and above the nuclear density. From that moment on the gravitational forces working to compress the star will be counterbalanced by nuclear forces. Atomic nuclei in this star will be tightly pushed together. Knowing the dimensions of atomic nuclei (10^-13 cm) and their number, astrophysicists have determined the radius of a star like that (- 10 km). M. Baade and F. Zwicky named such celestial bodies neutron stars. That's how the ancient science of astronomy witnessed a truly revolutionary event in the early 1930s as theoretical physicists predicted a new class of objects in the universe.

Neutron stars were identified only 35 years after. In July 1967 a team of British radio astronomers under Antony Hewish discovered radio pulsars. And in 1968 a radio pulsar was spotted in the Crab Nebula, the Crab pulsar-its period proved equal to 0.033 s; only a neutron star could rotate as fast as that. Thus both Lev Landau's and Fritz Zwicky's predictions came true, in particular about a connection of neutron stars with supernova explosions (Zwicky and Baade hypothesis; the Crab Nebula appeared after the burst of a supernova anno 1054).

MAGNETIC FIELDS OF NEUTRON STARS

The most remarkable feature of neutron stars is that they possess a super magnetic field whose intensity on the stellar surface attains to 10¹² Gc. This came as a complete surprise to many astrophysicists. And

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yet three years before the publication of works on this phenomenon, the Soviet astrophysicist N. Kardashov (elected to the Russian Academy of Sciences in 1994) has shown that an ordinary star collapsing into a neutron one should give rise to a powerful magnetic field. Dr. Kardashov proposed that the magnetic fields of a rotating neutron star must be fueling the processes observed in the Crab Nebula. Just a few months before the discovery of radio pulsars two Soviet astrophysicists, Drs P. Amnuel and O. Gusseinov, had sent to press an article in which they discussed the accretion (fall) of matter on a neutron star in tight (attached) binary stellar systems. They supposed that the powerful magnetic field of a neutron star should distort the symmetric motion of its plasma to make the star's emission starkly anisotropic (changeable), and its

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rotation result in pulsating radiation. At about the same time P. Pacini, an American astrophysicist, looked into particle acceleration by the magnetic field of a spinning neutron star.

The presence of such strong magnetic fields in neutron stars makes them a special class of astronomical objects interacting with the ambient medium (matter) by means of two kinds of forces, the electromagnetic and the gravitational. This interaction is manifested in diverse observable pictures depending on the correlation of these two types of forces. The Soviet astrophysicist W. Schwarzmann was the first to explain this important phenomenon in 1970. He demonstrated that a young neutron star (radio pulsar) should slow down its rotation until the gravitational forces have become higher than the electromagnetic ones, and then under the gravity drag the plasma will be falling on the neutron star's surface. An X-ray pulsar should appear as a result.

Shortly after, such objects were discovered by a group of American astrophysicists under R. Giacconi. The discovery of radio and X-ray pulsars came off as a complete triumph.

X-RAY PULSARS - NEUTRON STARS

The X-ray pulsars discovered in tight (attached) binary stars were taken for neutron stars almost unanimously for two obvious reasons. To begin with, short-period pulsars (with a period of several seconds) were discovered, and it seemed most unlikely for a white dwarf (a neutron star's only competitor for an X-ray pulsar's role) to spin with a short period like that. And second, in line with theoretical calculations only a neutron star was thought to be a source of X-ray emission.

But things came to a head in the mid-1970s as most of the X-ray pulsars were found to have periods of several hundred seconds; and at the same time an X-ray emission was discovered from a white dwarf designated A. M. Hercules. So some other, crucial test was needed for telling apart neutron stars from white dwarfs.

This proved to be a very simple problem. We know that X-ray pulsar periods in binaries decrease with time as a rule, while radio pulsar periods tend to increase. This attests to the utterly different nature of their energy output. The cause of X-ray pulsar acceleration resides in the fact that in binary systems (with X-ray pulsars being observed only in them) the matter falling onto a neutron star from its twin usually possesses a rotational momentum. Losing it to the neutron star, the matter thus speeds up the star's rotation. The more of the matter lands on a compact star, the higher the acceleration. The amount of the incident matter is determined from observations on a pulsar's luminosity. However, the rotational moment cannot the infinitely high, for otherwise the centrifugal forces would prohibit the stellar matter from hitting the compact star's surface. Clearly, the acceleration momentum has an upper constraint for a particular amount of incident matter. This constraint likewise depends on the compact star's rotation, that is on its period and radius. Since white dwarfs are hundreds of times larger than neutron stars, the maximal acceleration for them should be many times lower. Comparing the observable accelerations with the upper constraint, astrophysicists proved X-ray pulsars to be neutron stars indeed.

In the ten years that followed hundreds of X-ray and gamma radiation sources with quite unexpected properties were detected, including X-ray bursters, gamma burst sources, the SS 433 source, among other objects.

CLASSIFICATION OF NEUTRON STARS

The copious observational data obtained by the late 1970s - their diversity in particular-impelled scientists of the P. K. Sternberg State Institute of Astronomy to work out a general theory predicated on what we know about the evolution of neutron stars. It is characterized by a slow change in the modes of a neutron star's interaction with the ambient medium (matter). We considered the possible stages of the star's evolution. The first computations showed that the number of various regimes of neutron stars' interaction with the ambient matter goes far beyond such phenomena as radio and X-ray pulsars.

Let us look into the stages of this evolution. Neutron stars must be born with very short periods of rotation (10^-2 - 10^-3 s). This follows from the law of rotational momentum conservation in a collapse - that is when an ordinary star collapses into a neutron one. Spinning very fast at first, such a star emits radio waves, electromagnetic radiation and relativistic particles - in about the same mode as does a radio pulsar. The electromagnetic radiation and fluxes of relativistic particles, getting "stuck" in the ambient plasma, seek to throw it off, while the neutron star's gravitational pull attracts the plasma to the star's surface. During this period of the neutron star's life the force that throws off the ambient matter by far exceeds the gravitational drag. We call this regime ejection and designate it by the capital E. Radio pulsars, too, are assigned to this type of neutron stars. They get their radiation energy from a neutron star's rotational momentum via a magnetic field. However, E type neutron stars do not always behave like radio pulsars. The point is that the pulsars' radiation (pulsating radiation), though being quite a spectacular sight, has nothing remarkable about it in terms of energy output. As a matter of fact, the energy that a radio pulsar loses in a radio band is thousands times as low as that carried away by relativistic particles.

Under certain conditions, e.g. in tight binary systems, radio emission is actually absorbed to the full in the solar wind of the other component (a twin star, which is an ordinary

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star); that is why it is well-nigh impossible to detect a radio pulsar there. At the ejection stage a neutron star should slow down its rotation, and the intensity of its emission decreases with a decrease of rotation. Gradually the pressure of plasma-scattering emission will diminish so much that the ambient matter falling onto the star will quench its radiation.

This stage goes on for about 10⁴ - 10⁶ years. Thereupon ejection is arrested to usher in a new regime which Drs A. Illarionov and R. Syunayev dubbed a "propeller regime". Here's what happens: the magnetic field intensity in the environs of a neutron star soars, and the magnetic field pressure at some distance becomes comparable to the pressure of gravitational pressure. Because of the high conductivity of plasma, electric currents and fields are induced in it, and the plasma is drawn off by the star's rotating magnetic field. That's how the magnetosphere of the neutron star crystallizes. However, due to its high rate of rotation, the linear velocity on the magnetosphere's boundary is far above the escape velocity and thus the matter attracted by the magnetic field is ejected back; hence the name of this regime, "propeller". In theory a quasistationary regime is possible without plasma ejection. But the magnetosphere of the neutron star - on account of its rotation-heats up the incident matter to a temperature that it (this matter, or substance) will cease to "react" to the neutron star's gravitation, and a hot turbulent halo builds up around the magnetosphere. So far a neutron star persisting in the "propeller regime" cannot be reliably identified with any other astronomical object.

Continuing in the "propeller regime", a neutron star slows down its rotation until its magnetic field will no longer inhibit gravitation. The regime of accretion (type A) sets in. Due to the high gravitational potential of a neutron star, the matter getting onto its surface radiates (emits) as much as 20 percent of its potential energy (which is hundreds of times higher in efficiency than thermonuclear reactions). For instance, a bright X-ray emission source with luminosity of 10³⁷ erg/s (or 25,000 times as much as that of the sun) will appear if 10¹⁷ g of matter (equivalent to a flow of 10 ⁹ M_Θ /year) falls on the neutron star's surface.

In tight binary systems ordinary stars supply neutron stars with incident (accretional) matter at a fast rate-they can lose as much as 10^-5 - 10^-6 M_Θ annually. It is in such binary stars that X-ray pulsars were detected; the total number of these pulsars within the Galaxy must not be above 100, with only some 20 observable today.

Related to type A neutron stars are also X-ray bursters. In low-mass binaries whose evolution is very slow, the dissipation of magnetic neutron stars has an essential part to play. As a result of pressure the magnetic field contracts so much that the neutron star's magnetosphere becomes pressed against its surface. The matter spreads to cover the larger part of the stellar surface, the emission pulse fades, and favorable conditions are obtained for thermonuclear bursts. When a sufficient amount of matter has built up, it goes off like a hydrogen bomb. Hence the name, X-ray burster.

The ejection, "propeller" and accretion phases do not exhaust all the regimes of interaction of neutron stars with the ambient matter. Under certain conditions a neutron star, even if retarding its rotation very much, skips stage A in its evolution. This occurs when the magnetic field pressure on the magnetosphere's boundary far exceeds the attraction forces. A scenario like that is realized in the interaction of the solar wind with the earth's magnetosphere. Near the earth the solar wind velocity reaches several hundred kilometers per second, or it is dozens of times as high as the escape velocity. Particles of the solar wind fly by the earth without responding to its gravitational field. Neutron stars with such kind of magnetospheres are called geo-like and designated by the symbol G (from the Greek Ge, earth). The magnetospheres of geo-like neutron stars reliably protect their surface against the incident matter; however, within these magnetospheres there may occur processes of relativistic particles acceleration and "polar lights" that might be detected someday. In very tight binary systems an ordinary star may happen to be submerged within a neutron star's magnetosphere, an exotic case labeled a magnetic binary, or M (from the adjective magnetic).

While considering the regimes of ejection "propeller" and accretion, we have implied that the energy released by the incidence of matter is not high and the resultant emission has no effect on the motion of matter. In actual fact there is a limit to luminous emittance (luminosity) - a critical value when the forces of radiation pressure become equal to those of gravitation. This critical value is called the Eddington limit, and for solar mass stars it is roughly equivalent to 10³⁸ erg/s. Say, a neutron star having an accretion of 10^-8 M_Θ /year could develop such luminosity. Every neutron star within a binary lives through a moment when its twin "disgorges" a flux of matter dozens of thousands of times as high in intensity. Had all of this matter reached the neutron star's surface, its radiation would have exceeded the Eddington limit 10,000 fold. But this is ruled out because the radiation pressure would have exceeded gravitation 10,000 times over, and accretion would have ceased.

Now, what next? The incident matter cannot fly in and out simultaneously!

But it can. In a binary star system such matter does not reach a compact star right away but forms an accretional disk around it. Should the accretion rate become supercritical, some part of the extra matter will be "blown away" by the emission of radiation across the disk.

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The regime of supercritical disk accretion with respect to a relativistic object was first considered by Drs N. Shakura and R. Syunayev in 1973.

The spinning magnetic field compounds the picture for a neutron star. Three regimes may appear: SE-supercritical disk and ejection; SP-supercritical disk and "propeller"; SA-supercritical disk accretion proper. The matter flowing across the disk proves to be absolutely opaque (impermeable) to hard radiation. An on-looker would see only the uppermost layers of the flowing envelope (photosphere). The photosphere may expand to stellar dimensions to appear just like an ordinary star with wide emission lines. The accretional disk may come to be within the photosphere, all of it. Possibly the supercritical regimes may be accompanied by a discharge of relativistic jets of matter, with the source SS 433 representing a neutron star like this.

"PERIOD-LUMINOSITY" DIAGRAM FOR NEUTRON STARS

The correlation between gravitational and electromagnetic forces is a function of three parameters: a neutron star's period of spin; a magnetic field value; and the amount of matter captured by the star's gravitational field. The latter quantity is called a potential rate of accretion. It is measured in energy units standing for a level of luminosity attained by a radiation source, had all of the matter captured by a neutron star fallen on its surface. This value is convenient since it is observable in accretional neutron stars (e.g. in X-ray pulsars) and is equivalent to X-ray luminosity.

In stars with equal magnetic fields only two parameters-period and luminosity, are measured; consequently, a diagram may show as good as all types of neutron stars. But two regimes, G and M, are not there, for they are materialized only if certain additional conditions are fulfilled. Neutron stars in the ejection regime find themselves at the bottom of the "period-luminosity" diagram (i.e. in the area of fast-spinning neutron stars), while accretional neutron stars land at the top, an area where the role of electromagnetic forces is small. What is remarkable about this diagram is that it allows to plot simultaneously the position of both X-ray and radio pulsars. Should we draw lines corresponding to a magnetic field on the surface of neutron stars as equal to 10¹² Gc, the radio pulsars will be placed in the field of ejection, while the X-ray pulsars, in that of accretion. Yet another four areas will remain void: those of supercritical accretion (SA), supercritical ejection (SE), "propeller" (P) and supercritical propeller (SP). Although there are no reliably observable candidates to these areas as yet, they certainly ought to be in existence in the universe.

Gamma bursts may come from a neutron star at stage P. In keeping with a model suggested by Ye. Moskalenko, N. Shakuro and the author of the present article, solitary neutron stars may become sources of gamma bursts-the stars that have slowed down their rotation so much that the ejection stage has already passed, while that of accretion has not set in as yet. As a result, part of the matter that cannot fall on a neutron star's surface builds up an envelope within its magnetosphere. When the envelope grows to a mass large enough and the gravitational force has surpassed the centrifugal one, the envelope will "dump" onto the neutron star's surface to generate a gamma burst. Here plasma instabilities similar to those observed in the terrestrial magnetosphere may play an essential part. Even though this model falls short of perfection, it offers a few intriguing clues. For instance, it shows that the nearest sources of gamma bursts are at a distance of 10 pc, and that they make up 10 percent of the overall number of neutron stars in the Galaxy, or dozens of millions. And another important prediction: the rotation period of these neutron stars should be above 4 - 5 s, since these periods usher in the "propeller" stage.

This diagram is suitable for studying the evolution of neutron stars. Their magnetic field has about the same role to play as the mass of an ordinary star during its evolution on the Herzsprung-Russel (H-R) diagram, that is the larger the magnetic field of a star, the faster its evolution proceeds.

Dr. W Kornilov and the author of this article have designed a computer-simulated model of the evolution of neutron stars in the Galaxy. This model allows to calculate the number of neutron stars persisting in this or that state within our Galaxy. As expected, the observable radio and X-ray pulsars are but the tip of the iceberg. The absolute majority of neutron stars in massive binaries find themselves in the state of ejection (E) and "propeller" (P), while among solitary neutron stars, the commonest in the Galaxy, stars of the types P, G and A predominate. They may be sources of gamma bursts.

The galaxy has five times as many X-ray pulsars as SA sources, or objects with the possible properties of SS 433; and X-ray pulsars exceed the number of SP type sources hundredfold.

We see that the theoretical picture of possible states of neutron stars, in part confirmed by observational data, is far broader in its scale and scope. This elates both the observers and the theoreticians toward new discoveries.

Zemlya i Vselennaya (Earth and Universe), No. 2, 1985

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