PULSARS AND COMPACT X-RAY SOURCES : COSMIC LABORATORIES FOR THE STUDY OF NEUTRON STARS AND HADRON MATTER

Abstract

This paper reviews the dependence of the properties of neutron stars — their maximum mass, mass-radius relation, crustal extent and dynamic response — on models for hadron-hadron interaction and the likely existence of hadron superfluidity. The extent to which it both has proved possible and might prove possible to determine these and other properties of neutron stars from observations on pulsars and compact X-ray sources, and especially the pulsating X-ray sources, is summarized. The conclusion is reached that observations are capable of providing, within the next decade, definitive information on both the existence of hadron superfluidity and the viability of some of the current models for neutron-neutron interaction inside neutron stars. I. Introductory remarks.Some seven years ago, Ruderman, Shaham, and I surveyed the extent to wich it was possible to obtain information concerning neutron star structure from astronomical observations. At that time, attention was focused on the origin of the which had been observed in the Vela and Crab pulsars, and on their post-glitch behavior, which provides evidence for hadron superfluidity in the liquid 2 interior of these neutron stars. Durxng the past seven years, the range of observational possibilities for determining neutron star properties has expanded considerably. Pulsating x-ray stars have been discovered and identified as accreting rotating magne3 tic neutron stars in close binary systems. X-ray observations of the Doppler shift of the period of these stars, when combined with optical observations of the companion star, yield information on neutron star mas4 ses. Their spectra can provide information about the strength of the magnetic 5 field near the stellar surface while secular changes in their period provide information on the neutron star magnetic moment, mass, and radius. Further valuable information concerning neutron star structure may come as well from the irregular shortterm period variations which have been observed in all those pulsating x-ray stars whose period variations have been studied in some detail. To cite another example, the bursts characteristic of many of the x-ray bursters are in all likelihood caused by thermonuclear runaway processes in. matter freshly P accreted on the surface of neutron stars, while a minimum radius for neutron stars may be deduced from the shape of the x-ray spectrum in the tail of these bursts. Observations which place upper limits on the surface temperature of neutron stars of known age are beginning to provide information about the states of matter and physical processes in the stellar interior which control the cooling of stars following their initial formation. It should further be noted that additional have been observed in the Crab and Vela pulsars, while a third, comparatively slow pulsar (PSR 1641-45) has 12 exhibited a giant glitch only an order of magnitude smaller than the four superPermanent address JOURNAL DE PHYSIQUE Colloque Cl, supplement au n° 3, Tome 41, mars 1980, page C2-111 Resume.Pulsars et sources X compactes : laboratoires cosmiques pour l'etude des etoiles a neutrons et de la matiere hadronique. Cet article passe en revue les proprietes des etoiles a neutrons-masse maximum, relation masse-rayon, epaisseur de la croute et reponse dynamique en fonction des modeles d'interaction hadron-hadron et de la probable superfluidite hadronique. On resume ce qui s'est avere possible (ou pourrait l'etre bientot) pour connaitre ces proprietes (ainsi que d'autres) a partir de l'observation des pulsars, des sources X compactes, et surtout des sources X puisantes. En conclusion il sembla que les observations pourront fournir, avant dix ans,.des renseignements determinants a la fois sur la superfluidite hadronique et sur les quelques modeles courants d'interaction neutron-neutron dans les etoiles a neutrons. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980219 c2-112 JOURNAL DE PHYSIQUE glitches observed ifi the Vela pulsar. 11 from the so-called equations of staThe maximum mass, mass-radius relation, te (derived from models for which the avecrustal extent, and dynamic response of a rage system interaction energy is attractineutron star are sensitive to hadron interve at nuclear densities) to equaaction and hadron superfluidity in the dentions of state (derived from models for sity region, lor4 g cm-3 lo1' cm-3, so which the average system interaction enerthat to the extent these properties can be gy becomes repulsive at sub-nuclear densideduced from observation, it is possible to ties). Representative examples of the corview pulsars and compact x-ray sources as responding models are the phenomenological laboratories for the study of hadron Reid (R) potential for neutron-neutron inmatter under conditions which are not accesteraction,16 and the tensor interaction sible in the terrestrial laboratory. In (TI) model which assumes that the attractithis talk I shall describe briefly the ranve part of the neutron-neutron interaction ge of theoretical possibilities for these comes from higher order pion exchange. 17 important properties of neutron stars, and The resulting interaction energies (as a then summarize the current output of these function of density) and mass vs. central cosmic laboratories. density curves calculated for these two models are shown in Fig.1, while cross-secNeutron Star Maximum Mass and Internal Structure tions of corresponding stars of 1.4 M@ are Extensive theoretical studies have shown shown in Fig.2. that neutron stars with a mass 1.4 Ma haAs may be seen in Fig. la, for a stiff ve radii of the order of 10-16 km, with a equation of state, the interaction energy solid outer crust, 1-5 km thick, contaibecomes repulsive at densities somewhat ning increasingly neutron-rich nuclei in a less than that of nuclear matter, and henperiodic array, free electrons, and free ce acts to assist the neutron kinetic enerneutrons, beneath which is a liquid integy in opposing the attractive gravitational rior which begins at densities somewhat forces which act to collapse the star. The less than the density of nuclear matter, result, seen in Fig, Lb, is that the maxi14 Po= 2.8 x 10 9 cm-3, and contains largemum Pass of stars based on a stiff equation ly superfluid neutrons. The behavior of neuState is greater than that Of stars batron star matter in the crustal region is sed On a soft equation of state while, as comparatively well the remaimay be seen in Fig. 2, stars calculated ning and key ingredient in determining the with a stiff equation of state have a lomaximum mass and internal structure of neuwer central density, a larger radius, and tron stars is the calculation of a reliable a considerably larger crustal volume, than equation if state for the neutron liquid do stars of the same mass calculated with phase. It is a difficult calculation, in a soft equation of state. Hence to the expart because the basic interaction between tent that such as the neutrons is still not perfectly known, in stellar radius, and the ratio of the moment part because, for a given interaction model, Of inertia Of the Outer 'cr calculation of the ground state energy for a system at nuclear densities and beyond is a far-from-trivial many-body problem. 14 Pandharipande , Pines, and smith15 have shown that one can construct a variety of models for the neutron interaction which are consistent with terrestrial constraints (the free nucleon scattering data and the experimentally known energy, equilibrium density, and symmetry energy of nuclear matter). The theoretical possibilities for the resulting equation of state span a range I Y z -20 -30 I 1 . I I 1 , 0.1 0-2 0.3 n (2 I Fiq. Ia : Interaction energy of neutron matFig. Ib : Neutron star mass as a function ter as calculated with two models of central density for two models of the N-N interaction. of the N-N interaction. The arrows indicate the maximum mass and central density.