Neutron stars play a unique role in physics and astrophysics. On the one hand, they contain matter under extreme physical conditions, and their theories are based on risky and far extrapolations of what we consider reliable physical theories of the structure of matter tested in laboratory. On the other hand, their observations offer the unique opportunity to test these theories. Moreover, neutron stars are important dramatic personae on the stage of modern astrophysics; they participate in many astronomical phenomena.

Neutron stars contain the matter of density ranging from a few g cm-3 at their surface, where the pressure is small, to more than 1015 g cm-3 at the center, where the pressure exceeds 1036 dyn cm-2. To calculate neutron star structure, one needs the dependence of the pressure on density, the so called equation of state (EOS), in this huge density range, taking due account of temperature, more than 109 K in young neutron stars, and magnetic fields, sometimes above

1015 G.

The present book is mainly devoted to the theory of the EOS of neutron star matter and its consequences for neutron star structure. As one moves from the neutron star surface to the center, the methods to calculate the EOS change. Atomic structure and plasma theories are used for the surface stellar layers. Deeper layers of the neutron star crust require nuclear theory combined with plasma physics, both in very exotic density-temperature regimes. Finally, the neutron star core necessitates many-body theory of dense strongly interacting systems, together with the physics of strong interactions of elementary particles.

Several not too old books treating the topic of the EOS of neutron stars are available in the literature. Many aspects of the EOS problem are considered by Shapiro & Teukolsky (1983) in the monograph Black Holes, White Dwarfs, and Neutron Stars. However, this excellent book reflects the state of the art by the beginning of the 1980s. Some aspects of the EOS problem, stellar stability and equilibrium are described in Stellar Physics by Bisnovatyi-Kogan (2001, 2002). Selected EOS models, based on the relativistic theories of hadronic matter, are discussed in detail by Glendenning (2000) in the monograph Compact Stars: Nuclear Physics, Particle Physics, and General Relativity and in the book by Weber (1999), Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics. However, neither of these two monographs gives the detailed description of the variety of possible EOSs in stellar cores and crusts.

The present monograph is complementary to those cited above. We describe all neutron star layers paying special attention to the theoretical basis of calculations, physical properties (especially the EOS) and observational manifestations. First we give an overview of neutron star theory and observations. Then we analyze current EOS models in the neutron star crusts and cores. We show that when the density increases the models become more numerous and different but less reliable. The most interesting density range is a few times the standard nuclear density and higher, where the composition of the matter becomes largely unknown. According to the different models, this dense matter may contain nucleons, hyperons, pion or kaon condensates, deconfined quarks or the mixture of these components. We analyze all these possibilities. Then we study the variety of models of neutron stars composed of the matter with the different EOSs. Finally, we compare theoretical neutron star models with observations and formulate current constraints on the EOS which result from this comparison.

By the time of this writing (2006) the EOS of the neutron star core remains not strongly constrained and the problem is thus open. This state of the art makes the problem especially exciting and intriguing. The progress in the neutron star theory and observations is tremendous. Forthcoming observations of neutron stars, combined with new theoretical achievements, should be crucial to strongly constrain theoretical models and solve thus the main mystery of neutron star physics — the composition and equation of state in neutron star cores. We expect that the monograph will be a useful guide-book in achieving this goal.

This book benefited from our teaching experiences at the University of Warsaw and University of Torun in Poland, at Universite de Paris and Observatoire de Paris in France (PH), and at the Saint-Petersburg State Polytechnical University in Russia (DGY, AYP), as well as at several international schools for young astrophysicists and physicists.

In our presentation we tried to get to the forefront of theoretical calculations. Nevertheless, we supplement the analysis of modern techniques and recent results with the description of the historical development of the ideas. On many occasions, re-establishing the true sequence of events turned out to be a fascinating experience. We hope that that the reader will find these fragments of the text interesting and entertaining.

We have made an effort to present the results of calculations in the form of formulae, which are easier to use than tables. Sometimes we give a critical analysis of theories and our suggestions how to improve them. Both the degree of criticism and the details of suggestions are of course subjective. The prophecy is a dangerous activity, but we took risks.

We have tried to make this book complete, but of course our selection of topics reflects our limited research interests and competence. The list of references is long and reflects the huge work done in the past. We apologize to those authors whose work was not cited because of the natural limitation of space. The book was mainly completed in November 2005 and reflects the state of the neutron star physics by that time. Some minor addenda were made in August 2006.

Many discoveries related to neutron stars, for instance, the discovery of the first pulsar or the first binary pulsar, were serendipitous. However, Pasteur once said that in research "Chance favors only the prepared mind" (in French: "La chance ne sourit qu'aux esprits bien prepares," Pasteur 1854). We hope that this book will serve the cause of preparing the readers for future discoveries. The book can be useful to those theoreticians and observers who are working in the field of neutron stars and related fields of physics and astrophysics. We expect that it can also be useful to students and to many scientists who are just interested in the fascinating world of neutron stars.

We are grateful to our colleagues who, over the years of book writing, helped us through their collaboration, discussions, and expertise: M.K. Abubekerov, N.E. Alexandrovich, D.A. Baiko, D.P. Barsukov, M. Bejger, V.S. Beskin, G.S. Bisnovatyi-Kogan, S. Bonazzola, A.M. Bykov, B. Carter, G. Chabrier, N. Chamel, A.M. Cherepashchuk, A.I. Chugunov, H.E. DeWitt, M.E. Gusakov, D. Gondek-Rosinska, E. Gourgoulhon, V.S. Imshennik, I.L. Iosilevskiy, J. Ka-iuzny, A.D. Kaminker, R.P. Kirshner, A.M. Krassilchtchikov, D. Lai, J.M. Lat-timer, K.P. Levenfish, B. Paczyfiski, G.G. Pavlov, C.J. Pethick, Yu.A. Shibanov, P.S. Shternin, R.A. Sunyaev, T. Takatsuka, R. Tamagaki, L. Titarchuk, A.I. Tsy-gan, V.A. Urpin, D.A. Varshalovich, J. Ventura, J.L. Zdunik, J. Ziolkowski. Our special thanks are to Olga Burstein, Maigosia Haensel, and Marina Potekhina for their careful attention, permanent support and encouragement.

Chapter 1

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