2007:05 DOCTORAL T H E SI S Exotic Phases of Matter in Compact Stars Fredrik Sandin Luleå University of Technology Department of Applied Physics and Mechanical Engineering Division of Physics 2007:05|: 02-544|: - -- 07⁄05 -- Doctoral Thesis in Physics Exotic Phases of Matter in Compact Stars Jan Fredrik Sandin from Ostavall¨ Division of Physics Lule˚a University of Technology SE-971 87 Lule˚a Sweden To my parents, for giving me a curious character ABSTRACT This doctoral thesis in physics at Lule˚a University of Technology is devoted to the phenomenology of compact stars, and theoretical models of their interior. Particle physics has provided fundamental concepts and details needed to develop a descrip- tion of matter and the evolution of the universe. It is, however, difficult to obtain information about the properties of matter at low temperature and high density from such experiments. In this context, astrophysical observations constitute an impor- tant source of information, thanks to the high resolution of present and near-future terrestrial and space-based observatories. The density of matter in neutron stars ex- ceedsthatinatomicnuclei,andlittleisknownaboutthenatureoftheirinterior.It is clear that the interaction between the smallest observed building blocks of atomic nuclei, the quarks, becomes weaker with increasing density. Matter should therefore dissolve into a state of nearly free quarks at high densities, and models of classical superconductivity advocate that this state is a superconductor. The argument for this is simple: a low-temperature Fermi system with a weak attractive interaction is unstable with respect to formation of Cooper pairs. It is not known if this state of matter exists in neutron stars, but models suggest that it is possible. The major part of the work summarised in this thesis is the development of a model of superconduct- ing quark matter, and its consequences for the phenomenology of neutron stars and their formation in the collapse of massive stars. It is a Nambu–Jona-Lasinio model with self-consistently calculated quark masses and pairing gaps, which properly ac- counts for the β-equilibrium and/or charge neutrality constraints in compact stars and heavy-ion collisions. Phase diagrams and equations of state of superconduct- ing quark matter are presented, and the influence of different assumptions about the effective quark interaction is investigated. The effect of neutrino untrapping in hypothetical quark cores of newborn neutron stars is investigated, and phase dia- grams for quark matter with trapped neutrinos are presented. While no evidence for the presence of quark matter in neutron stars exists, it is explicitly shown that observations do not contradict this possibility. On the contrary, the presence of a quark matter core in neutron stars can overcome problems with hadronic equations of state. In contrast to the expectation from more simple model calculations, the results presented here suggest that strange quarks do not play a significant role in the physics of compact stars. While there is some room for bare strange stars, such models suffer from low maximum masses, and the presence of a hadronic shell tends to render stars with strange matter cores unstable. Regardless of the nature of mat- vi ter in neutron stars, general relativity and the standard model of particle physics limit their density to 1016 g/cm3. In the light of established theory, any object with a density exceeding this limit should be a black hole. It is suggested in this thesis that if quarks and leptons are composite objects, as suggested, e.g.,bythe three particle generations in the standard model, a yet unobserved class of compact objects with extremely high densities could exist. As the hypothetical pre-quark particles are called preons, these objects are named ‘preon stars’. The properties of preon stars are estimated, and it is shown that their maximum mass depends on the quark compositeness energy scale. In general, the mass of these objects should not exceed that of the Earth, and their maximum size is of the order of metres. Several methods to observationally detect preon stars are discussed, notably, by gravita- tional lensing of gamma-ray bursts and by measuring high-frequency gravitational waves from binary systems. To have a realistic detection rate, i.e.,tobeobservable, they must constitute a significant fraction of cold dark matter. This condition could be met if they formed in a primordial phase transition, at a temperature of the or- der of the quark compositeness energy scale. Some unexplained features observed in spectra of gamma-ray bursts are discussed, as they are similar to the signature ex- pected from a preon-star gravitational lensing event. An observation of objects with these characteristics would be a direct vindication of physics beyond the standard model. Keywords: Compact stars – Neutron stars – Quark stars – Hybrid stars – Protoneu- tron stars – Preon stars – Preons – Compositeness – Colour superconductivity. Appended Papers Paper I J. Hansson and F. Sandin, “Preon stars: a new class of cosmic compact objects”, Physics Letters B616, 1 (2005); astro-ph/0410417. Paper II F. Sandin, “Compact stars in the standard model – and beyond”, The European Physical Journal C40 S2, 15 (2005); astro-ph/0410407. Also to appear in “How and where to go beyond the standard model”, proceedings of the International School of Subnuclear Physics, Erice, ed. A. Zichichi: World Scientific (2007). Paper III D. Blaschke, S. Fredriksson, H. Grigorian, A. M. Oztas¨ ¸ and F. Sandin, “The phase diagram of three-flavor quark matter under compact star constraints”, Physical Review D72, 065020 (2005); hep-ph/0503194. Paper IV F. Sandin and A. M. Oztas¨ ¸, “Condition for gapless color-antitriplet excita- tions in Nambu–Jona-Lasinio models”, Physical Review C73, 035203 (2006); hep- ph/0512087. Paper V T. Klahn,¨ D. Blaschke, F. Sandin, Ch. Fuchs, A. Faessler, H. Grigorian, G. Ropke¨ and J. Trumper¨ , “Modern compact star observations and the quark matter equation of state”, submitted to Physics Letters B; nucl-th/0609067. Paper VI F. Sandin and J. Hansson, “The observational legacy of preon stars – probing new physics beyond the LHC”, to be submitted; astro-ph/0701768. Paper VII F. Sandin and D. Blaschke, “The quark core of protoneutron stars in the phase diagram of quark matter”, submitted to Physical Review D; astro-ph/0701772. vii Other Publications Articles in popular magazines J. Hansson and F. Sandin,“Preonstj¨arnor - en ny sorts himlakropp?”, Popul¨ar Astronomi 4, 8 (2005). J. Hansson and F. Sandin, “Stor som en kula men tyngrean ¨ jorden”, Forskning och Framsteg 7, 40 (2005). Numerical software F. Sandin, “On-line 3-flavour colour superconductivity calculator”, http://3fcs.dyndns.org. F. Sandin, “On-line gravitational femtolensing calculator”, http://femtolensing.dyndns.org. ix Preface This thesis is devoted to the physics of compact stars and some exotic phases of matter that could exist in these fascinating objects. By tradition, it consists of an introduction and appended research papers. The former provides some essential background needed to grasp the content of the papers. As the physics of compact stars is a multi-diciplinary field, a proper introduction is beyond the scope of this thesis. I therefore focus on essential topics, in particular technical aspects applied in the theoretical derivations and numerical calculations. References are given to textbooks and research papers that cover some complementary topics. I am pleased by the combination of main-stream research and investigations on topics of more hypothetical nature that underlays this thesis. The former constitutes a basis for the scientific content of the work, and has been performed in a highly active field of physics in collaboration with leading experts in an international con- text. This work has resulted in useful experiences, four completed papers and about an equal amount of present projects. The numerical software developed in this work is partially available on-line for cross-checking, and for others to use. The work on preon stars is of more hypothetical nature and have resulted in valuable experiences. It is clear that theoretical physics needs both “good” and “bad” new ideas, as it is notoriously difficult to correctly judge the value of a new idea at an early stage in its development. Nevertheless, it takes courage and a sensible type of confidence to develop them, and that need some trial and error. The preon star hypothesis has been awarded with a prize on suggestion by Gerard ’t Hooft and Antonino Zichichi, and it has resulted in three scientific papers. Preon stars have been recognised also in several popular magazines, and the first publication was on Science Direct’s top- 25 list of most read (downloaded) articles. It is a great joy to see that the work has stimulated others to consider the idea. The research presented in this thesis has been performed in collaboration, mainly with David Blaschke, Sverker Fredriksson, Hovik Grigorian, Johan Hansson, Thomas Kl¨ahn, and Ahmet Ozta¸¨ s, and to some extent also with Amand Faessler, Chris- tian Fuchs, Gerd R¨opke, and Joachim Tr¨umper. I thank David Blaschke for his hospitality during my visits to Rostock and Dubna, for his guidance and support in the daily work, and for introducing me in a group of great people and a fruit- ful collaboration. I would also like to express my gratitude to Mark Alford, Jens xi xii Berdermann, Michael Buballa, Mike Cruise, Ed Fenimore, Huben Ganev, Achim Geiser, Jeremy Goodman, Pawel Haensel, Abuki Hiroaki, Gerard ’t Hooft, Hen- ning Knutsen, Kostas Kokkotas, John Ralston, Sanjay Reddy, Avetis Sadoyan, Igor Shovkovy, Andrew Steiner, and Stefan Typel for useful discussions, and for their helpful and inspiring attitude. The numerical results presented in the appended papers were calculated on a local FreeBSD computer cluster that belongs to Hans Weber, I am most grateful to him for giving me unlimited access to his computers, and for useful discussions on classical superconductivity and statistical physics.