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Neutrino Emission from Neutron Stars

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Neutrino Emission from Neutron Stars Neutrino Emission from Neutron Stars D.G. Yakovlev1;5, A.D. Kaminker1 O.Y. Gnedin2, and P. Haensel3;4 1Ioffe Physical Technical Institute, Politekhnicheskaya 26, 194021, St.-Petersburg, Russia e-mail: [email protected]ffe.rssi.ru and [email protected]ffe.rssi.ru 2Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, England e-mail: [email protected] 3Copernicus Astronomical Center, Bartycka 18, PL-00-716, Warsaw, Poland e-mail: [email protected] 4 D´epartment of d'Astrophysique Relativiste et de Cosmologie { UMR 8629du CNRS, Observatoire de Paris, F-92195 Meudon Cedex, France 5 Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA Abstract We review the main neutrino emission mechanisms in neutron star crusts and cores. Among them are the well-known reactions such as the electron-positron annihilation, plasmon decay, neutrino bremsstrahlung of electrons colliding with atomic nuclei in the crust, as well as the Urca processes and neutrino bremsstrahlung in nucleon-nucleon collisions in the core. We emphasize recent theoretical achievements, for instance, band structure effects in neutrino emission due to scattering of electrons in Coulomb crystals of atomic nuclei. We consider the standard composition of matter (neutrons, protons, electrons, muons, hyperons) in the core, and also the case of exotic constituents such as the pion or kaon condensates and quark matter. We discuss the reduction of the neutrino emissivities by nucleon superfluidity, as well as the specific neutrino emission produced by Cooper pairing of the superfluid particles. We also analyze the effects of strong magnetic fields on some reactions, such as the direct Urca process and the neutrino synchrotron emission of electrons. The results are presented in the form convenient for practical use. We illustrate the effects of various neutrino reactions on the cooling of neutron stars. In particular, the neutrino emission in the crust is critical in setting the initial thermal relaxation between the core and the crust. Finally, we discuss the prospects of exploring the properties of supernuclear matter by confronting cooling simulations with observations of the thermal radiation from isolated neutron stars. 1 Contents 1 Overview 3 1.1 Introduction . 3 1.2 Structure of neutron stars . 4 2 Neutrino emission from neutron star crusts 9 2.1 Main neutrino reactions . 9 2.2 Annihilation of electron-positron pairs . 12 2.3 Plasmon decay . 20 2.4 Neutrino synchrotron emission by degenerate electrons . 24 2.5 Other electron-photon neutrino processes . 28 2.6 Neutrino bremsstrahlung in collisions of electrons with atomic nuclei . 29 2.7 Beta processes . 40 2.8 Neutrino emission connected with strong interaction of free neutrons . 45 2.9 Neutrino luminosity of a neutron star crust . 50 3 Neutrino emission in non-superfluid cores 54 3.1 Wealth of neutrino reactions . 54 3.2 Neutron beta decay . 57 3.3 Direct Urca processes . 59 3.4 Modified Urca process . 66 3.5 Non-equilibrium Urca processes . 72 3.6 Neutrino bremsstrahlung in baryon-baryon collisions . 75 3.7 Other neutrino reactions . 79 3.8 Neutrino emission from exotic phases of dense matter . 82 4 Neutrino emission from superfluid and magnetized cores 86 4.1 Reduction and enhancement of neutrino emission by superfluidity and magnetic fields 86 4.2 Bogoliubov transformation, energy gaps and critical temperatures . 87 4.3 Superfluid reduction of direct Urca process . 91 4.4 Modified Urca processes in superfluid matter . 98 4.5 Neutrino bremsstrahlung in superfluid matter . 102 4.6 Similarity criteria . 104 4.7 Neutrino emission due to Cooper pairing of baryons . 106 4.8 Leading reactions in superfluid cores . 110 4.9 Direct Urca process in strong magnetic fields . 113 4.10 Neutrino emission due to scattering of electrons off fluxoids . 118 5 Neutrino emission and neutron star cooling 125 5.1 Cooling equations and cooling code . 125 5.2 Cooling of non-superfluid neutron stars . 129 5.3 Thermal relaxation in the crust . 132 5.4 The relaxation time . 136 5.5 Cooling of superfluid neutron stars . 137 5.6 Cooling of neutron stars with strong internal magnetic fields . 143 2 5.7 Other aspects of neutron star cooling . 146 6 Conclusions 148 3 1 Overview 1.1 Introduction Neutron stars are the most fascinating stars known in the Universe. Indeed, measured masses of these tiny stars are around M 1:4 M , but they are expected to have very small radii, R 10 km. Accordingly, they possess an' enormous gravitational energy, GM 2=R 5 1053 erg 0:2 'Mc2, ∼ × ∼ and surface gravity, GM=R2 2 1014 cm s−2. Since the gravitational energy constitutes a large fraction of the rest-mass energy∼, neutron× stars are relativistic objects; space-time is essentially curved within and around them, implying they can behave as strong gravitational lenses (e.g., Zavlin et al. 1995). Neutron stars are very dense. Their mean density ρ¯ 3M=(4πR3) 7 1014 g cm−3 is several times the standard nuclear density, ρ = 2:8 1014 g'cm−3. The cen'tral ×density is larger, 0 × reaching up to (10{20) ρ0. Thus, the cores of neutron stars are composed of a strongly compressed nuclear matter. This compression, which cannot be reproduced in laboratory, is provided by the very strong gravitational force. Accordingly, neutron stars can be treated as unique astrophysical laboratories of superdense matter. The main constituents of neutron star cores are thought to be strongly degenerate neutrons with the admixture of protons and electrons, although other particles may also be available. Observationally, neutron stars manifest themselves in different ways, for instance, as radio pulsars, X-ray pulsars, anomalous X-ray pulsars (e.g., Mereghetti et al. 1998), X-ray bursters (e.g., Lewin et al. 1995), X-ray transients (e.g., Campana et al. 1998), sources of quasiperiodic X-ray oscillations (e.g., Psaltis et al. 1998, Kluzniak 1998), and soft-gamma repeaters (e.g., Cline et al. 1999 and references therein). They are the sources of electromagnetic radiation in all wavelength bands, from radio to hardest gamma-rays, and they are known to work as efficient accelerators of highly energetic particles. Their birth in supernova explosions is accompanied by the most powerful neutrino outburst. One of them was detected by the underground neutrino detectors as a signal of the 1987A supernova explosion in the Large Magellanic Cloud (e.g., Imshennik and Nadezhin 1988, Burrows 1990). Evolution of orbital parameters of the double neutron star binary containing PSR 1913+16, the Hulse{Taylor pulsar, indicates that the binary system emits gravitational waves. Merging neutron stars are thought to be among the best candidates for direct detection of gravitational waves. In other words, neutron stars are extremely interesting to observe and study theoretically. Their main \mystery" is the equation of state of dense matter in their cores. It cannot be derived from first principles since the exact calculation would require the exact theory of nuclear interactions and the exact many-body theory to account for in-medium effects. While lacking both of these theories, many model equations of state have been constructed in the last decades (e.g., Shapiro and Teukolsky 1983, Glendenning 1996, Weber 1999, Lattimer and Prakash 2000). They vary widely from the soft to the moderate and stiff ones and produce very different structure of neutron stars. This opens a possibility to constrain the equation of state by comparing theory with observations in many ways. The majority of methods are based on the determination (constraint) of the stellar mass and/or radius and the comparison with the mass-radius diagrams for different equations of state. In particular, one can use the data obtained from the mass measurements in close binaries containing neutron stars, the minimum spin periods of the millisecond pulsars, the identification of the kilohertz quasi-periodic oscillations with the orbital frequency in the last stable orbit, and from other related methods. Unfortunately, no decisive argument has been given so far in favor of the stiff, moderate or soft equations of state. One can definitely rule out only the ultra-soft equations of state which give 4 the maximum stellar mass lower than 1:44 M , the accurately measured mass of the Hulse{Taylor pulsar (Thorsett and Chakrabarty 1999). In this review we focus on another method to explore the internal structure of neutron stars | by comparing the theory of neutron star cooling with observations of the thermal radiation from the surfaces of isolated neutron stars. For about 105{106 years after their birth in supernova explosions, neutron stars cool mainly via neutrino emission from their interiors. Although their matter is very dense, they become fully transparent for neutrinos about 20 seconds after the birth (e.g., Burrows and Lattimer 1986, Prakash et al. 1997). Thus, the neutrinos produced in numerous reactions leave neutron stars freely, providing a powerful source of cooling. Therefore, it is important to study the whole variety of neutrino reactions in different neutron star layers in order to analyze the cooling. Some mechanisms have been reviewed not long ago by Bisnovatyi-Kogan (1989), Pethick (1992), Itoh et al. (1996), and Yakovlev et al. (1999b). More references to the original and review papers are given in subsequent chapters. The present review differs from other papers in several respects. First, we discuss the neutrino mechanisms in all neutron star layers, from the crust to the inner core, paying attention to open theoretical problems. Second, we consider the neutrino emission in the non-superfluid and non- magnetized matter as well as in the presence of superfluidity of baryons and the possible strong magnetic field. In particular, we analyze the neutrino emission due to Cooper pairing of baryons, which is forbidden in non-superfluid matter, and the synchrotron neutrino emission of electrons forbidden without the magnetic field.
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