Force autocorrelation function in linear response theory and the origin of friction

Vanishing of the equilibrium Green-Kubo fluctuation expression for the friction coefficient of a massive particle moving in a finite-volume liquid is usually interpreted as an unphysical consequence of the finite volume. Here I show that it is a physical consequence of the finite mass of the rest of the system, which allows it to be dragged by the moving particle. As a consequence, it is sufficient to have two infinite masses in the liquid for the friction coefficient to be finite. In addition, I give the physical interpretation of different friction coefficients for two infinite-mass particles moving in the liquid.Comment: 24 pages text and figure

Natal Kicks of Stellar-Mass Black Holes by Asymmetric Mass Ejection in Fallback Supernovae

Integrating trajectories of low-mass X-ray binaries containing black holes within the Galactic potential, Repetto, Davies & Sigurdsson recently showed that the large distances of some systems above the Galactic plane can only be explained if black holes receive appreciable natal kicks. Surprisingly, they found that the distribution of black hole kick velocities (rather than that of the momenta) should be similar to that of neutron stars. Here I argue that this result can be understood if neutron star and black hole kicks are a consequence of large-scale asymmetries created in the supernova ejecta by the explosion mechanism. The corresponding anisotropic gravitational attraction of the asymmetrically expelled matter does not only accelerate new-born neutron stars by the "gravitational tug-boat mechanism". It can also lead to delayed black-hole formation by asymmetric fallback of the slowest parts of the initial ejecta onto the transiently existing neutron star, in course of which the momentum of the black hole can grow with the fallback mass. Black hole kick velocities will therefore not be reduced by the ratio of neutron star to black hole mass as would be expected for kicks caused by anisotropic neutrino emission of the nascent neutron star.Comment: 7 pages, 1 figure (3 eps files); submitted to MNRA

Neutrino Emission from Supernovae

Supernovae are the most powerful cosmic sources of MeV neutrinos. These elementary particles play a crucial role when the evolution of a massive star is terminated by the collapse of its core to a neutron star or a black hole and the star explodes as supernova. The release of electron neutrinos, which are abundantly produced by electron captures, accelerates the catastrophic infall and causes a gradual neutronization of the stellar plasma by converting protons to neutrons as dominant constituents of neutron star matter. The emission of neutrinos and antineutrinos of all flavors carries away the gravitational binding energy of the compact remnant and drives its evolution from the hot initial to the cold final state. The absorption of electron neutrinos and antineutrinos in the surroundings of the newly formed neutron star can power the supernova explosion and determines the conditions in the innermost supernova ejecta, making them an interesting site for the nucleosynthesis of iron-group elements and trans-iron nuclei. In this Chapter the basic neutrino physics in supernova cores and nascent neutron stars will be discussed. This includes the most relevant neutrino production, absorption, and scattering processes, elementary aspects of neutrino transport in dense environments, the characteristic neutrino emission phases with their typical signal features, and the perspectives connected to a measurement of the neutrino signal from a future galactic supernova.Comment: Author version of chapter for 'Handbook of Supernovae,' edited by A. Alsabti and P. Murdin, Springer. 30 pages, 9 figure

Global Anisotropy Versus Small-Scale Fluctuations in Neutrino Flux in Core-Collapse Supernova Explosions

Effects of small-scale fluctuations in the neutrino radiation on core-collapse supernova explosions are examined. Through a parameter study with a fixed radiation field of neutrinos, we find substantial differences between the results of globally anisotropic neutrino radiation and those with fluctuations. As the number of modes of fluctuations increases, the shock positions, entropy distributions, and explosion energies approach those of spherical explosion. We conclude that global anisotropy of the neutrino radiation is the most effective mechanism of increasing the explosion energy when the total neutrino luminosity is given. This supports the previous statement on the explosion mechanism by Shimizu and coworkers.Comment: 14 pages, including 12 figures. To be published in the Astrophysical Journa

Monte Carlo Study of Supernova Neutrino Spectra Formation

The neutrino flux and spectra formation in a supernova core is studied by using a Monte Carlo code. The dominant opacity contribution for nu_mu and nu_tau is elastic scattering on nucleons. In addition we switch on or off a variety of processes which allow for the exchange of energy or the creation and destruction of neutrino pairs, notably nucleon bremsstrahlung, the e^+ e^- pair annihilation process and nu_e-bar nu_e -> nu_{mu,tau} nu_{mu,tau}-bar, recoil and weak magnetism in elastic nucleon scattering, elastic scattering on electrons and positrons and elastic scattering on electron neutrinos and anti-neutrinos. The least important processes are neutrino-neutrino scattering and e^+ e^- annihilation. The formation of the spectra and fluxes of nu_mu is dominated by the nucleonic processes, i.e. bremsstrahlung and elastic scattering with recoil, but also nu_e nu_e-bar annihilation and nu_mu e^\pm scattering contribute significantly. When all processes are included, the spectral shape of the emitted neutrino flux is always ``pinched,'' i.e. the width of the spectrum is smaller than that of a thermal spectrum with the same average energy. In all of our cases we find that the average nu_mu-bar energy exceeds the average nu_e-bar energy by only a small amount, 10% being a typical number. Weak magnetism effects cause the opacity of nu_mu to differ slightly from that of nu_mu-bar, translating into differences of the luminosities and average energies of a few percent. Depending on the density, temperature, and composition profile, the flavor-dependent luminosities L_{nu_e}$, L_{nu_e-bar}, and L_{nu_mu} can mutually differ from each other by up to a factor of two in either direction.Comment: 33 pages, 16 eps-figs, submitted to ApJ. Sections added: weak magnetism, discussion of different analytic fits to the spectra and detailed spectral shap

The r-Process in Black Hole Winds

All the current r-process scenarios relevant to core-collapse supernovae are facing severe difficulties. In particular, recent core-collapse simulations with neutrino transport show no sign of a neutron-rich wind from the proto-neutron star. In this paper, we discuss nucleosynthesis of the r-process in an alternative astrophysical site, "black hole winds", which are the neutrino-driven outflow from the accretion torus around a black hole. This condition is assumed to be realized in double neutron star mergers, neutron star - black hole mergers, or hypernovae.Comment: 6 pages, 4 figures, invited talk at OMEG10, March 2010, to be published in the proceedings of OMEG10 (AIP