Sanjay Reddy

Evolution of Proto-Neutron Stars

We study the thermal and chemical evolution during the Kelvin-Helmholtz phase of the birth of a neutron star, employing neutrino opacities that are consistently calculated with the underlying equation of state (EOS). Expressions for the diffusion coefficients appropriate for general relativistic neutrino transport in the equilibrium diffusion approximation are derived. The diffusion coefficients are evaluated using a field-theoretical finite-temperature EOS that includes the possible presence of hyperons. The variation of the diffusion coefficients is studied as a function of EOS and compositional parameters. We present results from numerical simulations of proto-neutron star cooling for internal stellar properties as well as emitted neutrino energies and luminosities. We discuss the influence of the initial stellar model, the total mass, the underlying EOS, and the addition of hyperons on the evolution of the proto-neutron star and on the expected signal in terrestrial detectors. We find that the differences in predicted luminosities and emitted neutrino energies do not depend much upon the details of the initial models or the underlying high-density EOS for early times (t<10 s), provided that opacities are calculated consistently with the EOS. The same holds true for models that allow for the presence of hyperons, except when the initial mass is significantly larger than the maximum mass for cold, catalyzed matter. For times larger than about 10 s, and prior to the occurrence of neutrino transparency, the neutrino luminosities decay exponentially with a time constant that is sensitive to the high-density properties of matter. We also find the average emitted neutrino energy increases during the first 5 s of evolution and then decreases nearly linearly with time. In general, increasing the proto-neutron star mass increases the average energy and the luminosity of neutrinos, as well as the overall evolutionary timescale. The influence of hyperons or variations in the dense matter EOS is increasingly important at later times. Metastable stars, those with hyperons that are unstable to collapse upon deleptonization, have relatively long evolution times, which increase the nearer the mass is to the maximum mass supportable by a cold, deleptonized star.

Hybrid Stars that Masquerade as Neutron Stars

We show that a hybrid (nuclear+quark matter) star can have a mass-radius relationship very similar to that predicted for a star made of purely nucleonic matter. We show this for a generic parameterization of the quark matter equation of state and also for an MIT bag model, each including a phenomenological correction based on gluonic corrections to the equation of state. We obtain hybrid stars as heavy as 2 M☉ for reasonable values of the bag model parameters. For nuclear matter, we use the equation of state calculated by Akmal and coworkers using many-body techniques. Both mixed and homogeneous phases of nuclear and quark matter are considered.

The maximum mass and radius of neutron stars and the nuclear symmetry energy

We calculate the equation of state of neutron matter with realistic two- and threenucleon interactions using Quantum Monte Carlo techniques, and demonstrate that the short-range three-neutron interaction determines the correlation between neutron matter energy at nuclear saturation density and the higher densities relevant to neutron stars. Our model for the nuclear interactions makes an experimentally testable prediction for the correlation between the neutron matter energy (which in turn is related to the symmetry energy) and its density dependence. This correlation is solely determined by the strength of the short-range 3 neutron force. The same force also provides a stringent constraint on the maximum mass and radius of neutron stars. An experimental measurement of the symmetry energy with an accuracy of < 1 MeV will enable model predictions for neutron star structure that can be tested with current and anticipated constraints on the masses and radii of neutron stars from x-ray observations.

Neutrino interactions in hot and dense matter

We study the charged and neutral current weak interaction rates relevant for the determination of neutrino opacities in dense matter found in supernovae and neutron stars. We establish an efficient formalism for calculating differential cross sections and mean free paths for interacting, asymmetric nuclear matter at arbitrary degeneracy. The formalism is valid for both charged and neutral current reactions. Strong interaction corrections are incorporated through the in-medium single particle energies at the relevant density and temperature. The effects of strong interactions on the weak interaction rates are investigated using both potential and effective field-theoretical models of matter. We investigate the relative importance of charged and neutral currents for different astrophysical situations, and also examine the influence of strangeness-bearing hyperons. Our findings show that the mean free paths are significantly altered by the effects of strong interactions and the multicomponent nature of dense matter. The opacities are then discussed in the context of the evolution of the core of a protoneutron star.

Asymmetric Two-Component Fermion Systems in Strong Coupling

We study the phase structure of a dilute two-component Fermi system with attractive interactions as a function of the coupling and a finite number asymmetry or polarization. In weak coupling, a number asymmetry results in phase separation. A mixed phase containing symmetric superfluid matter and an asymmetric normal phase is favored. For strong coupling we show that the stress on the superfluid phase to accommodate a number asymmetry increases. Near the infinite-scattering length, we calculate the single-particle excitation spectrum and the ground-state energy. A picture of weakly interacting quasiparticles emerges for modest polarizations. In this regime a homogeneous phase with a finite population of quasiparticle states characterized by a gapless spectrum is favored over the phase separated state. These states may be realized in cold atom experiments.

Minimal color-flavor-locked--nuclear interface

At nuclear matter density, electrically neutral strongly interacting matter in weak equilibrium is made of neutrons, protons and electrons. At sufficiently high density, such matter is made of up, down and strange quarks in the colorflavor locked phase, with no electrons. As a function of increasing density (or, perhaps, increasing depth in a compact star) other phases may intervene between these two phases which are guaranteed to be present. The simplest possibility, however, is a single first order phase transition between CFL and nuclear matter. Such a transition, in space, could take place either through a mixed phase region or at a single sharp interface with electron-free CFL and electron-rich nuclear matter in stable contact. Here we construct a model for such an interface. It is characterized by a region of separated charge, similar to an inversion layer at a metal-insulator boundary. On the CFL side, the charged boundary layer is dominated by a condensate of negative kaons. We then consider the energetics of the mixed phase alternative. We find that the mixed phase will occur only if the nuclear-CFL surface tension is significantly smaller than dimensional analysis would indicate.

Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints

▪ Abstract We review theoretical developments in studies of dense matter and its phase structure of relevance to compact stars. Observational data on compact stars, which can constrain the properties of dense matter, are presented critically and interpreted.

Extra dimensions, SN1987a, and nucleon-nucleon scattering data

Abstract One of the strongest constraints on the existence of large, compact, “gravity-only” dimensions comes from SN1987a. If the rate of energy loss into these putative extra dimensions is too high, then the neutrino pulse from the supernova will differ from that actually seen. The dominant mechanism for the production of Kaluza–Klein gravitons and dilatons in the supernova is via gravistrahlung and dilastrahlung from the nucleon–nucleon system. In this paper we compute the rates for these processes in a model-independent way using low-energy theorems which relate the emissivities to the measured nucleon–nucleon cross section. This is possible because for soft gravitons and dilatons the leading contribution to the energy-loss rate is from graphs in which the gravitational radiation is produced from external nucleon legs. Previous calculations neglected these mechanisms. We re-evaluate the bounds on toroidally-compactified “gravity-only” dimensions, and find that consistency with the observed SN1987a neutrino signal requires that if there are two such dimensions then their radius must be less than 1 micron.

Medium modification of the charged-current neutrino opacity and its implications

Previous work on neutrino emission from proto-neutron stars which employed full solutions of the Boltzmann equation showed that the average energies of emitted electron neutrinos and antineutrinos are closer to one another than predicted by older, more approximate work. This in turn implied that the neutrino driven wind is proton rich during its entire life, precluding r-process nucleosynthesis and the synthesis of Sr, Y, and Zr. This work relied on charged-current neutrino interaction rates that are appropriate for a free nucleon gas. Here, it is shown in detail that the inclusion of the nucleon potential energies and collisional broadening of the response significantly alters this conclusion. Isovector interactions, which give rise to the nuclear symmetry energy, produce a difference between the neutron and proton single-particle energies ΔU=U_n−U_p and alter the kinematics of the charged-current reactions. In neutron-rich matter, and for a given neutrino/antineutrino energy, the rate for ν_e + n → e^− + p is enhanced while ν_e + p → n + e^+ is suppressed because the Q value for these reactions is altered by ±ΔU, respectively. In the neutrino decoupling region, collisional broadening acts to enhance both νe and ν_e cross sections, and random-phase approximation (RPA) corrections decrease the νe cross section and increase the ν_e cross section, but mean field shifts have a larger effect. Therefore, electron neutrinos decouple at lower temperature than when the nucleons are assumed to be free and have lower average energies. The change is large enough to allow for a reasonable period of time when the neutrino driven wind is predicted to be neutron rich. It is also shown that the electron fraction in the wind is influenced by the nuclear symmetry energy.

Neutrino opacities in nuclear matter

Abstract Neutrino–matter cross sections and interaction rates are central to the core-collapse supernova phenomenon and, very likely, to the viability of the explosion mechanism itself. In this paper, we describe the major neutrino scattering, absorption, and production processes that together influence the outcome of core collapse and the cooling of protoneutron stars. One focus is on energy redistribution and many-body physics, but our major goal is to provide a useful resource for those interested in supernova neutrino microphysics.