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Prospects of establishing the radii of massive neutron stars in PSR J1614-2230 and PSR J0740+6620 from NICER and Chandra observatories hold the potential to constrain the equation of state (EoS) of matter to densities well beyond those encountered in canonical stars of mass $\sim 1.4\,{\rm M}_{\odot}$. In this work, we investigate the relation between the radii of very massive neutron stars up to the maximum mass, $M_{\rm max}$, supported by dense matter EoSs. Results from models with hadronic matter are contrasted with those that include a first-order hadron-to-quark phase transition. We find that a lower bound on $M_{\rm max}$ with an upper bound on the radius of massive pulsars serves to rule out too soft quark matter, and an upper bound on $M_{\rm max}$ with a lower bound on the radius of massive pulsars strongly disfavors a transition into too-stiff quark matter appearing at low densities. The complementary role played by radius inferences from future gravitational wave events of inspiraling binary neutron stars is also briefly discussed., 15 pages, 10 figures, 3 tables; discussions and references added

The possible detection of a compact object in the remnant of SN 1987A presents an unprecedented opportunity to follow its early evolution. The suspected detection stems from an excess of infrared emission from a dust blob near the compact object's predicted position. The infrared excess could be due to the decay of isotopes like 44Ti, accretion luminosity from a neutron star or black hole, magnetospheric emission or a wind originating from the spindown of a pulsar, or thermal emission from an embedded, cooling neutron star (NS 1987A). It is shown that the last possibility is the most plausible as the other explanations are disfavored by other observations and/or require fine-tuning of parameters. Not only are there indications the dust blob overlaps the predicted location of a kicked compact remnant, but its excess luminosity also matches the expected thermal power of a 30 year old neutron star. Furthermore, models of cooling neutron stars within the Minimal Cooling paradigm readily fit both NS 1987A and Cas A, the next-youngest known neutron star. If correct, a long heat transport timescale in the crust and a large effective stellar temperature are favored, implying relatively limited crustal n-1S0 superfluidity and an envelope with a thick layer of light elements, respectively. If the locations don't overlap, then pulsar spindown or accretion might be more likely, but the pulsar's period and magnetic field or the accretion rate must be rather finely tuned. In this case, NS 1987A may have enhanced cooling and/or a heavy-element envelope., Comment: 21 pages, 6 figures, to be published in ApJ

Recent developments in the theory of pure neutron matter and experiments concerning the symmetry energy of nuclear matter, coupled with recent measurements of high-mass neutron stars, now allow for relatively tight constraints on the equation of state of dense matter. We review how these constraints are formulated and describe the implications they have for neutron stars and core-collapse supernovae. We also examine thermal properties of dense matter, which are important for supernovae and neutron star mergers, but which cannot be nearly as well constrained at this time by experiment. In addition, we consider the role of the equation of state in medium-energy heavy-ion collisions., Comment: 87 pages, 20 figures, Accepted for Phys. Rep (Gerald E. Brown's Memorial Volume)

Some of the means through which the possible presence of nearly deconfined quarks in neutron stars can be detected by astrophysical observations of neutron stars from their birth to old age are highlighted., Comment: 8 pages, 6 figures, Plenary talk in Quark Matter 2006 to appear in J. Phys. G: Nucl. Part. Phys. 34 (2007)

We investigate how current and proposed observations of neutron stars can lead to an understanding of the state of their interiors and the key unknowns: the typical neutron star radius and the neutron star maximum mass. A theoretical analysis of neutron star structure, including general relativistic limits to mass, compactness, and spin rates is made. We consider observations made not only with photons, ranging from radio waves to X-rays, but also those involving neutrinos and gravity waves. We detail how precision determinations of structural properties would lead to significant restrictions on the poorly understood equation of state near and beyond the equilibrium density of nuclear matter., 70 pages, 19 figures, submitted to Hans Bethe Centennial Physics Reports

We investigate the effects of very strong magnetic fields upon the equation of state of dense bayonic matter in which hyperons are present. In the presence of a magnetic field, the equation of state above nuclear density is significantly affected both by Landau quantization and magnetic moment interactions, but only for field strengths $B>5\times10^{18}$ G. The former tends to soften the EOS and increase proton and lepton abundances, while the latter produces an overall stiffening of the EOS. Each results in a supression of hyperons relative to the field-free case. The structure of a neutron star is, however, primarily determined by the magnetic field stress. We utilize existing general relativistic magneto-hydrostatic calculations to demonstrate that maximum average fields within a stable neutron are limited to values $B\le 1-3 \times10^{18}$ G. This is not large enough to significantly influence particle compositions or the matter pressure, unless fluctuations dominate the average field strengths in the interior or configurations with significantly larger field gradients are considered., 12 pages, 3 figures. To be submitted to Phys. Lett. B

The presence of quark matter in neutron star interiors may have distinctive signatures in basic observables such as (i) masses and radii [1], (ii) surface temperatures versus age [2], (iii) spin-down rates of milli-second pulsars [3], and (iv) neutrino luminosities from future galactic core collapse supernovae [4]. I highlight recent developments in some of these areas with a view towards assessing how theory may be confirmed by $\nu-$signals from future galactic supernovae in detectors like SuperK, SNO and others under consideration, including UNO [5], and by multi-wavelength photon observations with new generation satellites such as the HST, Chandra, and XMM., Comment: 4 pages, 2 figures. To appear in the proceedings of QM 2001. Uses fleqn.sty and espcrc1.sty

Gerry Brown has had the most influence on my career in Physics, and my life after graduate studies. This article gives a brief account of some of the many ways in which Gerry shaped my research. Focus is placed on the significant strides on neutron star research made by the group at Stony Brook, which Gerry built from scratch. Selected puzzles about neutron stars that remain to be solved are noted., Suggestions of the referee and the editor incorporated. 24 pages, 11 figures, 2 tables, Contribution to "Gerry Brown's Memorial Meeting", 45 Years of Nuclear Theory at Stony Brook: A Tribute To Gerald E. Brown. Article in press as: M. Prakash, Neutron star news and puzzles, Nuclear Physics A (2014), http://dx.doi.org/10.1016/j.nuclphysa.2014.04.017

Neutron stars have long been regarded as extra-terrestrial laboratories from which we can learn about extreme energy density matter at low temperatures. In this article, I highlight some of the recent advances made in astrophysical observations and related theory. Although the focus is on the much needed information on masses and radii of several individual neutron stars, the need for additional knowledge about the many facets of neutron stars is stressed. The extent to which quark matter can be present in neutron stars is summarized with emphasis on the requirement of non-perturbative treatments. Some longstanding and new questions, answers to which will advance our current status of knowledge, are posed., 18 pages, 3 figures, 3 tables, Review submitted to Pramana

Baryon and quark superfluidity in the cooling of neutron stars are investigated. Observations could constrain combinations of the neutron or Lambda-hyperon pairing gaps and the star's mass. However, in a hybrid star with a mixed phase of hadrons and quarks, quark gaps larger than a few tenths of an MeV render quark matter virtually invisible for cooling. If the quark gap is smaller, quark superfluidity could be important, but its effects will be nearly impossible to distinguish from those of other baryonic constituents., Comment: 4 pages, 3 ps figures, uses RevTex(aps,prl). Submitted to Phys. Rev. Lett

A first order phase transition at high baryon density implies that a mixed phase can occupy a significant region of the interior of a neutron star. In this article we investigate the effect of a droplet phase on neutrino transport inside the core. Two specific scenarios of the phase transition are examined, one having a kaon condensate and the other having quark matter in the high density phase. The coherent scattering of neutrinos off the droplets greatly increases the neutrino opacity of the mixed phase. We comment on how the existence of such a phase will affect a supernova neutrino signal., Comment: 7 pages, 4 figures

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 protoneutron 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 protoneutron star and upon the expected signal in terrestrial detectors., Comment: 67 pages, 25 figures

A protoneutron star is formed immediately after the gravitational collapse of the core of a massive star. At birth, the hot and high density matter in such a star contains a large number of neutrinos trapped during collapse. Trapped neutrinos generally inhibit the presence of exotic matter — hyperons, a kaon condensate, or quarks. However, as the neutrinos diffuse out in about 10–15 s, the threshold for the appearance of strangeness is reduced; hence, the composition and the structure of the star can change significantly. The effect of exotic, negatively-charged, strangeness-bearing components is always to soften the equation of state, and the possibility exists that the star collapses to a black hole at this time. This could explain why no neutron star has yet been seen in the remnant of supernova SN1987A, even though one certainly existed when neutrinos were detected on Feb. 23, 1987. With new generation neutrino detectors it is feasible to test different theoretical scenarios observationally.

A protoneutron star is formed immediately after the gravitational collapse of the core of a massive star. At birth, the hot and high density matter in such a star contains a large number of neutrinos trapped during collapse. Trapped neutrinos generally inhibit the presence of exotic matter -- hyperons, a kaon condensate, or quarks. However, as the neutrinos diffuse out in about 10-15 s, the threshold for the appearance of strangeness is reduced; hence, the composition and the structure of the star can change significantly. The effect of exotic, negatively-charged, strangeness-bearing components is always to soften the equation of state, and the possibility exists that the star collapses to a black hole at this time. This could explain why no neutron star has yet been seen in the remnant of supernova SN1987A, even though one certainly existed when neutrinos were detected on Feb. 23, 1987. With new generation neutrino detectors it is feasible to test different theoretical scenarios observationally., Comment: 19 pages, 10 Postscript figures, Strangeness 96 paper to appear in Heavy Ion Physics

The structure of newborn hot neutron stars is compared with that of cold catalyzed configurations. The role of the nuclear equation of state on the structural changes is investigated and some of the astrophysical consequences are briefly discussed.

The supernova remnant Cassiopeia A contains the youngest known neutron star which is also the first one for which real time cooling has ever been observed. I n order to explain the rapid cooling of this neutron star, we first present the fundamental proper ties of neutron stars that control their thermal evolution with emphasis on the neutrino emission processes and neutron/proton superfluidity/superconductivity. Equipped with these results, we present a scenario in which the observed cooling of the neutron star in Cassiopeia A is interpreted as being due to the recent onset of neutron superfluidity in the core of the star. The manner in which the earlier occurrence of proton superconductivity determines the observed rapidity of thi s neutron star’s cooling is highlighted. This is the first direct evidence that superfluidity and super conductivity occur at supranuclear densities within neutron stars.

The determination of neutron star masses is reviewed in light of a new measurement of 1.97 M$_\odot$ for PSR J1614-2230 and an estimate of 2.4 M$_\odot$ for the black widow pulsar. Using a simple analytic model related to the so-called maximally compact equation of state, model-independent upper limits to thermodynamic properties in neutron stars, such as energy density, pressure, baryon number density and chemical potential, are established which depend upon the neutron star maximum mass. Using the largest well-measured neutron star mass, 1.97 M$_\odot$, it is possible to show that the energy density can never exceed about 2 GeV, the pressure about 1.3 GeV, and the baryon chemical potential about 2.1 GeV. Further, if quark matter comprises a significant component of neutron star cores, these limits are reduced to 1.3 GeV, 0.9 GeV, and 1.5 GeV, respectively. We also find that the maximum binding energy of any neutron star is about 25% of the rest mass. Neutron matter properties and astrophysical constraints additionally imply an upper limit to the neutron star maximum mass of about 2.4 M$_\odot$. A measured mass of 2.4 M$\odot$ would be incompatible with hybrid star models containing {\it significant} proportions of exotica in the form of hyperons, Bose condensates or quark matter.

Gravitational waves from the final stages of inspiralling binary neutron stars are expected to be one of the most important sources for ground-based gravitational wave detectors. The masses of the components are determinable from the orbital and chirp frequencies during the early part of the evolution during which tidal effects provide small correction; however, during this phase the signal is relatively clean. The accumulated phase shift due to tidal corrections is characterized by a single quantity, the Love number, which is sensitive to the compactness parameter M/R and the star's internal structure, and its determination could constrain the star's radius. We show that the Love number of normal neutron stars are much different from those of self-bound strange quark matter stars and could therefore provide an important way to distinguish between these two classes of stars., 18 pages, 17 figures, 1 table

The minimal cooling paradigm for neutron star cooling assumes that enhanced cooling due to neutrino emission from any direct Urca process, due either to nucleons or to exotica such as hyperons, Bose condensates, or deconfined quarks, does not occur. This scenario was developed to replace and extend the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation processes that occur near the critical temperature for superfluid/superconductor pairing. Recently, it has been found that Cooper-pair neutrino emission from the vector channel is suppressed by a large factor compared to the original estimates that violated vector current conservation. We show that Cooper-pair neutrino emission remains, nevertheless, an efficient cooling mechanism through the axial channel. As a result, the elimination of neutrino emission from Cooper-paired nucleons through the vector channel has only minor effects on the long-term cooling of neutron stars within the minimal cooling paradigm. We further quantify precisely the effect of the size of the neutron 3P2 gap and demonstrate that consistency between observations and the minimal cooling paradigm requires that the critical temperature T_c for this gap covers a range of values between T_c^min < 0.2 x 10^9 K up to T_c^max > 0.5 \times 10^9 K in the core of the star. In addition, it is required that young neutron stars have heterogenous envelope compositions: some must have light-element compositions and others must have heavy-element compositions. Unless these two conditions are fulfilled, about half of the observed young cooling neutron stars are inconsistent with the minimal cooling paradigm and provide evidence for the existence of enhanced cooling., 13 pages, 9 figures, submitted to ApJ

The shear viscosity of the crust might have a damping effect on the amplitude of r-modes of rotating neutron stars. This damping has implications for the emission of gravitational waves. We calculate the contribution to the shear viscosity coming from the ions using both semi-analytical methods, that consider binary collisions, and Molecular Dynamics simulations. We compare these results with the contribution coming from electrons. We study how the shear viscosity depends on density for conditions of interest in neutron star envelopes and outer crusts. In the low density limit, we find good agreement between results of our molecular dynamics simulations and classical semi-analytic calculations., 13 pages, 14 figures, Subsection added

The roles of isospin asymmetry in nuclei and neutron stars are investigated using a range of potential and field-theoretical models of nucleonic matter. The parameters of these models are fixed by fitting the properties of homogeneous bulk matter and closed-shell nuclei. We discuss and unravel the causes of correlations among the neutron skin thickness in heavy nuclei, the pressure of beta-equilibrated matter at a density of 0.1 fm$^{-3}$, the derivative of the nuclear symmetry energy at the same density and the radii of moderate mass neutron stars. Constraints on the symmetry properties of nuclear matter from the binding energies of nuclei are examined. The extent to which forthcoming neutron skin measurements will further delimit the symmetry properties is investigated. The impact of symmetry energy constraints for the mass and moment of inertia contained within neutron star crusts and the threshold density for the nucleon direct Urca process, all of which are potentially measurable, is explored. We also comment on the minimum neutron star radius, assuming that only nucleonic matter exists within the star., 49 pages, 17 figures, Phys. Rep. (in press); made improvements to "RAPR" and corrected transition densities

Neutrino processes in semi-transparent supernova matter, opaque to semi-transparent protoneutron star matter, and catalyzed neutron stars are discussed.

The photon emissivity from the bremsstrahlung process ee-> ee��occuring in the electrosphere at the bare surface of a strange quark star is calculated. For surface temperatures T, 17 pages, 6 figures

Neutron stars are some of the densest manifestations of massive objects in the universe. They are ideal astrophysical laboratories for testing theories of dense matter physics and provide connections among nuclear physics, particle physics and astrophysics. Neutron stars may exhibit conditions and phenomena not observed elsewhere, such as hyperon-dominated matter, deconfined quark matter, superfluidity and superconductivity with critical temperatures near ${10^{10}}$ kelvin, opaqueness to neutrinos, and magnetic fields in excess of $10^{13}$ Gauss. Here, we describe the formation, structure, internal composition and evolution of neutron stars. Observations that include studies of binary pulsars, thermal emission from isolated neutron stars, glitches from pulsars and quasi-periodic oscillations from accreting neutron stars provide information about neutron star masses, radii, temperatures, ages and internal compositions., Comment: 22 pages, 4 figures and 1 table

The mergers of black hole-neutron star binaries are calcuated using a pseudo-general relativistic potential that incorporates ${\mathcal O}(v^2/c^2)^3$ post-Newtonian corrections. Both normal matter neutron stars and self-bound strange quark matter stars are considered as black hole partners. As long as the neutron stars are not too massive relative to the black hole mass, orbital decay terminates in stable mass transfer rather than an actual merger. For a normal neutron star, mass transfer results in a widening of the orbit but the stable transfer ends before the minimum neutron star mass is reached. For a strange star, mass transfer does not result in an appreciable enlargement of the orbital separation, and the stable transfer continues until the strange star essentially disappears. These differences might be observable through their respective gravitational wave signatures., Contribution to QM04 proceedings. Submitted to Journal of Physics G

A new classification of neutron star cooling scenarios, involving either ``minimal'' cooling or ``enhanced'' cooling is proposed. The minimal cooling scenario replaces and extends the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation process. This emission dominates that due to the modified Urca process for temperatures close to the critical temperature for superfluid pairing. Minimal cooling is distinguished from enhanced cooling by the absence of neutrino emission from any direct Urca process, due either to nucleons or to exotica. Within the minimal cooling scenario, theoretical cooling models can be considered to be a four parameter family involving the equation of state of dense matter, superfluid properties of dense matter, the composition of the neutron star envelope, and the mass of the neutron star. Consequences of minimal cooling are explored through extensive variations of these parameters. Results are compared with the inferred properties of thermally-emitting neutron stars in order to ascertain if enhanced cooling occurs in any of them. All stars for which thermal emissions have been clearly detected are at least marginally consistent with the lack of enhanced cooling. The two pulsars PSR 0833-45 (Vela) and PSR 1706-44 would require enhanced cooling in case their ages and/or temperatures are on the lower side of their estimated values whereas the four stars PSR 0656+14, PSR 1055-52, Geminga, and RX J0720.4-3125 may require some source of internal heating in case their age and/or luminosity are on the upper side of their estimated values. The new upper limits on the thermal luminosity of PSR J0205+6449 and RX J0007.0+7302 are indicative of the occurrence of some enhanced neutrino emission beyond the minimal scenario., Comment: Version to appear in ApJ Supplements. Minor modifications in text and discussion of updated data with new figures

Observations to date cannot distinguish neutron stars from self-bound bare quark stars on the basis of their gross physical properties such as their masses and radii alone. However, their surface luminosity and spectral characteristics can be significantly different. Unlike a normal neutron star, a bare quark star can emit photons from its surface at super-Eddington luminosities for an extended period of time. We present a calculation of the photon bremsstrahlung rate from the bare quark star's surface, and indicate improvements that are required for a complete characterization of the spectrum. The observation of this distinctive photon spectrum would constitute an unmistakable signature of a strange quark star and shed light on color superconductivity at stellar densities., Comment: 8 pages, 5 figures; contribution to proceedings of the 26th annual Montreal-Rochester-Syracuse-Toronto Conference (MRST 2004) on High Energy Physics: From Quarks to Cosmology, May 12 - 14 (2004), Concordia University, Montreal, Quebec, Canada

The differential rates and emissivities of neutrino pairs from an equilibrium plasma are calculated for the wide range of density and temperature encountered in astrophysical systems. New analytical expressions are derived for the differential emissivities which yield total emissivities in full agreement with those previously calculated. The photon and plasmon pair production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are provided. The appropriate Legendre coefficients of these kernels, in forms suitable for multi-group flux-limited diffusion schemes are also computed., 27 pages and 10 figures. Submitted to Phys. Rev. C

We contrast the evolution of gravitational binary mergers for the two cases of a black hole and a normal neutron star, and a black hole and a self-bound strange quark matter star. In both cases inspiral continues until the Roche limit is reached, at which point it is expected that stable mass transfer to the balck hole ensues. Whereas a neutron star would then outspiral, the strange quark matter star barely moves out at all. Eventually, the strange quark star loses all its mass to the black hole, as compared to the neutron star whose outspiral continues until stable mass transfer terminates and inspiral resumes. These scenarios result in distinctly different gravitational wave signatures., Comment: 10 pages with 6 figures - Submitted to the Strange Quark Matter 2003 Conference Proceedings

Explicit expressions for the differential and total rates and emissivities of neutrino pairs from the photo-neutrino process $e^\pm + \gamma \to e^\pm + \nu + \bar\nu$ in hot and dense matter are derived. Full information about the emitted neutrinos is retained by evaluating the squared matrix elements for this process which was hitherto bypassed through the use of Lenard's identity in obtaining the total neutrino emissivities. Accurate numerical results are presented for widely varying conditions of temperature and density. Analytical results helpful in understanding the qualitative behaviors of the rates and emissivities in limiting situations are derived. The corresponding production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are developed. The appropriate Legendre coefficients of these kernels, in forms suitable for multigroup flux-limited diffusion schemes are also provided., Comment: 26 pages and 7 figures. Version as accepted in Phys. Rev. D; three figures and related discussion revised

We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are $\sim 100$ MeV while the masses of Goldstone modes are on the order of 10 MeV. For the same reason, the specific heat of the CFL phase is also dominated by the Goldstone modes. Notwithstanding this, both the emissivity and the specific heat from the massive modes remain rather small, because of their extremely small number densities. The values of the emissivity and the specific heat imply that the timescale for the cooling of the CFL core in isolation is $\sim 10^{26}$ y, which makes the CFL phase invisible as the exterior layers of normal matter surrounding the core will continue to cool through significantly more rapid processes. If the CFL phase appears during the evolution of a proto-neutron star, neutrino interactions with Goldstone bosons are expected to be significantly more important since temperatures are high enough ($\sim 20-40$ MeV) to admit large number densities of Goldstone modes., 29 pages, no figures. slightly modified text, one new eqn. and new refs. added

Recent Chandra observations have raised expectations that the objects RX J185635-3754 and 3C58 are either bare strange quark stars or stars with extended quark cores. However, these observations can also be interpreted in terms of normal neutron stars. Essential requirements for either explanation are that they simultaneously account for the observed (i) spectral features (i.e., thermal or nonthermal, possible lines), (ii) bounds on the inferred mass (M) and radius (R), and (iii) the cooling curves (effective temperatures T and luminosities L vs. age). Compact stars offer the promise of delineating QCD at finite baryon density (Lattimer and Prakash, 2001) in a fashion complementary to relativistic heavy ion collider experiments, which largely address the finite temperature, but baryon poor regime., Comment: 4 pages, 1 figure, uses espcrc1.sty (included)

For the low energy Standard Model neutrino-matter interactions, we calculate neutrino pair ($\nu\bar\nu$) emissivites in superfluid quark matter. Just below the critical temperature, Cooper pairs continuously break and recombine, resulting in the emission of $\nu\bar \nu$ pairs with a rate that greatly exceeds the standard quark modified Urca and bremsstrahlung rates. At the same baryon density in baryonic and quark matter, the ratio of baryon to quark $\nu\bar\nu$ emissivites lies in the range 2-5 for the densities of interest in the long-term cooling of solar mass compact stars. We also find that in matter containing hyperons, $\nu\bar\nu$ emission can occur with hyperons of all species., Comment: 10 pages, no figures

Even the elusive neutrinos are trapped in matter, albeit transiently, in several astrophysical circumstances. Their interactions with the ambient matter not only reveal the properties of such exotic matter itself, but also shed light on the fundamental properties of the neutrinos themselves. The physical sites of interest include the early universe, supernovae, and newly-born neutron stars. Detection of neutrinos from these vastly different eras using the new generation of neutrino detectors holds great promise for enhancing our understanding of neutrino-matter interactions and astrophysical phenomena., 77 pages, 13 figures; a final version of this manuscript is scheduled to be published in the Annual Review of Nuclear & Particle Science, Vol. 51, December 2001 (www.AnnualReviews.org)

Neutrino fluxes from proto-neutron stars with and without quarks are studied. Observable differences become apparent after 10--20 s of evolution. Sufficiently massive stars containing negatively-charged, strongly interacting, particles collapse to black holes during the first minute of evolution. Since the neutrino flux vanishes when a black hole forms, this is the most obvious signal that quarks (or other types of strange matter) have appeared. The metastability timescales for stars with quarks are intermediate between those containing hyperons and kaon condensates., 4 pages including 4 figures. Version with minor revisions. To be published in Physical Review Letters

Neutrino opacities important in the evolution of a proto-neutron star containing quark matter are studied. The results for pure quark matter are compared with limiting expressions previously derived, and are generalized to the temperatures, neutrino degeneracies and lepton contents encountered in a proto-neutron star's evolution. We find that the appearance of quarks in baryonic matter drastically reduces the neutrino opacity for a given entropy, the reduction being sensitive to the thermodynamic conditions in the mixed quark-hadron phase., 15 pages including 3 figures

Using a chirally invariant effective Lagrangian, we calculate the density and isospin dependences of the in-medium axial coupling, $g_A^*$, in spatially uniform matter present in core collapse supernovae and neutron stars. The quenching of $g_A^*$ with density in matter with different proton fractions is found to be similar. However, our results suggest that the quenching of the nucleon's $g_A^*$ in matter with hyperons is likely to be significantly greater than in matter with nucleons only., Comment: 4 pages revtex, 2 eps figures

The main stages in the evolution of a neutron star, from its birth as a proto-neutron star, to its old age as a cold, catalyzed configuration, are described. A proto-neutron star is formed in the aftermath of a successful supernova explosion and its evolution is dominated by neutrino diffusion. Its neutrino signal is a valuable diagnostic of its internal structure and composition. During its transformation from a hot, leptonrich to a cold, catalyzed remnant, the possibility exists that it can collapse into a black hole, which abruptly terminates neutrino emissions. The essential microphysics, reviewed herein, that controls its evolution are the equation of state of dense matter and its associated neutrino opacities. Several simulations of the proto-neutron star evolution, involving different assumptions about the composition of dense matter, are described. After its evolution into a nearly isothermal neutron star a hundred or so years after its birth, it may be observable through its thermal emission in X-rays during its life in the next million years. Its surface temperature will depend upon the rapidity of neutrino emission processes in its core, which depends on the composition of dense matter and whether or not its constituents exhibit superfluidity and superconductivity. Observations of thermal emission offer the best hope of a determination of the radius of a neutron star. The implications for the underlying dense matter equation of state of an accurate radius determination are explored.

We study static neutron stars with poloidal magnetic fields and a simple class of electric current distributions consistent with the requirement of stationarity. For this class of electric current distributions, we find that magnetic fields are too large for static configurations to exist when the magnetic force pushes a sufficient amount of mass off-center that the gravitational force points outward near the origin in the equatorial plane. (In our coordinates an outward gravitational force corresponds to $\partial\ln g_{tt}/\partial r>0$, where $t$ and $r$ are respectively time and radial coordinates and $g_{tt}$ is coefficient of $dt^2$ in the line element.) For the equations of state (EOSs) employed in previous work, we obtain configurations of higher mass than had been reported; we also present results with more recent EOSs. For all EOSs studied, we find that the maximum mass among these static configurations with magnetic fields is noticeably larger than the maximum mass attainable by uniform rotation, and that for fixed values of baryon number the maximum mass configurations are all characterized by an off-center density maximum., Submitted to the Astrophysical Journal. 37 pages, 8 figures, uses aastex macros

Immediately after they are born, neutron stars are characterized by an entropy per baryon of order unity and by the presence of trapped neutrinos. If the only hadrons in the star are nucleons, these effects slightly reduce the maximum mass relative to cold, catalyzed matter. However, if stangeness-bearing hyperons, a kaon condensate, or quarks are also present, these effects result in an increase in the maximum mass of up to $\sim 0.3{\rm M}_{\odot}$ compared to that of a cold, neutrino-free star. This makes a sufficiently massive proto-neutron star metastable, so that after a delay of 10--100 seconds, the PNS collapses into a black hole. Such an event might be straightforward to observe as an abrupt cessation of neutrinos when the instability is triggered., 7 pages, 4 figures, Presented at the XIX Conference on Neutrino Physics and Astrophysics (Neutrino2000)

We present simulations of the evolution of a proto-neutron star in which kaon-condensed matter might exist, including the effects of finite temperature and trapped neutrinos. The phase transition from pure nucleonic matter to the kaon condensate phase is described using Gibbs' rules for phase equilibrium, which permit the existence of a mixed phase. A general property of neutron stars containing kaon condensates, as well as other forms of strangeness, is that the maximum mass for cold, neutrino-free matter can be less than the maximum mass for matter containing trapped neutrinos or which has a finite entropy. A proto-neutron star formed with a baryon mass exceeding that of the maximum mass of cold, neutrino-free matter is therefore metastable, that is, it will collapse to a black hole at some time during the Kelvin-Helmholtz cooling stage. The effects of kaon condensation on metastable stars are dramatic. In these cases, the neutrino signal from a hypothetical galactic supernova (distance $\sim8.5$ kpc) will stop suddenly, generally at a level above the background in the SuperK and SNO detectors, which have low energy thresholds and backgrounds. This is in contrast to the case of a stable star, for which the signal exponentially decays, eventually disappearing into the background. We find the lifetimes of kaon-condensed metastable stars to be restricted to the range 40--70 s and weakly dependent on the proto-neutron star mass, in sharp contrast to the significantly larger mass dependence and range (1--100 s) of hyperon-rich metastable stars., 25 pages, 14 figures. Submitted to Astrophysical Journal

The equation of state (EOS) of dense matter plays an important role in the supernova phenomenon, the structure of neutron stars, and in the mergers of compact objects (neutron stars and black holes). During the collapse phase of a supernova, the EOS at subnuclear densities controls the collapse rate, the amount of deleptonization and thus the size of the collapsing core and the bounce density. Properties of nuclear matter that are especially crucial are the symmetry energy and the nuclear specific heat. The nuclear incompressibility, and the supernuclear EOS, play supporting roles. In a similar way, although the maximum masses of neutron stars are entirely dependent upon the supernuclear EOS, other important structural aspects are more sensitive to the equation of state at nuclear densities. The radii, moments of inertia, and the relative binding energies of neutron stars are, in particular, sensitive to the behavior of the nuclear symmetry energy. The dependence of the radius of a neutron star on its mass is shown to critically influence the outcome of the compact merger of two neutron stars or a neutron star with a small mass black hole. This latter topic is especially relevant to this volume, since it stems from research prompted by the tutoring of David Schramm a quarter century ago., 37 pages, 13 figures, accepted for publication in Physics Reports (David Schramm Memorial Volume)

The structure of neutron stars is considered from theoretical and observational perspectives. We demonstrate an important aspect of neutron star structure: the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density. In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure. For equations of state with extreme softening, or those that are self-bound, the radius is more sensitive to the mass. Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state. We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles. In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the star's compactness. These features can be understood by considering two analytic, yet realistic, solutions of Einstein's equations, due, respectively, to Buchdahl and Tolman. We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the presssure at the core-crust interface., Comment: 51 pages, 10 figures, submitted to ApJ

An extensive study of the effects of correlations on both charged and neutral current weak interaction rates in dense matter is performed. Both strong and electromagnetic correlations are considered.The propagation of particle-hole interactions in the medium plays an important role in determining the neutrino mean free paths. The effects due to Pauli-Blocking and density, spin, and isospin correlations in the medium significantly reduce the neutrino cross sections. Due to the lack of experimental information at high density, these correlations are necessarily model dependent. For example, spin correlations in nonrelativistic models are found to lead to larger suppressions of neutrino cross sections compared to those of relativistic models. This is due to the tendency of the nonrelativistic models to develop spin instabilities. Notwithstanding the above caveats, and the differences between nonrelativistic and relativistic approaches such as the spin- and isospin-dependent interactions and the nucleon effective masses, suppressions of order 2--3, relative to the case in which correlations are ignored, are obtained. Neutrino interactions in dense matter are especially important for supernova and early neutron star evolution calculations. The effects of correlations for protoneutron star evolution are calculated. Large effects on the internal thermodynamic properties of protoneutron stars, such as the temperature, are found. These translate into significant early enhancements in the emitted neutrino energies and fluxes, especially after a few seconds. At late times, beyond about 10 seconds, the emitted neutrino fluxes decrease more rapidly compared to simulations without the effects of correlations, due to the more rapid onset of neutrino transparency in the protoneutron star, Comment: 79 pages, 35 Figures

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 multi-component nature of dense matter. The opacities are then discussed in the context of the evolution of the core of a protoneutron star., 41 pages, 25 figures

We calculate neutrino cross sections from neutral current reactions in the dense matter encountered in the evolution of a newly born neutron star. Effects of composition and of strong interactions in the deleptonization and cooling phases of the evolution are studied. The influence of the possible presence of strangeness-rich hyperons on the neutrino scattering cross sections is explored. Due to the large vector couplings of the Sigma-minus and Cascade-minus, |C_V|~2, these particles, if present in protoneutron star matter, give significant contributions to neutrino scattering. In the deleptonization phase, the presence of strangeness leads to large neutrino energies, which results in large enhancements in the cross sections compared to those in matter with nucleons only. In the cooling phase, in which matter is nearly neutrino free, the response of the Sigma-minus hyperons to thermal neutrinos is the most significant. Neutrinos couple relatively weakly to the Lambda hyperons and, hence, their contributions are significant only at high density., Comment: 51 pages, 13 figures, ApJ in press

Neutrino processes in dense matter play a key role in the dynamics, deleptonization and the early cooling of hot protoneutron stars formed in the gravitational collapse of massive stars. Here we calculate neutrino mean free paths from neutrino-hyperon interactions in dense matter containing hyperons. Significant contributions to the neutrino opacity arise from scattering involving the Σ- hyperon, and absorption processes involving the neutral and Σ- hyperons. The estimates given here emphasize the need for (a) opacities which incorporate many-body effects in a multi-component mixture, and (b) new calculations of thermal and leptonic evolution of protoneutron stars with neutrino transport and equations of state with strangeness-rich matter.

We investigate the structure of neutron stars shortly after they are born, when the entropy per baryon is of order 1 or 2 and neutrinos are trapped on dynamical timescales. In all cases, the thermal effects for an entropy per baryon of order 2 or less are small when considering the maximum neutron star mass. Neutrino trapping, however, significantly changes the maximum mass due to the abundance of electrons. When matter is allowed to contain only nucleons and leptons, trapping decreases the maximum mass by an amount comparable to, but somewhat larger than, the increase due to finite entropy. When matter is allowed to contain strongly interacting negatively charged particles, in the form of strange baryons, a kaon condensate, or quarks, trapping instead results in an increase in the maximum mass of order $0.2M_\odot$, which adds to the effects of finite entropy. The presence of negatively-charged particles has two major implications. First, the value of the maximum mass will decrease during the early evolution of a neutron star as it loses trapped neutrinos, so that if a black hole forms, it either does so immediately after the bounce or it is delayed for a neutrino diffusion timescale of $\sim 10$ s. The latter case is most likely if the maximum mass of the hot star with trapped neutrinos is near $1.5M_\odot$. In the absence of negatively-charged hadrons, black hole formation would be due to accretion and therefore is likely to occur only immediately after bounce. Second, the appearance of hadronic negative charges results in a general softening of the equation of state that may be observable in the neutrino luminosities and average energies. Further, these additional negative charges decrease the electron fraction and may be observed in the relative excess of electron neutrinos compared to other neutrinos., Comment: 83 pages, 30 postscript figures, Physics Reports, to be published

We consider the rate at which energy is emitted by neutrinos from the dense interior of neutron stars containing a Bose condensate of pions or kaons. The rates obtained are larger, by a factor of 2, than those found earlier, and are consistent with those found for the direct Urca processes., Comment: RevTeX, 10 pages

We investigate the possibility of kaon condensation in the dense interior of neutron stars through the s--wave interaction of kaons with nucleons. We include nucleon--nucleon interactions by using simple parametrizations of realistic forces, and include electrons and muons in $\beta$--equilibrium. The conditions under which kaon condensed cores undergo a transition to quark matter containing strange quarks are also established. The critical density for kaon condensation lies in the range (2.3--5.0)$~\rho_0$, where $\rho_0=0.16$~fm$^{-3}$ is the equilibrium density of nuclear matter. For too large a value of the strangeness content of the proton, matter with a kaon condensate is not sufficiently stiff to support the lower limit of $1.44 M_\odot$ for a neutron star. Kaon condensation dramatically increases the proton abundance of matter and even allows positrons to exist inside the core. We also consider the case when neutrinos are trapped in the matter. Neutrino trapping shifts both kaon condensation and the quark matter transition to higher densities than in the case of cold, catalyzed matter. A newly--formed neutron star is expected to have a rather low central density, the density rising only after mass accretion onto the star ends after a few seconds. Thus, it is likely that if kaon condensation and/or the quark--hadron phase transition occur, they do so only during or after the mass accretion and neutrino trapping stages. We suggest that neutrino observations from a galactic supernova may provide direct evidence for or against a condensate and/or a quark--hadron transition., Comment: 31 Pages, 8 Tables ( LaTeX ), 14 uuencoded, tar-compressed postscript figures, NORDITA-93/29 N, SUNY-NTG-92-33