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Nuclear Astrophysics is a field at the intersection of nuclear physics and astrophysics, which seeks to understand the nuclear engines of astronomical objects and the origin of the chemical elements. This white paper summarizes progress and status of the field, the new open questions that have emerged, and the tremendous scientific opportunities that have opened up with major advances in capabilities across an ever growing number of disciplines and subfields that need to be integrated. We take a holistic view of the field discussing the unique challenges and opportunities in nuclear astrophysics in regards to science, diversity, education, and the interdisciplinarity and breadth of the field. Clearly nuclear astrophysics is a dynamic field with a bright future that is entering a new era of discovery opportunities., Comment: 96 pages. Submitted to Journal of Physics G

Nuclear pasta, with nucleons arranged into tubes, sheets, or other complex shapes, is expected in core collapse supernovae (SNe) at just below nuclear density. We calculate the additional opacity from neutrino-pasta coherent scattering using molecular dynamics simulations. We approximately include this opacity in simulations of SNe. We find that pasta slows neutrino diffusion and greatly increases the neutrino signal at late times of 10 or more seconds after stellar core collapse. This signal, for a galactic SN, should be clearly visible in large detectors such as Super-Kamiokande., Comment: 6 pages, 4 figures

A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope $L$ of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We find that the variation of either the density slope $L$ or the high-density behavior of nuclear symmetry energy leads to large changes in the binding energy of neutron stars. The difference in predictions using the GR and the scalar-tensor theory appears only for massive neutron stars, and even then is significantly smaller than the difference resulting from variations in the symmetry energy., Comment: To appear in the Proceedings of the 13th international symposium on Origin of Matter and Evolution of Galaxies (OMEG2015) , June 24-27, 2015, Beijing, China

There is a degeneracy between the equation of state (EOS) of superdense neutron-rich nuclear matter and the strong-field gravity in understanding properties of neutron stars. While the EOS is still poorly known, there are also longstanding ambiguities in choosing General Relativity or alternative gravity theories in the not-so-well tested strong-field regime. Besides possible appearance of hyperons and new phases, the most uncertain part of the nucleonic EOS is currently the density dependence of nuclear symmetry energy. To provide information that may help break the EOS-gravity degeneracy, we investigate effects of symmetry energy within its uncertain range determined by terrestrial nuclear laboratory experiments on the gravitational binding energy and spacetime curvature of neutron stars within GR and the scalar-tensor (ST) theory of gravity. In particular, we focus on effects of the following parameters characterizing the EOS of neutron-rich nucleonic matter: (1) the incompressibility $K_0$ of symmetric nuclear matter, (2) the slope $L$ of symmetry energy at saturation density and (3) the high-density behavior of symmetry energy. We find that the variation of either the density slope $L$ or the high-density behavior of symmetry energy leads to large changes in both the binding energy and curvature of neutron stars while effects of varying the more constrained $K_0$ are negligibly small. The difference in predictions using the GR and the ST theory appears only for massive neutron stars, and is significantly smaller than the differences resulting from variations in the symmetry energy. We conclude that within the ST theory of gravity, the EOS-gravity degeneracy has been broken by the recent relativistic pulsar measurements, and that measurements of neutron star properties sensitive to the compactness constrain mainly the density dependence of the symmetry energy., Comment: Note a title change in the second version. An additional section has been added. 17 pages, 8 figures (3 additional figures), 1 table

We investigate induced oscillations by the gravitational field of a fast stellar object, such as a neutron star or a black-hole in a near miss collision with another star. Non-adiabatic collision conditions may lead to large amplitude oscillations in the star. We show that for a solar-type star a resonant condition can be achieved by a fast moving stellar object with velocity in the range of 100 km/s to 1000 km/s, passing at a distance of a few multiples of the star radius. Although such collisions are rare, they are more frequent than head-on collisions, and their effects could be observed through a visible change of the star luminosity occurring within a few hours., Comment: 5 pages, 5 figures

According to the Hugenholtz-Van Hove theorem, the nuclear symmetry energy $S(\rho)$ and its slope $L(\rho)$ at arbitrary densities can be decomposed in terms of the density and momentum dependence of the single-nucleon potentials in isospin-asymmetric nuclear matter which are potentially accessible to experiment. We quantify the correlations between several well-known isovector observables and $L(\rho)$ to locate the density range in which each isovector observable is most sensitive to the density dependence of the $S(\rho)$. We then study the correlation coefficients between those isovector observables and all the components of the $L(\rho)$. The neutron skin thickness of $^{208}$Pb is found to be strongly correlated with the $L(\rho)$ at a subsaturation density of $\rho = 0.59 \rho_0$ through the density dependence of the first-order symmetry potential. Neutron star radii are found to be strongly correlated with the $L(\rho)$ over a wide range of supra-saturation densities mainly through both the density and momentum dependence of the first-order symmetry potential. Finally, we find that although the crust-core transition pressure has a complex correlation with the $L(\rho)$, it is strongly correlated with the momentum derivative of the first-order symmetry potential, and the density dependence of the second-order symmetry potential., Comment: 6 pages, 7 figures

Gravitational wave (GW) astronomy opens up an entirely new window on the Universe to probe the equations of state (EOS) of neutron-rich matter. With the advent of next generation GW detectors, measuring the gravitational radiation from coalescing binary neutron star systems, mountains on rotating neutron stars, and stellar oscillation modes may become possible in the near future. Using a set of model EOSs satisfying the latest constraints from terrestrial nuclear experiments, state of the art nuclear many-body calculations of the pure neutron matter EOS, and astrophysical observations consistently, we study various GW signatures of the high-density behavior of the nuclear symmetry energy, which is considered among the most uncertain properties of dense neutron-rich nucleonic matter. In particular, we find the tidal polarizability of neutron stars, potentially measurable in binary systems just prior to merger, is more sensitive to the high density component of the nuclear symmetry energy than the symmetry energy at nuclear saturation density. We also find that the upper limit on the GW strain amplitude from elliptically deformed stars is very sensitive to the density dependence of the symmetry energy. This suggests that future developments in modeling of the neutron star crust, and direct gravitational wave signals from accreting binaries will provide a wealth of information on the EOS of neutron-rich matter. We also review the sensitivity of the $r$-mode instability window to the density dependence of the symmetry energy. Whereas models with larger values of the density slope of the symmetry energy at saturation seem to be disfavored by the current observational data, within a simple $r$-mode model, we point out that a subsequent softer behavior of the symmetry energy at high densities (hinted at by recent observational interpretations) could rule them in., Comment: 14 pages, 11 figures, 3 tables; submitted to EPJA Special Volume on Nuclear Symmetry Energy

In order to assess the ability of purely crust-driven glitch models to match the observed glitch activity in the Vela pulsar, we conduct a systematic analysis of the dependence of the fractional moment of inertia of the inner crustal neutrons on the stiffness of the nuclear symmetry energy at saturation density $L$. We take into account both crustal entrainment and the fact that only a fraction $Y_{\rm g}$ of the core neutrons may couple to the crust on the glitch-rise timescale. We use a set of consistently-generated crust and core compositions and equations-of-state which are fit to results of low-density pure neutron matter calculations. When entrainment is included at the level suggested by recent microscopic calculations and the core is fully coupled to the crust, the model is only able to account for the Vela glitch activity for a 1.4$M_{\odot}$ star if the equation of state is particularly stiff $L>100$ MeV. However, an uncertainty of about 10\% in the crust-core transition density and pressure allows for the Vela glitch activity to be marginally accounted for in the range $L\approx30-60$MeV consistent with a range of experimental results. Alternatively, only a small amount of core neutrons need be involved. If less than 50\% of the core neutrons are coupled to the crust during the glitch, we can also account for the Vela glitch activity using crustal neutrons alone for EOSs consistent with the inferred range of $L$. We also explore the possibility of Vela being a high-mass neutron star, and of crustal entrainment being reduced or enhanced relative to its currently predicted values., Comment: 10 pages, 6 figures

The modeling of many neutron star observables incorporates the microphysics of both the stellar crust and core, which is tied intimately to the properties of the nuclear matter equation of state (EoS). We explore the predictions of such models over the range of experimentally constrained nuclear matter parameters, focusing on the slope of the symmetry energy at nuclear saturation density $L$. We use a consistent model of the composition and EoS of neutron star crust and core matter to model the binding energy of pulsar B of the double pulsar system J0737-3039, the frequencies of torsional oscillations of the neutron star crust and the instability region for r-modes in the neutron star core damped by electron-electron viscosity at the crust-core interface. By confronting these models with observations, we illustrate the potential of astrophysical observables to offer constraints on poorly known nuclear matter parameters complementary to terrestrial experiments, and demonstrate that our models consistently predict $L<70$ MeV., Comment: 11 pages, 5 figures, talk given at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS)

Using a set of model equations of state satisfying the latest constraints from both terrestrial nuclear experiments and astrophysical observations as well as state-of-the-art nuclear many-body calculations of the pure neutron matter equation of state, the tidal polarizability of canonical neutron stars in coalescing binaries is found to be a very sensitive probe of the high-density behavior of nuclear symmetry energy which is among the most uncertain properties of dense neutron-rich nucleonic matter. Moreover, it changes less than $\pm 10%$ by varying various properties of symmetric nuclear matter and symmetry energy around the saturation density within their respective ranges of remaining uncertainty., Comment: 6 pages, 5 figures

In this review, we will discuss the results of our recent work to study the general optimization of the pure isovector parameters of the popular relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) nuclear energy-density functionals (EDFs), using constraints on the pure neutron matter (PNM) equation of state (EoS) from recent {\sl ab initio} calculations. By using RMF and SHF parameterizations that give equivalent predictions for ground-state properties of doubly magic nuclei and properties of symmetric nuclear matter (SNM) and PNM, we found that such optimization leads to broadly consistent symmetry energy $J$ and its slope parameter $L$ at saturation density within a tight range of $\sigma(J) < 2$ MeV and $\sigma(L) < 6$ MeV. We demonstrate that a clear model dependence shows up (a) in the curvature parameter of the symmetry energy $K_{\rm sym}$, (b) the symmetry energy at supra-saturation densities, and (c) the radius of neutron stars., Comment: Talk given at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS)

We study the nuclear symmetry energy S(rho) and related quantities of nuclear physics and nuclear astrophysics predicted generically by relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simple prescription for preparing equivalent RMF and SHF parametrizations starting from a minimal set of empirical constraints on symmetric nuclear matter, nuclear binding energy and charge radii, enforcing equivalence of their Lorenz effective masses, and then using the pure neutron matter (PNM) equation of state (EoS) obtained from ab-initio calculations to optimize the pure isovector parameters in the RMF and SHF models. We find the resulting RMF and SHF parametrizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of <~2 MeV and <~6 MeV respectively, but that clear model dependence shows up in the predictions of higher-order symmetry energy parameters, leading to important differences in (a) the slope of the correlation between J and L from the confidence ellipse, (b) the isospin-dependent part of the incompressibility of nuclear matter K_tau, (c) the symmetry energy at supra-saturation densities, and (d) the predicted neutron star radii. The model dependence can lead to about 1-2 km difference in predictions of the neutron star radius given identical predicted values of J, L and symmetric nuclear matter (SNM) saturation properties. Allowing the full freedom in the effective masses in both models leads to constraints of 30<~J<~31.5 MeV, 35<~L<~60 MeV, -330<~K_tau<~-216 MeV for the RMF model as a whole and 30<~J<~33 MeV, 28<~L<~65 MeV, -420<~K_tau<~-325 MeV for the SHF model as a whole. Notably, given PNM constraints, these results place RMF and SHF models as a whole at odds with some constraints on K_tau inferred from giant monopole resonance and neutron skin experimental results., Comment: 15 pages, 7 figures, 4 tables

Using a simple model of a neutron star with a perfectly rigid crust constructed and a set of crust and core equations of state that span the range of nuclear experimental uncertainty in the density dependence of the symmetry energy from 25 MeV (soft EOS) to 115 MeV (stiff EOS), we calculate the instability window for the onset of the Chandrasekhar-Friedmann-Schutz (CFS) instability in r-mode oscillations for canonical neutron stars (1.4 M_{\odot}) and massive neutron stars (2.0 M_{\odot}). In these models the crust-core transition density, and thus crustal thickness, is calculated consistently with the core equation of state (EOS). For the canonical neutron star, the lower bound of the r-mode instability window is reduced in frequency by \approx150 Hz from the softest to the stiffest symmetry energy used, independent of mass and temperature. The instability window also drops by \approx 100 Hz independent of EOS when the mass is raised from 1.4 M_{\odot} to 2.0 M_{\odot}. Where temperature estimates are available, the observed neutron stars in low mass X-ray binaries (LMXBs) have frequencies below the instability window for the 1.4 M_{\odot} models, while some LMXBs fall within the instability window for 2.0 M_{\odot} stars if the symmetry energy is relatively stiff, indicating that a softer symmetry energy is more consistent with observations within this model. Thus we conclude that smaller values of L help stabilize neutron stars against runaway r-mode oscillations. The critical temperature, below which no star can reach the instability window without exceeding its Kepler frequency, varies by nearly an order of magnitude from soft to stiff symmetry energies. When the crust thickness and core EOS are treated consistently, a thicker crust corresponds to a lower critical temperature, the opposite result to previous studies in which the transition density was independent of the core EOS., Comment: 10 pages, 6 figures, accepted for publication in Physical Review C

We present a systematic survey the range of predictions of the neutron star inner crust composition, crust-core transition densities and pressures, and density range of the nuclear `pasta' phases at the bottom of the crust provided by the compressible liquid drop model in the light of current experimental and theoretical constraints on model parameters. Using a Skyrme-like model for nuclear matter, we construct baseline sequences of crust models by consistently varying the density dependence of the bulk symmetry energy at nuclear saturation density, $L$, under two conditions: (i) that the magnitude of the symmetry energy at saturation density $J$ is held constant, and (ii) $J$ correlates with $L$ under the constraint that the pure neutron matter (PNM) EoS satisfies the results of ab-initio calculations at low densities. Such baseline crust models facilitate consistent exploration of the $L$ dependence of crustal properties. The remaining surface energy and symmetric nuclear matter parameters are systematically varied around the baseline, and different functional forms of the PNM EoS at sub-saturation densities implemented, to estimate theoretical `error bars' for the baseline predictions. Inner crust composition and transition densities are shown to be most sensitive to the surface energy at very low proton fractions and to the behavior of the sub-saturation PNM EoS. Recent calculations of the energies of neutron drops suggest that the low-proton-fraction surface energy might be higher than predicted in Skyrme-like models, which our study suggests may result in a greatly reduced volume of pasta in the crust than conventionally predicted., Comment: 37 Pages, 16 figures, accepted for publication in Astrophysical Journal Supplement Series

The effects of the existence of exotic nuclear shapes at the bottom of the neutron star inner crust - nuclear `pasta' - on observational phenomena are estimated by comparing the limiting cases that those phases have a vanishing shear modulus and that they have the shear modulus of a crystalline solid . We estimate the effect on torsional crustal vibrations and on the maximum quadrupole ellipticity sustainable by the crust. The crust composition and transition densities are calculated consistently with the global properties, using a liquid drop model with a bulk nuclear equation of state (EoS) which allows a systematic variation of the nuclear symmetry energy. The symmetry energy J and its density dependence L at nuclear saturation density are the dominant nuclear inputs which determine the thickness of the crust, the range of densities at which pasta might appear, as well as global properties such as the radius and moment of inertia. We show the importance of calculating the global neutron star properties on the same footing as the crust EoS, and demonstrate that in the range of experimentally acceptable values of L, the pasta phase can alter the crust frequencies by up to a factor of three, exceeding the effects of superfluidity on the crust modes, and decrease the maximum quadrupole ellipticity sustainable by the crust by up to an order of magnitude. The signature of the pasta phases and the density dependence of the symmetry energy on the potential observables highlights the possibility of constraining the EoS of dense, neutron-rich matter and the properties of the pasta phases using astrophysical observations., Comment: 8 pages, 7 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

We show that the gravitational binding energy of a neutron star of a given mass is correlated with the slope of the nuclear symmetry energy at 1-2 times nuclear saturation density for equations of state without significant softening (i.e., those that predict maximum masses $M_{\rm max} > 1.44M_{\odot}$ in line with the largest accurately measured neutron star mass). Applying recent laboratory constraints on the slope of the symmetry energy to this correlation we extract a constraint on the baryon mass of the lower mass member of the double pulsar binary system, PSR J0737-3039B. We compare with independent constraints derived from modeling the progenitor star of J0737-3039B up to and through its collapse under the assumption that it formed in an electron capture supernova. The two sets of constraints are consistent only if $L \lesssim$ 70 MeV., Comment: 18 pages, 4 figures

The first results of a new three-dimensional, finite temperature Skyrme-Hartree-Fock+BCS study of the properties of inhomogeneous nuclear matter at densities and temperatures leading to the transition to uniform nuclear matter are presented. A constraint is placed on the two independent components of the quadrupole moment in order to self-consistently explore the shape phase space of nuclear configurations. The scheme employed naturally allows effects such as (i) neutron drip, which results in an external neutron gas, (ii) the variety of exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii) the subsequent dissolution of these nuclei into nuclear matter. In this way, the equation of state can be calculated across phase transitions from lower densities (where one dimensional Hartree-Fock suffices) through to uniform nuclear matter without recourse to interpolation techniques between density regimes described by different physical models., Comment: 10 pages, 9 figures, Proceedings of the 5th FRIB Workshop on Bulk Nuclear Properties

A comprehensive microscopic study of the properties of bulk matter at densities just below nuclear saturation $\rho_s = 2.5 \sim 10^{14}$ g cm$^{-3}$, zero and finite temperature and high neutron fraction, is outlined, and preliminary results presented. Such matter is expected to exist in the inner crust of neutron stars and during the core collapse of massive stars with $M \gtrsim 8M_{\odot}, Comment: 4 pages, 2 figures. Participant Contribution at the ``Dense Matter in Heavy Ion Collisions and Astrophysics" Summer School, JINR, Dubna, Aug. 21 - Sept. 1, 2006. To be published in PEPAN letters

First results from a fully self-consistent, temperature-dependent equation of state that spans the whole density range of neutron stars and supernova cores are presented. The equation of state (EoS) is calculated using a mean-field Hartree-Fock method in three dimensions (3D). The nuclear interaction is represented by the phenomenological Skyrme model in this work, but the EoS can be obtained in our framework for any suitable form of the nucleon-nucleon effective interaction. The scheme we employ naturally allows effects such as (i) neutron drip, which results in an external neutron gas, (ii) the variety of exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii) the subsequent dissolution of these nuclei into nuclear matter. In this way, the equation of state is calculated across phase transitions without recourse to interpolation techniques between density regimes described by different physical models. EoS tables are calculated in the wide range of densities, temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000 processors simultaneously., Comment: 6 pages, 11 figures. Published in conference proceedings Journal of Physics: Conference Series 46 (2006) 408. Extended version to be submitted to Phys. Rev. C

The double pulsar J0737--3039 has become an important astrophysical laboratory for testing fundamental physics. Here we demonstrate that the low measured mass of Pulsar B can be used to constrain the equation of state of neutron star matter {\em under the assumption} that it formed in an electron-capture supernova. We show that the observed orbital parameters as well as the likely evolutionary history of the system support such a hypothesis and discuss future refinements that will improve the constraints this test may provide., Comment: 8 pages, 3 figures, to be published in MNRAS

A method of calculating giant resonance strength functions using Time-Dependent Hartree-Fock techniques is described. An application to isoscalar giant monopole resonances in spherical nuclei is made, thus allowing a comparison between independent 1-, 2- and 3-Dimensional computer codes., Comment: Talk given at "10th Nuclear Physics Conference, Marie and Pierre Curie", Kazimierz Dolny, Poland, 24-28 Sept 2003