The nuclear symmetry energy plays a role in determining both the nuclear properties of terrestrial matter as well as the astrophysical properties of neutron stars. The first measurement of the neutron star tidal deformability, from gravitational wave
event GW170817, provides a new way of probing the symmetry energy. In this work, we report on new constraints on the symmetry energy from GW170817. We focus in particular on the low-order coefficients: namely, the value of the symmetry energy at the nuclear saturation density, S_0, and the slope of the symmetry energy, L_0. We find that the gravitational wave data are relatively insensitive to S_0, but that they depend strongly on L_0 and point to lower values of L_0 than have previously been reported, with a peak likelihood near L_0 ~ 20 MeV. Finally, we use the inferred posteriors on L_0 to derive new analytic constraints on higher-order nuclear terms.
The first detection of gravitational waves from a neutron star-neutron star merger, GW170817, has opened up a new avenue for constraining the ultradense-matter equation of state (EOS). The deviation of the observed waveform from a point-particle wave
form is a sensitive probe of the EOS controlling the merging neutron stars structure. In this topical review, I discuss the various constraints that have been made on the EOS in the year following the discovery of GW170817. In particular, I review the surprising relationship that has emerged between the effective tidal deformability of the binary system and the neutron star radius. I also report new results that make use of this relationship, finding that the radius inferred from GW170817 lies between 9.8 and 13.2 km at 90% confidence, with distinct likelihood peaks at 10.8 and 12.3 km. I compare these radii, as well as those inferred in the literature, to X-ray measurements of the neutron star radius. I also summarize the various maximum mass constraints, which point towards a maximum mass < 2.3 M_sun, depending on the fate of the remnant, and which can be used to additionally constrain the high-density EOS. I review the constraints on the EOS that have been performed directly, through Bayesian inference schemes. Finally, I comment on the importance of disentangling thermal effects in future EOS constraints from neutron star mergers.
Observations of isolated neutron stars place constraints on the equation of state (EOS) of cold, neutron-rich matter, while nuclear physics experiments probe the EOS of hot, symmetric matter. Many dynamical phenomena, such as core-collapse supernovae
, the formation and cooling of proto-neutron stars, and neutron star mergers, lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions. In this paper, we introduce a new framework to accurately calculate the thermal pressure of neutron-proton-electron matter at arbitrary density, temperature, and proton fraction. This framework can be expressed using a set of five physically-motivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure. We base two of these parameters on a new approximation of the Dirac effective mass, with which we reproduce the thermal pressure to within <~30% for a variety of realistic EOS at densities of interest. Three additional parameters, based on the behavior of the symmetry energy near the nuclear saturation density, allow for the extrapolation of any cold EOS in beta-equilibrium to arbitrary proton fractions. Our model thus allows a user to extend any cold nucleonic EOS, including piecewise-polytropes, to arbitrary temperature and proton fraction, for use in calculations and numerical simulations of astrophysical phenomena. We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of <~20% and offers a 1-3 orders-of-magnitude improvement over existing ideal-fluid models.
The mass distribution of compact objects provides a fossil record that can be studied to uncover information on the late stages of massive star evolution, the supernova explosion mechanism, and the dense matter equation of state. Observations of neut
ron star masses indicate a bimodal Gaussian distribution, while the observed black hole mass distribution decays exponentially for stellar-mass black holes. We use these observed distributions to directly confront the predictions of stellar evolution models and the neutrino-driven supernova simulations of Sukhbold et al. (2016). We find excellent agreement between the black hole and low-mass neutron star distributions created by these simulations and the observations. We show that a large fraction of the stellar envelope must be ejected, either during the formation of stellar-mass black holes or prior to the implosion through tidal stripping due to a binary companion, in order to reproduce the observed black hole mass distribution. We also determine the origins of the bimodal peaks of the neutron star mass distribution, finding that the low-mass peak (centered at ~1.4 M_sun) originates from progenitors with M_zams ~ 9-18 M_sun. The simulations fail to reproduce the observed peak of high-mass neutron stars (centered at ~1.8 M_sun) and we explore several possible explanations. We argue that the close agreement between the observed and predicted black hole and low-mass neutron star mass distributions provides new promising evidence that these stellar evolution and explosion models are accurately capturing the relevant stellar, nuclear, and explosion physics involved in the formation of compact objects.
One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. We present here a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample
of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parametrized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, rho_sat, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ~30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, towards larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.
The increasing number and precision of measurements of neutron star masses, radii, and, in the near future, moments of inertia offer the possibility of precisely determining the neutron star equation of state. One way to facilitate the mapping of obs
ervables to the equation of state is through a parametrization of the latter. We present here a generic method for optimizing the parametrization of any physically allowed EoS. We use mock equations of state that incorporate physically diverse and extreme behavior to test how well our parametrization reproduces the global properties of the stars, by minimizing the errors in the observables mass, radius, and the moment of inertia. We find that using piecewise polytropes and sampling the EoS with five fiducial densities between ~1-8 times the nuclear saturation density results in optimal errors for the smallest number of parameters. Specifically, it recreates the radii of the assumed EoS to within less than 0.5 km for the extreme mock equations of state and to within less than 0.12 km for 95% of a sample of 42 proposed, physically-motivated equations of state. Such a parametrization is also able to reproduce the maximum mass to within 0.04 M_sun and the moment of inertia of a 1.338 M_sun neutron star to within less than 10% for 95% of the proposed sample of equations of state.
A precise moment of inertia measurement for PSR J0737-3039A in the double pulsar system is expected within the next five years. We present here a new method of mapping the anticipated measurement of the moment of inertia directly into the neutron sta
r structure. We determine the maximum and minimum values possible for the moment of inertia of a neutron star of a given radius based on physical stability arguments, assuming knowledge of the equation of state only at densities below the nuclear saturation density. If the equation of state is trusted up to the nuclear saturation density, we find that a measurement of the moment of inertia will place absolute bounds on the radius of PSR J0737-3039A to within $pm$1 km. The resulting combination of moment of inertia, mass, and radius measurements for a single source will allow for new, stringent constraints on the dense-matter equation of state.
