arXiv subjects

James M. Lattimer

Publications and source records attributed to James M. Lattimer.

At least 37 records · Page 2Linked to original sources

arXiv2018

Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817

We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars' dimensionless tidal deformabilities are determined by the binary's mass ratio $q$ by $Λ_1/Λ_2 = q^6$. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90$\%$ credible interval is $\tildeΛ=222^{+420}_{-138}$ for a uniform component mass prior, $\tildeΛ=245^{+453}_{-151}$ for a component mass prior informed by radio observations of Galactic double neutron stars, and $\tildeΛ=233^{+448}_{-144}$ for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of $8.9 \le \hat{R} \le 13.2$ km, with a mean value of $\langle \hat{R} \rangle = 10.8$ km. Our results are the first measurement of tidal deformability with a physical constraint on the star's equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.

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arXiv2018

Tidal Deformabilities and Neutron Star Mergers

Finite size effects in a neutron star merger are manifested, at leading order, through the tidal deformabilities (Lambdas) of the stars. If strong first-order phase transitions do not exist within neutron stars, both neutron stars are described by the same equation of state, and their Lambdas are highly correlated through their masses even if the equation of state is unknown. If, however, a strong phase transition exists between the central densities of the two stars, so that the more massive star has a phase transition and the least massive star does not, this correlation will be weakened. In all cases, a minimum Lambda for each neutron star mass is imposed by causality, and a less conservative limit is imposed by the unitary gas constraint, both of which we compute. In order to make the best use of gravitational wave data from mergers, it is important to include the correlations relating the Lambdas and the masses as well as lower limits to the Lambdas as a function of mass. Focusing on the case without strong phase transitions, and for mergers where the chirp mass M_chirp<1.4M_sun, which is the case for all observed double neutron star systems where a total mass has been accurately measured, we show that the dimensionless Lambdas satisfy Lambda_1/Lambda_2= q^6, where q=M_2/M_1 is the binary mass ratio; $M$ is mass of each star, respectively. Moreover, they are bounded by q^{n_-}>Lambda_1/Lambda_2> q^{n_{0+}+qn_{1+}}, where n_-<n_{0+}+qn_{1+}; the parameters depend only on M_chirp, which is accurately determined from the gravitational-wave signal. We also provide analytic expressions for the wider bounds that exist in the case of a strong phase transition. We argue that bounded ranges for Lambda_1/Lambda_2, tuned to M_chirp, together with lower bounds to Lambda(M), will be more useful in gravitational waveform modeling than other suggested approaches.

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arXiv2017

Symmetry Parameter Constraints From A Lower Bound On The Neutron-Matter Energy

We propose the existence of a lower bound on the energy of pure neutron matter (PNM) on the basis of unitary-gas considerations. We discuss its justification from experimental studies of cold atoms as well as from theoretical studies of neutron matter. We demonstrate that this bound results in limits to the density-dependent symmetry energy, which is the difference between the energies of symmetric nuclear matter and PNM. In particular, this bound leads to a lower limit to the volume symmetry energy parameter $S_0$. In addition, for assumed values of $S_0$ above this minimum, this bound implies both upper and lower limits to the symmetry energy slope parameter $L$, which describes the lowest-order density dependence of the symmetry energy. A lower bound on the neutron-matter incompressibility is also obtained. These bounds are found to be consistent with both recent calculations of the energies of PNM and constraints from nuclear experiments. Our results are significant because several equations of state that are currently used in astrophysical simulations of supernovae and neutron star mergers, as well as in nuclear physics simulations of heavy-ion collisions, have symmetry energy parameters that violate these bounds. Furthermore, below the nuclear saturation density, the bound on neutron-matter energies leads to a lower limit to the density-dependent symmetry energy, which leads to upper limits to the nuclear surface symmetry parameter and the neutron-star crust-core boundary. We also obtain a lower limit to the neutron-skin thicknesses of neutron-rich nuclei. Above the nuclear saturation density, the bound on neutron-matter energies also leads to an upper limit to the symmetry energy, with implications for neutron-star cooling via the direct Urca process.

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arXiv2015

The Equation of State of Hot, Dense Matter and Neutron Stars

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.

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arXiv2015

Degenerate limit thermodynamics beyond leading order for models of dense matter

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic mean-field theoretical models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects, but in the case of finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Numerical computations are performed to compare results from our analytical formulas with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid.

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arXiv2015

Thermal properties of hot and dense matter with finite range interactions

We explore the thermal properties of hot and dense matter using a model that reproduces the empirical properties of isospin symmetric and asymmetric bulk nuclear matter, optical model fits to nucleon-nucleus scattering data, heavy-ion flow data in the energy range 0.5-2 GeV/A, and the largest well-measured neutron star mass of 2 $\rm{M}_\odot$. Results of this model which incorporates finite range interactions through Yukawa type forces are contrasted with those of a zero-range Skyrme model that yields nearly identical zero-temperature properties at all densities for symmetric and asymmetric nucleonic matter and the maximum neutron star mass, but fails to account for heavy-ion flow data due to the lack of an appropriate momentum dependence in its mean field. Similarities and differences in the thermal state variables and the specific heats between the two models are highlighted. Checks of our exact numerical calculations are performed from formulas derived in the strongly degenerate and non-degenerate limits. Our studies of the thermal and adiabatic indices, and the speed of sound in hot and dense matter for conditions of relevance to core-collapse supernovae, the thermal evolution of neutron stars from their birth and mergers of compact binary stars reveal that substantial variations begin to occur at sub-saturation densities before asymptotic values are reached at supra-nuclear densities.

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arXiv2014

Stellar Superfluids

Neutron stars provide a fertile environment for exploring superfluidity under extreme conditions. It is not surprising that Cooper pairing occurs in dense matter since nucleon pairing is observed in nuclei as energy differences between even-even and odd-even nuclei. Since superfluids and superconductors in neutron stars profoundly affect neutrino emissivities and specific heats, their presence can be observed in the thermal evolution of neutron stars. An ever-growing number of cooling neutron stars, now amounting to 13 thermal sources, and several additional objects from which upper limits to temperatures can be ascertained, can now be used to discriminate among theoretical scenarios and even to dramatically restrict properties of nucleon pairing at high densities. In addition, observations of pulsars, including their spin-downs and glitch histories, additionally support the conjecture that superfluidity and superconductivity are ubiquitous within, and important to our understanding of, neutron stars.

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arXiv2014

Neutron Star Masses and Radii from Quiescent Low-Mass X-ray Binaries

We perform a systematic analysis of neutron star radius constraints from five quiescent low-mass X-ray binaries and examine how they depend on measurements of their distances and amounts of intervening absorbing material, as well as their assumed atmospheric compositions. We construct and calibrate to published results a semi-analytic model of the neutron star atmosphere which approximates these effects for the predicted masses and radii. Starting from mass and radius probability distributions established from hydrogen-atmosphere spectral fits of quiescent sources, we apply this model to compute alternate sets of probability distributions. We perform Bayesian analyses to estimate neutron star mass-radius curves and equation of state (EOS) parameters that best-fit each set of distributions, assuming the existence of a known low-density neutron star crustal EOS, a simple model for the high-density EOS, causality, and the observation that the neutron star maximum mass exceeds $2~M_\odot$. We compute the posterior probabilities for each set of distance measurements and assumptions about absorption and composition. We find that, within the context of our assumptions and our parameterized EOS models, some absorption models are disfavored. We find that neutron stars composed of hadrons are favored relative to those with exotic matter with strong phase transitions. In addition, models in which all five stars have hydrogen atmospheres are found to be weakly disfavored. Our most likely models predict neutron star radii that are consistent with current experimental results concerning the nature of the nucleon-nucleon interaction near the nuclear saturation density.

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arXiv2014

Constraints on the Symmetry Energy Using the Mass-Radius Relation of Neutron Stars

The nuclear symmetry energy is intimately connected with nuclear astrophysics. This contribution focuses on the estimation of the symmetry energy from experiment and how it is related to the structure of neutron stars. The most important connection is between the radii of neutron stars and the pressure of neutron star matter in the vicinity of the nuclear saturation density $n_s$. This pressure is essentially controlled by the nuclear symmetry energy parameters $S_v$ and $L$, the first two coefficients of a Taylor expansion of the symmetry energy around $n_s$. We discuss constraints on these parameters that can be found from nuclear experiments. We demonstrate that these constraints are largely model-independent by deriving them qualitatively from a simple nuclear model. We also summarize how recent theoretical studies of pure neutron matter can reinforce these constraints. To date, several different astrophysical measurements of neutron star radii have been attempted. Attention is focused on photospheric radius expansion bursts and on thermal emissions from quiescent low-mass X-ray binaries. While none of these observations can, at the present time, determine individual neutron star radii to better than 20% accuracy, the body of observations can be used with Bayesian techniques to effectively constrain them to higher precision. These techniques invert the structure equations and obtain estimates of the pressure-density relation of neutron star matter, not only near $n_s$, but up to the highest densities found in neutron star interiors. The estimates we derive for neutron star radii are in concordance with predictions from nuclear experiment and theory.

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arXiv2014

Thermal properties of supernova matter: The bulk homogeneous phase

We investigate the thermal properties of the potential model equation of state of Akmal, Pandharipande and Ravenhall. This equation of state approximates the microscopic model calculations of Akmal and Pandharipande, which feature a neutral pion condensate. We treat the bulk homogeneous phase for isospin asymmetries ranging from symmetric nuclear matter to pure neutron matter and for temperatures and densities relevant for simulations of core-collapse supernovae, proto-neutron stars, and neutron star mergers. Numerical results of the state variables are compared with those of a typical Skyrme energy density functional with similar properties at nuclear densities, but which differs substantially at supra-nuclear densities. Analytical formulas, which are applicable to non-relativistic potential models such as the equations of state we are considering, are derived for all state variables and their thermodynamic derivatives. A highlight of our work is its focus on thermal response functions in the degenerate and non-degenerate situations, which allow checks of the numerical calculations for arbitrary degeneracy. These functions are sensitive to the density dependent effective masses of neutrons and protons, which determine the thermal properties in all regimes of degeneracy. We develop the "thermal asymmetry free energy" and establish its relation to the more commonly used nuclear symmetry energy. We also explore the role of the pion condensate at supra-nuclear densities and temperatures. Tables of matter properties as functions of baryon density, composition (i.e., proton fraction) and temperature are being produced which are suitable for use in astrophysical simulations of supernovae and neutron stars.

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arXiv2013

Constraining the Symmetry Parameters of the Nuclear Interaction

One of the major uncertainties in the dense matter equation of state has been the nuclear symmetry energy. The density dependence of the symmetry energy is important in nuclear astrophysics, as it controls the neutronization of matter in core-collapse supernovae, the radii of neutron stars and the thicknesses of their crusts, the rate of cooling of neutron stars, and the properties of nuclei involved in r-process nucleosynthesis. We show that fits of nuclear masses to experimental masses, combined with other experimental information from neutron skins, heavy ion collisions, giant dipole resonances and dipole polarizabilities, lead to stringent constraints on parameters that describe the symmetry energy near the nuclear saturation density. These constraints are remarkably consistent with inferences from theoretical calculations of pure neutron matter, and, furthermore, with astrophysical observations of neutron stars. The concordance of experimental, theoretical and observational analyses suggests that the symmetry parameters S_v and L are in the range 29.0 - 32.7 MeV and 40.5 - 61.9 MeV, respectively, and that the neutron star radius, for a 1.4 M_sun star, is in the narrow window 10.7 km < R < 13.1 km (90% confidence). We can also set tight limits to the size of neutron star crusts and the fractional moment of inertia they contain, as well as the overall moment of inertia and quadrupole polarizability of 1.4 M_sun stars. Our results also have implications for the disk mass and ejected mass of compact mergers involving neutron stars.

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arXiv2013

The Nuclear Equation of State and Neutron Star Masses

Neutron stars are valuable laboratories for the study of dense matter. Recent observations have uncovered both massive and low-mass neutron stars and have also set constraints on neutron star radii. The largest mass measurements are powerfully influencing the high-density equation of state because of the existence of the neutron star maximum mass. The smallest mass measurements, and the distributions of masses, have implications for the progenitors and formation mechanisms of neutron stars. The ensemble of mass and radius observations can realistically restrict the properties of dense matter, and, in particular, the behavior of the nuclear symmetry energy near the nuclear saturation density. Simultaneously, various nuclear experiments are progressively restricting the ranges of parameters describing the symmetry properties of the nuclear equation of state. In addition, new theoretical studies of pure neutron matter are providing insights. These observational, experimental and theoretical constraints of dense matter, when combined, are now revealing a remarkable convergence.

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arXiv2012

The Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter

The equation of state (EOS) of dense matter has been a long-sought goal of nuclear physics. Equations of state generate unique mass versus radius (M-R) relations for neutron stars, the ultra-dense remnants of stellar evolution. In this work, we determine the neutron star mass-radius relation and, based on recent observations of both transiently accreting and bursting sources, we show that the radius of a 1.4 solar mass neutron star lies between 10.4 and 12.9 km, independent of assumptions about the composition of the core. We show, for the first time, that these constraints remain valid upon removal from our sample of the most extreme transient sources or of the entire set of bursting sources; our constraints also apply even if deconfined quark matter exists in the neutron star core. Our results significantly constrain the dense matter EOS and are, furthermore, consistent with constraints from both heavy-ion collisions and theoretical studies of neutron matter. We predict a relatively weak dependence of the symmetry energy on the density and a value for the neutron skin thickness of lead which is less than 0.20 fm, results that are testable in forthcoming experiments.

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arXiv2011

Superfluid Neutrons in the Core of the Neutron Star in Cassiopeia A

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. In order to explain the rapid cooling of this neutron star, we first present the fundamental properties 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 this neutron star's cooling is highlighted. This is the first direct evidence that superfluidity and superconductivity occur at supranuclear densities within neutron stars.

astro-ph.HE↗

arXiv2011

Rapid Cooling of the Neutron Star in Cassiopeia A Triggered by Neutron Superfluidity in Dense Matter

We propose that the observed cooling of the neutron star in Cassiopeia A is due to enhanced neutrino emission from the recent onset of the breaking and formation of neutron Cooper pairs in the 3P2 channel. We find that the critical temperature for this superfluid transition is ~0.5x10^9 K. The observed rapidity of the cooling implies that protons were already in a superconducting state with a larger critical temperature. Our prediction that this cooling will continue for several decades at the present rate can be tested by continuous monitoring of this neutron star.

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arXiv2010

What a Two Solar Mass Neutron Star Really Means

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.

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arXiv2010

The Equation of State from Observed Masses and Radii of Neutron Stars

We determine an empirical dense matter equation of state from a heterogeneous dataset of six neutron stars: three type I X-ray bursters with photospheric radius expansion, studied by Ozel et al., and three transient low-mass X-ray binaries. We critically assess the mass and radius determinations from the X-ray burst sources and show explicitly how systematic uncertainties, such as the photospheric radius at touchdown, affect the most probable masses and radii. We introduce a parameterized equation of state and use a Markov Chain Monte Carlo algorithm within a Bayesian framework to determine nuclear parameters such as the incompressibility and the density dependence of the bulk symmetry energy. Using this framework we show, for the first time, that these parameters, predicted solely on the basis of astrophysical observations, all lie in ranges expected from nuclear systematics and laboratory experiments. We find significant constraints on the mass-radius relation for neutron stars, and hence on the pressure-density relation of dense matter. The predicted symmetry energy and the equation of state near the saturation density are soft, resulting in relatively small neutron star radii around 11-12 km for M=1.4 Msun. The predicted equation of state stiffens at higher densities, however, and our preferred model for X-ray bursts suggests that the neutron star maximum mass is relatively large, 1.9-2.2 Msun. Our results imply that several commonly used equations of state are inconsistent with observations.

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arXiv2009

Neutrino Emission from Cooper Pairs and Minimal Cooling of Neutron Stars

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.

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