Dense Matter Equation Of State Research Articles

Mass-radius constraints for the neutron star EoS - Bayesian analysis

We suggest a new Bayesian analysis (BA) using disjunct M-R constraints for extracting probability measures for cold, dense matter equations of state (EoS). One of the key issues of such an analysis is the question of a deconfinement transition in compact stars and whether it proceeds as a crossover or rather as a first order transition. We show by postulating results of not yet existing radius measurements for the known pulsars with a mass of 2Mq that a radius gap of about 3 km would clearly select an EoS with a strong first order phase transition as the most probably one. This would support the existence of a critical endpoint in the QCD phase diagram under scrutiny in present and upcoming heavy-ion collision experiments.

Neutron Star Physics and EOS

Neutron stars are important because measurement of their masses and radii will determine the dense matter equation of state. They will constrain the nuclear matter symmetry energy, which controls the neutron star matter pressure and the interior composition, and will influence the interpretation of nuclear experiments. Astrophysical observations include pulsar timing, X-ray bursts, quiescent low-mass X-ray binaries, pulse profiles from millisecond pulsars, neutrino observations from gravitational collapse supernovae,and gravitational radiation from compact object mergers. These observations will also constrain the neutron star interior, including the properties of superfluidity there, and determine the existence of a possible QCD phase transition.

Compactness of Neutron Stars.

Recent progress in the determination of both masses and radii of neutron stars is starting to place stringent constraints on the dense matter equation of state. In particular, new theoretical developments together with improved statistical tools seem to favor stellar radii that are significantly smaller than those predicted by models using purely nucleonic equations of state. Given that the underlying equation of state must also account for the observation of 2M⊙ neutron stars, theoretical approaches to the study of the dense matter equation of state are facing serious challenges. In response to this challenge, we compute the underlying equation of state associated with an assumed mass-radius template similar to the "common radius" assumption used in recent studies. Once such a mass-radius template is adopted, the equation of state follows directly from the implementation of Lindblom's algorithm; assumptions on the nature or composition of the dense stellar core are not required. By analyzing mass-radius profiles with a maximum mass consistent with observation and common radii in the 8-11 km range, a lower limit on the stellar radius of a 1.4M⊙ neutron star of RNS≳10.7 km is required to prevent the equation of state from violating causality.

Mass and radius constraints for compact stars and the QCD phase diagram

We suggest a new Bayesian analysis using disjunct M-R constraints for extracting probability measures for cold, dense matter equations of state. One of the key issues of such an analysis is the question of a deconfinement transition in compact stars and whether it proceeds as a crossover or rather as a first order transition. The latter question is relevant for the possible existence of a critical endpoint in the QCD phase diagram under scrutiny in present and upcoming heavy-ion collision experiments.

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.

Constraints on physics of neutron stars from X-ray observations

I summarize some constraints on the physics of neutron stars arising from X-ray observations of the surfaces of neutron stars, focusing on using models of low-magnetic-field neutron star atmospheres to interpret their X-ray spectra. I discuss observations of spectral lines, pulsation profiles, X-ray bursts, radius measurements of transiently accreting neutron stars in quiescence, crust and core cooling measurements of transiently accreting neutron stars, and cooling of young neutron stars. These observations have constrained the neutron star mass and radius (and thus the internal composition, and dense matter equation of state), the superfluidity and neutrino emissivity properties of the core, and the composition and superfluid state of the crust.

Does a hadron-quark phase transition in dense matter preclude the existence of massive neutron stars?

AbstractWe study the impact of a hadron-quark phase transition on the maximum neutron-star mass. The hadronic part of the equation of state relies on the most up-to-date Skyrme nuclear energy density functionals, fitted to essentially all experimental nuclear mass data and constrained to reproduce the properties of infinite nuclear matter as obtained from microscopic calculations using realistic forces. We show that the softening of the dense matter equation of state due to the phase transition is not necessarily incompatible with the existence of massive neutron stars like PSR J1614–2230.

The role of binding energies of neutron stars on the accretion-driven evolution

Abstract Millisecond pulsars are believed to descend from low-mass X-ray binaries. Observable parameters of binary millisecond pulsars, e.g. mass of the pulsar, mass of the companion, spin period of the pulsar, orbital period, orbital eccentricity, etc., are used to probe the past accretion history of the millisecond pulsars. However, unfortunately in these studies the binding energy of the neutron star is not commonly considered. We show that the effect of the binding energy is significant in the estimation of the amount of mass accretion, and thus should be incorporated in models for binary evolutions. Moreover, different equations of state for dense matter give different values for the accreted mass for the same amount of increase in the gravitational mass of the neutron star, implying the need of constraining dense matter equations of state even to understand the spin-up procedure properly.

Neutron stars and the dense matter equation of state

Neutron stars provide a unique laboratory with which to study cold, dense matter. The observational quantities of primary astrophysics interest are the maximum mass and the typical radius of a neutron star. These quantities are related to the relative stiffness of neutron-rich matter at supernuclear densities and the density dependence of the nuclear symmetry energy near the nuclear saturation density. The measurements of these nuclear properties via nuclear systematics and structure, heavy-ion collisions and parity-violating electron scattering from neutron-rich nuclei, are discussed. Several new observations, including mass measurements of binary pulsars and a confirmed distance determination for a nearby cooling neutron star, will be summarized. Additionally addressed will be observations of thermal emissions from cooling neutron stars in globular clusters and thermonuclear explosions from accreting stars. It will be demonstrated how this astrophysical data is shedding light on the pressure-density relation of extremely dense matter.

THE EQUATION OF STATE FROM OBSERVED MASSES AND RADII OF NEUTRON STARS

We determine an empirical dense matter equation of state (EOS) from a heterogeneous data set of six neutron stars: three Type-I X-ray bursters with photospheric radius expansion, studied by Özel 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 EOS 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 EOS near the saturation density are soft, resulting in relatively small neutron star radii around 11–12 km for M = 1.4 M☉. The predicted EOS 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 M☉. Our results imply that several commonly used equations of state are inconsistent with observations.

How strange are compact star interiors?

We discuss a Nambu–Jona–Lasinio (NJL)-type quantum field theoretical approach to the quark matter equation of state with color superconductivity and construct hybrid star models on this basis. It has recently been demonstrated that with increasing baryon density, the different quark flavors may occur sequentially, starting with down-quarks only, before the second light quark flavor and at highest densities the strange quark flavor also appears. We find that color superconducting phases are favorable over non-superconducting ones, which entails consequences for thermodynamic and transport properties of hybrid star matter. In particular, for NJL-type models no strange quark matter phases can occur in compact star interiors due to mechanical instability against gravitational collapse, unless a sufficiently strong flavor mixing as provided by the Kobayashi–Maskawa–'t Hooft determinant interaction is present in the model. We discuss observational data on mass–radius relationships of compact stars which can put constraints on the properties of the dense matter equation of state.

Neutron star equation of state

New observations of neutron stars from sources such as radio pulsars, X-ray binaries, quasi-periodic oscillators, X-ray bursters and thermally-emitting isolated neutron stars, can ultimately constrain the dense matter equation of state. Observable quantities include neutron star masses, radii, rotation rates, radiation radii, redshifts, moments of inertia, temperatures and ages. Several ways in which these quantities can lead to theoretical limits are discussed.

Members of the double pulsar system PSR J0737-3039: Neutron stars or strange stars?

One interesting method of constraining the dense matter Equations of State is to measure the advancement of the periastron of the orbit of a binary radio pulsar (when it belongs to a double neutron star system). There is a great deal of interest on applicability of this procedure to the double pulsar system PSR J0737-3039 (A/B). Although the above method can be applied to PSR A in future within some limitations, for PSR B this method cannot be applied. On the other hand, the study of genesis of PSR B might be useful in this connection and its low mass might be an indication that it could be a strange star.

Attributes of a rotating neutron star with a hyperon core

We study the effect of rotation on the global properties of a neutron star with a hyperon core in an effective chiral model with varying nucleon effective masses within a mean-field approach. The resulting gross properties of the rotating compact star sequences are then compared and analyzed with other theoretical predictions and observations from neutron stars. The maximum mass of the compact star predicted by the model lies in the range of $(1.4\text{\ensuremath{-}}2.4){M}_{\ensuremath{\bigodot}}$ at Kepler frequency ${\ensuremath{\Omega}}_{K}$, which is consistent with recent observations of high mass stars, thereby reflecting the sensitivity of the underlying nucleon effective mass in the dense matter equation of state. We also discuss the implications of the experimental constraints from the flow data from heavy-ion collisions on the global properties of rotating neutron stars.

The equation of state of dense matter: from nuclear collisions to neutron stars

The equation of state (EoS) of dense matter represents a central issue in the study of compact astrophysical objects and heavy ion reactions at intermediate and relativistic energies. We have derived a nuclear EoS with nucleons and hyperons within the Brueckner–Hartree–Fock approach, and joined it with quark matter EoS. For that, we have employed the MIT bag model, as well as the Nambu–Jona-Lasinio and the color dielectric models, and found that the NS maximum masses are not larger than 1.7 solar masses. A comparison with available data supports the idea that dense matter EoS should be soft at low density and quite stiff at high density.

Constraints on the dense matter equation of state from the measurements of PSR J0737-3039A moment of inertia and PSR J0751+1807 mass

The moment of inertia of the pulsar A in the neutron star binary J0737-3039 will soon be measurable through detailed measurements of the periastron advance. We present the calculation of the moment of inertia of neutron stars with the masses of the components of the binary J0737-3039 for a broad range of equations of state of dense matter and discuss the implications of such measurement for constraining the equation of state. An observational determination of the moment of inertia of the pulsar A in J0737-3039 with the accuracy of 10% shall narrow down considerably the range of viable equations of state. We also show that limits on maximal mass of a neutron star provide a complementary set of constraints on the properties of dense nuclear matter.

Discovery of the Neutron Star Spin Frequency in EXO 0748-676

We report the results of a search for burst oscillations during thermonuclear X-ray bursts from the low mass X-ray binary (LMXB) EXO 0748-676. With the proportional counter array (PCA) onboard the Rossi X-ray Timing Explorer (RXTE) we have detected a 45 Hz oscillation in the average power spectrum of 38 thermonuclear X-ray bursts from this source. We computed power spectra with 1 Hz frequency resolution for both the rising and decaying portions of 38 X-ray bursts from the public RXTE archive. We averaged the 1 Hz power spectra and detected a significant signal at 45 Hz in the decaying phases of the bursts. The signal is detected at a significance level of 4 x 10 (exp -8) similar signal was detected in the rising intervals. The oscillation peak is unresolved at 1 Hz frequency resolution, indicating an oscillation quality factor, Q = nu (sub 0)/Delta nu (sub fwhm) greater than 45, and the average signal amplitude is approximately equal to 3% (rms) The detection of 45 Hz burst oscillations from EXO 0748-676 provides compelling evidence that this is the neutron star spin frequency in this system. We use the inferred spin frequency to model the widths of absorption lines from the neutron star surface and show that the widths of the absorption lines from EXO 0748-676 recently reported by Cottam et al. are consistent with a 45 Hz spin frequency as long as the neutron star radius is in the range from about 9.5 - 15 km. With a known spin frequency, precise modelling of the line profiles from EXO 0748-676 holds great promise for constraining the dense matter equation of state.

Equation of state of dense matter and maximum mass of neutron stars

Theoretical models of the equation of state (EOS) of neutron-star matter (starting with the crust and ending at the densest region of the stellar core) are reviewed. Apart from a broad set of baryonic EOSs, strange quark matter, and even more exotic (abnormal and Q-matter) EOSs are considered. Results of calculations of M_max for non-rotating neutron stars and exotic compact stars are reviewed, with particular emphasis on the dependence on the dense-matter EOS. Rapid rotation increases M_max, and this effect is studied for both neutron stars and exotic stars. Theoretical results are then confronted with measurements of masses of neutron stars in binaries, and the consequences of such a confrontation and their possible impact on the theory of dense matter are discussed.

Evolution of Proto–Neutron Stars

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

Effect of Pion Condensation on Keplerian Angular Frequency of Rotating Neutron Stars

How fast can neutron star rotate? This problem is of growing interest, stimulated by the observation of millisecond pulsars, PSR 1937 + 214 (with the period P= 1.558 msY) and PSR 1957 + 20 (P= 1.607 ms),2) and in particular by the recent report finding a submillisecond pulsar in SN 1987 A (P=0.508 ms).3) Although the latter turned out to be erroneous,4) it motivated intensive studies5)-13) on the interplay between the maximum rotation rate and the properties of the equation of state (EOS) for dense matter. Keplerian angular frequency Sk of a rotating neutron star, at which mass shedding begins at the equator, places an upper limit on the rotation rate. Of interest is that it depends importantly on the EOS; for the same mass star, softer EOS generally leads to larger Sk. The softness, however, is limited by the requirement that the maximum mass should exceed 1.44 Me, the observed mass of PSR 19IJ+ 1614); Mmax <1.44Me (maximum mass condition). In addition, the speed of sound Vs, which increases with the density p and becomes maximum at the center of the maximummass neutron star, should not exceed the speed of light c; vs:S c (causality condition).· In connection with the softer EOS, it is of special interest to take account of the effect of pion condensation since it plays a dramatic role in softening the dense matter EOS. The aim of this paper is to study to what extent the Sk is affected by the inclusion of pion condensation. So far only one case has been touched for the pion-condensed EOS.7),ll) Here we make more thorough investigation by considering various EOS's with pion condensation.