Stiff Equation Of State Research Articles

Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity

A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong shock waves. In this paper we apply this scheme in full general relativity (involving {\it dynamical} spacetimes), and assess its suitability by performing test simulations for oscillations of rapidly rotating neutron stars and merger of binary neutron stars. It is demonstrated that this HRC scheme can yield results as accurate as those by the so-called high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers. Furthermore, the adopted HRC scheme has increased computational efficiency as it avoids the costly solution of Riemann problems and has practical advantages in the modeling of neutron star spacetimes. Namely, it allows simulations with stiff equations of state by successfully dealing with very low-density unphysical atmospheres. These facts not only suggest that such a HRC scheme may be a desirable tool for hydrodynamical simulations in general relativity, but also open the possibility to perform accurate magnetohydrodynamical simulations in curved dynamic spacetimes.

Momentum-dependent mean field in π0 production in Nb + Nb collisions

The Boltzmann-Nordheim-Vlasov (BNV) equation has been solved by using a microscopic momentum-dependent (MD) nuclear mean field. This potential has been calculated in the framework of the self-consistent Brueckner theory up to the second order in the G-matrix. Comparison with the so-called soft and stiff Equation of State (EOS) is presented, using the Skyrme force. Calculations have been performed for the 93Nb + 93Nb reaction at Elab = 100, 250, 400A MeV. Our results show that the subthreshold π0 production cross-section is very sensitive to the momentum-dependent mean field, resulting, at the lowest energy, in a total cross-section a factor of 7 larger than that obtained with a local potential. The effect decreases as the bombarding energy increases.

Growth of primordial black holes in a universe containing a massless scalar field

The evolution of primordial black holes in a flat Friedmann universe with a massless scalar field is investigated in fully general relativistic numerical relativity. A primordial black hole is expected to form with a scale comparable to the cosmological apparent horizon, in which case it may go through an initial phase with significant accretion. However, if it is very close to the cosmological apparent horizon size, the accretion is suppressed due to general relativistic effects. In any case, it soon gets smaller than the cosmological horizon and thereafter it can be approximated as an isolated vacuum solution with decaying mass accretion. In this situation the dynamical and inhomogeneous scalar field is typically equivalent to a perfect fluid with a stiff equation of state $p=\ensuremath{\rho}$. The black hole mass never increases by more than a factor of 2, despite recent claims that primordial black holes might grow substantially through accreting quintessence. It is found that the gravitational memory scenario, proposed for primordial black holes in Brans-Dicke and scalar-tensor theories of gravity, is highly unphysical.

An upper bound on the energy of a gravitationally redshifted electron-positron annihilation line from the Crab pulsar

We present a causally consistent and pulsationally stable two component neutron star model on the basis of the criterion that for each assigned of σ(≡(P0/E0) ≡ the ratio of pressure to energy-density), the compactness ratio u(≡(M/R), where M is the total mass and R is the radius of the configuration) of the static configuration does not exceed the compactness ratio, uh, of the homogeneous density sphere (that is, u ≤ uh). The core of this model is given by the stiffest equation of state (EOS), dP/dE = 1 (in geometrized units) and the envelope is characterized by the well-known EOS of a classical polytrope d ln P/ dl nρ =Γ 1((4/3) ≤ Γ1 ≤ 2). The models yield an upper bound on surface redshift, zR � 0.77, of neutron stars corresponding to the case of Γ1 = 5/3 envelope, whereas a model-independent upper bound on neutron star masses, Mmax ≤ 4.1 M� , is obtained for a conservative choice of the Eb = 2.7 × 10 14 gc m −3 ,a t the core-envelope boundary. If the observational constraint of the glitch healing parameter, Q ≥ 0.7, of the Crab pulsar is imposed on these models, the strong lower bounds on surface redshift zR ≥ 0.2234 and mass M � 1.721 Mare obtained for the Crab pulsar. However, if the other observational constraint of the recently evaluated of the moment of inertia for the Crab pulsar (based upon the newly estimated value of the Crab nebula mass M(nebula) � 4.6 M� ) is also imposed on these models together with the observational constraint of the central weighted mean Q ≈ 0.72, the model with the Γ1 = 5/3 envelope itself yields the of matching density, Eb = 2.7 × 10 14 gc m −3 , adopted in this study and in this sense does not represent a fiduciary quantity. For these constraints, the minimum surface redshift and mass of the Crab pulsar are slightly increased to the values zR � 0.2350 and M � 1.807 Mrespectively. The confirmation of these results requires evidence of the observation of the gravitationally redshifted electron-positron annihilation line in the energy range of about 0.414-0.418 MeV from the Crab pulsar, which is in agreement with the energy of the gamma-ray line at about 0.40 MeV, observed in the mid 1970s.

Perturbations in a holographic universe and in other stiff fluid cosmologies

We examine the generation and evolution of perturbations in a universe dominated by a fluid with stiff equation of state $p=\rho$. The recently proposed Holographic Universe is an example of such a model. We compute the spectrum of scalar and tensor perturbations, without relying on a microphysical description of the $p=\rho$ fluid. The spectrum is scale invariant deep inside the Hubble horizon. In contrast, infrared perturbations that enter the Hubble horizon during the stiff fluid dominated (holographic) phase yield oscillatory and logarithmic terms in the power spectrum. We show that vector perturbations grow during the stiff fluid dominated epoch and may result in a turbulent and anisotropic Universe at the end of the holographic phase. Therefore, the required period of inflation following the holographic phase cannot be much shorter than that required in standard inflationary models.

Collapse of Uniformly Rotating Stars to Black Holes and the Formation of Disks

Simulations in general relativity show that the outcome of collapse of a marginally unstable, uniformly rotating star spinning at the mass-shedding limit depends critically on the equation of state. For a very stiff equation of state, which is likely to characterize a neutron star, essentially all of the mass and angular momentum of the progenitor are swallowed by the Kerr black hole formed during the collapse, leaving nearly no residual gas to form a disk. For a soft equation of state with an adiabatic index \Gamma - 4/3 << 1, which characterizes a very massive or supermassive star supported predominantly by thermal radiation pressure, as much as 10% of the mass of the progenitor avoids capture and goes into a disk about the central hole. We present a semi-analytic calculation that corroborates these numerical findings and shows how the final outcome of such a collapse may be determined from simple physical considerations. In particular, we employ a simple energy variational principle with an approximate, post-Newtonian energy functional to determine the structure of a uniformly rotating, polytropic star at the onset of collapse as a function of polytropic index n, where \Gamma = 1+1/n. We then use this data to calculate the mass and spin of the final black hole and ambient disk. We show that the fraction of the total mass that remains in the disk falls off sharply as 3-n (equivalently, \Gamma - 4/3) increases.

The puzzles of RX J1856.5-3754: neutron star or quark star?

We discuss recent Chandra and XMM-Newton observations of the bright isolated neutron star RX J1856.5-3754 and suggest that the absence of any line features is due to effects of a high magnetic field strength (~10^13 G). Using different models for the temperature distribution across the neutron star surface assuming blackbody emission to fit the optical and X-ray spectrum and we derive a conservative lower limit of the apparent neutron star radius of 16.5 km x (d/117 pc). This corresponds to the radius for the true (de-redshifted) radius of 14 km for a 1.4 Msun neutron star, indicating a stiff equation of state at high densities. A comparison of the result with mass-radius diagrams shows that quark stars and neutron stars with quark matter cores can be ruled out with high confidence.

Mass dependence of disappearance of transverse in-plane flow

A complete theoretical study is presented for the disappearance of flow, for the first time, by analyzing 15 reactions with masses between 47 and 476 units. We demonstrate that the effect of nucleon-nucleon cross-section reduces to insignificant level for heavier colliding nuclei in agreement with previous studies. A stiff equation of state with nucleon-nucleon cross-sections of 35-40 mb is able to explain all the measured balance energies within few percent. A power law is also given for the mass dependence of the disappearance of flow which is in excellent agreement with experimental data.

Accretion dynamics in neutron star-black hole binaries

We perform three-dimensional, Newtonian hydrodynamic simulations with a nuclear equation of state to investigate the accretion dynamics in neutron star black hole systems. We find as a general result that non-spinning donor stars yield larger circularization radii than corotating donors. Therefore, the matter from a neutron star without spin will more likely settle into an accretion disk outside the Schwarzschild radius. With the used stiff equation of state we find it hard to form an accretion disk that is promising to launch a gamma-ray burst. In all relevant cases the core of the neutron star survives and keeps orbiting the black hole as a mini neutron star for the rest of the simulation time (up to several hundred dynamical neutron star times scales). The existence of this mini neutron star leaves a clear imprint on the gravitational wave signal which thus can be used to probe the physics at supra-nuclear densities.

Reaction dynamics and multifragmentation in Fermi energy heavy ion reactions

The reaction systems, 64Zn + 58Ni, 64Zn + 92Mo, 64Zn + 197Au, at 26A, 35A and 47A MeV, have been studied both in experiments with a 4$\pi$ detector array, NIMROD, and with Antisymmetrized Molecular Dynamics model calculations employing effective interactions corresponding to soft and stiff equations of state (EOS). Direct experimental observables, such as multiplicity distributions, charge distributions, energy spectra and velocity spectra, have been compared in detail with those of the calculations and a reasonable agreement is obtained. The velocity distributions of $\alpha$ particles and fragments with Z >= 3 show distinct differences in calculations with the soft EOS and the stiff EOS. The velocity distributions of $\alpha$ particle and Intermediate Mass Fragments (IMF's) are best described by the stiff EOS. Neither of the above direct observables nor the strength of the elliptic flow are sensitive to changes in the in-medium nucleon-nucleon (NN) cross sections. A detailed analysis of the central collision events calculated with the stiff EOS revealed that multifragmentation with cold fragment emission is a common feature predicted for all reactions studied here. A possible multifragmentation scenario is presented; after the preequilibrium emission ceases in the composite system, cold light fragments are formed in a hotter gas of nucleons and stay cold until the composite system underdoes multifragmentation. For reaction with 197Au at 47A MeV a significant radial expansion takes place. For reactions with 58Ni and 92Mo at 47A MeV semi-transparency becomes prominent. The differing reaction dynamics drastically change the kinematic characteristics of emitted fragments. This scenario gives consistent explanations for many existing experimental results in the Fermi energy domain.

A charged spherically symmetric solution

We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.

Quasiequilibrium sequences of synchronously rotating binary neutron stars with constant rest masses in general relativity: Another approach without using the conformally flat condition

We compute quasiequilibrium sequences of synchronously rotating compact binary star systems with constant rest masses. This computation is carried out by using a numerical scheme which is different from the scheme based on the conformally flat assumption about the space. Stars are assumed to be polytropes with polytropic indices of $N=0.5,$ $N=1.0,$ and $N=1.5.$ Since we compute binary star sequences with a constant rest mass, they provide approximate evolutionary tracks of binary star systems. For relatively stiff equations of state $(N&lt;1.0),$ there appear turning points along the quasiequilibrium sequences plotted in the angular momentum---angular velocity plane. Consequently a secular instability against exciting internal motion sets in at those points. Qualitatively, these results agree with those of Baumgarte et al. who employed the conformally flat condition. We further discuss the effect of different equations of state and a different strength of gravity by introducing two kinds of dimensionless quantities which represent the angular momentum and the angular velocity. The strength of gravity is renormalized in these quantities so that the quantities are transformed to values around unity. Therefore we can clearly see relations among quasiequilibrium sequences for a wide variety of strength of gravity and for different compressibility.

A study of accretion discs around rapidly rotating neutron stars in general relativity and its applications to four low mass X–ray binaries

We calculate the accretion disc temperature profiles, disc luminosities and boundary layer luminosities for rapidly rotating neutron stars considering the full effect of general relativity. We compare the theoretical values of these quantities with their values inferred from EXOSAT data for four low mass X–ray binary sources: XB 1820-30, GX 17+2, GX 9+1 and GX 349+2 and constrain the values of several properties of these sources. According to our calculations, the neutron stars in GX 9+1 and GX 349+2 are rapidly rotating and stiffer equations of state are unfavoured.

Bounds on Compactness for Low‐Mass X‐Ray Binary Neutron Stars from X‐Ray Burst Oscillations

We have modeled X-ray burst oscillations observed with the Rossi X-Ray Timing Explorer from two low-mass X-ray binaries (LMXB): 4U 1636-53 with a frequency of 580 Hz and 4U 1728-34 at a frequency of 363 Hz. We have computed least-squares fits to the oscillations observed during the rising phase of bursts using a model that includes emission from either a single circular hot spot or a pair of circular antipodal hot spots on the surface of a neutron star. We model the spreading of the thermonuclear hot spots by assuming that the hot spot angular size grows linearly with time. We calculate the flux as a function of rotational phase from the hot spots and take into account photon deflection in the relativistic gravitational field of the neutron star, assuming the exterior spacetime is the Schwarzschild metric. We find acceptable fits with our model in a χ2 sense and use these to place constraints on the compactness of the neutron stars in these sources. For 4U 1636-53, in which detection of a 290 Hz subharmonic supports the two-spot model, we find that the compactness (i.e., mass/radius ratio) is constrained to be M/R < 0.163 at 90% confidence (G = c = 1). This requires a relatively stiff equation of state (EOS) for the stellar interior. For example, if the neutron star has a mass of 1.4 M☉, then its radius must be greater than 12.8 km. Fits using a single hot spot model are not as highly constraining. We discuss the implications of our findings for recent efforts to calculate the EOS of dense nucleon matter and the structure of neutron stars.

Radiating sources in higher-dimensional gravity

We study a time-dependent five-dimensional (5D) metric which contains a static four-dimensional (4D) sub-metric whose three-dimensional (3D) part is spherically symmetric. An expansion in the metric coefficient allow us to obtain close-to Schwarzschild approximation to a class of spherically symmetric solutions. Using Campbell’s embedding theorem and the induced-matter formalism we obtain two 4D solutions. One describes a source with the stiff equation of state believed to be applicable to dense astrophysical objects, and the other describes a spherical source with a radial heat flow.

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. II. Newtonian limits

We study equilibrium sequences of close binary systems composed of identical polytropic stars in Newtonian gravity. The solving method is a multidomain spectral method which we have recently developed. An improvement is introduced here for accurate computations of binary systems with a stiff equation of state $(\ensuremath{\gamma}&gt;2).$ The computations are performed for both cases of synchronized and irrotational binary systems with adiabatic indices $\ensuremath{\gamma}=3, 2.5, 2.25, 2,$ and $1.8.$ It is found that the turning points of total energy along a constant-mass sequence appear only for $\ensuremath{\gamma}&gt;~1.8$ for synchronized binary systems and $\ensuremath{\gamma}&gt;~2.3$ for irrotational ones. In the synchronized case, the equilibrium sequences terminate by the contact between the two stars. On the other hand, for irrotational binaries, it is found that the sequences terminate at a mass shedding limit which corresponds to a detached configuration.

NEUTRON STARS: RECENT DEVELOPMENTS

Recent developments in neutron star theory and observation are discussed. Based on modern nucleon-nucleon potentials more reliable equations of state for dense nuclear matter have been constructed. Furthermore, phase transitions such as pion, kaon and hyperon condensation, superfluidity and quark matter can occur in cores of neutron stars. Specifically, the nuclear to quark matter phase transition and its mixed phases with intriguing structures are treated. Rotating neutron stars with and without phase transitions are discussed and compared to observed masses, radii and glitches. The observations of possible heavy ~2M⊙ neutron stars in X-ray binaries and quasi-periodic oscillations require relatively stiff equations of state and restrict strong phase transitions to occur at very high nuclear densities only.

Stability and instability of a hot and dilute nuclear droplet

The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with the same growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragment-mass distributions (in particular the power-law behavior) are consistent with the instability properties of an expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of bulk and surface modes (spinodal decomposition).

Covariant vortex in superconducting-superfluid-normal fluid mixtures with a stiff equation of state

Using a covariant description, we obtain the integrals of motion for a cylindrically symmetric, stationary vortex configuration in a mixture of interacting superconductors, superfluids and normal fluids. We then integrate the stress-energy density and find a very simple, closed expression for the energy per unit length and the relevant stress coefficients of the vortex with respect to a vortex-free reference state. This result is found assuming a ``stiff'' equation of state for the fluid mixture, which is the least compressible but still causal equation of state (contrary to the incompressible case). As an illustration for these general results, we discuss some applications to ``real'' superfluid-superconducting systems that are contained as special cases. These include the two-fluid model for He-II, uncharged binary superfluid mixtures, conventional superconductors and the superfluid neutron-proton-electron plasma in the outer core of neutron stars.

Newtonian hydrodynamics of the coalescence of black holes with neutron stars — III. Irrotational binaries with a stiff equation of state

We present a numerical study of the hydrodynamics in the final stages of inspiral of a black hole-neutron star binary, when the binary separation becomes comparable to the stellar radius. We use a Newtonian three-dimensional Smooth Particle Hydrodynamics (SPH) code, and model the neutron star with a soft (adiabatic index Gamma=5/3) polytropic equation of state and the black hole as a Newtonian point mass which accretes matter via an absorbing boundary at the Schwarzschild radius. Our initial conditions correspond to tidally locked binaries in equilibrium, and we have explored configurations with different values of the mass ratio q=Mns/Mbh, ranging from q=1 to q=0.1. The dynamical evolution is followed for approximately 23 ms, and in every case studied here we find that the neutron star is tidally disrupted on a dynamical timescale, forming a dense torus around the black hole that contains a few tenths of a solar mass. A nearly baryon-free axis is present in the system throughout the coalescence, and only modest beaming of a fireball that could give rise to a gamma-ray burst would be sufficient to avoid excessive baryon contamination. We find that some mass (on the order of 0.01 to 0.001 solar masses) may be dynamically ejected from the system, and could thus contribute substantially to the amount of observed r-process material in the galaxy. We calculate the gravitational radiation waveforms and luminosity in the quadrupole approximation.