Piecewise Polytropic Equation Of State Research Articles

Scalarized hybrid neutron stars in scalar tensor gravity

Hybrid neutron stars, the compact objects consisting hadronic matter and strange quark matter, can be considered as the probes for the scalar tensor gravity. In this work, we explore the scalarization of hybrid neutron stars in the scalar tensor gravity. For the hadronic phase, we apply a piecewise polytropic equation of state constrained by the observational data of GW170817 and the data of six low-mass X-ray binaries with thermonuclear burst or the symmetry energy of the nuclear interaction. In addition, to describe the strange quark matter inside the hybrid neutron star, different MIT bag models are employed. We study the effects of the value of bag constant, the mass of s quark, the perturbative quantum chromodynamics correction parameter, and the density jump at the surface of quark-hadronic phase transition on the scalarization of hybrid neutron stars. Our results confirm that the scalarization is more sensitive to the value of bag constant, the mass of s quark, and the density jump compared to the perturbative quantum chromodynamics correction parameter.

Thermodynamically adaptive piecewise polytropic equation of state for neutron stars

Thermodynamically adaptive piecewise polytropic equation of state for neutron stars

Simulating the Collapse of Rotating Primordial Gas Clouds to Study the Possibility of the Survival of Population III Protostars

It has been argued that the low-mass primordial stars (m Pop III ≤ 0.8 M ⊙) are likely to enter the main sequence and hence may possibly be found in present-day galaxies. However, due to limitations in existing numerical capabilities, current three-dimensional (3D) simulations of disk fragmentation are only capable of following a few thousand years of evolution after the formation of the first protostar. In this work, we use a modified version of the Gadget-2 smoothed particle hydrodynamics code to present the results of the nonlinear collapse of the gas clouds associated with various degrees of initial solid body rotation (parameterized by β) using a piecewise polytropic equation of state. The 3D simulations are followed until the epoch that occurs when 50M ⊙ of mass has been accreted in protostellar objects, which is adequate enough to investigate the dynamics of the protostars with the surrounding gaseous medium and to determine the mass function, accretion rate, and possibility of the survival of these protostellar objects to the present epoch. We found that evolving protostars that stay within slow-rotating parent clouds can become massive enough to survive, due to accretion in the absence of radiative feedback, whereas 10%–12% of those formed within fast-rotating clouds (β ≥ 0.1) could possibly be ejected from the gravitational bound cluster as low-mass stars.

Constraining the Parameterized Neutron Star Equation of State with Astronomical Observations

Abstract We utilize the phenomenologically parameterized piecewise polytropic equations of state to study various neutron star properties. We investigate the compliance of these equations of state with several astronomical observations. We also demonstrate that the theoretical estimates of the fractional moment of inertia cannot explain all the pulsar glitches observed. We model the crust as a solid spheroidal shell to calculate the fractional moment of inertia of fast-spinning neutron stars. We also show that the braking index obtained in a simple magnetic dipole radiation model with a varying moment of inertia deviates significantly from the observed data. Future developments in both theory and observations may allow us to use the fractional moment of inertia and braking index as observational constraints for neutron star equation of state.

Neutron stars in scalar–tensor gravity with quartic order scalar potential

In this work we investigate the effects of a non-minimally coupled quartic order scalar model on static neutron stars, with the non-minimal coupling in the Jordan frame being of the form f(ϕ)=1+ξϕ2. Particularly we derive the Einstein frame Tolman–Oppenheimer–Volkoff equations, and by numerically integrating them for both the interior and the exterior of the neutron star, using a double shooting python 3 based numerical code, we extract the masses and radii of the neutron stars evaluated finally in the Jordan frame, along with several other related physical quantities of interest. With regard to the equation of state for the neutron star, we use a piecewise polytropic equation of state with the central part being Skyrme-Lyon (SLy), Akmal–Pandharipande–Ravenhall (APR) or the Wiringa–Fiks–Fabrocini (WFF1) equations of state. The resulting M–R graphs are compatible with the observational bounds imposed by the GW170817 event which require the radius of a static M∼1.6M⊙ neutron star to be larger than R=10.68−0.04+15km and the radius of a static neutron star corresponding to the maximum mass of the star to be larger than R=9.6−0.03+0.14km. Moreover, the WFF1 EoS, which was excluded for static neutron stars in the context of general relativity, for the quartic order scalar model neutron star model provides realistic results compatible with the GW170817 event.

Accretion onto black holes inside neutron stars with piecewise-polytropic equations of state: Analytic and numerical treatments

We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star.

Universal inflationary attractors implications on static neutron stars

We study static neutron stars in the context of a class of non-minimally coupled inflationary potentials, the universal attractors. Universal attractors are known to generate a viable inflationary era, and they fall into the same category of inflationary phenomenology as the R 2 model and other well-known cosmological attractors. We present the essential features of universal attractors in both the Einstein and Jordan frame, and we extract the Tolman–Oppenheimer–Volkoff equations in the Einstein frame using the usual notation of theoretical astrophysics. We use a python 3 based double shooting numerical code for our numerical analysis and we construct the M–R graphs for the universal attractor potential, using piecewise polytropic equation of state the small density part of which is the WFF1 or the APR or the SLy equation of state. As we show, all the studied cases predict larger maximum masses for the neutron stars, and all the results are compatible with the GW170817 constraints imposed on the radii of the neutron stars.

Effects of high density phase transitions on neutron star dynamics

Various theoretical arguments motivate an expectation of a phase transition in matter at extreme densities above nuclear density, accompanied by hopes that gravitational wave observations may reveal the properties of such a transition. Instead of adopting a particular theory, we consider here a generic form of first order phase transition using a piecewise polytropic equation of state, and evolve both isolated neutron stars and neutron star binaries, including unequal mass binaries and, in some cases, magnetic field, looking at dynamical effects. Of particular interest are effects that may be observable either via gravitational waves or electromagnetic observations.

Neutron stars phenomenology with scalar–tensor inflationary attractors

In this work we shall study the implications of a subclass of E -models cosmological attractors, namely of a -attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the a -attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of a -attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical units frequently used in theoretical astrophysics contexts, we shall derive the Tolman–Oppenheimer–Volkoff equations in the Einstein frame. Assuming a piecewise polytropic equation of state, the lowest density part of which shall be chosen to be the WFF1, or APR or the SLy EoS, we numerically solve the Tolman–Oppenheimer–Volkoff equations using a double shooting python-based “LSODA” numerical code. The resulting picture depends on the value of the parameter a characterizing the a -attractors. As we show, for large values of a , which do not produce a viable inflationary era, the M – R graphs are nearly identical to the general relativistic result, and these two are discriminated at large central densities values. Also, for large a -values, the WFF1 equation of state is excluded, due to the GW170817 constraints on the radius of an M ∼ 1 . 6 M ⊙ neutron star, which must be larger than R = 10 . 6 8 − 0 . 04 + 15 km and on the radius corresponding to the maximum mass which must be larger than R = 9 . 6 − 0 . 03 + 0 . 14 km. In addition, the small a cases produce larger masses and radii compared to the general relativistic case and are compatible with the GW170817 constraints on the radii of neutron stars. A notable feature is that as the parameter a decreases, the radii of the static hydrodynamically stable neutron stars increase. Our results indicate deep and not yet completely understood connections between non-minimal inflationary attractors and neutron stars phenomenology in scalar–tensor theory.

Numerical-relativity simulations of long-lived remnants of binary neutron star mergers

We analyze the properties of the gravitational wave signal emitted after the merger of a binary neutron star system when the remnant survives for more than a 80 ms (and up to 140ms). We employ four different piecewise polytropic equations of state supplemented by an ideal fluid thermal component. We find that the post-merger phase can be subdivided into three phases: an early post-merger phase (where the quadrupole mode and a few subdominant features are active), the intermediate post-merger phase (where only the quadrupole mode is active) and the late post-merger phase (where convective instabilities trigger inertial modes). The inertial modes have frequencies somewhat smaller than the quadrupole modes. In one model, we find an interesting association of a corotation of the quadrupole mode in parts of the star with a revival of its amplitude. The gravitational wave emission of inertial modes in the late post-merger phase is concentrated in a narrow frequency region and is potentially detectable by the planned third-generation detectors. This allows for the possibility of probing not only the cold part of the equation of state, but also its dependence on finite temperature. In view of these results, it will be important to investigate the impact of various type of viscosities on the potential excitation of inertial modes in binary neutron star merger remnants.

Convective Excitation of Inertial Modes in Binary Neutron Star Mergers.

We present the first very long-term simulations (extending up to ∼140 ms after merger) of binary neutron star mergers with piecewise polytropic equations of state and in full general relativity. Our simulations reveal that, at a time of 30-50ms after merger, parts of the star become convectively unstable, which triggers the excitation of inertial modes. The excited inertial modes are sustained up to several tens of milliseconds and are potentially observable by the planned third-generation gravitational-wave detectors at frequencies of a few kilohertz. Since inertial modes depend on the rotation rate of the star and they are triggered by a convective instability in the postmerger remnant, their detection in gravitational waves will provide a unique opportunity to probe the rotational and thermal state of the merger remnant. In addition, our findings have implications for the long-term evolution and stability of binary neutron star remnants.

Neutron stars with spin polarized self-interacting dark matter

Dark matter, one of the important portion of the universe, could affect the visible matter in neutron stars. An important physical feature of dark matter is due to the spin of dark matter particles. Here, applying the piecewise polytropic equation of state for the neutron star matter and the equation of state of spin polarized self-interacting dark matter, we investigate the structure of neutron stars which are influenced by the spin polarized self-interacting dark matter. The behavior of the neutron star matter and dark matter portions for the stars with different values of the interaction between dark matter particles and spin polarization of dark matter is considered. In addition, we present the value of the gravitational redshift of these stars in different cases of spin polarized and self-interacting dark matter.

Parameterized neutron star and proto-neutron star equation of state at finite temperature

Read et al. proposed a parameterized equation of state (EOS) giving the pressure \(P\) as a function of the rest mass density \(\rho\) in a piecewise polytropic form for the study of neutron stars. The parameterized piecewise polytropic EOS can accurately represent many realistic EOS tables at zero temperature. We showed that the treatment can be extended to finite temperature to cover the study of neutron star at non zero temperature and proto-neutron stars. At finite temperature, two types of thermodynamic relations are needed, one for the pressure \(P\) and one for the internal energy density \(u\). We show that for many finite temperature realistic EOS tables, both the \(P\) and \(u\) can be accurately represented in piecewise polytropic forms as functions of the rest mass density \(\rho\) and temperature \(T\). The polytropic parameterization provides a framework to compare and understand the properties of the different realistic EOSs.

Exploring tidal effects of coalescing binary neutron stars in numerical relativity. II. Long-term simulations

We perform new longterm (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein's equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than 1 radian. We then compare the extrapolated waveforms with those calculated by the latest effective-one-body (EOB) formalism in which the so-called tidal deformability, higher post-Newtonian corrections, and gravitational self-force effects are taken into account. We show that for a binary of compact neutron stars with their radius 11.1 km, the waveform by the EOB formalism agrees quite well with the numerical waveform so that the total phase error is smaller than 1 radian for the total phase of $\sim 200$ radian up to the merger. By contrast, for a binary of less compact neutron stars with their radius 13.6 km, the EOB and numerical waveforms disagree with each other in the last few wave cycles, resulting in the total phase error of $\sim 3$ radian.

Quasiequilibrium sequences of binary neutron stars undergoing dynamical scalarization

We calculate quasiequilibrium sequences of equal-mass, irrotational binary neutron stars (BNSs) in a scalar-tensor (ST) theory of gravity that admits dynamical scalarization. We model neutron stars with realistic equations of state (notably through piecewise polytropic equations of state). Using these quasiequilibrium sequences we compute the binary's scalar charge and binding energy versus orbital angular frequency. We find that the absolute value of the binding energy is smaller than in general relativity (GR), differing at most by ~14% at high frequencies for the cases considered. We use the newly computed binding energy and the balance equation to estimate the number of gravitational-wave (GW) cycles during the adiabatic, quasicircular inspiral stage up to the end of the sequence, which is the last stable orbit or the mass-shedding point, depending on which comes first. We find that, depending on the ST parameters, the number of GW cycles can be substantially smaller than in GR. In particular, we obtain that when dynamical scalarization sets in around a GW frequency of ~130 Hz, the sole inclusion of the ST binding energy causes a reduction of GW cycles from ~120 Hz up to the end of the sequence (~1200 Hz) of ~11% with respect to the GR case. We estimate that when the ST energy flux is also included the reduction in GW cycles becomes of ~24%. Quite interestingly, dynamical scalarization can produce a difference in the number of GW cycles with respect to the GR point-particle case that is much larger than the effect due to tidal interactions, which is on the order of only a few GW cycles. These results further clarify and confirm recent studies that have evolved BNSs either in full numerical relativity or in post-Newtonian theory, and point out the importance of developing accurate ST-theory waveforms for systems composed of strongly self-gravitating objects, such as BNSs.

Gravitational waves from spinning black hole-neutron star binaries: dependence on black hole spins and on neutron star equations of state

We study the merger of black hole (BH)-neutron star (NS) binaries with a variety of BH spins aligned or anti-aligned with the orbital angular momentum, and with the mass ratio in the range MBH/MNS = 2--5, where MBH and MNS are the mass of the BH and NS, respectively. We model NS matter by systematically parametrized piecewise polytropic equations of state. The initial condition is computed in the puncture framework adopting an isolated horizon framework to estimate the BH spin and assuming an irrotational velocity field for the fluid inside the NS. Dynamical simulations are performed in full general relativity by an adaptive mesh refinement code, SACRA. The treatment of hydrodynamic equations and estimation of the disk mass are improved. We find that the NS is tidally disrupted irrespective of the mass ratio when the BH has a moderately large prograde spin, whereas only binaries with low mass ratios, MBH/MNS <~ 3 or small compactnesses of the NSs, bring the tidal disruption when the BH spin is zero or retrograde. The mass of the remnant disk is accordingly large as >~ 0.1 Msun, which is required by central engines of short gamma-ray bursts, if the BH spin is prograde. Information of the tidal disruption is reflected in a clear relation between the compactness of the NS and an appropriately defined "cutoff frequency" in the gravitational-wave spectrum, above which the spectrum damps exponentially. We find that the tidal disruption of the NS and excitation of the quasinormal mode of the remnant BH occur in a compatible manner in high mass-ratio binaries with the prograde BH spin. The correlation between the compactness and the cutoff frequency still holds for such cases. It is also suggested by extrapolation that the merger of an extremely spinning BH and an irrotational NS binary does not lead to formation of an overspinning BH.

The properties of pre-stellar discs in isolated and multiple pre-stellar systems

We present high-resolution 3D smoothed particle hydrodynamics simulations of the formation and evolution of protostellar discs in a turbulent molecular cloud. Using a piecewise polytropic equation of state, we perform two sets of simulations. In both cases we find that isolated systems undergo a fundamentally different evolution than members of binary or multiple systems. When formed, isolated systems must accrete mass and increase their specific angular momentum, leading to the formation of massive, extended discs, which undergo strong gravitational instabilities and are susceptible to disc fragmentation. Fragments with initial masses of 5.5 M_jup, 7.4 M_jup and 12 M_jup are produced in our simulations. In binaries and small clusters, we observe that due to competition for material from the parent core, members do not accrete significant amounts of high specific angular momentum gas relative to isolated systems. We find that discs in multiple systems are strongly self-gravitating but that they are stable against fragmentation due to disc truncation and mass profile steeping by tides, accretion of high specific angular momentum gas by other members, and angular momentum being redirected into members' orbits. In general, we expect disc fragmentation to be less likely in clusters and to be more a feature of isolated systems.

The star formation efficiency and its relation to variations in the initial mass function

We investigate how the dynamical state of a turbulently supported, 1000 solar mass, molecular cloud affects the properties of the cluster it forms, focusing our discussion on the star formation efficiency (SFE) and the initial mass function (IMF). A variety of initial energy states are examined in this paper, ranging from clouds with PE = 0.1 KE to clouds with PE = 10 KE, and for both isothermal and piece-wise polytropic equations of state (similar to that suggested by Larson). It is found that arbitrary star formation efficiencies are possible, with strongly unbound clouds yielding very low star formation efficiencies. We suggest that the low star formation efficiency in the Maddelena cloud may be a consequence of the relatively unbound state of its internal structure. It is also found that competitive accretion results in the observed IMF when the clouds have initial energy states of PE >= KE. We show that under such conditions the shape of the IMF is independent of time in the calculations. This demonstrates that the global accretion process can be terminated at any stage in the cluster's evolution, while still yielding a distribution of stellar masses that is consistent with the observed IMF. As the clouds become progressively more unbound, competitive accretion is less important and the protostellar mass function flattens. These results predict that molecular clouds should be permeated with a distributed population of stars that follow a flatter than Salpeter IMF.