High frequency oscillations during magnetar flares

The effect of isospin-dependent nuclear forces on the inner crust of neutron stars is modeled within the framework of Quantum Molecular Dynamics (QMD). To successfully control the density dependence of the symmetry energy of neutron-star matter below nuclear saturation density, a mixed vector-isovector potential is introduced. This approach is inspired by the baryon density and isospin density-dependent repulsive Skyrme force of asymmetric nuclear matter. In isospin-asymmetric nuclear matter, the system shows nucleation, as nucleons are arranged into shapes resembling nuclear pasta. The dependence of clusterization in the system on the isospin properties is also explored by calculating two-point correlation functions. We show that, as compared to previous results that did not involve such mixed interaction terms, the energy symmetry slope L is successfully controlled by varying the corresponding coupling strength. Nevertheless, the effect of changing the slope of the nuclear symmetry energy L on the crust-core transition density does not seem significant. To the knowledge of the authors, this is the first implementation of such a coupling in a QMD model for isospin asymmetric matter, which is relevant to the inner crust of neutron and proto-neutron stars.

The cell structure of $\ensuremath{\beta}$-stable clusters in the inner crust of cold and warm neutron stars is studied within the Thomas--Fermi approach by using relativistic mean-field nuclear models. The relative size of the inner crust and the pasta phase of neutron stars is calculated, and the effect of the symmetry energy slope parameter $L$ on the profile of the neutron star crust is discussed. It is shown that, while the size of the total crust is mainly determined by the incompressibility modulus, the relative size of the inner crust depends on $L$. It is found that the inner crust represents a larger fraction of the total crust for smaller values of $L$. Finally, it is shown that, at finite temperature the pasta phase in $\ensuremath{\beta}$-equilibrium matter essentially melts above $5\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}6$ MeV, and that the onset density of the rod-like and slab-like structures does not depend on the temperature.

We explore the impact of a magnetar giant flare (GF) on the neutron star (NS) crust, and the associated baryon mass ejection. We consider that sudden magnetic energy dissipation creates a thin high-pressure shell above a portion of the NS surface, which drives a relativistic shockwave into the crust, heating a fraction of these layers sufficiently to become unbound along directions unconfined by the magnetic field. We explore this process using spherically symmetric relativistic hydrodynamical simulations. For an initial shell pressure PGF we find the total unbound ejecta mass roughly obeys the relation $M_{\rm {ej}}\sim 4\!-\!9\times 10^{24}\, \rm {g}\, (P_{\rm GF}/10^{30}\, \rm {erg}\, \rm {cm}^{-3})^{1.43}$. For $P_{\rm {GF}}\sim 10^{30}\!-\!10^{31}\, \rm {erg}\, \rm {cm}^{-3}$ corresponding to the dissipation of a magnetic field of strength $\sim 10^{15.5}\!-\!10^{16}\, \rm {G}$, we find $M_{\rm {ej}}\sim 10^{25}\!-\!10^{26}\, \rm {g}$ with asymptotic velocities vej/c ∼ 0.3–0.6 compatible with the ejecta properties inferred from the afterglow of the 2004 December GF from SGR 1806-20. Because the flare excavates crustal material to a depth characterized by an electron fraction Ye ≈ 0.40–0.46, and is ejected with high entropy and rapid expansion time-scale, the conditions are met for heavy element r-process nucleosynthesis via the alpha-rich freeze-out mechanism. Given an energetic GF rate of roughly once per century in the Milky Way, we find that magnetar GFs could be an appreciable heavy r-process source that tracks star formation. We predict that GFs are accompanied by short ∼minutes long, luminous $\sim 10^{39}\, \rm {erg}\, \rm {s}^{-1}$ optical transients powered by r-process decay (nova brevis), akin to scaled-down kilonovae. Our findings also have implications for the synchrotron nebulae surrounding some repeating fast radio burst sources.

We develop a method for implementing a proposal on utilizing knowledge of neutron star (NS) equation of state (EoS) for inferring the Hubble constant from a population of binary neutron star (BNS) mergers. This method is useful in exploiting BNSs as standard sirens when their redshifts are not available. Gravitational wave (GW) signals from compact object binaries provide a direct measurement of their luminosity distances, but not their redshifts. Unlike in the past, here we employ a realistic EoS parametrization in a Bayesian framework to simultaneously measure the Hubble constant and refine the constraints on the EoS parameters. The uncertainty in the redshift depends on the uncertainties in the EoS and the mass parameters estimated from GW data. Combining the inferred BNS redshifts with the corresponding luminosity distances, one constructs a redshift-distance relation and deduces the Hubble constant from it. Here, we show that in the Cosmic Explorer era, one can measure the Hubble constant to a precision of $\lesssim 5\%$ (with a $90\%$ credible interval) with a realistic distribution of a thousand BNSs, while allowing for uncertainties in their EoS parameters. Such a measurement can potentially resolve the current tension in the measurements of the Hubble constant from the early- and late-time universe. The methodology implemented in this work demonstrates a comprehensive prescription for inferring the NS EoS and the Hubble constant by simultaneously combining GW observations from merging NSs, while employing a simple population model for NS masses and keeping the merger rate of NSs constant in redshift. This method can be immediately extended to incorporate merger rate, population properties, and additional cosmological parameters.

Aql X-1 is a prolific transient neutron star low-mass X-ray binary that exhibits an accretion outburst approximately once every year. Whether the thermal X-rays detected in intervening quiescent episodes are the result of cooling of the neutron star or due to continued lowlevel accretion remains unclear. In this work, we use Swift data obtained after the long and bright 2011 and 2013 outbursts, as well as the short and faint 2015 outburst, to investigate the hypothesis that cooling of the accretion-heated neutron star crust dominates the quiescent thermal emission in Aql X-1. We demonstrate that the X-ray light curves and measured neutron star surface temperatures are consistent with the expectations of the crust cooling paradigm. By using a thermal evolution code, we find that 1.2-3.2 MeV nucleon -1 of shallow heat release describes the observational data well, depending on the assumed mass-accretion rate and temperature of the stellar core. We find no evidence for varying strengths of this shallow heating after different outbursts, but this could be due to limitations of the data. We argue that monitoring Aql X-1 for up to 1 yr after future outbursts can be a powerful tool to break model degeneracies and solve open questions about the magnitude, depth, and origin of shallow heating in neutron star crusts.

Recently exploratory studies were performed on the possibility of constraining the neutron star equation of state (EOS) using signals from coalescing binary neutron stars, or neutron star-black hole systems, as they will be seen in upcoming advanced gravitational wave detectors such as Advanced LIGO and Advanced Virgo. In particular, it was estimated to what extent the combined information from multiple detections would enable one to distinguish between different equations of state through hypothesis ranking or parameter estimation. Under the assumption of zero neutron star spins both in signals and in template waveforms and considering tidal effects to 1 post-Newtonian (1PN) order, it was found that O(20) sources would suffice to distinguish between a hard, moderate, and soft equation of state. Here we revisit these results, this time including neutron star tidal effects to the highest order currently known, termination of gravitational waveforms at the contact frequency, neutron star spins, and the resulting quadrupole-monopole interaction. We also take the masses of neutron stars in simulated sources to be distributed according to a relatively strongly peaked Gaussian, as hinted at by observations, but without assuming that the data analyst will necessarily have accurate knowledge of this distribution for use as a mass prior. We find that especially the effect of the latter is dramatic, necessitating many more detections to distinguish between different EOS and causing systematic biases in parameter estimation, on top of biases due to imperfect understanding of the signal model pointed out in earlier work. This would get mitigated if reliable prior information about the mass distribution could be folded into the analyses.

The magnetic field strength at birth is arguably one of the most important properties to determine the evolutionary path of a neutron star. Objects with very high fields, collectively known as magnetars, are characterized by high X‐ray quiescent luminosities, occurrence of outbursts, and, for some of them, sporadic giant flares. While the magnetic field strength is believed to drive their collective behaviour, however, the diversity of their properties, and, especially, the observation of magnetar‐like bursts from “low‐field” pulsars, has been a theoretical puzzle. In this review, we discuss results of long‐term simulations following the coupled evolution of the X‐ray luminosity and the timing properties for a large, homogeneous sample of X‐ray emitting isolated neutron stars, accounting for a range of initial magnetic field strengths, envelope compositions, and neutron star masses. In addition, by following the evolution of magnetic stresses within the neutron star crust, we can also relate the observed magnetar phenomenology to the physical properties of neutron stars, and in particular to their age and magnetic field strength and topology. The dichotomy of “high‐B” field pulsars versus magnetars is naturally explained, and occasional outbursts from old, low B‐field neutron stars are predicted. We conclude by speculating on the fate of old magnetars, and by presenting observational diagnostics of the neutron star crustal field topology. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The electron capture of Gamow-Teller transition on iron group nuclei is investigated in a strong magnetic field at the crusts of neutron stars. The results show that the magnetic field has only a slight effect on the electron capture rates with the range of the magnetic fields (109 ∼ 1013 G) on surfaces of most neutron stars, whereas for some magnetars whose range of the magnetic field is 1013 ∼ 1018 G, the electron capture rates of most iron group nuclei would be debased greatly and may be even decreased overrun 3 orders of magnitude by the strong magnetic field.

We study the impact of strong magnetic fields on the pasta phases that are expected to exist in the inner crust of neutron stars. We employ the relativistic mean field model to describe the nucleon interaction and use the self-consistent Thomas-Fermi approximation to calculate the nonuniform matter in neutron star crust. The properties of pasta phases and crust-core transition are examined. It is found that as the magnetic field strength $B$ is less than ${10}^{17}$ G, the effects of magnetic field are not evident comparing with the results without magnetic field. As $B$ is stronger than ${10}^{18}$ G, the onset densities of pasta phases and crust-core transition density decrease significantly, and the density distributions of nucleons and electrons are also changed obviously.

In a coalescing neutron star–neutron star or neutron star–black hole binary, oscillation modes of the neutron star can be resonantly excited by the companion during the final minutes of the binary inspiral, when the orbital frequency sweeps up from a few Hz to a few thousand Hz. The resulting resonant energy transfer between the orbit and the neutron star speeds up or slows down the inspiral, depending on whether the resonant mode has positive or negative energy, and induces a phase change in the emitted gravitational waves from the binary. While only g-modes can be excited for a non-rotating neutron star, f-modes and r-modes can also be excited when the neutron star is spinning. A tidal resonance, designated by the index ( jk, m) ({ jk} specifies the angular order of the mode, as in the spherical harmonic Yjk), occurs when the mode frequency equals m times the orbital frequency. For the f-mode resonance to occur before coalescence, the neutron star must have rapid rotation, with spin frequency νs≳710 Hz for the (22,2)-resonance and νs≳570 Hz for the (33,3)-resonance (assuming canonical neutron star mass, M=1.4 M⊙, and radius, R=10 km; however, for R=15 km, these critical spin frequencies become 330 and 260 Hz, respectively). Although current observations suggest that such high rotation rates may be unlikely for coalescing binary neutron stars, these rates are physically allowed. Because of their strong tidal coupling, the f-mode resonances induce a large change in the number of orbital cycles of coalescence, ΔNorb, with the maximum ΔNorb∼10–1000 for the (22,2)-resonance and ΔNorb∼1 for the (33,3)-resonance. Such f-mode resonant effects, if present, must be included in constructing the templates of waveforms used in searching for gravitational wave signals. Higher order f-mode resonances can occur at slower rotation rates, but the induced orbital change is much smaller (ΔNorb≲0.1). For the dominant g-mode (22,2)-resonance, even modest rotation (νs≲100 Hz) can enhance the resonant effect on the orbit by shifting the resonance to a smaller orbital frequency. However, because of the weak coupling between the g-mode and the tidal potential, ΔNorb lies in the range 10−3–10−2 (depending strongly on the neutron star equation of state) and is probably negligible for the purpose of detecting gravitational waves. Resonant excitations of r-modes require misaligned spin–orbit inclinations, and the dominant resonances correspond to octopolar excitations of the jk=2 mode, with (jk, m)=(22,3) and (22,1). Since the tidal coupling of the r-mode depends strongly on rotation rate, ΔNorb≲10−2(R/10 km)10(M/1.4 M⊙)−20/3 is negligible for canonical neutron star parameters, but can be appreciable if the neutron star radius is larger.

The gravitational radiation has been proposed a long time before, as an explana- tion for the observed relatively low spin frequencies of young neutron stars and of accreting neutron stars in low-mass X-ray binaries as well. In the present work we studied the effects of the neutron star equation of state on the r-mode instability window of rotating neutron stars.

The new generation of X-ray telescopes will provide simultaneous measurements of the radius and mass of a number of neutron stars (NSs), potentially constraining their equation of state (EoS). However the use of non-unified EoSs, that are based on different nuclear models for the crust and core, can introduce an uncertainty on the NS radius of the order of the precision expected from these instruments. Two solutions to this problem are presented. First a large number of unified EoSs and second an approximate approach to the NS crust that allows to obtain with a very large precision the relation between the NS mass and radius with no need to use an EoS for the crust. Correlations between the NS radius and nuclear parameters, which are properties of the EoS that can be indirectly measured in laboratory, are discussed. These open the possibility of constraining the NS radius with experiments on Earth. Finally, the appearance of hyperons in the core of NSs is examined. They are included in the EoS models consistently with available measurements on the hyperon properties. Because of the scarcity of these experimental data one can not exclude that hyperons appear at high densities in NSs in spite of the observations of massive NSs.

Conditions in neutron stars are more extreme than almost any encountered on Earth: densities exceed those of atomic nuclei, and matter has a large neutron excess. During the past quarter of a century, the challenge of understanding neutron stars has stimulated physicists to confront conditions far different from those normally encountered terrestrially. Laboratory studies have in turn yielded important input for the studies of neutron stars. We discuss a number of examples of this continuing interplay between physics and astrophysics. The first is the equation of state of dense matter, which is the basis for all theoretical models of neutron stars. The second is the composition of dense matter. This has profound influence on neutrino generating processes in neutron stars, and hence on their cooling. A third example is nuclei with a large neutron excess, such as are expected to be present in the crusts of neutron stars. Properties of similar nuclei play an important role in theories of element production.

Superfluid dilute neutron matter and ultracold gas, close to the unitary regime, exhibit several similarities. Therefore, to a certain extent, fermionic ultracold gases may serve as emulators of dilute neutron matter, which forms the inner crust of neutron stars and is not directly accessed experimentally. Quantum vortices are one of the most significant properties of neutron superfluid, essential for comprehending neutron stars’ dynamics. The structure and dynamics of quantum vortices as a function of pairing correlations’ strength are being investigated experimentally and theoretically in ultracold gases. Certain aspects of these studies are relevant to neutron stars. We provide an overview of the characteristics of quantum vortices in s-wave-type fermionic and electrically neutral superfluids. The main focus is on the dynamics of fermionic vortices and their intrinsic structure.

Within the Bayesian framework, using an explicitly isospin-dependent parametric equation of state (EOS) for the core of neutron stars (NSs), we studied how the NS EOS behaves when we confront it with the tidal deformabilities of canonical NSs with different error and different lower boundaries, and with the tidal deformabilities of massive NSs. We found that it does not significantly improve the constraints on the NS EOS but has a weak effect on narrowing down the slope parameter of the symmetry energy by decreasing the measurement errors of . Both the isospin-dependent and isospin-independent parts of the NS EOS were significantly constrained and raised as the tidal deformabilities of massive NSs were adopted in the calculations, especially in high-density regions. We also found that is more competent to limit the curvature parameter than the slope parameter of the symmetry energy, whereas the opposite occurs for the radius of canonical NSs . The tidal deformability of an NS with two times the solar mass is more sensitive to skewness than the curvature parameter of the symmetry energy, and and have no correlation with the former.