Do Neutron Star Gravitational Waves Carry Superfluid Imprints?

Isolated neutron stars undergoing non-radial oscillations are expected to emit gravitational waves in the kilohertz frequency range. To date, radio astronomers have located about 1,300 pulsars, and can estimate that there are about 2×10⁸ neutron stars in the galaxy. Many of these are surely old and cold enough that their interiors will contain matter in the superfluid or superconducting state. In fact, the so-called glitch phenomenon in pulsars (a sudden spin-up of the pulsar's crust) is best described by assuming the presence of superfluid neutrons and superconducting protons in the inner crusts and cores of the pulsars. Recently there has been much progress on modelling the dynamics of superfluid neutron stars in both the Newtonian and general relativistic regimes. We will discuss some of the main results of this recent work, perhaps the most important being that superfluidity should affect the gravitational waves from neutron stars (emitted, for instance, during a glitch) by modifying both the rotational properties of the background star and the modes of oscillation of the perturbed configuration. Finally, we present an analysis of the so-called zero-frequency subspace (i.e., the space of time-independent perturbations) and determine that it is spanned by two sets of polar (or spheroidal) and two sets of axial (or toroidal) degenerate perturbations for the general relativistic system. As in the Newtonian case, the polar perturbations are the g-modes which are missing from the pulsation spectrum of a non-rotating configuration, and the axial perturbations should lead to two sets of r-modes when the degeneracy of the frequencies is broken by having the background rotate.     

Analyzing gravitational waves with general relativity

After a short review of prominent properties of gravitational waves and of the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent discoveries of gravitational waves. They are used to build theoretical template banks for searching and analyzing the signals in the ground-based detectors LIGO and Virgo, and, further ahead, space-based LISA-like detectors. In particular, the post-Newtonian approximation describes with high accuracy the early inspiral of compact binary systems, made of black holes or neutron stars. It mainly consists of extending the Einstein quadrupole formula by a series of relativistic corrections up to high order. The compact objects are modeled by point masses with spins. The practical calculations face difficult problems of divergences, which have been solved thanks to dimensional regularization. In the last rotations before the merger, the finite size effects and the internal structure of neutron stars (notably the internal equation of state) affect the evolution of the orbit and the emission of gravitational waves. We describe these effects within a simple Newtonian model.     

Alternating vorticity bands in a solution of wormlike micelles

We report on structural characterization of vorticity bands formed in a wormlike micellar solution by Rheo--small-angle neutron scattering and video imaging experiments. Below a critical shear stress tau{c} in Newtonian and shear-thinning regime, only a minor flow alignment of the micelles is observed. Above tau{c}, in the shear-thickening regime, alternating transparent and turbid bands are formed. Triggered small-angle neutron scattering shows different anisotropic patterns in both bands indicating strongly aligned structures. By high-speed video imaging, we show that such an alignment of micelles does not correspond to a phase of lower viscosity.     

NEUTRON SPIN INTERFERENCE,PRINCIPLE OF SPINOR SUPERPOSITION AND INFLUENCE OF EARTH GRAVITY ON THE NSE

The interfererice between the spinor components of the potarized neutron beam passing through a Mezei-coil investiga-ted. The authors proposed a method to detect the phase shift of the spinor Components a to test the principle of the fermion spin superposition. The influence of the earth gravity on the spinor interference is considered. The results show that the Planck's constant h and the Newtonian gravitational constant G(or q) both are involved in the phase shift θ, which is independent of the neutron mass.     

Covariant Newtonian and relativistic dynamics of (magneto)-elastic solid model for neutron star crust

This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.     

Effective Hamiltonian for non-minimally coupled scalar fields

In the post Newtonian limit, a non-relativistic Hamiltonian is derived for scalar fields with quartic self-interaction and non-minimal coupling to the curvature scalar of the background spacetime. These effects are found to contribute to the non-relativistic Hamiltonian by adding nonlinearities and by modifying the gravitational Darwin term. As we discuss briefly in the text, the impact of these novel structures can be sizable in dense media like neutron star core, and can have observable signatures in phase transitions, for example.     

Classical,Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons

We present a comprehensive simulation study of the Newtonian and quantum model of a Stern–Gerlach experiment with cold neutrons. By solving Newton’s equation of motion and the time-dependent Pauli equation for a wide range of uniform magnetic field strengths, we scrutinize the role of the latter for drawing the conclusion that the magnetic moment of the neutron is quantized. We then demonstrate that a marginal modification of the Newtonian model suffices to construct, without invoking any concept of quantum theory, an event-based subquantum model that eliminates the shortcomings of the classical model and yields results that are in qualitative agreement with experiment and quantum theory. In this event-by-event model, the intrinsic angular momentum can take any value on the sphere, yet, for a sufficiently strong uniform magnetic field, the particle beam splits in two, exactly as in experiment and in concert with quantum theory.     

Constraints on new interactions from neutron scattering experiments

Constraints for the constants of hypothetical Yukawa-type corrections to the Newtonian gravitational potential are obtained from analysis of neutron scattering experiments. Restrictions are obtained for the interaction range between 10⁻¹² and 10⁻⁷ cm, where Casimir force experiments and atomic-force microscopy are not sensitive. Experimental limits are obtained also for nonelectromagnetic inverse-power-law neutron-nucleus potentials. Some possibilities are discussed to strengthen these constraints. The text was submitted by the author in English.     

新生中子星的性质与三体核力效应

在Brueckner-Hartree-Fock理论框架内, 研究了新生中子星的状态方程和性质, 计算了新生中子星的最大质量和新生中子星中质子占总核子数的丰度, 特别是讨论了三体核力和中微子束缚效应的影响以及三体核力和中微子束缚效应的相互影响. 结果表明, 无论是否考虑三体核力, 中微子束缚对新生中子星的状态方程和质子丰度均有明显影响. 中微子束缚导致新生中子星物质中的质子丰度显著增大. 三体核力的贡献是使新生中子星的状态方程变硬并导致新生中子星中质子丰度明显增大. 束缚在中子星物质中的中微子显著减弱了三体核力对于中子星物质中质子丰度的影响.     

122~125Sn中子谱因子的实验研究

多个Sn同位素位于慢速中子俘获（s-）过程路径上,其中子谱因子可用于计算ASn（n,γ） A+1Sn直接辐射俘获的天体物理反应率,并可研究Sn同位素对s-过程核合成的贡献。本工作在中国原子能科学研究院HI-13串列加速器Q3D磁谱仪上,对实验室系下8°~66°范围内的122,124Sn（d,p）和（p,d）单中子转移反应角分布进行了测量。利用DWBA理论计算了转移反应角分布,并提取了122-125Sn的基态以及123,125Sn第一激发态的中子谱因子。其中,122Sn和124Sn的基态中子谱因子是首次从实验上获得。由于本工作成功鉴别开了123,125Sn的基态和第一激发态的效应,因此给出的谱因子比前人的结果更可信。Several Tin isotopes are on the path of slow neutron capture (s-) process, and the direct components of (n, γ) reactions can be derived from their neutron spectroscopic factors. In the present work, the angular distributions of 122,124Sn(p, d) and (d, p) reactions are obtained using the high-precision Q3D magnetic spectrograph in Beijing HI-13 tandem accelerator in China Institute of Atomic Energy. The distorted-wave Born approximation (DWBA) calculations are performed to extract the neutron spectroscopic factors of the ground state of 122-125Sn and the first excited state of 123,125Sn. The neutron spectroscopic factors of the ground state of 122Sn and 124Sn are firstly obtained in this work. As the events of the ground state and first excited state of 123,125Sn can be distinguished clearly by our experiment, the neutron spectroscopic factories of 123,125Sn are more reliable.     

Letter: Weitzenböck Spacetime Outside a Rapidly Rotating Object and the Motion of a Dirac Particle

The tetrad and the torsion fields due to a rapidly rotating massive object are found. The motion of a spin particle in the Weitzenböck spacetime is studied. It is shown that the axial-vector torsion is the entity responsible for the gravitomagnetic component of the gravitational field.The influences of the quadrupole moment of the rapidly rotating object on the motion of the particle are discussed. It is pointed out that the influences of the quadrupole moment are negligible for Kerr black holes, but are as important as that of the Newtonian potential for a rapidly rotating neutron star.     

The Properties of Pure Neutron Star

For a given equation of state of neutron matter in the relativistic σ-ω model, ๏๏๏๏๏ including the vacuum fluctuation of neutron and σ meson, the properties of pure neutron star are studied. We find that the maximum mass of pure neutron star is ～ 2.0 M_{\odot}. At the same time, the influence of incompressibility of the nuclear matter to the properties of neutron star is also studied. We also find that the maximum mass of neutron stars decreases as equation of state of neutron matter becomes softer.     

THE POSSIBLE ORIGIN OF STRCNG MAGNETIC FIELD OF NEUTRON STAR:FERROMAGNETIC STATE

The magnetic susceptibility of neutron matter was calculated by means of Owen's LOCV method. The results showed that a transition to a ferromagnetic state can exist for HJ, IY and M-S potentials, but there is no transition for Reid soft-core potential .By analyses, we concluded that the ferromagnetic state is a possible origin of strong magnetic field within the neutron star. We also considered an influence of the ferromagnetic state on the mass, radius and moment of inertia of the neutron star.Finally we discussed the effect of magnetization on physical state in the neutron star.     

完整力学系统的高阶运动微分方程

从质点系的牛顿动力学方程出发,引入系统的高阶速度能量,导出完整力学系统的高阶Lagrange方程、高阶Nielsen方程以及高阶Appell方程,并证明了完整系统三种形式的高阶运动微分方程是等价的.结果表明,完整系统高阶运动微分方程揭示了系统运动状态的改变与力的各阶变化率之间的联系,这是牛顿动力学方程以及传统分析力学方程不能直接反映的.因此,完整系统高阶运动微分方程是对牛顿动力学方程及传统Lagrange方程、Nielsen方程、Appell方程等二阶运动微分方程的进一步补充. 关键词： 高阶速度能量 高阶Lagrange方程 高阶 Nielsen方程 高阶Appell方程     

The Effect of Hyperon-Hyperon Interaction on Neutron Stars

The equations of state of the neutron star matter are calculated in the relativistic mean-field approximation with different hyperon coupling constants. The properties of neutron stars are studied by solving the Oppenheimer-Volkoff equation. It manifests the properties of neutron stars — change explicitly as different hyperon coupling constants are concerned.     

Hadron masses in medium and neutron star properties

We investigate the properties of the neutron star with relativistic mean-field models. We incorporate in the quantum hadrodynamics and in the quark-meson coupling models a possible reduction of meson masses in nuclear matter. The equation of state for neutron star matter is obtained and is employed in Oppenheimer-Volkov equation to extract the maximum mass of the stable neutron star. We find that the equation of state, the composition and the properties of the neutron stars are sensitive to the values of the meson masses in medium.     

Solid state effects during deuterium implantation into copper and titanium

Results of neutron counting experiments during deuterium implantation into titanium and copper are reported. Models for neutron yield have been developed by taking into account different solid state effects like energy degradation of incident ions, energy dependent d-d fusion cross section and diffusion of implanted deuterium possibly influenced by surface desorption and formation of metal deuterides. The asymptotic time dependence of the neutron yield during implantation has been compared with the experimental results. Using these results, solid state processes that might occur during deuterium implantation into these metals are inferred.     

Effects of temperature on the structure of neutron stars at high temperature

In Newtonian physics, higher temperature leads to higher thermal pressure, which provides stronger support against the gravitational contraction of stars. However, in the temperature range of tens of MeV involved in the evolution of a proto-neutron star or a higher massive neutron star, the effects of temperature are richer. We showed that, for a high temperature neutron star (HTNS) constructed with a realistic equation of state (EOS), the HTNS may expand or contract during cooling, the central density may increase or decrease, the quasi-normal mode oscillation frequencies may increase or decrease, and in particular, (i) independent of the EOS, for a HTNS of a given mass, there exists a maximum temperature \(T_{max}\) that it could ever attend at birth (with the value of \(T_{max}\) different for different EOS), and (ii) for the Hempel EOS and the Shen EOS, there is a range of mass that the HTNS may gravitationally collapse after a period of radiative cooling; however, for the Lattimer–Swesty EOS and Banik EOS, no delayed collapse is possible. Our study, which describes the cooling of HTNSs with simple quasi-stationary TOV sequences, provides an understanding of the effects of the thermal energy/pressure at high temperature, and a demonstration that different EOSs can lead to qualitatively different evolution paths.     

Observations of neutron stars and the equation of state of matter at high densities

We summarize the constraints on the equation of state of high-density nuclear matter derived from neutron star observations. The most stringent constraints are provided by the largest mass, the largest radius, the highest rotational frequency, and the maximum surface gravity observed for neutron stars. The combination of these constraints allows only nuclear equations of state which are quite stiff.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.