Quasi-normal modes and gravitational wave astronomy

We review the main results obtained in the literature on quasi-normal modes (QNM) of compact stars and black holes, in the light of recent exciting developments of gravitational wave (GW) detectors. QNMs are a fundamental feature of the gravitational signal emitted by compact objects in many astrophysical processes; we will show that their eigenfrequencies encode interesting information on the nature and on the inner structure of the emitting source and we will discuss whether we are ready for a GW asteroseismology.     

Quasi-normal modes of extremal black holes from hidden conformal symmetry

In this Letter, we construct the quasi-normal modes of three-dimensional extremal black holes in an algebraic way. We show that the infinite towers of the quasi-normal modes of scalar, vector and tensor could be constructed as the descendents of the highest weight modes. Our investigation shows that the hidden conformal symmetry suggested in Chen et al. (2010) [5] is an intrinsic property of the extremal black hole. Moreover, we notice that we need to fix the freedom in defining the local vector fields and find the right hidden conformal symmetry to obtain the physical quasi-normal modes.     

Untersuchungen zu den Existenzbereichen und Typen von ac-Entladungen. II. Das Verhalten der Entladungstypen in Ne/Ar-Gemischen und der Vergleich mit Ne/N2-Gemischen

The investigations on the transition between the discharge modes in Ne? N₂ mixtures are described in [1]. In the present paper we investigate Ne? Ar mixtures with a view to comparing the behaviour of these different mixtures. The measurements confirm the transition mechanism between the bistable pulse mode and the non-bistable continous mode in Ne-Penning mixtures. The life time of metastable atoms is important for the existence of the continuous mode. If the life time is changed by varying the cross sections for the Penning ionization Q_p (e.g. in other mixtures), the transition frequency of both these discharge modes shows a corresponding shift, which, for both mixtures, is in good agreement with literature values of Q_p. The second part presents a study of the quasiglow mode. The transition between the pulse mode and the quasiglow mode correlates to the ion transit time. The three discharge modes are represented in the existence diagram.     

Quasi-normal oscillations of a schwarzschild black hole

The modes of oscillation of a Schwarzschild black hole are determined within an analytic framework. These quasi-normal modes are related to the bound states of the inverted black hole potential which is approximated by the inverted Eckart potential. For a given angular momentum parameter j, the real part of the quasi-normal frequency decreases as the mode number n (or, equivalently, the damping factor) increases, in agreement with the results of numerical studies.     

Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole

We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole rotates slowly enough, we show that these poles form a discrete subset of \mathbb C{\mathbb C} . As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed.     

光学无源谐振腔的矩阵理论(柱坐标)(Ⅱ)——轴对称稳定光学无源谐振腔的计算

本文的目的是探讨应用文献[1]中提出的光学无源谐振腔的矩阵方程,解决腔中振荡横模的具体计算方法问题,并讨论其精度。为了便于与已有公式较可靠的结果相比,我们挑选了由两面对称的球面反射镜组成的、菲涅耳数N≤1的各种稳定腔作为计算对象;还分别用数学试验法和文献[1]中得出的误差上限公式,求出所得结果的误差。结果表明:对于基横模,所得结果与文献[3,6]的结果在报道的精度内很好地符合;对于包括高阶模在内的各阶横模,文献[1]中所得公式的误差上限都是正确的,但往往大大偏高。计算结果实际上往往具有高得多的精度。文中对g=0,0.5,0.8,0.9,0.95,菲涅耳数N=1的稳定腔,列出了l=0,p=0,1,2,3,4,5的各阶横模的本征值;绘出了l=0,1,2,p=0,1,2各阶横模场的相对振幅与位相分布曲线。还绘出了上述诸类稳定腔中N=1/π时TEM₀₀,TEM₀₁模的场分布曲线。从所得结果中得出了一些新的规律,并进行了某些讨论。本文结果表明:用这种矩阵理论,确实可以较为方便地一次求得模损耗不极近于1的、角模数l任意给定而径模数p不同的、所有各阶横模的性质,并能给出所得结果的误差上限,保证其具有相当高的精度。由于所用坐标系关系,本方法仅适用于具有理想轴对称性的谐振腔。 关键词：     

Gravitational radiation from an extreme Kerr black hole

We analytically investigate gravitational radiation induced by a test particle falling into an extreme Kerr black hole. Assuming the radiation is dominated by the infinite sequence of quasi-normal modes which has the limiting frequencym/(2M), wherem is an azimuthal eigenvalue andM is the mass of the black hole. we find the radiated energy diverges logarithmically in time. Then we evaluate the back reaction to the black hole by appealing to the energy and angular momentum conservation laws. We find the radiation has a tendency to increase the ratio of the angular momentum to mass of the black hole, which is completely different from the non-extreme case, while the contribution of the test particle is to decrease it.     

Letter: Solutions of All One-Dimensional Wave Equations with Time Independent Potential and Separable Variables

Solutions, in terms of special functions, of all wave equations u _xx – u _tt = V(x) u(t,x), characterised by eight inequivalent time independent potentials and by variables separation, have been found. The real valueness and the properties of the solutions produced by computer algebra programs are not always manifest and in this work we provide ready to use solutions. We discuss especially the potential (m ₁ + m ₂ sinh x)cosh^–2x. Such potential approximates the Schwarzschild black hole potential and its use for determining black holes quasi-normal modes is hinted to.     

<Emphasis Type="Italic">q</Emphasis>-Breathers and thermalization in acoustic chains with arbitrary nonlinearity Index

Nonlinearity shapes lattice dynamics affecting vibrational spectrum, transport and thermalization phenomena. Beside breathers and solitons one finds the third fundamental class of nonlinear modes, q-breathers, i.e., periodic orbits in nonlinear lattices, exponentially localized in the reciprocal mode space. To date, the studies of q-breathers have been confined to the cubic and quartic nonlinearity in the interaction potential. In this paper we study the case of arbitrary nonlinearity index γ in an acoustic chain. We uncover qualitative difference in the scaling of delocalization and stability thresholds of q-breathers with the system size: there exists a critical index γ* = 6, below which both thresholds (in nonlinearity strength) tend to zero, and diverge when above. We also demonstrate that this critical index value is decisive for the presence or absence of thermalization. For a generic interaction potential the mode space localized dynamics is determined only by the three lowest order nonlinear terms in the power series expansion.     

Nonlinear r-modes in rapidly rotating relativistic stars

The r-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications, provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3D general-relativistic hydrodynamical evolutions. We find that (1) on dynamical time scales, there is no strong nonlinear coupling of r-modes to other modes at amplitudes of order one-the maximum r-mode amplitude is of order unity. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes. (3) The kinematical drift associated with r-modes appears to be present in our simulations, but confirmation requires more precise initial data.     

长周期光纤光栅中的包层模谐振

本文给出了光纤中包层模的电场形式,指出包层膜的电场形式与弱导光纤中导模的电场形式不同,对光纤中基模与包层模电场沿光纤横截面分布的重叠情况的分析表明,长周期光纤光栅除了能将HE₁₁导模耦合到HE_1p包层模外,也可以将其耦合到EH_1p包层模。基于耦合模理论的计算表明,耦合到EH_1p和EH_1,p-1包层模的耦合波长相近,对于典型的单模光纤,当p>4时耦合到这两个模式的耦合系数是可比的。     

Quasi-normal Modes of Rerssner-Nordström Black Hole

The minimum interval of event horizon area of Rerssner-Nordström black hole was calculated via using the loop quantum gravity theory. Based on the first law of black hole thermodynamics, the real part of quasi-normal modes frequency of the black hole was calculated. The expression of asymptotically quasi-normal mode frequency of Rerssner-Nordström black hole was deduced strictly. By analyzing the value of the minimum spin j _{m i n} , the two families of quasi-normal mode spectra of the charged black hole were obtained for j _{m i n} = 1/2 and j _{m i n} = 1 respectively. Our conclusion is in complete agreement with the analytical results of Hod. Our results provide the theoretical basis for the source of the real part of the quasi-normal mode frequency of the black hole.     

掺镱钒酸钇晶体的晶格振动光谱

掺镜钒酸钇晶体是一种很有应用前景的晶体材料,由于它适合于半导体激光器泵浦的全固态激光器的要求而受到人们的普遍关注。拉曼光谱是研究材料的声子能谱分布的方法。本文根据群论对称性分类,计算了掺镜钒酸钇晶体的拉曼和红外活性振动模。选择不同几何配置的拉曼光谱,获得了不同的晶格振动模并计算了不同晶格振动模的散射效率。实验证明最强的振动模来自钒氧四面体的振动。     

孔径光阑输出对太赫兹激光器模式特性的影响

孔径光阑耦合技术是大功率光泵气体太赫兹激光器的一种常用谐振腔设计方法。在不考虑波导对腔内模式形成的影响下,采用传输矩阵的特征向量法,针对孔径光阑耦合太赫兹谐振腔的腔内本征模式以及输出光束特性进行了数值模拟,得到了该种谐振腔在不同g参数下损耗最低的几种本征模式及其相应的衍射损耗;采用衍射积分与矩阵光学结合的方法计算了孔径光阑输出太赫兹激光的光束特性,得到不同本征模式的远场衍射光斑及发散角。研究工作为孔径光阑耦合的气体太赫兹激光器设计提供了理论参考。     

Local and global gravity

Our long experience with Newtonian potentials has inured us to the view that gravity only produces local effects. In this paper we challenge this quite deeply ingrained notion and explicitly identify some intrinsically global gravitational effects. In particular we show that the global cosmological Hubble flow can actually modify the motions of stars and gas within individual galaxies, and even do so in a way which can apparently eliminate the need for galactic dark matter. Also we show that a classical light wave acquires an observable, global, pathdependent phase in traversing a gravitational field. Both of these effects serve to underscore the intrinsic difference between nonrelativistic and relativistic gravity.     

LAMOST medium-resolution spectroscopic survey of binarity and exotic star (LAMOST-MRS-B): Observation strategy and target selection

LAMOST-MRS-B is one of the sub-surveys of LAMOST medium-resolution ($R\sim7500$) spectroscopic survey. It aims at studying the statistical properties (e.g., binary fraction, orbital period distribution, mass ratio distribution) of binary stars and exotic stars. We intend to observe about 30000 stars ($10 {\rm mag}\leq G < 14.5$ mag) with at least 10 visits in five years. We first planned to observe 25 plates around the galactic plane in 2018. Then the plates were reduced to 12 in 2019 because of the limitation of observation. At the same time, two new plates located at the high galactic latitude were added to explore binary properties influenced by the different environments. In this survey project, we set the identified exotic and low-metallicity stars with the highest observation priorities. For the rest of the selected stars, we gave the higher priority to the relatively brighter stars in order to obtain high quality spectra as many as possible. Spectra of 49129 stars have been obtained in LAMOST-MRS-B field and released in DR8, of which 28828 and 3375 stars have been visited more than twice and ten times with $\rm SNR \geq 10$, respectively. Most of the sources are B-, A-, and F-type stars with $\rm -0.6< [Fe/H] < 0.4 $ dex. We also obtain 347 identified variable and exotic stars and about 250 stars with $\rm [Fe/H] <-1$ dex. We measure radial velocities (RVs) by using 892233 spectra of the stars. The uncertainties of RV achieve about $1$ ${\rm km \cdot s^{-1}}$and $10$ ${\rm km \cdot s^{-1}}$ for 95% of late- and early-type stars, respectively. The datasets presented in this paper are available at http://www.doi.org/10.57760/sciencedb.j00113.00035.     

Multiple helical scans and the reconstruction of over FOV-sized objects in cone-beam CT

In cone-beam computed tomography(CBCT),there are often cases where the size of the specimen is larger than the field of view(FOV)(referred to as over FOV-sized(OFS)).To acquire the complete projection data for OFS objects,some scan modes have been developed for long objects and short but over-wide objects.However,these modes still cannot meet the requirements for both longitudinally long and transversely wide objects.In this paper,we propose a multiple helical scan mode and a corresponding reconstruction algorithm for both longitudinally long and transversely wide objects.The simulation results show that our model can deal with the problem and that the results are acceptable,while the OFS object is twice as long compared with the FOV in the same latitude.     

On low-degree p mode rotational splitting

This paper is devoted to the measurement of low-degree p mode rotational splitting, which is one of the most urgent problems in helioseismology. The last three years witnessed considerable progress in this field. It can be stated with confidence that the angular velocity of solar core rotation exceeds only marginally or even does not exceed the rotation velocity of the Sun envelope, except for an area of radius 0.1R in the deep interior of the core. Further progress in this avenue encounters a variety of serious difficulties for lack of reliable data on g modes. These difficulties are due to the physical nature of the p modes themselves and the imperfection of the analytical techniques.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 10, pp. 1218–1221, October, 1996.