Seismology of sunspot atmospheres

The present work deals with the theory of oscillations with periods of about 3 min observed in the chromosphere above sunspot umbrae. The model of these oscillations (slow mode magneto-acoustic waves trapped in a chromospheric resonant cavity) provides an independent method of checking empirical models of the chromosphere above sunspots. Making use of this method, we investigate sunspot models which have been derived from spectroscopic data; the calculated periods of the oscillations fit well the observed periods.     

Parameters of oscillation generation regions in open star cluster models

We determine the masses and radii of central regions of open star cluster (OCL) models with small or zero entropy production and estimate the masses of oscillation generation regions in clustermodels based on the data of the phase-space coordinates of stars. The radii of such regions are close to the core radii of the OCL models. We develop a new method for estimating the total OCL masses based on the cluster core mass, the cluster and cluster core radii, and radial distribution of stars. This method yields estimates of dynamical masses of Pleiades, Praesepe, and M67, which agree well with the estimates of the total masses of the corresponding clusters based on proper motions and spectroscopic data for cluster stars.We construct the spectra and dispersion curves of the oscillations of the field of azimuthal velocities v _φ in OCL models. Weak, low-amplitude unstable oscillations of v _φ develop in cluster models near the cluster core boundary, and weak damped oscillations of v _φ often develop at frequencies close to the frequencies of more powerful oscillations, which may reduce the non-stationarity degree in OCL models. We determine the number and parameters of such oscillations near the cores boundaries of cluster models. Such oscillations points to the possible role that gradient instability near the core of cluster models plays in the decrease of the mass of the oscillation generation regions and production of entropy in the cores of OCL models with massive extended cores.     

The energy dependence of burst oscillations from the accreting millisecond pulsar XTE J1814−338

The nature of the asymmetry that gives rise to Type I X-ray burst oscillations on accreting neutron stars remains a matter of debate. Of particular interest is whether the burst oscillation mechanism differs between the bursting millisecond pulsars and the non-pulsing systems. One means to diagnose this is to study the energy dependence of the burst oscillations: here we present an analysis of oscillations from 28 bursts observed during the 2003 outburst of the accreting millisecond pulsar XTE J1814−338. We find that the fractional amplitude of the burst oscillations falls with energy, in contrast to the behaviour found by Muno et al. in the burst oscillations from a set of non-pulsing systems. The drop with energy mirrors that seen in the accretion-powered pulsations; in this respect XTE J1814−338 behaves like the other accreting millisecond pulsars. The burst oscillations show no evidence for either hard or soft lags, in contrast to the persistent pulsations, which show soft lags of up to 50 μs. The fall in amplitude with energy is inconsistent with current surface-mode and simple hotspot models of burst oscillations. We discuss improvements to the models and uncertainties in the physics that might resolve these issues.     

Effects of rotation and tidal distortions on the shapes of radial velocity curves of polytropic models of pulsating variable stars

Anharmonic oscillations of rotating stars have been studied by various authors in literature to explain the observed features of certain variable stars. However, there is no study available in literature that has discussed the combined effect of rotation and tidal distortions on the anharmonic oscillations of stars. In this paper, we have created a model to determine the effect of rotation and tidal distortions on the anharmonic radial oscillations associated with various polytropic models of pulsating variable stars. For this study we have used the theory of Rosseland to obtain the anharmonic pulsation equation for rotationally and tidally distorted polytropic models of pulsating variable stars. The main objective of this study is to investigate the effect of rotation and tidal distortions on the shapes of the radial velocity curves for rotationally and tidally distorted polytropic models of pulsating variable stars. The results of the present study show that the rotational effects cause more deviations in the shapes of radial velocity curves of pulsating variable stars as compared to tidal effects.     

Spectrum of the free oscillations of the moon

The determination of the internal structure of the Moon using bulk waves is largely complicated due to inhomogeneities in its uppermost layer. We investigate the possibility of studying the Moon’s interior by a sensing method using the free oscillations of the Moon. The spectrum of the free oscillations is calculated for two current models of the internal structure of the Moon derived from the analysis of the Apollo seismic network data, based on new methods: the MG (Garsia, et al., 2011) and MW (Weber, et al., 2011) models. In contrast to the MG model, the MW model includes a solid inner core. In this latter model, we estimate how the shear modulus of the inner core affects the structure of the oscillations.     

Model of local oscillations in sunspots

We have analyzed the properties of oscillations in a sunspot based on SDO observations with a duration of 6 h. The 3-min oscillation spectrum has turned out to consist of dozens of spectral lines. The line widths are at the spectral resolution limit. The oscillations in a sunspot have been broken down into individual areas with a size of a few arcseconds, each having its own oscillation spectrum. These oscillation properties cannot be explained in terms of the existing models based on the assumption that the sunspot oscillates as a whole. We propose a model of local oscillations that explains the complex spectrum of the oscillations and their locality. We show that in addition to the chromospheric resonator, there exists a subphotospheric resonator for slow MHD waves. The existence of this resonance layer allows the locality of the oscillations and their complex spectrum to be explained in terms of Parker’s model.     

日冕中无衰减振荡的研究进展

日冕中冕环的无衰减横向振荡(简称无衰减振荡)自2012年被发现以来,受到了广泛的关注.无衰减振荡具有在日冕中广泛存在以及振幅无明显变小的特性,使之在解释日冕加热和冕震学诊断上都具有相当的潜力.总结了日冕中无衰减振荡的研究进展,包括观测研究得到的一系列结果、提出的理论和数值模型以及基于无衰减振荡进行冕震学诊断的一些尝试,并且展望了未来可以进一步开展的研究.     

Quasi-sinusoidal oscillations of the angular velocity of pulsars

We study the oscillations of the angular velocity of pulsars, obtaining an equation for the angular velocity and its derivative taking account of the curvature of vortices. We show that this equation has a quasisinusoidal solution and find the period of these oscillations. We show that the estimates for the value of the periods for various models of neutron stars give quantities of the order of tens of days, which is in agreement with the observations of the quasi-periodic oscillations and fluctuations of the angular velocity of pulsars.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

Solar models with low opacity

Solar Physics - Evolutionary models of the present Sun with standard and artifically low opacity of stellar matter are obtained and adiabatic nonradial oscillations of the models are computed. The...     

Oscillations of rapidly rotating superfluid stars

Using time evolutions of the relevant linearized equations, we study non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two-fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass-shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in β-equilibrium and co-exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non-radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non-axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation.     

Instabilities in a nonstationary model of self-gravitating disks. II. Warp modes of vertical oscillations

Gravitational instabilities with respect to warp modes of vertical oscillations are examined for nonlinearly nonequilibrium disk models with isotropic and anisotropic velocity diagrams. Nonstationary analogs of the dispersion relations for vertical oscillations in these models are derived in a general form. A detailed study is made of the major large scale oscillatory modes, which correspond primarily to the most common type of warp in the form of an integral sign, as well as to dome-shaped, U-shaped, and precessional warps. Critical diagrams showing the initial virial relation as a function of the rotation parameter for the nonstationary model are constructed for each of these vertical oscillation modes. A comparative analysis is made of the growth rates of the instabilities for these modes in order to determine the dependence of the characteristic times for their appearance on the basic physical parameters of the two models.     

Effect of central condensation on the modes of nonradial oscillations of stellar models

Modes of nonradial oscillations of six composite polytropic models have been investigated numerically to study the effect of central condensation parameter being the density at the centre and the mean density of a stellar model) on the modes of nonradial oscillations of stellar models.     

160-min oscillations of the Sun as the mean of study of its internal structure

The investigation of the models of the contemporary Sun with a mixed core has shown that the amplitude of some gravity modes of oscillations of the star can be mainly concentrated in the central region. This phenomenon takes place if the node of the amplitude of radial displacement coincides with the boundary of the mixed core. In this case the core can be regarded as a driving generator of the oscillations, determining their period and phase. It is suggested as the explanation of the observational properties of the 160-min oscillation.

     

Interpretation of oscillations in UV lines observed above sunspot umbrae

Our theory of a resonator for slow magneto-atmospheric waves in the chromosphere of a sunspot umbra has been used to check different models of the structure of the chromosphere and transition region. Oscillations of velocity and intensity in Civ, Siiv, and Oiv lines observed by Gurman et al. (1982) on the SMM spacecraft have been compared with the calculated oscillations. The observed spectrum of resonant peaks could well be explained by a gradient model of the umbral chromosphere. Different assumptions concerning the structure of the transition region do not influence the calculated resonance periods, but the amplitudes and phases of oscillations are modified. There is strong evidence for a concentration of the observed oscillations in cold fine structure elements of the transition region, even if the filling factor of such elements is very small (some few percent). Isothermal rather than adiabatic oscillations in the cold elements should be assumed in order to explain the observed fluctuations of line intensity; the relative amplitudes of pressure oscillations in the hot main component with a steep gradient of temperature are too small to explain the observed intensity fluctuations.     

Quasi-periodic oscillations in low-mass X-ray binaries and constraints on the equation of state of neutron star matter

Recently discovered quasi-periodic oscillations in the X-ray brightness of low-mass X-ray binaries are used to derive constraints on the mass of the neutron star component and the equation of state of neutron star matter. The observations are compared with models of rapidly rotating neutron stars which are calculated by means of an exact numerical method in full relativity. For the equations of state we select a broad collection of models representing different assumptions about the many-body structure and the complexity of the composition of superdense matter. The mass constraints differ from their values in the approximate treatment by ∼10 per cent. Under the assumption that the maximum frequency of the quasi-periodic oscillations originates from the innermost stable orbit, the mass of the neutron star is in the range M ∼1.92–2.25 M_⊙. The quasi-periodic oscillation in the Atoll-source 4U 1820−30 in particular is only consistent with equations of state that are rather stiff at high densities, which is explainable, so far, only with pure nucleonic/leptonic composition. This interpretation contradicts the hypothesis that the protoneutron star formed in SN 1987A collapsed to a black hole, since this would demand a maximum neutron star mass below 1.6 M_⊙. The recently suggested identification of quasi-periodic oscillations with frequencies of about 10 Hz with the Lense–Thirring precession of the accretion disc is found to be inconsistent with the models studied in this work, unless it is assumed that the first overtone of the precession is observed.     

Seismology of a Sunspot Atmosphere

Two competing theories of sunspot oscillations are discussed. It is pointed out that the normal mode (eigenoscillations) theory is in contradiction with a number of observations. The reasons for this are discussed. The revised filter theory of the three-minute sunspot oscillations is outlined. It is shown that the reason for the occurrence of the multipassband filter for the slow waves is the interference that appears from the multilayer structure of the sunspot atmosphere. In contrast with Zhugzhda and Locans (Sov. Astron. Lett. 7, 25?–?27, 1981) it is shown that along with the Fabry?–?Perot chromospheric passband the cutoff frequency passband and a number of the high-frequency passbands occur. The effect of the nonlinearity of the sunspot oscillations in the upper chromosphere and the transition region is taken into account. The spectra of the distinct empirical models of the sunspot atmosphere are explored. An example of the interpretation of the sunspot oscillations based on the revised filter theory is presented. Only the filter theory can explain the complicated behavior of the oscillations across the sunspot. The observations provide evidence of the nonuniformity of the sunspot atmosphere.     

Effects of rotation and tidal distortion on the periods of small adiabatic oscillations of the polytropic models of the stars

The averaging technique of Kippenhahn and Thomas (1970) has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials to determine the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of polytropic models of the stars.     

Radiation pressure effects in the oscillations of compressible rotating homogeneous spheroids

Earlier models of compressible, rotating, and homogeneous ellipsoids with gas pressure are generalized to include the presence of radiation pressure. Under the assumptions of a linear velocity field of the fluid and a bounded ellipsoidal surface, the dynamical behaviour of these models can be described by ordinary differential equations. These equations are used to study the finite oscillations of massive radiative models with masses 10M and 30M in which the effects of radiation pressure are expected to be important.Models with two different degrees of equilibrium are chosen: an equilibrium (i.e., dynamically stable) model with an initial asymmetric inward velocity, and a nonequilibrium model with a nonequilibrium central temperature and which falls inwards from rest. For each of these two degrees of equilibrium, two initial configurations are considered: rotating spheroidal and nonrotating spherical models.From the numerical integration of the differential equations for these models, we obtain the time evolution of their principal semi-diametersa ₁ anda ₃, and of their central temperatures, which are graphically displayed by making plots of the trajectories in the (a ₁,a ₃) phase space, and of botha ₁ and the total central pressureP _c against time.It is found that in all the equilibrium radiative models (in which radiation pressure is taken into account), the periods of the oscillations of botha ₁ andP _c are longer than those of the corresponding nonradiative models, while the reverse is true for the nonequilibrium radiative models. The envelopes of thea ₁ oscillations of the equilibrium radiative models also have much longer periods; this result also holds for the nonequilibrium models whenever the envelope is well defined. Further, as compared to the nonradiative models, almost all the radiative models collapse to smaller volumes before rebouncing, with the more massive model undergoing a larger collapse and attaining a correspondingly larger peakP _c.When the mass is increased, the dynamical behavior of the radiative model generally becomes more nonperiodic. The ratio of the central radiation pressure to the central gas pressure, which is small for low mass models, increases with mass, and at the center of the more massive model, the radiation pressure can be comparable in magnitude to the gas pressure. In all the radiative models, the average periods as well as the average amplitudes of both thea ₁ andP _c oscillations also increase with mass.When either rotation or radiation pressure effects or both are included in the equilibrium nonradiative model, the period of the envelope of thea ₁ oscillations is increased. The presence of rotation in the equilibrium radiative model, however, decreases this period.Some astrophysical implications of this work are briefly discussed.     

The autoparametric 3:2 resonance in conservative systems

In the resonance model, high‐frequency quasi‐periodic oscillations (QPOs) are supposed to be a consequence of nonlinear resonance between modes of oscillations occurring within the innermost parts of an accretion disk. Several models with a prescribed mode–mode interaction were proposed in order to explain the characteristic properties of the resonance in QPO sources. In this paper, we examine nonlinear oscillations of a system having a quadratic nonlinearity and we show that this case is particularly relevant for QPOs. We present a very convenient way how to study autoparametric resonances of a fully general system using the method of multiple scales. We concentrate to conservative systems and discuss their behavior near the 3:2 parametric resonance. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Infrared synchrotron oscillations in GRS 1915+105

We report simultaneous observations of the black hole candidate X-ray transient GRS 1915+105 in the infrared (IR) at K and in the radio at 2 cm. Oscillations of period 26 min were observed in both wavebands, having (dereddened) peak–peak amplitudes of about 40 mJy and with the IR leading the radio by 7 min, or perhaps by 33 or 59 min. A synchrotron origin for the oscillations continues to seem very likely. We consider a range of problems raised by these observations, and briefly discuss the applicability of expanding-synchrotron source or conical jet models to the oscillations. Comparing simplistic estimates of the ejecta mass to the missing inner disc mass in the model of Belloni et al., we find that a significant fraction of the inner disc may be ejected during the oscillations.