Modal selection in oscillator model equations with two-mode nonresonant coupling

We present a revised criterion for the double-mode pulsation in oscillator model equations with two-mode nonresonant coupling. By applying the criterion, we demonstrate that there are four cases, namely, mode 0-only, mode 1-only, either-or, and double-mode ones on limiting amplitude space. We also show that models with evolutionary masses are preferable for double-mode pulsations. Moreover, we study numerically modal selection properties of the oscillator model equations corresponding to various limiting amplitudes. The results show the suggested criterion to be useful for prediction of modal selection properties. Some examples of the phase-locking behaviour are also shown.     

Coupled-oscillators

Modal coupling oscillation models for the stellar radial pulsation and coupled-oscillators are reviewed. Coupled-oscillators with the second-order and third-order terms seemed to behave non-systematically. Using the equation by Schwarzschild and Savedoff (1949) with the dissipation term of van del Pol's type which is third-order, we demonstrate the effect of each term. The effects can be understood by the terms of the nonlinear dynamics, which is recently developing, that is. phase-locking, quasi-periodicity, period doubling, and chaos. As the problem of stellar pulsation, especially of double-mode cepheids on the period-ratio, we examine the dependence on the stellar structure from which the coupling constants in the second-order terms are derived. Eigen functions for adiabatic pulsations had been used for the calculation of the constants. It is noted that only two set of the constants are available, that is, for the polytrope model withn = 3 and a cepheid model without convection. Some examples of nonlinear dynamical effects will be shown.It is shown that if the constants were suitable values, the period-ratio of double-mode cepheids is probably realized. The possibility is briefly suggested.     

Frequency analysis of Cepheids in the Large Magellanic Cloud: new types of classical Cepheid pulsators

We have performed a detailed systematic search for multiperiodicity in the Population I Cepheids of the Large Magellanic Cloud. In this process, we have identified for the first time several new types of Cepheid pulsational behaviour. We have found two triple-mode Cepheids pulsating simultaneously in the first three radial overtones. In 9 per cent of the first overtone (FO) Cepheids, we have detected weak but well-resolved secondary periodicities. They appear either very close to the primary pulsation frequency or at a much higher frequency with a characteristic period ratio of 0.60–0.64. In either case, the secondary periodicities must correspond to non-radial modes of oscillation. This result presents a major challenge to the theory of stellar pulsations, which predicts that such modes should not be excited in Cepheid variables. Non-radial modes have also been found in three of the fundamental first overtone (FU/FO) double-mode Cepheids, but no such oscillations have been detected in single-mode Cepheids pulsating in the FU mode.
In 19 per cent of double-mode Cepheids pulsating in the first two radial overtones (FO/SO type), we have detected a Blazhko-type periodic modulation of amplitudes and phases. Both modes are modulated with a common period, which is always longer than 700 d. Variations of the two amplitudes are anticorrelated, and maximum of one amplitude always coincides with minimum of the other. We have compared observations of modulated FO/SO Cepheids with predictions of theoretical models of the Blazhko effect, showing that the currently most popular models cannot account for properties of these stars. We propose that the Blazhko effect in FO/SO Cepheids can be explained by a non-stationary resonant interaction of one of the radial modes with another, perhaps non-radial, mode of oscillations.     

Multimode stellar pulsations

We apply the two time method to weakly anharmonic (nonlinear) stellar pulsations. The problem contains two small parameters: -the ratio of the dynamical and the thermal timescale and -the measure of the anharmonicity in the oscillator equation. The 0(⁰) system is solved up to 0() by the use of an asymptotic perturbation method. This solution is then used within the framework of the two time method to obtain the slow evolution of the amplitudes and entropy. Both monomode and double-mode pulsations are treated in a non-resonance case.Work supported by the National Science Foundation (AST79-20024).     

Double-mode stellar pulsation

The current observational and theoretical status of the double-mode variables is reviewed. Focusing mostly on the RR Lyrae stars, we address the question of the observational evidence ofmodal stability. The problem of stationarity is a crucial issue in the modelling of these stars.We mention past efforts in hydrodynamical and analytical modelling together with a detailed discussion of some very recent results. It is suggested that stochastic forcing due to turbulent convection may play a crucial role in exciting some marginally stable modes in the limiting pulsation. The latest hydrodynamical results first demonstrate that purelyradiative models are able to showpermanent double-mode behavior in the relevant period regime of RRd stars. The reason for the previous lack of double-mode behavior is attributed to the large dissipation,i.e. artificial viscosity, generally used in the codes to ensure numerical stability and to obtain amplitudes comparable to the observed ones.We think that better models should include some physical dissipation, most probably turbulent convection, and a more accurate numerical treatment of the radiative hydrodynamics.     

Multi-Wavelength Observations of Quasi-Periodic Pulsations in a Solar Flare

We have performed a search for flares and quasi-periodic pulsations (QPPs) from low-mass M-dwarf stars using Transient Exoplanet Survey Satellite (TESS) two-minute cadence data. We find seven stars that show evidence of QPPs. Using Fourier and empirical mode decomposition techniques, we confirm the presence of 11 QPPs in these seven stars with a period between 10.2 and 71.9 minutes, including an oscillation with strong drift in the period and a double-mode oscillation. The fraction of flares that showed QPPs (7%) is higher than other studies of stellar flares, but it is very similar to the fraction of solar C-class flares. Based on the stellar parameters taken from the TESS Input Catalog, we determine the lengths and magnetic-field strengths of the flare coronal loops using the period of the QPPs and various assumptions about the origin of the QPPs. We also use a scaling relationship based on flares from the Sun and solar-type stars and the observed energy, plus the duration of the flares, finding that the different approaches predict loop lengths that are consistent to within a factor of about two. We also discuss the flare frequency of the seven stars determining whether this could result in ozone depletion or abiogenesis in any orbiting exoplanet. Three of our stars have a sufficiently high rate of energetic flares, which are likely to cause abiogenesis. However, two of these stars are also in the range where ozone depletion is likely to occur. We speculate on the implications of the flare rates, loop lengths, and QPPs for life on potential exoplanets orbiting in their host star’s habitable zone.

     

Stability of equilibrium self-gravitating models and the possibility of black hole formation in the jordan-brans-dicke theory

We show that, starting from the qualitative analysis of the solutions of the vacuum equations, one can conclude that, in contrast to the general theory of relativity, in the Jordan-Brans-Dicke theory gravitational collapse does not lead to the formation of black holes, but that no reliable determination of the existence or nonexistence of black holes in the Jordan-Brans-Dicke theory will be possible until the time-dependent equations have been solved numerically. We propose a method of solving the problem of stability of equilibrium self-gravitating configurations with respect to radial pulsations and state a criterion for stability.Translated fromAstrofizika, Vol. 38, No. 3, 1995.     

Pulsating type IV solar radio bursts

Several models for pulsating type IV radio bursts are presented based on the assumption that the pulsations are the result of fluctuations in the synchrotron emission due to small variations in the magnetic field of the source. It is shown that a source that is optically thick at low frequencies due to synchrotron self-absorption exhibits pulsations that occur in two bands situated on either side of the spectral peak. The pulsations in the two bands are 180° out of phase and the band of pulsations at the higher frequencies is the more intense. In contrast, a synchrotron source that is optically thin at all frequencies and whose low frequency emission is suppressed due to the Razin effect develops only a single band of pulsations around the frequency of maximum emission. However, the flux density associated with the later model would be too small to explain the more intense pulsations that have been observed unless the source area is considerably larger than presently seems reasonable.     

Nonresonant mode coupling in double-mode pulsators

The simplest model for the evolution to steady nonlinear stellar pulsation is nonresonant interaction involving two linearly unstable modes. One scenario models a double-mode pulsator, while another one shows evolution to classic pulsators. In all cases exact shock-like solutions have been obtained.     

Search for Evolutionary Changes in the Periods of the Double-Mode Cepheid AS Cas

Astronomy Letters - For both periods of the double-mode classical Cepheid AS Cas we have constructed $$O-C$$ diagrams spanning a time interval of 132 years. The $$O-C$$ diagrams have the shape of...     

Search for Evolutionary Changes in the Periods of the Double-Mode Cepheid TU Cas

Astronomy Letters - For both periods of the double-mode classical Cepheid TU Cas we have constructed $$O-C$$ diagrams spanning a time interval of 117 years. The $$O-C$$ diagrams have the shape of...     

Nonlinear RR Lyrae models with new livermore opacities

A. N. Cox recently showed that a 20% opacity decrease in the 20,000-30,000 K region as indicated by the new Livermore OPAL opacities reconciles the discrepancy between pulsation and evolution masses of double-mode RR Lyrae variables. Nonlinear hydrodynamic calculations were performed for RR Lyrae models of mass 0.75M , 51L , andZ = 0.0001 (Osterhoff II type) including this opacity decrease. The Stellingwerf periodic relaxation method was used to converge the models to a limit cycle, and the Floquet matrix eigenvalues calculated to search for a tendency of the fundamental mode to grow from the full-amplitude overtone solution, and the overtone mode to grow from the full-amplitude fundamental solution, thereby predicting double-mode behavior. Models ofT _eff < 7000 K with the opacity decrease have positive fundamental-mode growth rates in the overtone solution, in contrast to earlier results by Hodson and Cox (1982), and models withT _eff > 7000 have positive 1st overtone growth rates in the fundamental-mode solution, but double-mode behavior was not found.     

The relationship between the strength of the IMF and the frequency of magnetic pulsations on the ground and in the solar wind

It has been established for some time that there is a correlation between the frequency of Pc 3–4 geomagnetic pulsations observed on the ground and the strength of the interplanetary magnetic field (IMF). The recent discovery of an apparently similar relationship between pulsations in the same frequency band in the solar wind and the strength of the IMF led to the suggestion that some magnetospheric Pc 3–4 pulsations have an exogenic source.In this paper we offer a statistical reappraisal of some of the earlier results, and an analysis of newly available ground and solar wind pulsation data sets, which suggest that on the basis of a frequency-field strength relationship alone, the case for an exogenic source is still unproven.We do, however, find support for the frequency-field strength relationship (for ground pulsations), which was the original basis for the Borok B index for prediction of the strength of the IMF. We also confirm that pulsation frequency is, at best, an imprecise predictor and show that any derived relationship is strongly dependent on the data sets used.     

Subsecond (0.1 s) Pulsations in the 11 April 2001 Radio Event

Radio pulsations observed during the 11 April 2001 event at six single frequencies (237, 327, 408, 610, 1420, and 2695 MHz) by the Trieste radio-polarimeter with a time resolution 10 ms are analyzed. A wavelet analysis method as well as time delay and polarization measurements are used. Both methods reveal pulsations with a period of about 0.1 s at all observed frequencies. Furthermore, the 0.1 s pulsations drift toward higher and lower frequencies, starting at about 1420 MHz. The polarization of pulsations increases with frequency and time. The remarkable fact that the detected 0.1 s period of pulsations does not depend on frequency in a very broad frequency range is discussed in terms of existing models of pulsations.     

The role of the Hermanus Magnetic Observatory in geomagnetic field research

Geomagnetic field research carried out at the Hermanus Magnetic Observatory over the past decade is reviewed. An important aspect of this research has been the study of geomagnetic field variations, with particular emphasis on ULF geomagnetic pulsations. Features of geomagnetic pulsations which are unique to low latitude locations have been investigated, such as the cavity mode nature of low latitude Pi 2 pulsations and the role played by ionosphericO ⁺ ions in the field line resonances responsible for Pc 3 pulsations. A theoretical model has been developed which is able to account for the observed relationships between geomagnetic pulsations and oscillations in the frequency of HF radio waves traversing ionospheric paths. Other facets of the research have been geomagnetic field modelling, aimed at improving the accuracy and resolution of regional geomagnetic field models, and the development of improved geomagnetic activity indices.     

A Search for Pulsating, Mass-Accreting Components in Algol-Type Eclipsing Binaries

We present a status report on the search for pulsations in primary componants of Algols systems (oEA stars). Analysis of 21 systems with A0-F2 spectral type primaries revealed pulsations in two systems suggesting that of the order of ten persent of Algols primaries in this range are actually pulsators.     

A time profile of millisecond pulsations of solar microwave radio bursts

An hypothesis on the interference origin of millisecond pulsations of solar-burst microwave radio emissions based on the fact that the signal scintillation appears as a result of radio-wave propagation through an inhomogeneous turbulent corona is considered. It is shown that the time profile of pulsations depends on the phase difference of interfering waves and can either look like pulses of “emission” and “absorption” or it can have a sawtooth form with slow buildup and fast drop. The observed properties of pulsations were compared with predictions of this model; this comparison showed that the formation of pulsations and their observed properties are satisfactorily explained by multipath propagation, which takes place at traversal of the coronal plasma by radio waves.     

Hard x-ray Pulsations in the Initial Phase of Flares

When analyzing light curves of hard X-ray bursts recorded by the Hard X-Ray Spectrometer on board the MTI satellite, we have found three events (all associated with major solar flares, two of them in the same active region) which show pulsations in the very initial phase of the burst. Periods of the pulsations range from 25 to 48 s. We compare them with other observations of pulsations of radio waves and in X-rays and conclude that pulsations of this kind have not been observed before. We mention several possible causes and prefer interactions between current-carrying loops as the most likely interpretation of the observed variations.     

Multisatellite observations of resonant hydromagnetic waves

Most measurements of long period ULF pulsations have come from ground based and single satellite observations. The observations have given strong support to the idea that these waves are resonant standing hydromagnetic waves on geomagnetic field lines. Simultaneous ground-satellite observations provide further details of the pulsation structure and are useful for examining the effect of the ionosphere on the transmission of the waves to the ground. Recently, multisatellite observations have been used to provide further insight into the nature of pulsations and we review the results obtained using this technique. Among the results presented are those from the ISEE 1 and 2 spacecraft which are closely spaced in identical orbits, making it possible to distinguish temporal from spatial structure in waves. The ISEE spacecraft have made measurements of resonant region widths and resonance harmonics. In addition, examples are shown of recent multisatellite observations of the global nature of some pulsations and the localization of Pi2 pulsations in space.     

Multipoint observations of low latitude ULF Pc3 waves in south-east Australia

Geomagnetic pulsations recorded on the ground are the signatures of the integrated signals from the magnetosphere. Pc3 geomagnetic pulsations are quasi-sinusoidal variations in the earth’s magnetic field in the period range 10–45 seconds. The magnitude of these pulsations ranges from fraction of a nT (nano Tesla) to several nT. These pulsations can be observed in a number of ways. However, the application of ground-based magnetometer arrays has proven to be one of the most successful methods of studying the spatial structure of hydromagnetic waves in the earth’s magnetosphere. The solar wind provides the energy for the earth’s magnetospheric processes. Pc3–5 geomagnetic pulsations can be generated either externally or internally with respect to the magnetosphere. The Pc3 studies undertaken in the past have been confined to middle and high latitudes. The spatial and temporal variations observed in Pc3 occurrence are of vital importance because they provide evidence which can be directly related to wave generation mechanisms both inside and external to the magnetosphere. At low latitudes (L < 3) wave energy predominates in the Pc3 band and the spatial characteristics of these pulsations have received little attention in the past. An array of four low latitude induction coil magnetometers were established in south-east Australia over a longitudinal range of 17 degrees at L = 1.8 to 2.7 for carrying out the study of the effect of the solar wind velocity on these pulsations. Digital dynamic spectra showing Pc3 pulsation activity over a period of about six months have been used to evaluate Pc3 pulsation occurrence. Pc3 occurrence probability at low latitudes has been found to be dominant for the solar wind velocity in the range 400–700 km/s. The results suggest that solar wind controls Pc3 occurrence through a mechanism in which Pc3 wave energy is convected through the magnetosheath and coupled to the standing oscillations of magnetospheric field lines.