Non-radial Oscillations Research Articles

Nonradial Oscillations: The Cause of Macroturbulence in Late-Type Stars?

A fundamental problem in contemporary stellar atmospheres research concerns the cause of what the spectroscoplst calls “macroturbulence.” Even in so well studied a star as the Sun, it is unclear as to which of the many resolved velocity fields is most responsible for the broadening of the disk-integrated spectrum. There are several uncertainties attached to the identification of this primary velocity field. To cite one, Beckers (1980) indicates in a recent review that the two principal contributors to macroturbulence, convective granulation and the five-minute nonradial oscilltion pattern, each add only an r.m. s. velocity of 1/2 km s at τ5000 = 0.1. According to him, even when they are put together with related unresolved patterns [e.g. subgranulation and short period (<30) oscilltions] the sum of all known velocities seems to fall short of macroturbulence obtained from line broadening studies [~ 3 km s-1; radial-tangential model (Gray 1977, Smith 1978)]. The most recent models of the solar granulation field (Keil 1980) suggest somewhat higher velocities, e.g. 1.1 km s-1 at τ5000 = 0.1, when revised corrections for terrestrial seeing are taken into account. Nonetheless, such corrections must be added to both the convection and oscillation amplitudes, so it is still not clear whether one of these fields dominates the line formation.

Rotational and Tidal Perturbations of Nonradial Oscillations In a Polytropic Star

AbstractThe degeneracy of frequencies of nonradial oscillations is resolved in the presence of rotation. As observed in an inertial frame the frequency of a nonradial oscillation in a uniformly rotating star is given as

On adiabatic non-radial oscillations with moderate or large L

On adiabatic non-radial oscillations with moderate or large L

Linear, nonadiabatic analysis of nonradial oscillations of massive near main sequence stars

The equations for linear, nonadiabatic, nonradial oscillations have been solved for models with 7 M/sub sun/, 12 M/sub sun/, and 20 M/sub sun/ in the core-hydrogen burning and hydrogen exhaustion phases. Although the nonadiabatic periods are essentially the same as those of the corresponding adiabatic ones for those models investigated, the e-folding times for the oscillation amplitude are considerably different from the results of a quasi-adiabatic analysis, in particular for f and p modes. All the modes investigated are stable. However, the opacity bump near the He/sup +/ ionization zone has a destabilizing influence on nonradial modes in the 7 M/sub sun/ models about as strong as on purely radial oscillations. The effective temperatures of the 12 M/sub sun/ and 20 M/sub sun/ models are too high for the opacity bump mehcanism to be effective as a destabilizing mechanism for nonradial modes. For the g/sup +/ modes another driving zone exists in the intermediate-to-high temperature region. This driving zone's effect on stability is larger than the destabilizing effect of the nuclear reactions of zero-age main-sequence models. The phase lag of maximum luminosity behind minimum radius is small except for relatively high order g/sup +/ modes, for which the maximum luminositymore » and the maximum temperature occur near the phase of maximum radius because of the dominant effect of horizontal motions. ''Avoided crossing'' of the modes in evolved models is also discussed.« less

Micropulses, drifting subpulses, and nonradial oscillations of neutron stars

Rotating, magnetized neutron stars can support a rich variety of oscillation modes. The periods of the modes are estimated and compared with periodicities found in the pulsars. The millisecond time scale quasi-periodic micropulsations observed in PSR 2016+28 and PSR 1133+16 can be identified as nonradial l=0 or 1 p-mode oscillations, if mode-beating or internal noise broadening can account for the apparent rapid variability of amplitude and frequency. Torsional oscillations of the neutron star crusts have periods in the range of the pulsar subpulses; and rotational splitting of modes with l=2, 3, or 4 can account qualitatively for subpulse drift. Long-period Alfven modes, as well as Tkachenko oscillations, should be excited by pulsar glitches, and postglitch data may contain direct evidence of these modes.

Nonradial pulsations of accretion disks - The nature of quasi-periodic oscillations in dwarf novae

Quasi-periodic oscillations on time scales from approx.30 s to approx.150 s, which have been observed in several dwarf novae during outburst, have been qualitatively interpreted as oscillations of the accretion disks in these systems. We investigate this suggestion quantitatively by showing that there exist nonradial oscillation modes of the disk that, being weakly coupled in the radial (omega-bar) direction, correspond to oscillations of individual disk annuli which are periodic in phi, z, and t. The frequencies of these oscillations are directly proportional to the rotation frequency of the annulus. Because the luminosity of an annulus is largest at some intermediate radius, the oscillations are expected to be most evident for annuli near this radius. For values of the parameters typical of dwarf novae, the corresponding oscillation periods are approx.20 s, with a range from approx.10 to approx.150 s. We suggest that these modes correspond to the observed quasi-periodic oscillations.

Non-Radial Oscillations in Red Giants

The structure of red giant stars allows non-radial oscillation modes which propagate as p-modes near the surface, to propagate below the convection zone as g-modes with very high radial wave number [Dziembowski (1971, 1977), Shibahashi and Osaki (1976)]. Under some conditions the oscillations in these two propagation regions can be treated as virtually independent normal modes [Shibahashi and Osaki (1976)]. This paper examines the situation in which this approximation is not good, and discusses possible observational consequences of the interaction of the two propagation regions.The linearized differential equations describing non-radial adiabatic oscillations in stars can be written in the form, 1a1b

Generation of Oscillatory Motions in the Stellar Atmosphere

AbstractThermal overstability of non-radial eigenmodes of stars is discussed as one of possible causes for generating non-thermal motions in the stellar atmosphere. The nature of oscillatory motions in stars is first considered both in the local and the global stand points. Then, the excitation of eigen-oscillations is discussed and results of numerical studies so far made are reviewed for the vibrational stability of various stellar models against non-radial oscillations. It is found that many of non-radial p-modes of high tesseral harmonics are likely excited in various stars of the HR diagram and that they possibly manifest themselves as non-thermal velocity fields in the stellar atmosphere.

Radial and nonradial oscillations in Delta Scuti stars

Mode identifications from the phase shift between the B-V color curves and the V light curves of Delta Scuti stars are discussed. For five Delta Scuti stars the frequency of highest amplitude is due to pulsation in a radial mode with one or more frequencies due to nonradial modes lying nearby. Thus there may be a resonance between the frequencies of radial and nonradial modes. This behavior has only been found in subgiant and giant stars so far, but this could easily be a selection effect. Theoretical predictions of frequencies for different 1-modes of the same overtone for main sequence, subgiant, and giant stars are needed to compare with these observations. Theoretical predictions of the strength of resonance coupling between radial and nonradial modes as a function of frequency separation are also needed.

Nonradial oscillations: The cause of macroturbulence in latetype stars?

Nonradial oscillations: The cause of macroturbulence in latetype stars?

Mode discrimination in nonradially oscillating stars from light, colour and velocity observations

Expressions for the amplitudes and phases of the light, colour and radial velocity variations are derived for a star in nonradial oscillation. For stars in the cepheid instability strip the spherical harmonic mode of the oscillation can be obtained from the phase difference between the light and colour variations. For β Cep stars the mode can be estimated from the amplitude ratio of the light and colour variations.

A review of: “Nonradial oscillations of stars”

Abstract By W. Unno, Y. Osaki, H. Ando, H. Shibahashi, University of Tokyo Press, 344 pp., Y5800 ($32.50, £16.50). (ISBN 0-86008-258-X) 1979.

Theoretical Review of Secular Instabilities in the Sun

In this review we discuss the problems raised by the discovery that the sun was, in the past, unstable towards non-radial oscillations.In 1972, Fowler (1972), in an attempt to explain the low-neutrino flux measured in Davis’ experiment (now 1.6 snu, while the standard solar model predicts 4.4 snu) suggested that the sun could have undergone, some 10 years ago, a change in structure because of sudden mixing of the inner core. During the same year Dilke and Gough (1972) suggested the sun is unstable to low-order gravity modes (g+ modes) of non-radial oscillation and that the mixing is triggered when the amplitude of the oscillation becomes large enough.

White Dwarf Pulsations

It has been known for a long time that white dwarfs are pulsationally unstable if nuclear burning takes place in their envelopes. Perturbation of energy generation rate promotes pulsational instability and this effect is frequently referred to as ε-mechanism. In recent years, with the advent of high-speed photometry, many rapidly varying white dwarfs have been discovered. However, periods of variability were found to be significantly longer than the periods of radial pulsations which were the only type of oscillations considered before the discovery. Furthermore, the case of ε-mechanism as being responsible for the observed variability has never been made strong for any of the observed objects.Variable white dwarfs are found among: Iosingle DA-type objects in the effective temperature range 10000-15000K; 2omembers of close, usually but not always, cataclysmic binary systems. Although, following an early suggestion by Warner and Robinson (1972), the excitation of nonradial oscillation is postulated in both cases, the two types represent very different physical situations and they will be discussed here separately.

Supergiant Pulsations

AbstractThe main data concerning the amplitudes and periods of super-giant variations are reviewed. The period-luminosity-colour relation of intermediate-term variations is compatible with pulsation motions. The Q-values seem to be larger than those corresponding to the fundamental mode and there are arguments favouring non-radial oscillations.

Rotational and tidal perturbations of nonradial oscillations in a polytropic star

where Xi,ks , Yi,k% and Zi,ks (i = 1,2) are quantities which are obtained by numerical computations, and M and M 2 are total masses of a pulsating star and of its companion star, respectively. In deriving equation (2), we em~loyed the assumption of rotation synchronous with the orbital motion. The term (X 1 k% + m2Yl k% ) is due to the second order effects of the Coriolis for~e and the'other terms in equation (2) are caused by the deformation of the equilibrium structure due to centrifugal and tidal forces. Numerical results are listed in Saio (1981) for the polytrope n = 3 and y = 5/3.

Realistic Line Models for Pulsating B Stars

Spectral line profiles in pulsating stars are affected by the interplay of a number of velocity fields. In addition to the basic velocities associated with the pulsation mode, the complications of stellar rotation, atmospheric velocity gradients, stellar winds and varying scales of turbulence may also be present. Initial modelling for line profiles in variables assumed a constant ‘intrinsic profile’ which was integrated over the limb-darkened stellar disk. This approach has been used even in recent work for nonradial pulsations (Stamford and Watson 1977; Kubiak 1978) because of computational ease. Employing an LTE analysis to predict centre-to-limb profile variations, which are then integrated over the disk, represents an improvement on this. This has been done, for example, by Parsons (1972) for radial pulsations in cepheids and by Smith (1978) for nonradial oscillations in B stars. Mihalas (1979) has recently made an even more detailed examination of profiles in expanding atmospheres which involved consideration of velocity gradients, departures from LTE and rotation.

Variational principles for the linear and adiabatic oscillations of a spherical star, and related definitions of canonical energy density and of canonical energy flux

Abstract It is examined how the variational principle of Chandrasekhar and Lebovitz for adiabatic non-radial oscillations of a spherical star. and the variational principle for wave motions in a horizontal atmospheric layer given by Tolstoy stem for Hamilton's principle. The known variational functionals are recovered from the Lagrangian that is defined as the difference between the change in kinetic energy and the sum of the changes in the internal and gravitational potential energies. Certain terms of the Lagrangian vanish because of the boundary conditions of the star's equilibrium. The implications for the canonical energy densities and the canonical energy fluxes that are derived from the various Lagrangians are considered.

The effect of radial and non-radial stellar oscillations on the light, colour and velocity variations

The effect of radial and non-radial stellar oscillations on the observed light, colour and velocity variations is examined. A method of estimating the phase lag, radius and other pulsation constants is applied to classical cepheids. Amplitude and phase relations for non-radially oscillating stars are discussed with particular emphasis on the quadrupole mode. The radial pulsation and quadrupole oscillation models for β Cep stars are discussed. Some effects are predicted for multiperiodic stars and a method of determining the radius and pulsation modes is suggested.

White dwarf seismology

view Abstract Citations (27) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS White dwarfs seimology. Hansen, C. J. ; van Horn, H. M. Abstract A cool, 1-solar mass, Fe-56 white dwarf model is analyzed to determine the effects of a shear-supporting crystalline core upon the nonradial oscillation periods in the Cowling approximation. Both spheroidal and toroidal modes with l = 1, 2, and 3 have been calculated. Of the spheroidal oscillations, only the g-modes are seriously shifted in frequency. The toroidal oscillations, which have nonzero frequencies because of the nonzero shear modulus of the solid core, have periods intermediate between those of the p- and g-modes. None of the low-order oscillation modes have frequencies comparable to those observed in the ZZ Ceti white dwarfs. Publication: The Astrophysical Journal Pub Date: October 1979 DOI: 10.1086/157386 Bibcode: 1979ApJ...233..253H Keywords: Metallic Stars; Seismology; Stellar Models; Stellar Motions; Stellar Structure; White Dwarf Stars; Approximation; Cores; Iron; Metal Crystals; Oscillations; Shear Properties; Astrophysics; Oscillations:White Dwarfs; White Dwarfs:Interiors; White Dwarfs:Models full text sources ADS |