Radial Oscillation Modes Research Articles

Quadratic and Cubic Couplings of Oscillation Modes of Stars

The strength of nonlinear interactions of oscillation modes of stars is determined by the amplitudes as well as by the eigenfunctions of the oscillation modes. The intrinsic couplings of modes through their eigenfunctions can be described by coupling coefficients. Here, we concentrate on quadratic and cubic coupling coefficients that describe the nonlinear coupling of modes with itself and are called self-coupling coefficients.We considered radial and nonradial oscillation modes of polytropic models with degrees of central condensation that correspond to central condensations of main sequence stars to highly condensed evolved stars. We study the influence of the radial order and the degree of the oscillation mode on the self- coupling coefficients.

Radial oscillations of finite-temperature white dwarfs

Models of finite temperature completely degenerate stellar configurations are considered. The frequencies of fundamental radial modes of oscillations for these white dwarf models have been computed for different values of the central degeneracy parameter 1/y02 and for uniform temperatures of 20×106 K and 108 K. A variational formulation as well as a direct approach is employed to calculate the temperature induced modifications in the frequencies of oscillation of these white-dwarf models.

On multimode pulsations of degenerate stellar models

Nonlinear dissipative radial oscillations of partially and completely degenerate stellar models have been studied. The general mathematical framework for the study of interaction between various radial modes of oscillation has been presented. The dynamical tools, e.g., Poincare surface of section and the spectrum of Liapunov exponents, have been used to investigate the nature of pulsation in the phase space. For simplicity, numerical computations have been made to study the interaction of only the first three modes, including the fundamental mode for both partially and completely degenerate stellar masses. For these models, with varying degrees of central degeneracy, the possible occurrence of quasi-periodic motions with as many as three irrationally related frequencies has been established in the dissipative regime. 56 refs.

Radial and nonradial pulsation of a rotating partially degenerate standard model

The effect of slow uniform rotation on the radial and nonradial modes of partially degenerate standard models has been investigated. For the case of the radial mode, it is shown that the destabilizing effect of slow uniform rotation reduces with increased central condensation of the model. However, it is found that the models with a strongly degenerate interior, become more unstable dynamically as a result of slow uniform rotation. Further, it is noted that the frequency of the nonradial modes of oscillation (Kelvin mode) increases due to the presence of rotation. Thus the period of radial modes of oscillation of a slowly uniformly rotating partially degenerate standard model are much larger than the corresponding periods of nonradial (Kelvin) modes.

Radial and nonradial oscillations of partially-degenerate stellar masses

The radial and nonradial modes of oscillation of partially degenerate stellar masses have been studied. It is found that the radial mode shows a decrease with increased central condensation and the configuration tends, therefore, towards a marginally stable point with increased degeneracy. The nonradial modes forl=2 and 3 also shows a similar trend. However, the decrease is slower than the corresponding radial mode.

Non-linear helioseismology

The differential equations for non-linearly coupled radial adiabatic oscillation modes are integrated for three detailed solar models. In all experiments the resulting power spectrum of the surface displacement shows a peak at a long period PL exceeding 2 hr.

Structure and Stability of Multielectron Bubbles in Liquid Helium

The charge-density distribution in multielectron bubbles is calculated with use of a generalized Thomas-Fermi method. The exchange and correlation effects are found crucial; these result in a density profile much narrower than that obtained by simple estimates. The observed stability of the bubbles is explained in terms of the nonlinear coupling between the radial and angular modes of oscillation. Above a threshold oscillation amplitude a period-doubling instability sets in.

Bulk attenuation in the Earth and viscosity of the core

Recent studies indicate that bulk absorption is required somewhere in the Earth to explain the damping of the radial modes of free oscillation. This excess absorption, if attributed to bulk viscosity in the core, requires a value of ~500 P. This is theoretically reasonable and may be due to structural or concentration fluctuations. The shear viscosity is at least several orders of magnitude smaller.

Radial modes of oscillation of cool stellar disks

view Abstract Citations (4) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Radial modes of oscillation of cool stellar disks. Zweibel, E. Abstract Equations describing long wavelength radial modes of oscillation for stellar disks are derived. The approach is applied to determine the density response of a cool stellar disk to radial potential perturbations and is exact for disks with zero velocity dispersion. The formulation may be applied to finite or infinite disks of arbitrary structure, so long as the length scale of the perturbation is larger than the epicyclic amplitude. Three functions - the unperturbed surface density, the epicyclic frequency, and the radial velocity dispersion - are involved in the expression of the equilibrium structure. The effects of differential rotation, halos, and velocity dispersion on axisymmetric stability are studied for some disk models. Publication: The Astrophysical Journal Pub Date: May 1978 DOI: 10.1086/156127 Bibcode: 1978ApJ...222..110Z Keywords: Galactic Structure; Oscillations; Vibration Mode; Distribution Functions; Perturbation Theory; Plane Waves; Rotating Disks; Steady State; Astrophysics; Galaxies:Stellar Dynamics; Oscillations:Stellar Disks full text sources ADS |

Linear radial and nonradial modes of oscillation of hot white dwarfs

Low-order linear radial and nonradial quadrupole modes of oscillation of hot white dwarfs with hydrogen envelopes are evaluated in the quasi-adiabatic approximation. Luminosities range from 10 to the 36th to 10 to the 38th power. Masses range between 0.6 and 1.4 solar masses. Models are found with unstable radial modes as high as the third harmonic. The first nonradial quadrupole gravity mode is always unstable. The results may be relevant to pulsating X-ray sources in general and are specifically applied to Cen X-3, Her X-1, and SMC X-1.

An Investigation of Accretion of Matter onto White Dwarfs as a Possible X-Ray Mechanism

view Abstract Citations (19) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS An Investigation of Accretion of Matter onto White Dwarfs as a Possible X-Ray Mechanism Degregoria, A. J. Abstract The accretion flow onto white dwarfs is investigated by numerically integrating the full nonlinear hydrodynamic equations under the assumption of spherical symmetry to determine the short-term time-dependent behavior, to determine the effects on the flow when radial modes of oscillation of the star are excited, to see if X-rays are produced, and to determine the radiation spectrum. Some applications of the results to known X-ray sources are suggestive. Subject headings: binaries - white dwarf stars - X-ray sources Publication: The Astrophysical Journal Pub Date: May 1974 DOI: 10.1086/152834 Bibcode: 1974ApJ...189..555D full text sources ADS |

Contributions of theoretical seismograms to the study of modes, rays, and the Earth

Theoretical seismograms, for both simplified and realistic models of the earth, can be calculated and analyzed to learn the relations between free oscillations and traveling waves. These studies can help to clarify the influence of the physical properties of the earth upon the generation, propagation, attenuation, and dispersion of elastic waves. Principal results include the equivalence of mantle and crustal Rayleigh waves to the fundamental radial modes of spheroidal free oscillations and the equivalence of G waves and ordinary Love waves to the fundamental radial modes of torsional free oscillations. In contrast, the higher radial modes produce all the direct, reflected, refracted, and diffracted body phases, as well as the higher‐mode surface waves. Stoneley‐wave propagation along the core‐mantle boundary introduces a large number of interesting phenomena into the propagation of the spheroidal overtones. The confinement of the Stoneley modes to the vicinity of this boundary is responsible for the discontinuities in the spectra and the relative difficulty in the excitation of long‐period P and SV diffracted arrivals, as compared with the corresponding SH phases. The trapping of body‐wave energy for sources within a velocity inversion is demonstrated. The particle motion ratio at the surface may be as useful as phase velocity in the understanding of the physical properties beneath a recording site; realistic curves of this parameter are presented for a wide range of periods and radial orders.

Radial Modes of Oscillation in an Axially Symmetric Combustion Chamber

A fundamental study of flame-driven transverse oscillations in an experimental burner is being made. These oscillations are similar to those occurring in the combustion chambers of rockets, ramjets, and afterburners. The first radial mode and six combined first radial and axial modes were obtained in an experimental combustion system. Data are given on the effect of velocity, composition, mixing-chamber length, and location of the burner head with respect to the combustion chamber. Sound-pressure-level surveys for a few modes also are presented. [The work described in this paper was conducted under the sponsorship of the Aeronautical Research Laboratory of the Wright Air Development Center, Contract No. AF 33(038)-12656.]