Umin Lee

Line profile variations caused by low-frequency nonradial pulsations of rapidly rotating stars

Line profile variations caused by low-frequency nonradial g-mode oscillations of a rotating star are presented. For a nonradial oscillation mode whose oscillation frequency in the corotating frame is comparable to or smaller than the rotation frequency, the latitudinal dependence of the oscillation amplitude deviates significantly from that for a nonrotating star. Rotation usually causes oscillations confined to a narrow equatorial belt as well as causing toroidal velocity fields. The concentration of the amplitude of the oscillation toward the equator leads to a reduction in the strength of the bumps in line profiles if the maximum velocity of nonradial pulsation is fixed. For the same normalization, the line profile variations due to the sectoral prograde mode are most visible, while those caused by retrograde waves are almost invisible due to a cancellation effect. The toroidal component generated by stellar rotation appreciably affects the line profile variation of some modes. 24 refs.

Energy of oscillation : the role of the negative energy mode in overstable nonradial oscillations of rotating stars

In the present treatment of adiabatic nonradial oscillation energies in both nonrotating and uniformly rotating stars, the resonance between two positive energy modes yields an avoided crossing, while the resonance between one positive energy mode and a negative one yields an overstable mode. It is found that while the oscillation energies of p- and g-modes in nonrotating stars, and g-modes of rotating stars, are definitely positive, the energy of an oscillatory convective mode of rotating stars is positive or negative, depending on the ratio of the frequencies of rotation to those of oscillation. For a negative energy oscillation, amplitude increases when energy is extracted from, rather than fed into, the oscillation; when a resonance occurs between a negative energy mode and a positive one, energy flows from the negative energy mode to the positive one, thereby forming an overstable oscillation. 16 refs.

Theory and evidence of global Rossby waves in upper main-sequence stars: r-mode oscillations in many Kepler stars

Asteroseismic inference from pressure modes (p modes) and buoyancy, or gravity, modes (g modes) is ubiquitous for stars across the Hertzsprung–Russell diagram. Until now, however, discussion of r modes (global Rossby waves) has been rare. Here we derive the expected frequency ranges of r modes in the observational frame by considering the visibility of these modes. We find that the frequencies of r modes of azimuthal order m appear as groups at slightly lower frequency than m times the rotation frequency. Comparing the visibility curves for r modes with Fourier amplitude spectra of Kepler light curves of upper main-sequence B, A, and F stars, we find that r modes are present in many γ Dor stars (as first discovered by Van Reeth et al.), spotted stars, and so-called heartbeat stars, which are highly eccentric binary stars. We also find a signature of r modes in a frequently bursting Be star observed by Kepler. In the amplitude spectra of moderately to rapidly rotating γ Dor stars, r-mode frequency groups appear at lower frequency than prograde g-mode frequency groups, while in the amplitude spectra of spotted early A to B stars, groups of symmetric (with respect to the equator) r-mode frequencies appear just below the frequency of a structured peak that we suggest represents an approximate stellar rotation rate. In many heartbeat stars, a group of frequencies can be fitted with symmetric m = 1 r modes, which can be used to obtain rotation frequencies of these stars.

On the Excitation Mechanism for the Nonradial Pulsations in ϵ Persei

We have examined whether the kappa-mechanism at the ”Z” opacity bump can excite overstable nonradial pulsation (NRP) modes such as those responsible for the line-profile variations ( lpv ) observed for ϵ Persei (Gies et al. 1999). From the lpv modeling with realistic stellar parameters and the state-of-the-art codes, we confirmed that the observed lpv can generally be explained by the modes with l values suggested by Gies et al. (1999). We have also found that some tesseral modes, which have smaller m than those of sectoral modes, can reproduce the observed lpv well for the periods of 3.51hr/3.84 hr and 4.06hr/4.54 hr. Our linear non-adiabatic nonradial pulsation analysis applied to massive (13M ⊙ ––14M ⊙ ) stars shows that the periods of higher | m | values in the co-rotating frame are too long to be excited by the Z-bump kappa-mechanism while the smaller | m | values give marginal consistency.

Low-frequency oscillations of rotating massive stars

Stellar rotation significantly modifies the property of nonradial oscillations when the frequencies (in the co-rotating frame) are comparable to or less than the frequency of rotation. The angular dependence of the amplitude of such an oscillation cannot be expressed by a single spherical harmonic, Ylm (θ, φ). The amplitude of a g-mode tends to be confined to a narrow equatorial region compared to the non-rotating case. In addition to g-modes, which exist in a radiative equilibrium region, inertial (oscillatory convective) modes exist in a convective region. Half of the inertial modes have negative energy, while all the g-modes have positive energy. When the oscillation frequency of a positive energy mode is close to that of a negative energy mode, resonance coupling between the two modes occurs and energy flows from the negative energy mode to the positive one to increase the amplitude of both modes; i.e., to lead to the overstability of the oscillations. Therefore, overstable g-mode oscillations are possible for all rotating stars with inner convective and outer radiative regions. The resonance excitation of g-modes in the radiative envelope by inertial oscillations in the rotating convective core give natural explanation for rapid variations of early type stars. From observed periods of a variable early type star we can obtain information on the superadiabatic temperature gradient and the angular rotation frequency of the convective core.

Asymptotic analysis of inertial waves in the convective envelope of the sun

Inertial waves are propagative in convective regions of rotating stars. Half of the inertial waves have positive energy of oscillations and the other half negative energy. The inertial waves with negative energy become overstable when they are in resonance with waves having positive energy such as internal gravity waves or when they dissipate energy of oscillations through nonadiabatic effects. We calculate a frequency spectrum of inertial (oscillatory convective) modes with negative energy propagating in the surface convective zone of the sun by using an asymptotic method of nonradial oscillations of rotating stars. It is shown that the inertial modes have large amplitudes only at high latitudes. The inertial modes with negative energy have very low frequencies seen in the corotating frame and hence if they are observed in an inertial frame their frequencies are approximately equal to −mΩ⊙.