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Register a new userExcitation and visibility of slow modes in rotating B-type stars
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Added by
Alexey A. Pamyatnykh
Publication date
2006
fields
Physics
and research's language is
English
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We use the traditional approximation to describe oscillations with frequencies comparable to the angular rotation rate. Validity of this approximation in application to main-sequence B stars is discussed. Numerical results regarding mode stability and visibility are presented for a model of the Be star HD 163868. For this object, Walker et al.(2005) detected a record number of mode frequencies using data from the small space telescope MOST. Our interpretation of these data differs from that of Walker et al. In particular, we interpret peaks in the lowest frequency range as retrograde g modes. We find instability in a large number of modes that remain undetectable because of unfavourable aspect and/or effect of cancellation. There is no clear preference to excitation of prograde modes.
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We study how rotation affects observable amplitudes of high-order g- and mixed r/g-modes and examine prospects for their detection and identification. Our formalism, which is described in some detail, relies on a nonadiabatic generalization of the traditional approximation. Numerical results are presented for a number of unstable modes in a model of SPB star, at rotation rates up to 250 km/s. It is shown that rotation has a large effect on mode visibility in light and in mean radial velocity variations. In most cases, fast rotation impairs mode detectability of g-modes in light variation, as Townsend (2003b) has already noted, but it helps detection in radial velocity variation. The mixed modes, which exist only at sufficiently fast rotation, are also more easily seen in radial velocity. The amplitude ratios and phase differences are strongly dependent on the aspect, the rotational velocity and on the mode. The latter dependence is essential for mode identification.
Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray dynamics to build an asymptotic theory for the subset of regular modes which are the easiest to observe and identify. Comparisons with 2D numerical simulations of oscillations in polytropic stars show that both the frequency and amplitude distributions of these modes can accurately be described by an asymptotic theory for almost all rotation rates. The spectra are mainly characterized by two quantum numbers; their extraction from observed spectra should enable one to obtain information about stellar interiors.
Several classes of stars (most notably O and B main-sequence stars, as well as accreting white dwarfs and neutron stars) rotate quite rapidly, at spin frequencies greater than the typical g-mode frequencies. We discuss how rapid rotation modifies the $kappa$-mechanism excitation and observability of g-mode oscillations. We find that, by affecting the timescale match between the mode period and the thermal time at the driving zone, rapid rotation stabilizes some of the g-modes that are excited in a non-rotating star, and, conversely, excites g-modes that are damped in absence of rotation. The fluid velocities and temperature perturbations are strongly concentrated near the equator for most g-modes in rapidly rotating stars, which means that a favorable viewing angle may be required to observe the pulsations. Moreover, the stability of modes of the same $l$ but different $m$ is affected differently by rotation. We illustrate this by considering g-modes in Slowly Pulsating B-type stars as a function of the rotation rate.
For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...). Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modeled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions. We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.
We present results of a search for identification of modes responsible for the six most significant frequency peaks detected in the rapidly rotating SPB star $mu$ Eridani. All published and some unpublished photometric data are used in our new analysis. The mode identification is carried out with the method developed by Daszynska-Daszkiewicz et al. employing the phases and amplitudes from multi-band photometric data and relying on the traditional approximation for the treatment of oscillations in rotating stars. Models consistent with the observed mean parameters are considered. For the five frequency peaks, the candidates for the identifications are searched amongst unstable modes. In the case of the third frequency, which is an exact multiple of the orbital frequency, this condition is relaxed. The systematic search is continued up to a harmonic degree $ell =6$. Determination of the angular numbers, $(ell,m)$, is done simultaneously with the rotation rate, $V_{rm rot}$, and the inclination angle, $i$, constrained by the spectroscopic data on the projected rotational velocity, $V_{rm rot}sin i$, which is assumed constant. All the peaks may be accounted for with g-modes of high radial orders and the degrees $ellle 6$. There are differences in some identifications between the models. For the two lowest--amplitude peaks the identifications are not unique. Nonetheless, the equatorial velocity is constrained to a narrow range of (135, 140) km/s. Our work presents the first application of the photometric method of mode identification in the framework of the traditional approximation and we believe that it opens a new promising direction in studies of SPB stars.
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