Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...273..135a&link_type=abstract
Astronomy and Astrophysics, Vol.273, NO. 1/JUNI, P. 135, 1993
Astronomy and Astrophysics
Astrophysics
43
Line: Profiles, Stars: Individual: Μ Cen, Ζ Oph, Stars: Oscillations, Stars: Rotation
Scientific paper
We present a theoretical expression for the components of the Lagrangian displacement field ξ for a rotating, pulsating star, taking into account the effect of the Coriolis force. We re-emphasize that for a rotating ξ star cannot be described by a single spherical harmonic; correction terms proportional to the ratio Ω/ω of the rotation and pulsation frequencies have to be taken into account. We show that this first-order correction to a mode with degree l and azimuthal number m consists of two toroidal terms, one with degree l - 1 and one with degree l + 1, and one spheroidal term with degree l, all sharing azimuthal number m. A second-order approximation, which would also take into account the effect of the centrifugal force, was not attempted, because of the extreme complexity of the problem if spherical symmetry does not apply. Our expressions thus apply to a monoperiodic pulsation with a period significantly shorter than the rotation period, i.e. for p-modes or low-order g-modes, or for high-order -modes in slow rotators.
We then redetermine the velocity of a point on the stellar surface in the direction of the observer and study the effect of the new terms on line profile variations. Comparison of theoretical profiles with various sets of input parameters shows that the effects are huge in most cases when Ω/ω is larger than 20%. The toroidal terms induce additional "bumps", in particular in the case of low-degree pulsations. Prograde modes are affected most; the symmetry with respect to m disappears. We compare theoretically generated profiles with the observations of some famous line profile variables and conclude that the assumption of having high l-values in these stars has to be questioned. An interesting result is that Baade's (1984) observations of μ Cen may be explained by a single l = -m = 2 mode. The implications of our results for the interpretation of early-type variables of different kinds are briefly addressed.
Aerts Christine
Waelkens Christoffel
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