Amplitudes of stellar oscillations: the implications for asteroseismology

There are no good predictions for the amplitudes expected from solar-like oscillations in other stars. In the absence of a definitive model for convection, which is thought to be the mechanism that excites these oscillations, the amplitudes for both velocity and luminosity measurements must be estimated by scaling from the Sun. In the case of luminosity measurements, even this is difficult because of disagreement over the solar amplitude. This last point has lead us to investigate whether the luminosity amplitude of oscillations ( L=L) can be derived from the velocity amplitude (vosc). Using linear theory and observational data, we show that p-mode oscillations in a large sample of pulsating stars satisfy ( L=L)bol / vosc=Teff . Using this relationship, together with the best estimate of vosc; = (23:4 1:4) cm s 1, we estimate the luminosity amplitude of solar oscillations at 550 nm to be ( L=L) = (4:7 0:3) ppm. Next we discuss how to scale the amplitude of solar-like (i.e., convectively-powered) oscillations from the Sun to other stars. The only predictions come from model calculations by Christensen-Dalsgaard & Frandsen (1983, Sol. Phys. 82, 469). However, their grid of stellar models is not dense enough to allow amplitude predictions for an arbitrary star. Nevertheless, although convective theory is complicated, we might expect that the general properties of convection – including oscillation amplitudes – should change smoothly through the colourmagnitude diagram. Indeed, we find that the velocity amplitudes predicted by the model calculations are well fitted by the relation vosc / L=M . These two relations allow us to predict both the velocity and luminosity amplitudes of solar-like oscillations in any given star. We compare these predictions with published observations and evaluate claims for detections that have appeared in the literature. We argue that there is not yet good evidence for solar-like oscillations in any star except the Sun. For solartype stars (e.g., Cen A and Hyi), observations have not yet reached sufficient sensitivity to detect the amplitudes we predict. For some F-type stars, namely Procyon and several Send offprint requests to: Tim Bedding ([email protected]) ? Present address: Institute of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark ([email protected]) members of M67, detection sensitivities 30–40% below the predicted amplitudes have been achieved. We conclude that these stars must oscillate with amplitudes less than has generally been assumed.