AMPLITUDES OF STELLAR OSCILLATIONS - THE IMPLICATIONS FOR ASTEROSEISMOLOGY

There are no good predictions for the amplitudes expected from solar-l ike oscillations in other stars. In the absence of a definitive model for convection, which is thought to be the mechanism that excites thes e oscillations, the amplitudes for both velocity and luminosity measur ements must be estimated by scaling from the Sun. In the case of lumin osity measurements, even this is difficult because of disagreement ove r the solar amplitude. This last point has lead us to investigate whet her the luminosity amplitude of oscillations delta L/L can be derived from the velocity amplitude (v(osc)). Using linear theory and observat ional data, we show that p-mode oscillations in a large sample of puls ating stars satisfy (delta L/L)(bol) proportional to v(osc)/T-eff. Usi ng this relationship, together with the best estimate of v(osc,.) = (2 3.4 +/- 1.4) cm s(-1), we estimate the luminosity amplitude of solar o scillations at 550 nm to be delta L/L = (4.7 +/- 0.3) ppm. Next we dis cuss how to scale the amplitude of solar-like (i.e., convectively-powe red) oscillations from the Sun to other stars. The only predictions co me from model calculations by Christensen-Dalsgaard and Frandsen (1983 , Sol. Phys. 82, 469). However, their grid of stellar models Is not de nse enough to allow amplitude predictions for an arbitrary star. Never theless, although convective theory is complicated, we might expect th at the general properties of convection - including oscillation amplit udes - should change smoothly through the colour-magnitude diagram. In deed, we find that the velocity amplitudes predicted by the model calc ulations are well fitted by the relation v(osc) proportional to L/M. T hese two relations allow us to predict both the velocity and luminosit y 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 i s not yet good evidence for solar-like oscillations in any star except the Sun. For solar-type stars (e.g., alpha Cen A and beta Hyi), obser vations have not yet reached sufficient sensitivity to detect the ampl itudes we predict. For some F-type stars, namely Procyon and several m embers of M67, detection sensitivities 30-40% below the predicted ampl itudes have been achieved. We conclude that these stars must oscillate with amplitudes less than has generally been assumed.