Amplitudes of Stellar Oscillations: The Implications for Asteroseismology

TL;DR

This paper investigates how to predict stellar oscillation amplitudes, especially luminosity variations, by relating velocity amplitudes to luminosity changes using observational data and linear theory, aiding asteroseismology.

Contribution

It derives a relation between luminosity and velocity amplitudes of stellar oscillations and discusses scaling these amplitudes from the Sun to other stars.

Findings

Luminosity amplitude (dL/L) is proportional to velocity amplitude (v_osc) divided by effective temperature (T_eff).

Estimated solar luminosity amplitude at 550 nm is approximately 4.7 ppm.

Model predictions suggest oscillation amplitudes change smoothly across different types of stars.

Abstract

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 (dL/L) can be derived from the velocity amplitude v_osc. Using linear theory and observational data, we show that p-mode oscillations in a large sample of pulsating stars satisfy (dL/L)_bol proportional to v_osc/T_eff. Using this relationship, together with the best estimate of v_osc(Sun) = (23.4 +/- 1.4) cm/s, we estimate the luminosity amplitude of solar oscillations at 550 nm to be dL/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, 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 colour-magnitude diagram. Indeed, we find that the velocity amplitudes predicted by the model