Photometric modal discrimination in Delta Scuti and Gamma Doradus stars

TL;DR

This paper evaluates photometric methods, especially Stromgren photometry, for identifying pulsation modes in delta Scuti and gamma Doradus stars, discussing limitations and potential for future space-based observations.

Contribution

It introduces two methods to calculate phase lags and departure from adiabaticity, demonstrating their effectiveness in mode discrimination for these variable stars.

Findings

Gamma Dor stars have phase lags near 0 degrees, opposite to delta Scuti stars.

Application to HADS confirms radial pulsation modes (l=0).

Multi-band photometry is highly effective for mode identification.

Abstract

The potential of photometric methods for the identification of l, the degree of spherical surface harmonic of a pulsating star, is investigated with special emphasis on Stromgren photometry applied to delta Scuti and gamma Dor variables. Limitations of actual model atmospheres when fine precision is required for the calculations of partial derivatives and integrals, which depend on limb darkening coefficients, are discussed. Two methods are discussed to calculate the phase lags, the angle between maximum temperature and minimum radius, and R, a parameter which describes departure from adiabaticity of the atmospheres of these pulsating stars. These quantities appear to be very dependent on the convection as parametrized by the mixing length theory. When one of the methods is applied to the gamma Dor stars gives phase lags close to 0 degrees, which are 90-180 degrees out of phase from typical delta Scuti stars. Examples are given for some High Amplitude Delta Scuti Stars (HADS) where the method can be easily applied and gives results consistent to interpret them as radial (l=0) pulsating stars. Other low amplitude delta Scuti stars could be oscillating in a non-radial (l=1, 2) mode. Multi-band photometry is concluded to be a very powerful tool for mode identification of delta Scuti and gamma Dor stars, specially with the more accurate photometry that will be achieved in the near future with the asteroseismological space missions now in progress.