A semi-analytical formula for the light variations due to low-frequency g modes in rotating stars

Through the adoption of the so-called ‘traditional approximation’, a new semi-analytical formula is derived for the light variations produced by low-frequency g modes in uniformly rotating stars. The formula is used to examine the influence of rotation on the variability produced by a stellar model representative of the slowly pulsating B-type class. It is found that, for all apart from prograde sectoral modes, the Coriolis force acts to trap pulsation within an equatorial waveguide. Towards rapid rotation and/or low pulsation frequency, this waveguide becomes so narrow that only a thin band around the stellar equator makes any appreciable contribution toward flux changes. As a result, unless viewed from near the poles, the variability exhibited by the star becomes very small, possibly explaining why recent photometric observations of rapidly rotating stars have failed to find much evidence for the presence of low-frequency modes. It is further demonstrated that the ratio between the variability amplitude in pairs of passbands depends, with the introduction of rotation, both on the azimuthal order of a mode, and on the location of the observer in relation to the rotation axis of the star. This means that the standard photometric techniques used to identify modes in non-rotating stars cannot easily be applied to systems where rotation is significant.