The Potential of Multicolor Photometry for Pulsating Subdwarf B Stars

Abstract

We investigate the potential of multicolor photometry for partial mode identification in both long- and short-period variable subdwarf B stars. The technique presented is based on the fact that the frequency dependence of an oscillation's amplitude and phase bears the signature of the mode's degree index l, among other things. Unknown contributing factors can be eliminated through the evaluation of the amplitude ratios and phase differences arising from the brightness variation in different wavebands, theoretically enabling the inference of the degree index from observations in two or more bandpasses. Employing a designated model atmosphere code, we calculate the brightness variation expected across the visible disk during a pulsation cycle in terms of temperature, radius, and surface gravity perturbations to the emergent flux for representative EC 14026 and PG 1716 star models. Nonadiabatic effects are considered in detail and found to be significant from nonadiabatic pulsation calculations applied to our state-of-the-art models of subdwarf B stars. Our results indicate that the brightness variations observed in subdwarf B stars are caused primarily by changes in temperature and radius, with surface gravity perturbations playing a small role. For PG 1716 stars, temperature effects dominate in the limit of long periods with the result that the oscillatory amplitudes and phases lose their period dependence and nonadiabatic effects become unimportant. Outside this regime, however, their values are strongly influenced by both factors. We find that the phase shifts between brightness variations in different wavebands are generally small but may lie above the experimental detection threshold in certain cases. The prospect of mode discrimination seems much more promising on the basis of the corresponding amplitude ratios. While in EC 14026 stars the amplitude ratios predicted are very similar for modes with l = 0, 1, or 2, they are well separated from those of modes with l = 3, l = 5, and l = 4 or 6, each of which form a distinct group. For the case of the PG 1716 stars it should be possible to discriminate between modes with l = 1, 2, 4, or 6 and those of degree indices l = 3 and l = 5. Identifying modes within a given group is challenging for both types of pulsator and requires multicolor photometry of extremely high quality. Nevertheless, we demonstrate that it is feasible using the example of the largest amplitude peak detected for the fast pulsator KPD 2109+4401 by Jeffery et al.