The period-luminosity relation for δ Scuti stars using Gaia DR2 parallaxes

We have examined the period-luminosity (P-L) relation for δ Scuti stars using Gaia DR2 parallaxes. We included 228 stars from the catalogue of Rodríguez et al., as well as 1124 stars observed in the 4-yr Kepler mission. For each star, we considered the dominant pulsation period, and used DR2 parallaxes and extinction corrections to determine absolute V magnitudes. Many stars fall along a sequence in the P-L relation coinciding with fundamental-mode pulsation, while others pulsate in shorter period overtones. The latter stars tend to have higher effective temperatures, consistent with theoretical calculations. Surprisingly, we find an excess of stars lying on a ridge with periods half that of the fundamental. We suggest this may be due to a 2:1 resonance between the third or fourth overtone and the fundamental mode.