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

We have examined the period-luminosity (P-L) relation for delta Scuti stars using Gaia DR2 parallaxes. We included 228 stars from the catalogue of Rodriguez et al. (2000), as well as 1124 stars observed in the four-year 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.