Population synthesis of delta Scuti stars: the instability strip, period-luminosity relation, and large-separation distribution

Interpreting the observed properties of intermediate-mass stars requires accounting for rotation, binarity, intrinsic population diversity, and measurement uncertainty. We combine these effects in population-synthesis models of 1.4-2.5 M stars that include pulsation properties of delta Sct variables. The synthetic populations successfully reproduce the distributions of stars observed in young associations, validating the mapping between intrinsic and observed stellar properties. Using these models, we infer a semi-empirical delta Sct instability strip by matching synthetic and observed populations. The resulting instability strip is systematically hotter than widely used theoretical prescriptions, implying that delta Sct stars are on average 0.1 M more massive than previously assumed, with 95% of the population spanning approximately 1.50-2.30 M. We then investigate the delta Sct period-luminosity relation and reproduce its recently identified second ridge with mixture models in which roughly one-third of stars have the fifth or sixth radial overtone as their dominant mode; the fraction increases in younger populations. In contrast, unresolved binarity does not account for the second ridge. Finally, we predict the population-wide distribution of asteroseismic large separations, nu, finding a peak between 6 and 7 d-1, in agreement with recent observations. We also demonstrate that nu is most reliably measured with the 'echelle technique, while autocorrelation methods can produce spurious detections when used in isolation. These results show that population synthesis provides a powerful framework for interpreting populations of delta Sct stars and for linking stellar evolution, pulsation, and observation.