An asteroseismic age estimate for the Pleiades using a neural-network emulator of rotating $\delta$ Scuti pulsation models

Abstract

Asteroseismology of $\delta$ Sct stars has strong potential for determining the ages of young stars through individual mode fitting. We present a neural-network emulator trained on approximately 46 million rotating pulsation models. From stellar mass, metallicity, age, and equatorial rotation velocity, it predicts 12 classical observables, two asteroseismic scalars, and the p mode, f mode and low-order g mode frequencies for degrees $\ell =0$-3, including the individual $m$ components of rotationally split multiplets. We couple the emulator to nested sampling through a multivariate likelihood that propagates correlated emulator residuals, making full Bayesian posterior exploration practical. Applied to five $\delta$ Sct stars in the Pleiades observed by TESS, the framework gives mutually consistent individual asteroseismic ages of 107-117 Myr. Combining their age posteriors gives a cluster age of $113.3\pm 4.5$ Myr (statistical), consistent with the $112\pm 5$ Myr lithium-depletion-boundary age and the 110-160 Myr range from rotating-isochrone fitting. Together with spectroscopic $v\sin i$, the inferred equatorial velocities also provide post-fit inclination estimates. Separate perturbed-grid tests using 100 matched synthetic pairs per input-physics variation give median absolute age shifts of $2.1$, $2.3$, and $5.2$ Myr for $|\Delta f_{\mathrm{ov}}|=0.005$, $|\Delta {\alpha }_{\mathrm{MLT}}|=0.1$, and $|\Delta Y|=0.02$, respectively; the corresponding 90th percentile shifts are $6.5$, $7.6$, and $16.2$ Myr. These tests describe conditional population sensitivities, not a systematic uncertainty on the Pleiades age. Together, the cluster-age agreement and the scale of these input-physics sensitivities support $\delta$ Sct asteroseismology as a complementary age estimation method for young stars.

arXiv comment26 pages, 21 figures, 14 tables