Period spacings and global seismic parameters for K2 red giants using deep learning

Gravity-mode period spacings (DPi_1) of red giants probe the stellar core directly, constraining its structure, mass and evolutionary state. Their measurement requires resolving narrow, densely spaced mixed modes and has so far relied on the four-year baseline of Kepler. Recovering DPi_1 from the much shorter ( 80-day) baselines typical of K2 remains largely unexplored at the ensemble scale. We develop an automated machine-learning technique to measure global asteroseismic parameters and gravity-mode period spacings for red giants from single-campaign K2 photometry. Two deep residual neural networks take the full-resolution power spectrum of an 80-day light curve as input, without background fitting or mode identification, and return a probability distribution for each parameter, yielding a point estimate and asymmetric uncertainties. They are trained on 8 million synthetic spectra and evaluated on held-out synthetics, on Kepler data degraded to K2-like resolution, and on K2 observations. On Kepler data at K2-like resolution, numax and Dnu are recovered for 96% and 91% of stars with robust dispersions of 3.6% and 1.2%; DPi_1 for 22%, with a dispersion of 0.9%. Applied to 18,704 K2 red giants, the inferred numax and Dnu agree with catalogue values to 5.8% and 1.9%, the additional scatter arising from known K2 artefacts. Among the 2,059 young red giants we obtain DPi_1 for 232 stars with a median fractional uncertainty of 1.3%, following the same Dnu-DPi_1 sequence as the Kepler sample although the training set carries no imprint of that relation. We show that numax, Dnu and - for a subset of young red giants - DPi_1 can be recovered from a single 80-day K2 campaign within an automated, probabilistic machine-learning framework. This approach can also be extended to short-baseline samples from TESS and, in future, Roman and PLATO.