Granulation signatures as seen by Kepler short-cadence data. II. A hierarchical route to inferring stellar radii from granulation

Stellar granulation arises from near-surface convection and is imprinted in stellar photometric time series, yet links between granulation observables and fundamental stellar properties remain underexploited. We aim to establish a statistically robust framework for inferring stellar radii directly from granulation signals in long-duration space-based photometry, aided by atmospheric parameters. We construct a Bayesian hierarchical model to connect stellar radius and granulation, relating radius through regression to the total granulation amplitude, primary characteristic frequency of the granulation, stellar effective temperature, and surface metallicity. The derivation is performed separately for three granulation models, propagating the marginal posteriors of the granulation parameters to account for intrinsic dispersion of the derived relations. Each background model yields a unique radius posterior, subsequently combined using Bayesian evidences as weights, producing posteriors that best represent the given star. The granulation-radius relations were derived from a heterogeneous sample of 363 stars, combining seismic and interferometric targets from multiple sources. Application to an independent sample of 367 stars recovers the reference radii within $1\sigma$ in ${\approx}73\%$ of cases. The distribution of residuals is consistent with a well-calibrated and unbiased inference. Across applications, the granulation-inferred radii achieve a precision of ${\approx}10\%$. The agreement with seismic and interferometric benchmarks demonstrates that granulation carries predictive information on stellar radii at a level comparable to several established techniques. Using granulation as a structural diagnostic enables the inference of stellar radii from granulation signals across diverse stellar populations; directly applicable to data from Kepler, TESS, and the upcoming ESA PLATO mission.