Inference of stellar parameters from brightness variations

It has been demonstrated that the time variability of a stars brightness at different frequencies can be used to infer its surface gravity, radius, mass, and age. With large samples of light curves now available from Kepler and K2, and upcoming surveys like TESS, we wish to quantify the overall information content of this data and identify where the information resides. As a first look into this question we ask which stellar parameters we can predict from the brightness variations in red-giant stars data and to what precision, using a data-driven model. We demonstrate that the long-cadence (30-minute) Kepler light curves for 2000 red-giant stars can be used to predict their $T_{rm eff}$ and $log g$. Our inference makes use of a data-driven model of a part of the autocorrelation function (ACF) of the light curve, where we posit a polynomial relationship between stellar parameters and the ACF pixel values. We find that this model, trained using 1000 stars, can be used to recover the temperature $T_{rm eff}$ to $<$100 K, the surface gravity to $<$ 0.1 dex, and the asteroseismic power-spectrum parameters $rm u_{max}$ and $rm Delta{ u}$ to $<11$ $mu$Hz and $<0.9$ $mu$Hz ($lesssim$ 15%). We recover $T_{rm eff}$ from range of time-lags 0.045 $<$ $T_{rm lag}$ $<$ 370 days and the $log g$, $rm u_{max}$ and $rm Delta{ u}$ from the range 0.045 $<$ $T_{rm lag}$ $<$ 35 days. We do not discover any information about stellar metallicity. The information content of the data about each parameter is empirically quantified using this method, enabling comparisons to theoretical expectations about convective granulation.