Analyzing and developing a model for the Radial Velocity data of Gamma Draconis’ Star

Gamma Draconis (also known as Eltanin) is a K5 III type star located 154.3 light years away from Earth. We are studying the radial velocity variability of Gamma Dra because it appeared to have a 10.7 MJ (Jupiter mass) planet during the years 2003-2011, but the velocity oscillations then decayed and phase-shifted (Hatzes et al. 2018). Gamma Dra is therefore a good test case for algorithms designed to disentangle true planet discoveries from false positives due to magnetic activity, rotation, oscillations, or granulation. Hatzes et al. suggest that Gamma Dra’s RV variations could be coming from oscillatory convective modes, but did not fit a model to the data. We have been studying the archival radial velocity data of Gamma Draconis, looking for a physically motivated mathematical model of the star’s RV variability. Since the RV time series is quasi-periodic, we have selected a Gaussian process (GP) model that combines two covariance kernels of sines squared, which encodes periodic variations, and squared exponential, which allows the periodic signal to decay with increasing time lag between two data points. We are also testing a variation of the quasi-periodic model that includes a second cycle with a much longer period than the ~700-day decaying signal reported by Hatzes et al. GP regression is a nonparametric machine learning algorithm with a Bayesian approach to model fitting. This method has several benefits such as working well on small datasets and having the ability to provide uncertainty measurements on the period and correlation time. Our objective is to run statistical hypothesis tests to prove if our model is reasonable and to make sure it is not overfitting the data. Our research will improve our understanding of the intrinsic variability of red giants, which will help with planet discovery validation on red giant-focused planet searches (e.g. Hrudkova’ et al. 2017). More generally, our goal is to improve modeling of quasi-periodic noise in all types of target stars, as stellar noise is the limiting factor in searches for earthlike planets orbiting sunlike stars.