Earl P. Bellinger

Pavan Vynatheya, Adrian S. Hamers, Rosemary A. Mardling et al.

We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the Mardling-Aarseth stability formula from 2001, where we introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as `stable' and `unstable'. To achieve this, we generate a large training data set of 10^6 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than previous stability criteria, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of 93 % and 95 % respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use Python script.

Earl P. Bellinger, George C. Angelou, Saskia Hekker et al.

Owing to the remarkable photometric precision of space observatories like Kepler, stellar and planetary systems beyond our own are now being characterized en masse for the first time. These characterizations are pivotal for endeavors such as searching for Earth-like planets and solar twins, understanding the mechanisms that govern stellar evolution, and tracing the dynamics of our Galaxy. The volume of data that is becoming available, however, brings with it the need to process this information accurately and rapidly. While existing methods can constrain fundamental stellar parameters such as ages, masses, and radii from these observations, they require substantial computational efforts to do so. We develop a method based on machine learning for rapidly estimating fundamental parameters of main-sequence solar-like stars from classical and asteroseismic observations. We first demonstrate this method on a hare-and-hound exercise and then apply it to the Sun, 16 Cyg A & B, and 34 planet-hosting candidates that have been observed by the Kepler spacecraft. We find that our estimates and their associated uncertainties are comparable to the results of other methods, but with the additional benefit of being able to explore many more stellar parameters while using much less computation time. We furthermore use this method to present evidence for an empirical diffusion-mass relation. Our method is open source and freely available for the community to use. The source code for all analyses and for all figures appearing in this manuscript can be found electronically at https://github.com/earlbellinger/asteroseismology

Earl P. Bellinger, Shashi M. Kanbur, Anupam Bhardwaj et al.

The period of pulsation and the structure of the light curve for Cepheid and RR Lyrae variables depend on the fundamental parameters of the star: mass, radius, luminosity, and effective temperature. Here we train artificial neural networks on theoretical pulsation models to predict the fundamental parameters of these stars based on their period and light curve structure. We find significant improvements to estimates of these parameters made using light curve structure and period over estimates made using only the period. Given that the models are able to reproduce most observables, we find that the fundamental parameters of these stars can be estimated up to 60% more accurately when light curve structure is taken into consideration. We quantify which aspects of light curve structure are most important in determining fundamental parameters, and find for example that the second Fourier amplitude component of RR Lyrae light curves is even more important than period in determining the effective temperature of the star. We apply this analysis to observations of hundreds Cepheids in the Large Magellanic Cloud and thousands of RR Lyrae in the Magellanic Clouds and Galactic bulge to produce catalogs of estimated masses, radii, luminosities, and other parameters of these stars. As an example application, we estimate Wesenheit indices and use those to derive distance moduli to the Magellanic Clouds of $μ_{\text{LMC},\text{CEP}} = 18.688 \pm 0.093$, $μ_{\text{LMC},\text{RRL}} = 18.52 \pm 0.14$, and $μ_{\text{SMC},\text{RRL}} = 18.88 \pm 0.17$ mag.