[Paper Review] Stellar Parameters in an Instant with Machine Learning: Application to Kepler LEGACY Targets

Earl P. Bellinger, George C. Angelou+4 more|May 18, 2017

Stellar, planetary, and galactic studies5 references3 citations

TL;DR

This paper presents a machine learning approach using regression trees to rapidly infer stellar parameters—such as mass, age, radius, and evolutionary model parameters—for 52 main-sequence Kepler LEGACY stars from asteroseismic data. The method achieves high precision, with median uncertainties of 3.6% for mass, 1.7% for radius, and 14.8% for age, while enabling fast, scalable estimation of previously intractable parameters like initial helium abundance and diffusion coefficients without iterative grid searches.

ABSTRACT

With the advent of dedicated photometric space missions, the ability to rapidly process huge catalogues of stars has become paramount. Bellinger and Angelou et al. (2016) recently introduced a new method based on machine learning for inferring the stellar parameters of main-sequence stars exhibiting solar-like oscillations. The method makes precise predictions that are consistent with other methods, but with the advantages of being able to explore many more parameters while costing practically no time. Here we apply the method to 52 so-called "LEGACY" main-sequence stars observed by the Kepler space mission. For each star, we present estimates and uncertainties of mass, age, radius, luminosity, core hydrogen abundance, surface helium abundance, surface gravity, initial helium abundance, and initial metallicity as well as estimates of their evolutionary model parameters of mixing length, overshooting coefficient, and diffusion multiplication factor. We obtain median uncertainties in stellar age, mass, and radius of 14.8%, 3.6%, and 1.7%, respectively. The source code for all analyses and for all figures appearing in this manuscript can be found electronically at: https://github.com/earlbellinger/asteroseismology

Motivation & Objective

• To develop a fast, scalable method for inferring stellar parameters from asteroseismic data without iterative grid searches.
• To estimate not only standard parameters like mass and radius but also complex evolutionary model parameters such as mixing length, overshooting, and diffusion coefficients.
• To apply the method to the high-quality Kepler LEGACY sample of 52 main-sequence stars with core hydrogen abundance ≥10⁻³.
• To quantify uncertainties and validate performance against theoretical limits and alternative methods.
• To enable rapid, precise, and comprehensive parameter estimation across large stellar samples, setting a new benchmark for efficiency and scope.

Proposed method

• The method employs classification and regression trees (CART) trained on a synthetic grid of stellar models generated with MESA and GYRE to map asteroseismic frequencies to physical parameters.
• It bypasses traditional iterative optimization by learning direct mappings from observed frequencies to stellar parameters, reducing computation to seconds per star.
• Posterior distributions of parameters are sampled via Monte Carlo methods, with uncertainties propagated through the trained model.
• A uniform prior is imposed on initial helium abundance $Y_0$ (0.22–0.34), and relative uncertainties are evaluated against theoretical maximums to assess reliability.
• The approach uses a truncated explained variance score $V_{\text{e, mean}}^{\text{trunc}}$ to evaluate predictive performance relative to random guessing, with truncation at 200 to avoid bias from zero-valued parameters.
• The method is applied to 52 stars from the Kepler LEGACY sample after excluding those with $X_c \leq 10^{-2}$, ensuring main-sequence status.

Experimental results

Research questions

• RQ1 Can machine learning enable fast, high-precision inference of stellar parameters from asteroseismic data without iterative grid searches?
• RQ2 How accurately can evolutionary model parameters such as mixing length, overshooting, and diffusion coefficients be estimated using this approach?
• RQ3 What are the relative uncertainties of key parameters like mass, radius, age, and surface gravity, and how do they compare to theoretical limits?
• RQ4 Why are certain parameters like diffusion multiplier $D$ and overshooting coefficient $\alpha_{\text{ov}}$ poorly constrained despite the method’s overall accuracy?
• RQ5 To what extent does the method outperform traditional optimization-based techniques in speed and parameter coverage?

Key findings

• The median uncertainty in stellar mass is 3.6%, with the best-constrained star (KIC 8760414) achieving 1.34% uncertainty.
• The median uncertainty in stellar radius is 1.7%, with surface gravity estimated to better than 0.26% on average, making it the most precisely constrained parameter.
• The initial helium abundance $Y_0$ is constrained with a median uncertainty of 3.14%, significantly below its theoretical maximum of 54.51%.
• The diffusion multiplier $D$ has a median uncertainty of 86.86%, with over a third of stars having uncertainty exceeding 100%, indicating strong degeneracy with initial composition and model limitations.
• The overshooting coefficient $\alpha_{\text{ov}}$ has a median uncertainty of 53.29% and a truncated explained variance score of only 0.483, indicating poor constraint and high degeneracy.
• The method achieves a truncated explained variance score of 0.932 for $\log g$, 0.906 for radius, and 0.830 for mass, indicating excellent predictive performance relative to random guessing.