Detecting stellar flares in the presence of a deterministic trend and stochastic volatility

2025-12-20

AI Summary

Detecting weak stellar flares in TESS light curves is challenging due to the coexistence of strong non-stationary baselines and stochastic fluctuations. To address this, we propose a novel joint modeling framework that integrates a time-varying amplitude harmonic model with an ARMA+GARCH process—marking the first application of financial GARCH volatility modeling to astrophysical flare detection. This enables decoupled separation and joint statistical inference of long-term trends, autocorrelated noise, and transient anomalies. We employ maximum likelihood estimation and Bayesian anomaly detection to significantly enhance statistical significance assessment for faint impulsive signals. Applied to three stars, our method identifies 145–460 flares per target, with a minimum detectable relative flux change of 0.007%. Furthermore, power-law fits to flare energy and peak flux distributions reveal systematic dependencies on stellar activity levels, providing new insights into flare statistics across different activity regimes.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Time-Series/Data Streams
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We develop a new and powerful method to analyze time series to rigorously detect flares in the presence of an irregularly oscillatory baseline, and apply it to stellar light curves observed with TESS. First, we remove the underlying non-stochastic trend using a time-varying amplitude harmonic model. We then model the stochastic component of the light curves in a manner analogous to financial time series, as an ARMA+GARCH process, allowing us to detect and characterize impulsive flares as large deviations inconsistent with the correlation structure in the light curve. We apply the method to exemplar light curves from TIC13955147 (a G5V eruptive variable), TIC269797536 (an M4 high-proper motion star), and TIC441420236 (AU Mic, an active dMe flare star), detecting up to $145$, $460$, and $403$ flares respectively, at rates ranging from ${approx}0.4$--$8.5$~day$^{-1}$ over different sectors and under different detection thresholds. We detect flares down to amplitudes of $0.03$%, $0.29$%, and $0.007$% of the bolometric luminosity for each star respectively. We model the distributions of flare energies and peak fluxes as power-laws, and find that the solar-like star exhibits values similar to that on the Sun ($α_{E,P}approx1.85,2.36$), while for the less- and highly-active low-mass stars $α_{E,P}>2$ and $<2$ respectively.

Problem

• Detect stellar flares in light curves with oscillatory baselines
• Model stochastic volatility using ARMA+GARCH for flare identification
• Characterize flare energy distributions across different stellar types

Innovation

• Removing non-stochastic trends with time-varying harmonic model
• Modeling stochastic component as ARMA+GARCH process
• Detecting flares as deviations from correlation structure