New Approach to Superflare Energy Determination

TL;DR

This paper introduces a new physically motivated method for estimating stellar flare energies that accounts for time-dependent temperature evolution, improving accuracy over traditional fixed-temperature approaches, especially for single-band observations.

Contribution

The paper presents a novel approach that models flare temperature as variable over time with a constant emitting area, validated on a large TESS flare dataset.

Findings

Reduces systematic errors in energy estimates up to ten times

Improves accuracy by using peak temperatures from semi-empirical models

Applicable to main-sequence stars of spectral types K4 and later

Abstract

We present a new method for estimating the total energy radiated by stellar flares in broad-band continua, which assumes a constant emitting area but incorporates a time-dependent temperature evolution. This physically motivated approach offers an alternative to the commonly used method that assumes a fixed flare temperature about of 10 000\,K and variable area. By allowing the temperature to vary over time while keeping the emitting area constant, our method captures more realistic flare behaviour. This time-dependent treatment of the flare temperature is supported by numerous solar observations, numerical simulations, and multiwavelength studies of active stars. We demonstrate that using peak flare temperatures estimated from a semi-empirical model grid, rather than assuming an ad-hoc flare temperature value, improves the accuracy of total energy estimates. Although the most precise results still require a multi-band photometry/spectroscopy or independently constrained flare temperatures, our method offers a practical and scalable solution for single-band observations. It is particularly well suited for main-sequence stars of spectral types K4 and later with known effective temperatures. Finally we discuss how the flare continuum behaves under varying chromospheric conditions. Our method improves flare energy estimates by incorporating a physically relevant time-dependent temperature evolution and empirically derived peak temperatures, rather than assuming a constant 10 000\,K value. This modification reduces systematic errors that can reach factors up to ten as compared to previous estimates. We proved this on a sample of 50,320 TESS flares.