The study of main-sequence star super-flare frequency, peculiar super-flares and empirical relations between stellar activity and rotation periods

Abstract

Stellar flares are unpredictable, explosive phenomena defined as sudden, intense brightening on the surface of a star caused by the release of magnetic energy during the reconnection of twisted magnetic fields in the outer atmospheres of stars. During a stellar flare, a sizable fraction of the energy is released as electromagnetic radiation with a wide range of wavelengths, from radio waves to gamma rays. The observations of the brightness increase across different wavelengths, especially in X-rays and UV, are frequently used to detect stellar flares. Most flares are observed on young, active stars or magnetically active stars like our Sun. Stellar flares have a significant impact on the environment, including the planetary system of the star. Additionally, flares can cause disturbances in the star’s magnetic field, leading to stellar storms and coronal mass ejections that may adversely affect life on nearby planets. Studying stellar flares helps us understand magnetic fields, stellar activity, and the interaction of stars and their planetary systems.

This thesis provides observations and statistical analysis of stellar flares found by an automated flare detection Python script, written for this purpose, that was used to search for super-flares on main sequence stars of types A, F, G, K, and M based on the entire Kepler’s long-cadence data. 4637 super-flares on 1896 G-type dwarfs were found, and it was determined that a super-flare on G-type dwarfs of energy of 10^35 erg occurs on a star once every 4360 years. Furthermore, 321, 1125, 4538 and 5445 super-flares were found on 136, 522, 770 and 312 dwarfs of types A, F, K and M, respectively. Moreover, the statistical properties of the occurrence rate of super-flares were studied and confirmed that the occurrence rate (dN/dE) of super-flares versus flare energy, E, follows a power law distribution with dN/dE ∝ E^(-α), where α ≃ 2.0 to 2.1 for the spectral types ranging from F-type to M-type stars. However, for A-type stars, the value of α is approximately 1.3. This indicates that A-type stars’ flare conditions differ from those of other spectral types.

In addition, the thesis presents new results of the occurrences of super-flares on slowly rotating Sun-like stars with rotation periods ranging from 24.5 to 44 days. This finding further supports previous, controversial results that the Sun may experience a surprise super-flare. Furthermore, the thesis describes newly found unusually large amplitude super-flares detected on G- and M-type main-sequence stars. A preliminary examination of these cases was provided, and the link between e-folding decay time, τ vs flare amplitude and flare energy was studied. The results show that for Sun-like stars with a slow rotation period, low τ values are associated with high flare energies, and high τ values are associated with low flare energies. Similarly, τ is large for small flare amplitudes, and τ is small for large amplitudes considered. However, there is no clear relation between these parameters for large amplitude super-flares in the main sequence G- and M-type stars, as we could not establish clear functional dependence between the parameters.

Previous studies have revealed short activity cycles in F-type and G-type stars, and the question investigated was whether or not short-term activity cycles are a common phenomenon in these stars. Also, extensive studies establish an empirical connection between a star’s activity cycle and rotation periods. Therefore, 138 Kepler IDs of F and G types main sequence stars with rotation periods less than a day (P_rot < 1 d) were collected using Kepler data and Gaia parameters to derive, as well as use plausible, established empirical relations between P_cyc and Prot to provide predictions for very short 5.09 ≤ P_cyc ≤ 38.46 d cases in a tabular form. Also, an alternative method for measuring very short P_cyc, using flare-detection algorithms applied to future space mission data, has been proposed.