Magnetic Activity of Different Types of Variable Stars Observed by TESS Mission

The investigation of the magnetic activity of different types of variable stars holds significant implications for our understanding of the physical processes and evolution of stars. This study’s International Variable Star Index (VSX) variable star catalog was cross-matched with Transiting Exoplanet Survey Satellite (TESS) data, resulting in 26,276 labeled targets from 76,187 light curves. A total of 25,327 stellar flare events were detected, including 245 eclipsing binaries, 2324 rotating stars, 111 pulsating stars, and 629 eruptive stars. The results showed that flares from eclipsing binaries, rotating stars, eruptive stars, and pulsating stars have durations such that 90% are less than 2 h, and 91% of their amplitudes are less than 0.3. Flare events mainly occurred in the temperature range of 2000 K to 3000 K. The power-law indices of different types of variable stars were <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.72</mn><mo>±</mo><mn>0.025</mn></mrow></semantics></math></inline-formula> (eclipsing binaries), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.82</mn><mo>±</mo><mn>0.062</mn></mrow></semantics></math></inline-formula> (rotating stars), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.80</mn><mo>±</mo><mn>0.0116</mn></mrow></semantics></math></inline-formula> (eruptive stars), and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.73</mn><mo>±</mo><mn>0.060</mn></mrow></semantics></math></inline-formula> (pulsating stars). Among them, the flare energy of pulsating stars is more concentrated in the high-energy range. In all samples, flare energies were distributed from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.99</mn><mo>×</mo><msup><mn>10</mn><mn>31</mn></msup></mrow></semantics></math></inline-formula> erg to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6.18</mn><mo>×</mo><msup><mn>10</mn><mn>38</mn></msup></mrow></semantics></math></inline-formula> erg. The LAMOST DR9 low-resolution spectral survey has provided H<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> equivalent widths for 398 variable stars. By utilizing these H<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> equivalent widths, we have determined the stellar activity of the variable stars and confirmed a positive correlation between the flare energy and H<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> equivalent width.