The Magnetic Connection Between Flares, Rotation, and Age for the Volume-Complete Sample of Fully Convective M Dwarfs within 15 Parsecs

Abstract

Fully convective M dwarfs display many magnetic phenomena motivating numerous questions of how these stars generate and sustain large scale coherent magnetic fields. Moreover, the terrestrial exoplanets that are most spectroscopically accessible will orbit such stars, hence we need to understand the stellar radiation environment that has sculpted these planetary atmospheres. I present an observational study of rotation periods, flare rates, and chromospheric activity indicators of a volume-complete sample of 219 M dwarfs with masses between 0.1--0.3$\msol$ and within 15 parsecs. I used photometric data from the Transiting Exoplanet Survey Satellite (TESS) and the MEarth Observatory to make the first determination of the rotation periods for 53 of these stars. I employed multi-epoch high-resolution spectroscopic observations from 1.5 meter telescopes in Arizona and Chile to measure radial velocities and equivalent widths of chromospheric spectroscopic indicators. I used the radial velocities coupled with proper motions and parallaxes from the Gaia mission to determine galactic kinematics, from which I estimated the ages of these stars based on their motion through the Galaxy. I found that these stars divide into two groups: 29% have $\ha$ in emission, a saturated flare rate corresponding to a Carrington-level flare once every 4 days, and kinematic ages less than 2 Gyr. The remaining 71% do not show $\ha$ in emission and have flare rates that are at least six orders of magnitude less than the saturated value, rotation periods that exceed 100 days, and ages in excess of 6 Gyr. I found that all mid-to-late M dwarfs display the same slope for the frequency of flares as a function of energy, with an index of 2, sufficient to explain coronal heating. The spectroscopic magnetic activity indicator $\ha$ is formed via magnetic heating of the chromosphere and shows variability with time, however the dominant mechanism causing the variability is not established. I conducted a multi-epoch high-resolution spectroscopic monitoring program of 13 fully convective M dwarfs with rotation periods spanning 0.2--92.0 days with the TRES spectrograph. For 9 of these stars, we found no correlation between $\ha$ and rotational phase, indicating that constant emission from fixed magnetic structures, such as starspots and plage, are unlikely to be the dominant source of the variability in $\ha$. In contrast, one star, G 7-34, shows a clear relationship between $\ha$ and the stellar rotational phase. High-cadence spectroscopic observations of three additional stars revealed that they are variable on timescales ranging from 20--45 minutes, which I postulated could be due to flaring behavior. To confirm whether flares were the dominant mechanism leading to $\ha$ variability, I obtained simultaneous photometry from TESS and spectroscopic observations for 5 fully convective stars; GJ 1111, Gl 54.1, G 7-34, G 99-49, and AP Col. I find 12 photometric flares in the TESS data that overlap with the spectroscopic observations, observations, all of which display enhanced $\ha$ emission during the flare. However, I also observed many $\ha$ flares for which I did not find a photometric counterpart. This indicates that the chromosphere, which is the source of the $\ha$ emission, is much more sensitive to the resultant effect of magnetic reconnection than the photosphere, which is the source of the photometric flare. We conclude that $\ha$ variability is likely a combination of stellar flaring and fixed magnetic structures rotating into and out of view, with stellar flares dominating for active fully convective M dwarfs.