Rotational modulation of spectroscopic Zeeman signatures in low-mass stars

Accurate tracers of the stellar magnetic field and rotation are cornerstones for the study of M dwarfs and for reliable detection and characterization of their exoplanetary companions. Such measurements are particularly challenging for old, slowly rotating, fully convective M dwarfs. To explore the use of new activity and rotation tracers, we examined multi-year near-infrared spectroscopic monitoring of two such stars -- GJ 699 (Barnard's Star) and Teegarden's Star -- carried out with Habitable Zone Planet Finder spectrograph. We detected periodic variations in absorption line widths across the stellar spectrum with higher amplitudes towards longer wavelengths. We also detected similar variations in the strength and width of the 12435.67 Angstrom neutral potassium (K I) line, a known tracer of the photospheric magnetic field. Attributing these variations to rotational modulation, we confirm the known $145\pm15$ d rotation period of GJ 699, and measure the rotation period of Teegarden's Star to be $99.6\pm1.4$ d. Based on simulations of the K I line and the wavelength-dependence of the line width signal, we argue that the observed signals are consistent with varying photospheric magnetic fields and the associated Zeeman effect. These results highlight the value of detailed line profile measurements in the near-infrared for diagnosing stellar magnetic field variability. Such measurements may be pivotal for disentangling activity and exoplanet-related signals in spectroscopic monitoring of old, low-mass stars.