Orbital motion and dynamical mass of the complex periodic variable binary system 2MASS J05082729-2101444

We used very long baseline interferometry to constrain the orbit of the binary system 2MASS J05082729-2101444. We observed the system with the VLBA in three epochs at a frequency of 4.85 GHz, which provides an angular resolution of about 3 mas. We combined the three radio astrometric observations, 119 RVs (60 VIS and 59 NIR) obtained with the CARMENES high-resolution spectrograph over a period of 8.1 years, and a relative astrometric measurement of an archival H-band Keck NIRC adaptive optics image to fit the orbital motion of the binary system. The VLBA observations resolved the binary system and show emission from both stellar components, with similar flux-density levels (0.34-0.67 mJy), and showing slight temporal flux variations. The emission appears quiescent, with no significant circular polarization, and with no flare events. We obtained an orbital motion fit of the binary system, which shows an eccentric orbit (e = 0.71), an orbital period of 2.19 yr, and a semimajor axis of 26.964 mas (1.3 au). The VLBA observations made it possible to resolve the binary system and identify both stars as radio-loud sources. The combined fit shows that 2M0508-21 is an M-dwarf binary with a total dynamical mass of $0.459\pm0.007$ M$_{\odot}$, assuming Gaia's parallax. This mass is slightly higher than those estimated from the luminosity and theoretical evolutionary models. The upper limit of the circular polarization at 4.85 GHz ($\lesssim$10\%), the persistence of the quiescent emission, and the relatively low brightness temperatures are consistent with a gyro-synchrotron or synchrotron origin of the radio emission. Further VLBA observations are needed to obtain the individual masses of the stars, as well as to verify Gaia's parallax of the system. A complete characterization of the system will help improve evolutionary models for young objects at the substellar boundary.