EBLM XV -- Revised dynamical masses for the circumbinary planet host Kepler-16 AB, using the SOPHIE spectrograph

Eclipsing binaries are perfect laboratories to measure precise, accurate and model-independent stellar radii and stellar masses, so long as both components are spectroscopically resolved. Resolving both components is difficult in high-contrast binaries, for instance, those composed of an FGK main-sequence star with an M-type companion. In those cases, the secondary can contribute <1% of the total flux in optical wavelengths. This makes measuring dynamical masses challenging and has typically only been attempted with large-aperture telescopes (8-10-m). The High-Resolution Cross-Correlation Spectroscopy (HRCCS) method was developed to extract weak emission and transmission spectra for exoplanet atmospheres. This method was recently adapted and applied to measure dynamical masses in high-contrast binaries. In this work, we apply the HRCCS method to optical spectra of the high-contrast binary and circumbinary planet host Kepler-16AB, obtained with the SOPHIE spectrograph at the 1.93-m telescope at the Observatoire de Haute-Provence. The secondary, which has a contrast ratio of ~ 6 x 10-3, is resolved with a detection significance of 9.5-sigma. We derive dynamical masses with a precision of 1.5% and 0.9% for the primary and secondary respectively. These are comparable, but slightly higher (within 2-7%) to previous mass-measurements, which has -- within the uncertainties -- no implication for the mass of the known circumbinary planet. This work demonstrates that dynamical mass measurements of high-contrast binaries can be done with 2-m class telescopes. We also investigate different analysis protocols to ensure we derive robust uncertainties for dynamical masses.