Updated Masses for the TRAPPIST-1 Planets

The newly detected TRAPPIST-1 system, with seven low-mass, roughly Earth-sized planets transiting a nearby ultra-cool dwarf, is one of the most important exoplanet discoveries to date. The short baseline of the available discovery observations, however, means that the planetary masses (obtained through measurement of transit timing variations of the planets of the system) are not yet well constrained. The masses reported in the discovery paper were derived using a combination of photometric timing measurements obtained from the ground and from the Spitzer spacecraft, and have uncertainties ranging from 30\% to nearly 100\%, with the mass of the outermost, $P=18.8\,{\rm d}$, planet h remaining unmeasured. Here, we present an analysis that supplements the timing measurements of the discovery paper with 73.6 days of photometry obtained by the K2 Mission. Our analysis refines the orbital parameters for all of the planets in the system. We substantially improve the upper bounds on eccentricity for inner six planets (finding $e<0.02$ for inner six known members of the system), and we derive masses of $0.79\pm 0.27 \,M_{\oplus}$, $1.63\pm 0.63\,M_{\oplus}$, $0.33\pm 0.15\,M_{\oplus}$, $0.24^{+0.56}_{-0.24}\,M_{\oplus}$, $0.36\pm 0.12\,M_{\oplus}$, $0.566\pm 0.038\,M_{\oplus}$, and $0.086\pm 0.084\,M_{\oplus}$ for planets b, c, d, e, f, g, and h, respectively.