Photo-dynamical mass determination of the multi-planetary system K2-19

K2-19 is the second multi-planetary system discovered with K2 observations. The system is composed of two Neptune size planets close to the 3:2 mean-motion resonance. To better characterise the system we obtained two additional transit observations of K2-19b and five additional radial velocity observations. These were combined with K2 data and fitted simultaneously with the system dynamics (photo-dynamical model) which increases the precision of the transit time measurements. The higher transit time precision allows us to detect the chopping signal of the dynamic interaction of the planets that in turn permits to uniquely characterise the system. Although the reflex motion of the star was not detected, dynamic modelling of the system allowed us to derive planetary masses of $M_b= 44 \pm 12\, M_{\oplus}$ and $M_c = 15.9 \pm 7.0\, M_{\oplus}$ for the inner and the outer planets respectively, leading to densities close to Uranus. We also show that our method allows the derivation of mass ratios using only the 80 days of observations during the first campaign of K2.