Size and shape of Chariklo from multi-epoch stellar occultations

We use data from five stellar occultations observed between 2013 and 2016 to constrain Chariklo's size and shape, and the ring reflectivity. We consider four possible models for Chariklo (sphere, Maclaurin spheroid, tri-axial ellipsoid and Jacobi ellipsoid) and we use a Bayesian approach to estimate the corresponding parameters. The spherical model has a radius $R=129\pm3$ km. The Maclaurin model has equatorial and polar radii $a=b=143^{+3}_{-6}$ km and $c=96^{+14}_{-4}$ km, respectively, with density $970^{+300}_{-180}$ kg m$^{-3}$. The ellipsoidal model has semiaxes $a=148^{+6}_{-4}$ km, $b=132^{+6}_{-5}$ km and $c=102^{+10}_{-8}$ km. Finally, the Jacobi model has semiaxes $a$=157$\pm$4 km, $b$=139$\pm$ 4 km and $c$=86$\pm$1 km, and density $796^{+2}_{-4}$ kg m$^{-3}$ . Depending on the model, we obtain topographic features of 6-11 km, typical of Saturn icy satellites with similar size and density. We constrain Chariklo's geometric albedo between 3.1\% (sphere) and 4.9\% (ellipsoid), while the ring $I/F$ reflectivity is less constrained between 0.6\% (Jacobi) and 8.9\% (sphere). The ellipsoid model explains both the optical light curve and the long-term photometry variation of the system, giving a plausible value for the geometric albedo of the ring particles of $10-15\%$. The derived Chariklo's mass of 6-8$\times10^{18}$ kg places the rings close to the 3:1 resonance between the ring mean motion and Chariklo's rotation period.