Are small radii of compact stars ruled out by GW170817/AT2017gfo?

The detection of GW170817 and its electromagnetic counterparts allows to constrain the equation of state of dense matter in new and complementary ways. Very stiff equations of state are ruled out by the upper limit on the average tidal deformability, $\tilde\Lambda \lesssim 800$, imposed by the detected gravitational wave signal. A lower limit, $\tilde\Lambda \gtrsim 400$, can also be extracted by considering the large amount of ejected matter which powers the kilonova AT2017gfo. By using several microscopic nucleonic equations of state, we first confirm the existence of a monotonic relation between $R_{1.5}$ (the radius of the $1.5M_{\odot}$ configuration) and $\tilde\Lambda$. This translates the limits on $\tilde\Lambda$ into limits on the radius: $11.8\,\text{km} \lesssim R_{1.5} \lesssim 13.1\,$km. We then show that the monotonic relation is violated, if a second branch of compact stars composed of quark matter exists, as in the two-families or the twin-stars scenarios. In particular, it is possible to fulfill the limits on $\tilde\Lambda$ while having $R_{1.5}$ significantly smaller than $12\,$km. In both those scenarios the event GW170817/AT2017gfo originates from the merger of a hadronic star and a star containing quark matter.