New Constraints on Radii and Tidal Deformabilities of Neutron Stars from GW170817.

We explore in a parameterized manner a very large range of physically plausible equations of state (EOSs) for compact stars for matter that is either purely hadronic or that exhibits a phase transition. In particular, we produce two classes of EOSs with and without phase transitions, each containing one million EOSs. We then impose constraints on the maximum mass (M<2.16  M_{⊙}) and on the dimensionless tidal deformability (Λ[over ˜]<800) deduced from GW170817, together with recent suggestions of lower limits on Λ[over ˜]. Exploiting more than 10^{9} equilibrium models for each class of EOSs, we produce distribution functions of all the stellar properties and determine, among other quantities, the radius that is statistically most probable for any value of the stellar mass. In this way, we deduce that the radius of a purely hadronic neutron star with a representative mass of 1.4  M_{⊙} is constrained to be 12.00<R_{1.4}/km<13.45 at a 2σ confidence level, with a most likely value of R[over ¯]_{1.4}=12.39  km; similarly, the smallest dimensionless tidal deformability is Λ[over ˜]_{1.4}>375, again at a 2σ level. On the other hand, because EOSs with a phase transition allow for very compact stars on the so-called "twin-star" branch, small radii are possible with such EOSs although not probable, i.e., 8.53<R_{1.4}/km<13.74 and R[over ¯]_{1.4}=13.06  km at a 2σ level, with Λ[over ˜]_{1.4}>35.5 at a 3σ level. Finally, since these EOSs exhibit upper limits on Λ[over ˜], the detection of a binary with a total mass of 3.4  M_{⊙} and Λ[over ˜]_{1.7}>461 can rule out twin-star solutions.