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-circle dot) and on the dimensionless tidal deformability (<(A)over tilde> < 800) deduced from GW170817, together with recent suggestions of lower limits on <(N)over tilde> 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-circle dot is constrained to be 12.00 < R-1.4/km < 13.45 at a 2 sigma confidence level, with a most likely value of (R) over bar (1.4) = 12.39 km; similarly, the smallest dimensionless tidal deformability is (A) over tilde (1.4) > 375, again at a 2 sigma 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 bar (1.4) = 13.06 km at a 2 sigma level, with (A) over tilde (1.)(4) > 35.5 at a 3 sigma level. Finally, since these EOSs exhibit upper limits on (A) over tilde, the detection of a binary with a total mass of 3.4 M-circle dot and (A) over tilde (1.7) > 461 can rule out twin-star solutions.