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