Maximally stiff equations of state and the structure of hybrid stars

The simultaneous reconciliation of the 1σ estimations on the mass (M) and radius (R) of the PSR J0030+0451 pulsar and the HESS J1731-347 remnant requires a region in the M-R plane where the slope dM/dR is positive. The latter reflects that the equation of state (EOS) should stiffen as the density increases, which requires a sufficiently large value for the speed of sound in dense matter. However, based on different theoretical assumptions, the sound velocity manifests an upper bound leading to a constraint on how stiff the resulting EOS can be. In the present contribution, we present our recent work on the possible simultaneous explanation of the aforementioned measurements in the context of hybrid EOSs, by describing the high-density phase as maximally incompressible (considering different suggestions for the upper speed of sound bound). A relevant discussion on possible constraints on the properties of first order transitions is also included.