Tidal deformability Λ as a function of mass for the CLC EOS (red) with the DH crust connected at ρ_u = ρ₀ (results obtained with the CLCacc EOS are indistinguishable), and for the DH EOS (green). The bottom horizontal line corresponds to the limit on the deformability of a 1.4 M_⊙ obtained from the observations of GW170817, the merger of two NSs: Λ ≤ 800. While the DH EOS is compatible with this observational constraint, the maximally stiff CLC EOS gives much higher values of Λ for M = 1.4 M_⊙. The top horizontal line corresponds to the tidal deformability in the case in which one of the components of the GW170817 merger was a black hole (or a very compact self-bound star) with vanishing deformability. This limiting Λ_1,max = 2777 was computed from the observational bound on (Eq. (10)) for marginal values of the component masses, M₁ = 1.17 M_⊙ (assumed NS, Λ ≠ 0) and M₂ = 1.6 M_⊙ (assumed BH, Λ ≡ 0) in the high-spin prior estimation case (see Table 1 in Abbott et al. 2017b for details).