tokens: that the crucial difference between both models is the much higher proton fraction in the BHF approach. In this case, the DU threshold is already reached at ρ = 0.44 fm −3 ( x p = 0.136), whereas with the APR it is delayed to ρ = 0.82 fm −3 ( x p = 0.140). Figure 1. Pressure and energy density (a), and proton and muon fractions (b) as functions of baryon number density ρ in beta-stable matter for the APR and BHF EOS. The lower panels show NS mass (d) and radius (c) as functions of the central density ρ c . The DU onset is indicated by vertical dotted lines. On the contrary, the APR EOS is somewhat stiffer, i.e. features a larger pressure and energy density. We also mention that the APR EOS becomes superluminal at ρ = 0.85 fm −3 , whereas BHF remains always below the critical threshold (Burgio Schulze 2010 ; Taranto et al. 2013 ). By solving the standard Tolman–Oppenheimer–Volkov equations for the NS structure, this input yields the NS (mass,radius) – central density relations shown in panels (c) and (d) of Fig. 1 . We remark that both models reach maximum masses (slightly) above two solar masses and predict very similar radii in spite of their different matter composition. With BHF the DU process is active in nearly all stars, M /M ⊙ > 1.10, while with APR only in the most heavy ones, M /M ⊙ > 2.03. This has profound consequences for the cooling behaviour. 3 PAIRING GAPS AND CRITICAL TEMPERATURES Of vital importance for any cooling simulation is the knowledge of the 1S0 and 3PF2 pairing gaps for neutrons and protons in beta-stable matter, which on one hand block the DU and MU reactions, and on the other hand open new cooling channels by the PBF mechanism for stellar matter in the vicinity of the critical temperature (Yakovlev et al. 2001 ). As usual, we focus in this work on the most important proton 1S0 (p1S0) and neutron 3PF2 (n3P2) pairing channels and neglect the less important remaining combinations. As stressed before, the gaps should be computed in a framework that is consistent with the determination of the EOS, i.e. be based on the same NN interaction and using the same medium effects (TBF and effective masses), and indeed we follow this procedure here, by using the results of Zhou et al. ( 2004 ), which employed the same V18+UIX nuclear interaction and BHF SP spectra for the calculation of the gaps. To be more precise, and focusing on the more general case of pairing in the coupled 3PF2 channel, the pairing gaps were computed on the BCS level by solving the (angle-averaged) gap equation (Amundsen Østgaard 1985 ; Baldo et al. 1992 , 1998 ; Takatsuka Tamagaki 1993 ; Elgarøy et al. 1996 ; Khodel, Khodel Clark 1998 ) for the two-component L = 1, 3 gap function, with while fixing the (neutron or proton) density, Here e ( k ) are the BHF SP energies, equation ( 2 ), containing contributions due to two-body and three-body forces, μ ≈ e ( k F ) is the (neutron) chemical potential determined self-consistently from equations ( 6 )–( 8 ), and
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