tokens: to the analytical Newtonian, adiabatic and steady-state wind model, referred to in the following as NASS, derived by Takahashi Janka ( 1997 ). It provides a simple, fully analytical description of the dynamics of the wind outflow at relatively late times or sufficiently far away from the PNS surface. The NASS wind model relies on the general assumptions listed above, in particular, those of a Newtonian PNS gravitational potential and of an adiabatic expansion. In addition, all the elementary and e − /e + weak interaction processes are assumed to be frozen out, nuclear β-decays not to affect Y e or s , and possible deviations from nuclear equilibrium with regard to strong and electromagnetic interactions to have no influence on the thermodynamical properties of the wind. Under such simplifying assumptions, the NASS model cannot predict any time variations of the entropy s , electron fraction Y e , or of the wind mass-loss rate , which are thus treated as constant input parameters. The basic NASS wind dynamics in the regime under consideration, and in particular for high enough entropies, is well approximated (Takahashi Janka 1997 ; Arnould et al. 2007 ) by where M * is the PNS mass, r the radius, v the velocity, T the temperature. The total energy per unit mass E may be obtained by setting a boundary condition and is usually expressed as a function of the wind energy: E = f w × E wind , where and v s equals the local adiabatic sound speed (Arnould et al. 2007 ). For f w = 1, the solutions correspond to a sonic wind, whereas for f w > 1, they are of sub-sonic wind type and usually referred to as breeze solutions. More details about the wind model can be found in Arnould et al. ( 2007 ). The entropy is dominated by photons, electrons and positrons in the wind so that the so-called radiation entropy is given by where f e = 1 in the high- T limit when electrons and positrons are highly relativistic, and decreases with T for high -values. In this study, it is approximated by , where T 9 is the temperature expressed in 10 9 K (Witti et al. 1994 ). Since the nucleosynthesis in the wind is followed by starting at a temperature of T 9 = 9, the total entropy is essentially equal to the radiation entropy (within a few per cent). Note that the ‘radiation entropy’ is measured here per baryon in units of the Boltzmann constant k B and includes both the photon and lepton contributions, but not the baryonic ones. For the initial conditions adopted here, the latter amounts to typically 9 k B /baryon. In the wind model of Takahashi Janka ( 1997 ), the radial evolution of the velocity, v ( r ), and density, ρ( r ), for specified total energy ( E ) per unit mass of outflow material (or, equivalent, for given f w ), given entropy and given mass-loss rate () is determined by the energy equation (based on Bernoulli's equation, see equation 1 ) and the continuity equation . The temperature then follows from the assumption of constant entropy, which couples
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