Annu. Rev. Astron. Astrophys. 1994. 32: 153-90 Copyright © 1994 by Annual Reviews. All rights reserved

3.4. The r-Process in Nascent Neutron Star Winds

Woosley & Hoffman (1992) proposed the winds from nascent neutron stars as the site of the r-process. In this section we discuss the physics of these winds. Only detailed models will allow us to determine whether these winds are indeed the site of the r-process. On the other hand, simple arguments will illustrate the basic features of these winds and why they are attractive as an r-process site.

A core-collapse (i.e. type II or Ib) supernova may leave a hot (kT 10 MeV) neutron star as a remnant (e.g. Bethe 1990). This neutron star cools by neutrino emission on a timescale of order 10 seconds. Salpeter & Shapiro (1981) were among the first to consider the thermal evolution of such a young neutron star. They were able to show that, although the neutrino luminosity is always sub-Eddington, the photon luminosity can be super-Eddington. Thus, for sufficiently hot nascent neutron stars, there is a neutrino-driven wind.

Duncan et al (1986) repeated the arguments of Salpeter & Shapiro and showed that a spherically symmetric, nascent neutron star of radius 10.6 km and mass 1.4M has a super-Eddington photon luminosity if the neutron star temperature is 0.4 MeV. Duncan et al also showed that the star cannot stabilize itself by changing its size or by transporting energy by convection. A wind must therefore blow from the surface of the neutron star. Moreover, Duncan et al showed that the mass loss rate in this wind is of order 10^-5 M s^-1, which gives, if the wind lasts for the early cooling time of the nascent neutron star (~ 10 s), about 10^-4 M. If this material forms r-process nuclei, the wind naturally gives the correct amount of r-process matter per supernova. [For more details on this wind, see Woosley et al (1994) and references therein]

What about the entropy in the wind? The net heating of a matter element lifting off the surface of the neutron star is governed by the heating due to neutrino interactions with the wind material and cooling due to emission by the matter. The heating goes as F <E>, where is the neutrino-matter interaction cross section, F is the number flux of neutrinos, and <E> is the average neutrino energy. F L <E>^-1 r^-2 where L is the neutrino luminosity and r is the radial position of the matter element, <E>² (e.g. Tubbs & Schramm 1975). The heating thus goes as L <E>² r^-2. <E> and L fall off on the neutron-star cooling timescale of roughly 10 seconds. The matter elements move out on timescales faster than 10 seconds, so the heating rate falls off roughly as r^-2. The cooling goes as T_m⁶ where T_m is the local matter temperature. Above the surface of the neutron star, T_m⁶ falls off more steeply than r^-2. As the mass element lifts off the star, the initial heating is slow because the matter and neutrino temperatures are nearly equal. As the mass element moves out, the matter temperature T_m drops. Once the mass element passes the "gain radius." where the heating and cooling rates are equal, T_m is too low for the material to cool off as fast as it is heated (Bethe & Wilson 1985). As heat is added, the entropy rises. In this way, the entropy can reach values of 100k or more before neutrino interactions with the wind material freeze out. These are the values required for a high entropy r-process.

Note that the entropy in mass elements leaving the neutron star at late times will be larger than in mass elements leaving the star at early times. This is because most of the heating occurs fairly near the surface of the neutron star because the neutrino flux and hence the net heating rate falls off as 1/r². As a neutron star ages, it shrinks in radius [from ~ 100 km at a few tenths of a second after core bounce to ~ 10 km at several seconds after bounce in the models of Wilson & Mayle (1993)]. The decrease in the initial r from which the mass elements begin increases the heating rate more than the slow fall off in L and <E> decrease it. The net heating and entropy in the later mass elements is thus larger.

The last question we must consider is the neutron richness of the wind material. Y_e is set in the wind by the reactions _e + n p + e^- and _e + p n + e⁺. If the fluxes and energies of the _e and _e were equal, Y_e would be slightly larger than 0.5 because the mass of the proton is slightly less than that of the neutron. As a nascent neutron star cools, however, it becomes neutron rich. The opacity for v_es becomes larger than that for _es because of the reaction _e + n p + e^-. The _es thus have a longer mean free path and originate deeper in the neutron star. This means that they are more energetic than the _es. This necessarily drives the material neutron rich. At late times (t 10 s after core bounce) <E_e> 2<E_e> which makes Y_e 0.33 (Qian et al 1993). This is certainly neutron rich enough for a high entropy r-process.

As a last point, let us re-emphasize that the entropy and Y_e in a mass element vary according to when that mass element lifts off the neutron star. Each mass element thus undergoes a somewhat different nucleosynthesis. The final r-process abundance distribution, however, is a sum of all of these different components. The r-process in nascent neutron star winds thus naturally satisfies the requirement imposed by the work of Kratz et al (1993). Notice that the wind dynamics and thermodynamics are completely determined by the mass, radius, and temperature of the neutron star. Any given neutron star probably passes through roughly the same sequence of temperatures and radii as a function of time as it cools. We thus expect to get essentially the same r-process out of every supernova. This satisfies our expectations from the observations of the r-process elements in old stars (see Section 3.3).

Does a solar system distribution naturally emerge in such a wind? Meyer et al (1992), using a schematic model based on output from Wilson & Mayle (1993), found the resulting abundances matched the solar system distribution quite well (see also Howard et al 1993 and Takahashi et al 1994). A more detailed model, using mass element trajectories calculated directly in Wilson and Mayle's supernova code produced abundances that also agree well with the solar distribution (Woosley et al 1994). This latter model also gives the correct amount of r-process mass per supernova (~ 10^-4 M). Confirmation of nascent neutron star winds as the site for the r-process will require a full survey of the nucleosynthesis in detailed, realistic wind models. Nevertheless, nascent neutron star winds seem extremely promising as the site for the r-process.