GENERAL RELATIVISTIC EFFECTS IN THE NEUTRINO-DRIVEN WIND AND r-PROCESS NUCLEOSYNTHESIS

We discuss general relativistic effects in the steady state neutrino-driven “wind” that may arise from nascent neutron stars. In particular, we generalize previous analytic estimates of the entropy per baryon S, the mass outflow rate Ṁ, and the dynamical expansion timescale tdyn. We show that S increases and tdyn decreases with increasing values of the mass-to-radius ratio describing the supernova core. Both of these trends indicate that a more compact core will lead to a higher number of neutrons per seed nucleus. Such an enhancement in the neutronyseed ratio may be required for successful r-process nucleosynthesis in neutrino-heated supernova ejecta. Subject headings: equation of state — nuclear reactions, nucleosynthesis, abundances — relativity — supernovae: general The production site of the r-process elements (Burbidge et al. 1957; Cameron 1957) is a long-standing problem (see Mathews & Cowan 1990). One of the most promising candidate sites for r-process nucleosynthesis is the neutrino-heated ejecta from the post–core-bounce environment of a Type II or Type Ib supernova (Meyer et al. 1992; Woosley & Hoffman 1992; Takahashi, Witti, & Janka 1994; Woosley et al. 1994). These r-process calculations, though promising, cannot reproduce the solar system r-process abundance pattern without an artificial increase in the neutron-to-seed nucleus ratio over that predicted in hydrodynamical calculations and simple wind models (see, e.g., Hoffman, Woosley, & Qian 1996; Meyer, Brown, & Luo 1996). Qian & Woosley (1996, hereafter QW) used a simple model of the neutrino-driven wind to obtain both analytic and numerical estimates of quantities upon which the nucleosynthesis abundance yield depends. These quantities include the electron fraction Ye, the entropy per baryon S, the mass outflow rate Ṁ, and the dynamic expansion timescale tdyn—all of which are important in setting the neutronyseed nucleus ratio prior to the epoch of rapid neutron capture. In this Letter we generalize the analytic derivations in QW to include general relativistic effects. Such effects are of potential interest in light of “soft” nuclear matter equations of state—involving, for example, kaon condensation (Thorsson, Prakash, & Lattimer 1994)—which could lead to very compact supernova cores and even black holes as supernova remnants (Bethe & Brown 1995; Woosley & Timmes 1996). While QW reported two sample numerical calculations involving postNewtonian corrections, they did not present corresponding analytic calculations. Numerical calculations reported in QW suggest that general relativistic effects go in the direction of making conditions more favorable for the r-process. We here allow for general relativistic effects in analytical calculations, including effects not included in the numerical calculations by QW, namely, the redshift of neutrino energies and bending of the neutrino trajectories. In the analytic approximations performed by QW, the calculation of the quantities S, Ṁ, and tdyn essentially decouples from the calculation of Ye. We will present analytic estimates for S, Ṁ, and tdyn; general relativistic effects on Ye have been considered in another paper (Fuller & Qian 1996). Unless units are explicitly given, we take \ 5 c 5 k 5 1. The wind equations in Duncan, Shapiro, & Wasserman (1986) and QW can be generalized to allow for relativistic outflow velocities and general relativistic effects in a static Schwarzschild spacetime. A detailed derivation and discussion will appear elsewhere (Cardall & Fuller 1997, hereafter CF). We here simply present the general relativistic analogs of equations (24)–(26) of QW, which give the radial evolution of the velocity, “flow energy” per baryon eflow, and entropy per baryon: