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

3. THE r-PROCESS

Nature does not endure sudden mutations without great violence.

Francois Rabelais, Gargantua

We turn now to a discussion of the r-process. We seek to understand in some detail how and where the r-process occurs. How the r-process occurs depends on whether it is a primary or secondary process. We will see that the evidence available to us today indicates that the r-process is a primary, freezeout from equilibrium process. As for where the r-process occurs, the rapid timescales associated with the r-process point to violent events such as supernovae or disruptions of neutron stars. Winds from nascent neutron stars are currently believed to be the most probable site. Our discussion will be brief. For more details, the reader should turn to the many excellent reviews in the literature (e.g. Hillebrandt 1978, Mathews & Cowan 1990, Cowan et al 1991).

3.1. The Primary r-Process

Let us return to the notion of a freezeout from equilibrium. As a system in NSE expands and cools, the abundances shift to maintain NSE. We have seen that in doing so the entropy of the system moves from the baryons into the photons and leptons and the abundance of heavier nuclei grows at the expense of free nucleons and light nuclei. Eventually the temperature of the system is too low or the abundance of reactants too small for certain reactions to go fast enough to maintain NSE. These reactions freeze out. The first reactions to freeze out are charged-particle reactions. Neutron-capture reactions can continue, however, because they are not impeded by a nuclear Coulomb barrier. The nuclei present at the time of the freezeout of the charged-particle reactions then eventually capture the remaining neutrons.

If we suppose that the system is quite neutron rich, many free neutrons should exist after freezeout of the charged-particle reactions. One might imagine that as we increase the neutron richness of the system, we simply have more neutron-rich isotopes of the nuclei present in the system. However, there is a limit to how neutron rich the nuclei can get. This is because the nuclei eventually encounter neutron drip, at which point the binding energy of the next neutron captured is negative. Once the nuclei reach neutron drip, they cannot contain any more neutrons. Thus, for sufficiently neutron-rich material, there may be many free neutrons at the time of charged-particle reaction freezeout. The system establishes an equilibrium between the neutron-capture (n, ) and neutron-disintegration (, n) reactions. Beta decays then occur which increase the charge on the nucleus and allow further neutron capture. This phase of the freezeout from equilibrium in which only neutron-capture, neutron-disintegration, and beta-decay reactions occur is the r-process.

How neutron rich must material be to undergo an r-process? We know that the r-process produces uranium (A = 238) from seed nuclei (A 50 - 100); therefore, there must be roughly 100 free neutrons per seed nucleus at the time of charged-particle reaction freezeout. The required neutron richness thus depends on the abundance of seed nuclei which in turn depends on the entropy per baryon in the system.

If the entropy per baryon is less than or roughly 10k, NSE favors iron-group nuclei. These are the seed nuclei for the r-process once the charged- particle reactions have frozen out. Because the r-process needs around 100 free neutrons per seed, a seed nucleus like ⁷⁸Ni, typical in a low entropy, neutron-rich freezeout, requires a total neutron-to-proton (n/p) ratio of (50 + 100)/28 5.4 or a Y_e = p / (n + p) 0.16. This is quite neutron-rich material.

If the entropy per baryon is high ( 100k), NSE favors ⁴He at high temperature. As the temperature drops in the expanding material, NSE begins to favor iron-group nuclei. For large entropy per baryon, this occurs late in the expansion. At this late time, the two reaction sequences that begin the assembly of alpha particles into iron-group nuclei, ⁴He + ⁴He + ⁴He ¹²C and ⁴He + ⁴He + n ⁹Be followed by ⁹Be + ⁴He ¹²C + n, may not be operating at a significant level or may even have frozen out. We note that these reaction sequences rely on three-body interactions which are highly sensitive to the density. The higher the entropy per baryon at a given temperature, the larger the photon-to-baryon ratio and the lower the density. A lower density results in slower three-body reaction rates. Thus the higher the entropy per baryon, the higher the temperature at which these three-body reactions freeze out and the lower the abundance of seed nuclei. Unlike the three-body reactions, alpha captures on ¹²C and heavier nuclei occur rapidly and build up heavy nuclei. As the system falls out of equilibrium, there will be more alpha particles around than there would be in NSE. Some of these alpha particles capture on the iron-group nuclei present to make heavier nuclei (A ~ 100). Eventually these reactions freeze out also, and the system is left with an abundance of free neutrons, seed nuclei, and many ⁴He nuclei. At this point the free neutrons can capture on the seed nuclei, but not on the ⁴He nuclei. In this way an r-process occurs.

The degree of neutron richness necessary for an r-process in a high entropy environment is less than in a low entropy environment. A typical composition for an entropy per baryon of 400k and a neutron-to-proton ratio of 1.6 (Y_e = 0.385) is 20% free neutrons by mass, 10% seed nuclei, and 70% alpha particles (Woosley & Hoffman 1992). Suppose the seed nucleus is Z = 35, A = 100 (also typical), then the free neutron-seed nucleus ratio is 200 in the case: more than sufficient for an r-process. We thus see that the degree of neutron richness we need for a primary r-process directly depends on the entropy per baryon.

We have to this point discussed how a primary r-process would occur in the freezeout from NSE in low entropy and high entropy environments. The r-process might also occur in a very low entropy or zero-entropy environment. Matter inside a neutron star is extremely neutron rich and highly-degenerate. If the neutron star is more than a few hours old, it is cold (T 10⁹ K) on a nuclear energy scale (e.g. Baym & Pethick 1979), implying that the entropy per baryon is quite low ( 0.5k). At densities below nuclear density ( 2 × 10¹⁴ g cm^-3) but above neutron-drip density ( 4 × 10¹¹ g cm^-3), extremely neutron-rich nuclei exist in strong equilibrium with degenerate neutrons and weak equilibrium with the degenerate electrons (Baym et al 1971). Above nuclear density, the material is comprised of free nucleons and electrons. Weak equilibrium forces the Y_e of the material to be of order 0.05 or less (Lattimer et al 1985, Lattimer & Swesty 1991).

Only the strong gravity of the neutron star keeps such matter from exploding apart. If a piece of cold neutron-star matter were to escape from the neutron star into interstellar space, it would decompress. If this escape occurred without too much violence, there would not be a dramatic increase in the entropy. The material would remain cold. The material would consist of neutrons and nuclei, and as the material expanded, an r-process could occur (Lattimer et al 1977, Meyer 1989). In such a system, the only heating that would occur would be from the beta decays and nuclear fissions during the r-process, which are irreversible processes. Notice that such an r-process would not be a freezeout from NSE. The system was not in nuclear statistical equilibrium prior to expansion, and it would not attain NSE later in the expansion unless the beta decays and nuclear fissions that occur could drive the temperature up high enough, something that probably does not happen (Meyer 1989). On the other hand, this would be a freezeout from weak equilibrium. Thus, such an r-process would be primary because it is the formation of the neutron star that creates the seed nuclei and the weak equilibrium would erase the entire previous history of the nucleons. Moreover, material that began at densities above nuclear matter density would experience a phase transition from free nucleons into neutrons and nuclei during the expansion. In this case, the seed nuclei would form during the decompression.

Now that we understand how the r-process occurs in freezeout from equilibrium, we may consider the question of what astrophysical sites could give low, very low, or high entropy r-processes. Let us begin with low entropy sites. The earliest site considered for a low entropy r-process was at the mass cut of a type II supernova (Burbidge et al 1957, Cameron 1957). The mass cut is the boundary between the matter that escapes into space from the supernova and the matter that remains as part of the remnant neutron star. The first serious time-dependent calculations of such an r-process were made by Seeger et al (1965), although this work assumed constant temperature and neutron number density. Later calculations treated the r-process as dynamical, that is, with varying temperature and neutron density (Cameron et al 1970, Schramm 1973, Sato 1974, Kodama & Takahashi 1975, Hillebrandt et al 1976, Hillebrandt 1978). While some of these workers found fairly good fits to the solar system r-process distribution, the models studied provided no natural way of explaining why the particular r-process distribution we see should emerge from a supernova and, more seriously, why a supernova should eject only a small mass of r-process matter (see Section 3.3). It is also important to note that current type II supernova models do not yield Y_e as low as 0.1-0.2 at the mass cut, as required by a low entropy r-process (e.g. Wilson & Mayle 1993, Woosley et al 1994).

Due to the difficulties with the mass-cut site, astrophysicists turned to other supernova scenarios. In particular, workers sought other means of ejecting low entropy, neutron-rich r-process matter. Rotating stellar cores with (LeBlanc & Wilson 1970, Meier et al 1976, Muller & Hillebrandt 1979) and without magnetic fields (Symbalisty 1984, Symbalisty et al 1985) can eject some neutron-matter. It is not clear, however, that the supernova cores can attain the high rotation rates and magnetic fields required for such ejection. Moreover, there is no natural explanation for why the material has just the right conditions to make a solar system r-process distribution.

What about very low entropy r-processes? Lattimer & Schramm (1974, 1976) considered the tidal disruption of a neutron star by a black hole. The ejected neutron-star matter could then undergo a very low entropy r-process (Lattimer et al 1977, Meyer 1989). Neutron star-neutron star collisions could also lead to the ejection of neutron-rich matter (Symbalisty & Schramm 1982, Eichler et al 1989; see also Kochanek l992 and Colpi et al 1989, 1991, 1993). If this material were not strongly disturbed during the collision, it would undergo a very low entropy r-process. It is likely in such an event, however, that the material would be shocked to entropies of order several k per baryon, so that in fact a low entropy would probably ensue (Evans & Mathews 1988). In any case, these sites suffer the two difficulties of uncertain occurrence rates and the lack of any natural reason a solar system r-process distribution should result.

This leaves the high entropy r-process. A promising site for such an r-process is in the neutrino-driven winds from nascent neutron stars. We consider this site in more detail in Section 3.4.