C. Freiburghaus

r-Process in Neutron Star Mergers

The production site of the neutron-rich heavy elements that are formed by rapid neutron capture (the r-process) is still unknown despite intensive research. Here we show detailed studies of a scenario that has been proposed earlier by Lattimer & Schramm, Symbalisty & Schramm, Eichler et al., and Davies et al., namely the merger of two neutron stars. The results of hydrodynamic and full network calculations are combined in order to investigate the relevance of this scenario for r-process nucleosynthesis. Sufficient material is ejected to explain the amount of r-process nuclei in the Galaxy by decompression of neutron star material. Provided that the ejecta consist of matter with a proton-to-nucleon ratio of Ye approximately 0.1, the calculated abundances fit the observed solar r-pattern excellently for nuclei that include and are heavier than the A approximately 130 peak.

Element synthesis in stars

Except for H-1, H-2, He-3, He-4, and Li-7, originating from the Big Bang, all heavier elements are made in stellar evolution and stellar explosions. Nuclear physics, and in many cases nuclear structure far from stability, enters in a crucial way. Therefore, we examine in this review the role of nuclear physics in astrophysics in general and in particular how it affects stellar events and the resulting nucleosynthesis. Stellar modeling addresses four major aspects: 1. energy generation and nucleosynthesis, 2. energy transport via conduction, radiation or possibly convection, 3. hydrodynamics/hydrostatics, and finally 4. thermodynamic properties of the matter involved. Nuclear Physics enters via nuclear reaction cross sections and nuclear structure (affecting the composition changes and nuclear energy generation), neutrino-nucleon and neutrino-nucleus cross sections (affecting neutrino opacities and transport), and e.g. the equation of state at and beyond nuclear densities which creates a relation between the nuclear many body problem and and hydrodynamic response like pressure and entropy. In the following we review these four topics by highlighting the role and impact of nuclear physics in each of these aspects of stellar modeling. The main emphasis is put on the connection to element synthesis.

An approximation for the rp-process

Hot (explosive) hydrogen burning, or the rapid proton capture process (rp-process), occurs in a number of astrophysical environments. Novae and X-ray bursts are the most prominent ones, but accretion disks around black holes and other sites are candidates as well. The expensive and often multidimensional hydrocalculations for such events require an accurate prediction of the thermonuclear energy generation while avoiding full nucleosynthesis network calculations. In the present investigation we present an approximation scheme that leads to accuracy of more than 15% for the energy generation in hot hydrogen burning from 108-1.5 × 109 K, which covers the whole range of all presently known astrophysical sites. It is based on the concept of slowly varying hydrogen and helium abundances and assumes a kind of local steady flow by requiring that all reactions entering and leaving a nucleus add up to a zero flux. This scheme can adapt itself automatically and covers low-temperature regimes, characterized by a steady flow of reactions, as well as high-temperature regimes where a (p, γ)-(γ, p)-equilibrium is established, while β+-decays or (α, p)-reactions feed the population of the next isotonic line of nuclei. In addition to a gain of a factor of 15 in computational speed over a full-network calculation and energy generation accurate to more than 15% this scheme also allows the correct prediction of individual isotopic abundances. Thus, it delivers all features of a full network at a highly reduced cost and can easily be implemented in hydrocalculations.

Nucleosynthesis calculations for the ejecta of neutron star coalescences

We present the results of fully dynamical r-process network calculations for the ejecta of neutron star mergers (NSMs). The late stages of the inspiral and the final violent coalescence of a neutron star binary have been calculated in detail using a 3D hydrodynamics code (Newtonian gravity plus backreaction forces emerging from the emission of gravitational waves) and a realistic nuclear equation of state. The found trajectories for the ejecta serve as input for dynamical r-process calculations where all relevant nuclear reactions (including beta-decays depositing nuclear energy in the expanding material) are followed. We find that all the ejected material undergoes r-process. For an initial Ye close to 0.1 the abundance distributions reproduce very accurately the solar r-process pattern for nuclei with A above 130. For lighter nuclei strongly underabundant (as compared to solar) distributions are encountered. We show that this behaviour is consistent with the latest observations of very old, metal-poor stars, despite simplistic arguments that have recently been raised against the possibility of NSM as possible sources of Galactic r-process material.

The QSE-Reduced Nuclear Reaction Network for Silicon Burning

Iron and neighboring nuclei are formed in massive stars shortly before core collapse and during their supernova outbursts, as well as during thermonuclear supernovae. Complete and incomplete silicon burning are responsible for the production of a wide range of nuclei with atomic mass numbers from 28 to 64. Because of the large number of nuclei involved,accuratemodelingofsiliconburningiscomputationallyexpensive.However,examinationofthephysicsof silicon burning has revealed that the nuclear evolution is dominated by large groups of nuclei in mutual equilibrium. We present a new hybrid equilibrium-network scheme which takes advantage of this quasi-equilibrium in order to reduce the number of independent variables calculated. This allows accurate prediction of the nuclear abundance evolution, deleptonization, and energy generation at a greatly reduced computational cost when compared to a conventional nuclear reaction network. During silicon burning, the resultant QSE-reduced network is approximately an order of magnitude faster than the full network it replaces and requires the tracking of less than a third as many abundance variables, without significant loss of accuracy. These reductions in computational cost and the number of species evolved make QSE-reduced networks well suited for inclusion within hydrodynamic simulations, particularly in multidimensional applications. Subject headingg methods: numerical — nuclear reactions, nucleosynthesis, abundances — stars: evolution — supernovae: general

The r-process in the high entropy bubble

We examined the r-process in the high entropy bubble within a detailed parameter study. Previous investigations ([1,2]) based on realistic supernovae models showed already that this model yields a very good fit to the solar system r-process abundance curve for masses above A = 120. For A < 120 their fit was relatively poor. We are concerned mainly with the question whether it is possible to obtain a good fit in the range below A = 120. Within a simple approach of an adiabatically expanding sphere we analyzed a broad parameter range, independent of specific explosion simulations. We varyied the electron abundance Ye and the entropy S and studied the resulting contributions as a function of the two parameters. We could show that the reproduction of the whole r-process pattern within the suggested high-entropy bubble scenario is not possible unless electron abundances as low as 0.35 are permitted.

Explosive nucleosynthesis and the astrophysical r-process

We give an overview of chemical equilibria in explosive burning and the role which neutron and/or proton separation energies play. We focus then on the rapid neutron-capture process (r-process) which encounters unstable nuclei far from beta-stability with neutron separation energies in the range 1-4 MeV. Its observable features, like the abundances, witness nuclear structure as well as the conditions in the appropriate astrophysical environment. With the remaining lack of a full understanding of its astrophysical origin, parametrized calculations are still necessary. The classical approach is based on (constant) neutron number densities n(n) and temperatures T over duration timescales tau. Recent investigations, motivated by the neutrino wind scenario from hot neutron stars after a supernova explosion, followed the expansion of matter with initial entropies S and electron fractions Y-e over expansion timescales tau. We compare the similarities and differences between the two approaches with respect to resulting abundance features and their relation to solar r-process abundances. Special emphasis is given to the questions (i) whether the same nuclear properties far from stability lead to similar abundance patterns and deficiencies in both approaches and (ii) whether some features can also provide clear constraints on the permitted astrophysical conditions.