Implications of low-energy fusion hindrance on stellar burning and nucleosynthesis

L. R. Gasques, E. F. Brown, A. Chieffi, C. L. Jiang, M. Limongi, C. Rolfs, M. Wiescher, and D. G. Yakovlev

Phys. Rev. C 76, 035802 – Published 14 September 2007

Abstract

We investigate the consequences of a new phenomenological model prediction of strongly reduced low-energy astrophysical $S$ -factors for carbon and oxygen fusion reactions on stellar burning and nucleosynthesis. The new model drastically reduces the reaction rates in stellar matter at temperatures $T ≲ (3 − 10) \times 10^{8}$ K, especially at densities $ρ ≳ 10^{9}$ g cm $^{- 3}$ , in a strongly screened or even pycnonuclear burning regime. We show that these modifications change the abundance of many isotopes in massive late-type stars and in particular strongly enhance the abundances of long-lived radioactive isotopes such as ${}^{26}{Al}$ and ${}^{60}{Fe}$ . The reduced reaction rates also significantly complicate carbon ignition (shift carbon ignition to higher temperatures and densities) in massive accreting white dwarfs exploding as type Ia supernovae and in accreting neutron stars producing superbursts. This would require much higher ignition densities for white dwarf supernovae and would widen the gulf between theoretical and inferred ignition depths for superbursts.

Received 9 May 2007

DOI:https://doi.org/10.1103/PhysRevC.76.035802

Authors & Affiliations

L. R. Gasques

Department of Nuclear Physics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia and Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA

E. F. Brown

Department of Physics & Astronomy and Joint Institute for Nuclear Astrophysics, National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA

A. Chieffi

Istituto Nationale di Astrofisica, Osservatorio Astronomico di Roma, Via Frascati 33, I-00040 Monteporzio Catone, Italy

C. L. Jiang

Physics Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439, USA

M. Limongi

Istituto Nationale di Astrofisica, Osservatorio Astronomico di Roma, Via Frascati 33, I-00040 Monteporzio Catone, Italy

C. Rolfs

Experimentalphysik III, Ruhr-Universität Bochum, Bochum, Germany

M. Wiescher

Department of Physics and Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA

D. G. Yakovlev

Ioffe Physical Technical Institute, Politekhnicheskaya 26, RU-194021 St.-Petersburg, Russia

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Issue

Vol. 76, Iss. 3 — September 2007

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Images

Figure 1
(Top) Astrophysical factors for the ${}^{12}C + {}^{12}C$ , ${}^{12}C + {}^{16}O$ , and ${}^{16}O + {}^{16}O$ reactions versus center-of-mass energy $E$ of colliding nuclei. Various symbols show experimental data. (Middle) Normalized rates of these reactions versus temperature neglecting plasma screening effects. (Bottom) Rates of the same reactions versus temperature for three values of the density ( $ρ = 10^{6}, 10^{9}$ , and $10^{10}$ g cm $^{- 3}, ρ_{6} \equiv ρ / 10^{6}$ g cm $^{- 3}$ ) in pure carbon matter (left), in a C-O mixture with 30% of carbon by mass (middle), and in pure oxygen matter (right). Thick lines refer to standard $S$ -factors (either recent model calculations [1, 2], denoted as Standard, or the formalism of Fowler et al. [5, 6]. denoted as Standard1); thin lines refer to reduced $S$ -factors (Jiang et al. [12]). See text for details.Reuse & Permissions
Figure 2
Deviations in isotopic abundances $Y_{rdc}$ for the reduced fusion rates from the abundances $Y_{std}$ for the standard rates [5, 6] at the endpoint of evolution of $20 M_{⊙}$ (left) and $60 M_{⊙}$ (right) stars. Shown are the abundances of 109 isotopes 1…109 from ${}^{12}C$ to ${}^{98}{Mo}$ .Reuse & Permissions
Figure 3
Abundance distributions of selected isotopes between ${}^{1}H$ and ${}^{60}{Fe}$ for the core and shell burning zones at different late evolution stages of the $20 M_{⊙}$ star. The thick solid lines correspond to the standard fusion rates, whereas the thin dashed lines are for the reduced rates. See text for details.Reuse & Permissions
Figure 4
Abundance distribution of the long-lived radioactive isotopes ${}^{26}{Al}$ and ${}^{60}{Fe}$ (left vertical scales) over the inner core and shell burning zones of $20 M_{⊙}$ and $60 M_{⊙}$ stars. The dashed and solid lines show the abundances at the end of stellar evolution and after passage of a shock induced by explosive burning, respectively. The dotted lines display the oxygen abundance (right vertical scales) before the shock passage. Thick lines are calculated with the standard reaction rates; thin lines are for the reduced rates.Reuse & Permissions
Figure 5
Carbon ignition curves in a core of a massive ${}^{12}C$ - ${}^{16}O$ white dwarf (WD; 30% of carbon by mass), in a neutron star (NS) crust with the same composition (dashed lines), and in a neutron star crust containing mixture of ashes of hydrogen and helium burning (solid lines). Thick lines refer to standard carbon burning rate, whereas thin lines are for the reduced rate. The upper axis gives the column depth $y_{NS} = P / g$ within a crust of an accreting $1.6 M_{⊙}$ neutron star with the radius of 10.8 km. The dotted line is a temperature profile within the crust of such a star assuming the crust is composed of ashes and the accretion rate $\approx 0.3$ of the Eddington rate. The filled and open dots position carbon ignition in such a crust for the standard and reduced carbon fusion rates, respectively. See text for details.Reuse & Permissions

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