The rp-Process in Core-collapse Supernovae
Shinya Wanajo
Research Center for the Early Universe, Graduate School of Science,
University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
Abstract
Recent hydrodynamic simulations of core-collapse supernovae with accurate neutrinotransport suggest that the bulk of the neutrino-heated ejecta is proton rich, in which the
production of some interesting proton-rich nuclei is expected. However, there are a numberof waiting point nuclei with the β + -lives of a few minutes, which prevent the production ofheavy proton-rich nuclei beyond iron in explosive events such as core-collapse supernovae. In
this study, it is shown that the rapid proton-capture (rp) process takes place by bypassingthese waiting points via neutron-capture reactions even in the proton-rich environment, if
there is an intense neutrino flux as expected during the early phase of the neutrino-driven
winds of core-collapse supernovae. The nucleosynthesis calculations imply that the neutrinodriven winds can be potentially the origin of light p-nuclei including 92,94 Mo and 96,98 Ru,
which cannot be explained by other astrophysical sites.

1

INTRODUCTION

The rapid proton-capture (rp) process has been expected to take place in proton-rich compositions with sufficiently high temperature [1] such as in X-ray bursts [2], whose nucleosynthetic
products might contribute to the Galactic chemical evolution of some proton-rich isotopes including p-nuclei. Recent hydrodynamic simulations of core-collapse supernovae with accurate
neutrino transport show that the bulk of the neutrino-heated ejecta during the early phase isproton rich [3], in which the production of some proton-rich nuclei is expected. However, there
are a number of waiting point nuclei with the β + -lives of a few minutes on the rp-process path,
which inhibit the production of heavy proton-rich nuclei beyond iron in core-collapse supernovae.
In this paper, it is shown that these waiting points are bypassed via (n, p) and (n, γ) reactions
even in proton-rich environments, if there is an intense neutrino flux as expected during the early
epoch of core-collapse supernovae (as also discussed in recent works [4, 5]). As a result, the rpprocess takes place that leads to the production of proton-rich nuclei beyond A ∼ 100. The
nucleosynthesis calculations are performed in order to demonstrate this effect, with the semianalytic neutrino-driven wind models [6, 7]. The results imply that this neutrino-induced rpprocess in core-collapse supernovae can be potentially the origin of the light p-nuclei including
92,94 Mo and 96,98 Ru, which cannot be explained even by the most successful scenario (i.e.,
the O/Ne layers in core-collapse supernovae [8]) of the p-nuclei production. A more detailed
discussion of the current results will be presented in a forthcoming paper [9].

2

NEUTRINO-DRIVEN WINDS

Assuming the spherical symmetry of the neutrino-driven winds from a nascent neutron star, theequations of baryon, momentum, and mass-energy conservation with the Schwarzschild metriccan be solved numerically [6]. Once the neutron star mass (M ), the neutrino sphere radius (Rν ),and the neutrino luminosity (Lν , of one flavor, where each flavor is assumed to have the same
luminosity) are specified along with the mass ejection rate (Ṁ ) as the boundary condition, the1

Figure 1: Model parameters (Rν , tpb , Ṁ ) are shown as functions of Lν . Also denoted are theobtained entropies for 1.4M¯ and 2.0M¯ cases.
wind solution can be obtained. In this study, Ṁ is chosen so as the wind crosses the sonic point
to be the transonic solution. The neutron star mass is taken to be 1.4M¯ and 2.0M¯ .

The time evolutions of Lν and Rν are assumed to be Lν (tpb ) = Lν0 (tpb /t0 )−1 and Rν (tpb ) =(Rν0 −Rνf )(tpb /t0 )−1 +Rνf , where tpb is the post-bounce time, t0 = 0.2 s, Lν0 = 4×1052 ergs s−1 ,Rν0 = 30 km, and Rνf = 10 km, which mimic the hydrodynamic results of the neutrinodriven winds in [10]. The wind trajectories are calculated for 54 constant Lν between 0.5 and
40 ergs s−1 (i.e., 0.2 < tpb < 16 s) with Rν (Lν ) = (Rν0 − Rνf )(Lν /Lν0 ) + Rνf deduced from theabove equations. Figure 1 shows the obtained entropies in winds for 1.4M¯ and 2.0M¯ cases
as functions of Lν , along with the morel parameters Ṁ , rν , and tpb . For more details on thesewind models, see [9].

3NUCLEOSYNTHESISThe nucleosynthetic yields for each wind trajectory are obtained by application of an extensive
nuclear reaction network that consists of ∼ 6000 species between the proton and neutron drip
lines along with all relevant nuclear reaction and weak rates. The neutrino captures on freenucleons are also included. Each calculation is initiated (t = 0 s) when the temperature decreases
to T9 = 9 (where T9 ≡ T /109 K).
Figure 2 shows the snapshot of nucleosynthesis at t = 0.02 s for the wind trajectory of
M = 2.0M¯ , Lν = 4.0 × 1051 ergs s−1 , tpb = 2.0 s, and Yei = 0.600, where the neutrino reactions
are turned off (left panel) and on (right panel). Yei is the initial electron fraction (number ofproton per baryon) at T9 = 9 (t = 0 s). The entropy obtained for this trajectory is 129NA k.
Without neutrino reactions, the abundances have a sharp peak at 56 Ni and the nuclear flow stops
at 64 Ge owing to its long half life (1.062 min) as well as the small proton-separation energies
around these species. In contrast, the inclusion of neutrino reactions leads to the nuclear flow
reaching the Z = 50 proton-magic number, resulting in the production of proton-rich isotopes
beyond A = 100. This neutrino-induced rp-process is a consequence of the presence of neutrons
2Figure 2: Snapshot of the nucleosynthesis at t = 0.02 s for the wind trajectory of M = 2.0M¯ ,Lν = 4.0 × 1051 ergs s−1 , tpb = 2.0 s, and Yei = 0.600, where the neutrino reactions are turnedoff (left panel) and on (right panel). The abundances are shown by the image in the nuclide
chart. The abundance curve as a function of mass number is shown in the upper left for eachpanel.
formed by the capture of anti-electron neutrinos on free protons. As a result, the waiting point
nuclei are bypassed via neutron captures (n, p) and (n, γ), and the proton capture proceeds.
The time evolution of Yei that determines the initial composition for each wind trajectoryis assumed as in the top panel of Figure 3, so as to mimic the hydrodynamic results in [10].
Yei is taken to be constant (Ye0 ) for t0 < tpb ≤ t1 and Ye (tpb ) = (Ye0 − Ye1 )(tpb /t1 )−1 + Yef
for t > t1 , where t1 = 4.0 s and Ye1 = 0.100. Ye0 is taken to be a free parameter, which varies
from 0.460 to 0.630 with the interval of 0.005 (35 cases). This gives Yei for each wind suchas Ye = Ye0 and Ye (Lν ) = (Ye0 − Ye1 )(Lν /Lν0 )(t1 /t0 ) + Ye1 for Lν ≥ 2.0 × 1051 ergs s−1 andLν < 2.0 × 1051 ergs s−1 , respectively. It should be noted that Ye changes during the α-process
phase (T9 ∼ 7 − 4), affected by the neutrino capture on free nucleons [11]. The bottom panel of
Figure 3 shows the shifts ∆Ye at tpb = 0.4, 1.0, and 4.0 s (Lν = 20, 8, and 2 × 1051 ergs s−1 ,respectively), when the temperature decreases to T9 = 3 (at which the rp-process sets in). The
left-top panel shows Yei (thin lines) and Yef ≡ Yei + ∆Ye (thick lines) for Ye0 = 0.600 (solidlines) and 0.460 (dotted lines).

4

CONTRIBUTION TO GALACTIC CHEMICAL EVOLUTION

In order to examine the contribution of this neutrino-induced rp-process to the Galactic chemical
evolution, the yields for each Yei model (35 cases) are mass-averaged over the 54 wind trajectories
weighted by Ṁ (Lν )∆tpb . The mass-averaged abundances of p-nuclei with respect to their solar
values for M = 1.4M¯ (top panel) and 2.0M¯ (bottom panel) cases are shown in Figure 4, as
functions of Yef (tpb = 4.0 s) (at Lν = 2.0 × 1051 ergs s−1 , as representative of different Yef s).
Note that the production of p-nuclei during later phase (t > 4.0 s) are negligible owing to theneutron richness (Figure 3, top panel), where the neutron capture nucleosynthesis takes place.
As can be seen, a variety of p-nuclei are produced with interesting amount for Yef > 0.5 models.
The heavier p-nuclei (up to A ≈ 110 − 120) appear for greater Yef models as well as for larger
3

Figure 3: Top panel: time evolution of Yei(thin lines) and Yef ≡ Yei + ∆Ye (thicklines) for Ye0 = 0.600 (solid lines) and
0.460 (dotted lines). Bottom panel: ∆Ye
at tpb = 0.4, 1.0, and 4.0 s (Lν = 20, 8,
and 2 × 1051 ergs s−1 , respectively), when
the temperature decreases to T9 = 3 (atwhich the rp-process sets in).

Figure 4: Top panel: mass-averaged abundances of p-nuclei (and 90 Zr for comparison purposes) with respect to theirsolar values for M = 1.4M¯ case asfunctions of Yef (tpb = 4.0 s). Also
shown is the histogram of the Ye distribution p(Ye ) of the neutrino-processed
ejecta in a two-dimensional “exploding”
core-collapse simulation by [3]. Bottom
panel: same as the right-top panel, but
for M = 2.0M¯ case.

M (= 2.0M¯ ) case (i.e., greater entropies, see Figure 1). It should be noted that 74 Se and 92 Mo
are most enhanced in slightly neutron-rich compositions (at Yef ≈ 0.48, see [9, 12]).
In reality, the neutrino-heated matter must have a certain distribution of Ye as can be seen ina two-dimensional hydrodynamic simulation of core-collapse supernova [3]. The Ye distributionof the neutrino-processed ejecta during the first 468 ms after core bounce for a 15M¯ progenitor
star obtained by [3] is overlaid in Figure 4, which has the maximum at Ye ≈ 0.5 and dominatesin the proton-rich side. To test the contributions of the winds for M = 1.4M¯ and 2.0M¯cases, the mass-averaged yields for each Yei model are further Ye -averaged (54 × 35 = 1890
winds in total) with p(Ye ) shown in Figure 4, assuming this distribution to be representative of
core-collapse supernovae. The resulting abundances with respect to their solar values are shownin Figure 5 for M = 1.4M¯ (top panel) and 2.0M¯ (bottom panel) cases as functions of mass
number. The p-nuclei are denoted with filled circles. The dotted horizontal lines indicate a“normalization band” between the largest production factor (84 Sr) and that by a factor of ten
less than that, along with a median value (dashed line).
As can be seen in Figure 5, the p-nuclei up to 92 Mo and 108 Cd for M = 1.4M¯ and 2.0M¯

4

Figure 5: Mass-Ye -averaged abundances with respect to their solar values for M = 1.4M¯(top panel) and 2.0M¯ (bottom panel) cases as functions of mass number. The isotopes (after
decay) are denoted by circles (even-Z) and triangles (odd-Z). The p-nuclei are denoted withfilled circles. The solid lines connect isotopes of a given element.
cases, respectively, fall within the normalization band, which are regarded to be the dominant
species produced by each event. Note that 74 Se and 92 Mo are mainly from the slightly neutronrich ejecta as described above, while other p-nuclei are synthesized by the neutrino-induced
rp-process in the proton-rich ejecta. The ejected masses by winds during the first 20 s are
2.8 × 10−3 M¯ and 1.1 × 10−3 M¯ for M = 1.4M¯ and 2.0M¯ cases, respectively. Given thatthe progenitor mass for each case to be, e.g., 15M¯ and 30M¯ , respectively, the overproduction
factor is expressed as ∼ 10−4 (Xej /X¯ ). The requisite overproduction factor of a given isotope forthe nucleosynthetic event to be the major source in the solar system is ∼ 10 [10], assuming that
all the core-collapse supernovae produce the same amount of the isotope. The overproduction
factors of ∼ 10 − 100 (see Figure 5) for the current models imply that the neutrino-driven winds
can be potentially the major astrophysical site of these light p-nuclei.
The neutron-capture nuclei with A > 100 result from winds during the later phase (tpb >4.0 s, see Figure 3, top panel), where the initial compositions are presumed to be neutron rich.
In fact, the high-entropy winds of M = 2.0M¯ case are those proposed to be the astrophysicalorigin of the heavy r-process nuclei [6, 13], while that of M = 1.4M¯ to be the origin of lightr-process nuclei up to A ∼ 130 [13]. It is interesting to note that no overproduction of theA ≈ 90 nuclei [6, 10] appears owing to the neutron deficiency in the ejecta [13].

5SUMMARY

It is shown that the interesting amounts of p-nuclei can be produced by the neutrino-induced
rp-process in the proton-rich neutrino-driven winds of core-collapse supernovae. This is due tothe presence of free neutrons by the anti-electron neutrino capture on free protons, which bypass
5the known waiting point nuclei along the nuclear path of the rp-process. The nucleosynthesis
calculations imply that this neutrino-induced rp-process in core-collapse supernovae can bepotentially the origin of light p-nuclei up to A ∼ 110, which cannot be easily explained by otherastrophysical scenarios.
This work was supported in part by a Grant-in-Aid for Japan-France Integrated Action Program (SAKURA) from the Japan Society for the Promotion of Science, and Scientific Research(17740108) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

References[1] R. K. Wallace and S. E. Woosley, Astrophys. J. 45, 389 (1981).
[2] O. Koike, M. Hashimoto, K. Arai, and S. Wanajo, Astron. Astrophys., 342, 464 (1999).
[3] R. Buras, M. Rampp, H. -Th Janka, and K. Kifonidis, Astron. Astrophys., in press (2005, astroph/0507135).
[4] J. Pruet, R. D. Hoffman, S. E. Woosley, R. Buras, and H. -Th. Janka, Astrophys. J., submitted (2005,
astro-ph/0511194).
[5] C. Fröhlich, et al. Astrophys. J., 637, 415 (2006).
[6] S. Wanajo, T. Kajino, G. J. Mathews, and K. Otsuki, Astrophys. J., 554, 578 (2001).
[7] S. Wanajo, N. Itoh, Y. Ishimaru, S. Nozawa, and T. C. Beers, Astrophys. J., 577, 853 (2002).
[8] M. Rayet, M. Arnould, M. Hashimoto, N. Prantzos, and K. Nomoto, Astron. Astrophys., 298, 517(1995).
[9] S. Wanajo, in preparation.
[10] S. E. Woosley, J. R. Wilson, G. J. Mathews, R. D. Hoffman, and B. S. Meyer, Astrophys. J., 433,
229 (1994).
[11] B. S. Meyer, G. C. McLaughlin, and G. M. Fuller, Phys. Rev. C, 58, 3696 (1998).
[12] R. D. Hoffman, S. E. Woosley, G. M. Fuller, and B. S. Meyer, Astrophys. J., 460, 478 (1996).
[13] S. Wanajo and I. Ishimaru, Nucl. Phys. A, in press (2006, doi:10.1016/j.nuclphysa.2005.10.012)

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