Neutrino-Induced Nucleosynthesis of A>64 Nuclei: The p Process
C. Fro
¨
hlich,
1
G. Martı
´
nez-Pinedo,
2,3
M. Liebendo
¨
rfer,
4,1
F.-K. Thielemann,
1
E. Bravo,
5
W. R. Hix,
6
K. Langanke,
3,7
and N. T. Zinner
8
1
Departement fu
¨
r Physik und Astronomie, Universita
¨
t Basel, CH-4056 Basel, Switzerland
2
ICREA and Institut d’Estudis Espacials de Catalunya, Universitat Auto
`
noma de Barcelona, E-08193 Bellaterra, Spain
3
Gesellschaft fu
¨
r Schwerionenforschung, D-64291 Darmstadt, Germany
4
Canadian Institute for Theoretical Astrophysics, Toronto, Ontario M5S 3H8, Canada
5
Departament de Fı
´
sica i Enginyeria Nuclear, Universitat Polite
`
cnica de Catalunya, E-08034 Barcelona, Spain
6
Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
7
Institut fu
¨
r Kernphysik, Technische Universita
¨
t Darmstadt, D-64289 Darmstadt, Germany
8
Institute for Physics and Astronomy, University of A
˚
rhus, DK-8000 A
˚
rhus C, Denmark
(Received 10 November 2005; published 10 April 2006)
We present a new nucleosynthesis process that we denote as the p process, which occurs in
supernovae (and possibly gamma-ray bursts) when strong neutrino fluxes create proton-rich ejecta. In
this process, antineutrino absorptions in the proton-rich environment produce neutrons that are immedi-
ately captured by neutron-deficient nuclei. This allows for the nucleosynthesis of nuclei with mass
numbers A>64, making this process a possible candidate to explain the origin of the solar abundances of
92;94
Mo and
96;98
Ru. This process also offers a natural explanation for the large abundance of Sr seen in a
hyper-metal-poor star.
DOI: 10.1103/PhysRevLett.96.142502 PACS numbers: 26.30.+k, 25.30.Pt, 97.60.Bw
Supernova explosions (the cataclysmic end point of
stellar evolution) produce iron and neighboring nuclei.
The production of elements beyond Fe has long been
postulated by three classical processes: the r and s pro-
cesses (caused by rapid or slow neutron capture) and the p
process, standing either for proton capture or alternative
means to produce heavy neutron deficient, stable isotopes
[1]. The s process acts during stellar evolution via neutron
captures on Fe produced in previous stellar generations
(thus being a ‘‘secondary process’’). The location, opera-
tion, and uniqueness of the r and the p process in astro-
physical sites are still a subject of debate. The r process is
required to be a primary process [2], meaning that the
production of such elements is independent of the initial
heavy element content in the star. Recent galactic chemical
evolution studies of Sr, Y, and Zr [3] suggest the existence
of a primary process, denoted the ‘‘lighter element primary
process’’ (LEPP), which is independent of the r process
[2,4] and operates very early in the Galaxy. Most of the p
nuclei are thought to be produced in hot (supernova)
environments, where disintegration of preexisting heavy
elements due to blackbody radiation photons can account
for the heavy p nuclei while the light ones are underpro-
duced (see, e.g., Refs. [5–7]). Currently, the mechanism
for the production of the light p nuclei,
92;94
Mo and
96;98
Ru,
is unknown. However, chemical evolution studies of the
cosmochronometer nucleus
92
Nb [8] imply a primary su-
pernova origin for these light p nuclei.
Observations of extremely ‘‘metal-poor’’ stars in the
Milky Way provide us with information about the nucleo-
synthesis processes operating at the earliest times in the
evolution of our Galaxy. They are thus probing supernova
events from the earliest massive stars, the fastest evolving
stellar species. The recently discovered hyper-metal-poor
stars in the Milky Way [9,10] may witness chemical en-
richment by the first generation of faint massive super-
novae which experience extensive matter mixing (due to
instabilities) and fallback of matter after the explosion
[11]. However, the detection of Sr=Fe (exceeding 10 times
the solar ratio) in the most metal-poor star known to date
[9] suggests the existence of a primary process, producing
elements beyond Fe and Zn.
In this Letter, we present a new nucleosynthesis process
that will occur in all core-collapse supernovae and could
explain the existence of Sr and other elements beyond Fe in
the very early stage of galactic evolution. We denote this
process the ‘‘p process’’ and suggest it as a candidate for
the postulated lighter element primary process LEPP [3].
It can also contribute to the nucleosynthesis of light
p-process nuclei. Here, we consider only the inner ejecta
of core-collapse supernovae, but the winds from the accre-
tion disk in the collapsar model of gamma-ray bursts [12–
14] may also be a relevant site for the p process. This
process is distinct from previous nucleosynthesis processes
involving neutrinos. The production of light p nuclei by
neutrino absorption on nuclei in alpha-rich freeze-outs
resulting from the neutron-rich neutrino wind that develops
in later phases of a supernova explosion [15,16]. The neu-
trino process, involving neutrino-induced spallation of nu-
cleons, has been discussed [17–19] for the production of
some selected nuclei. And finally, it has been suggested
that antineutrino absorption on protons may be a source of
neutrons for the production of light nuclei up to Li [17].
As a full understanding of the core-collapse supernova
mechanism is still pending and successful explosion simu-
lations are difficult to obtain [20], the composition of the
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innermost ejecta—directly linked to the explosion mecha-
nism—remains to a large extent unexplored. Recent su-
pernova simulations with accurate neutrino transport
[20–22] show the presence of proton-rich neutrino-heated
matter, both in the inner ejecta [20,21] and in the early
neutrino wind from the protoneutron star [20]. This matter
is subject to a large neutrino energy deposition by the
absorption of neutrinos and antineutrinos with initially
similar intensities and energy spectra. As soon as the
heating and expansion lifts the electron degeneracy, the re-
actions
e
n
!
p e
and
e
p
!
n e
drive the
composition proton rich due to the smaller mass of the
proton [23,24] (n, p, e
, e
,
e
, and
e
denote the neutron,
proton, electron, positron, neutrino, and antineutrino, re-
spectively). As this proton-rich matter expands and cools,
nuclei can form resulting in a composition dominated by
N Z nuclei, mainly
56
Ni and
4
He, and protons. Without
the further inclusion of neutrino and antineutrino reactions,
the composition of this matter will finally consist of pro-
tons, alpha particles, and heavy (Fe-group) nuclei (in nu-
cleosynthesis terms a proton- and alpha-rich freeze-out),
with enhanced abundances of
45
Sc,
49
Ti, and
64
Zn [23,24].
In these calculations the matter flow stops at
64
Ge with a
small proton capture probability and a beta-decay half-life
(64 s) that is much longer than the expansion time scale
( 10 s) [23].
Synthesis of nuclei heavier than A 64, including light
p nuclei, is possible in proton-rich ejecta if the entropy per
nucleon is in the range s 150–170k
B
(where k
B
is the
Boltzmann constant) [25]. Such large entropies are, how-
ever, not attained in core-collapse supernovae simulations
with detailed neutrino transport which give s 50–75k
B
[23,24]. Here we show that the synthesis of nuclei with
A>64 can also be obtained with realistic entropies, if one
explores the previously neglected effect of neutrino inter-
actions on the nucleosynthesis of heavy nuclei. N Z nu-
clei are practically inert to neutrino capture (converting a
neutron in a proton), because such reactions are endoergic
for neutron-deficient nuclei located away from the valley
of stability. The situation is different for antineutrinos that
are captured in a typical time of a few seconds, both on
protons and nuclei, at the distances at which nuclei form
(1000 km). This time scale is much shorter than the beta-
decay half-life of the most abundant heavy nuclei reached
without neutrino interactions (e.g.,
56
Ni and
64
Ge). As
protons are more abundant than heavy nuclei, antineutrino
capture occurs predominantly on protons, causing a resid-
ual density of free neutrons of 10
14
–10
15
cm
3
for several
seconds, when the temperatures are in the range 1–3 GK.
This effect is clearly seen in Fig. 1, where the time evolu-
tion of the abundances of protons, neutrons, alpha parti-
cles, and
56
Ni is shown (
56
Ni serves to illustrate when
nuclei are formed). The dashed lines show the results for
a calculation where neutrino absorptions are neglected
once the temperature drops below 6 GK. Without the
inclusion of antineutrino capture the neutron abundance
soon becomes too small to allow for any capture on heavy
nuclei. The figure also compares the evolution of Y
e
(de-
fined as the number of electrons per nucleon).
In our studies we use the detailed neutrino spectral infor-
mation provided by neutrino radiation-hydrodynamical
calculations [24] to determine the neutrino and antineu-
trino absorption rates at each point of the nucleosynthesis
trajectory (temperature, density, and radius). Our network
calculations follow the detailed abundances of 1435 iso-
topes between Z 1 and Z 54 plus neutrons, which
allows an accurate treatment of the changes in composition
induced by neutrino interactions.
The neutrons produced via antineutrino absorption on
protons can easily be captured by neutron-deficient N Z
nuclei (for example,
64
Ge), which have large neutron cap-
ture cross sections. The amount of nuclei with A>64
produced is then proportional to the number of antineutri-
nos captured. While proton capture (p; )on
64
Ge takes
too long, the (n; p) reaction dominates (with a lifetime of
0.25 s at a temperature of 2 GK), permitting the matter flow
to continue to nuclei heavier than
64
Ge via subsequent
proton captures with freeze-out at temperatures around
1 GK. This is different from r-process environments with
Y
e
< 0:5, i.e., neutron-rich ejecta, where neutrino capture
on neutrons provides protons that interact mainly with the
existing neutrons, producing alpha particles and light nu-
clei. Their capture by heavy nuclei is suppressed because
of the large Coulomb barriers [15,26]. Consequently, in
r-process studies an enhanced formation of the heaviest
nuclei does not take place when neutrino interactions are
included. In proton-rich ejecta, in contrast to expectation
[23], antineutrino absorption produces neutrons that do not
suffer from Coulomb barriers and are captured preferen-
tially by heavy neutron-deficient nuclei.
110
Time (s)
−22
−20
−18
−16
−14
−12
−10
−8
−6
−4
−2
0
log
10
(Y
i
)
0.51
0.53
0.55
Y
e
n
p
4
He
56
Ni
Y
e
FIG. 1 (color online). Evolution of the abundances of neutrons,
protons, alpha particles, and
56
Ni in a nucleosynthesis trajectory
resulting from model B07 of Ref. [24]. The abundance, Y,is
defined as the number of nuclei of the species i present divided
by the total number of nucleons which is conserved during the
calculation. The solid (dashed) lines display the nucleosynthesis
results which include (omit) neutrino and antineutrino absorp-
tion interactions after nuclei are formed. The abscissa measures
the time since the onset of the supernova explosion.
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Figure 2 shows the composition of supernova ejecta
obtained with the hydrodynamical model B07 described
in detail in Ref. [24]. In addition to the proton-rich con-
ditions in the innermost ejected zones visible in simula-
tions by different groups [20–22], our models consistently
include neutrino-absorption reactions in the nucleosynthe-
sis calculations allowing for the occurrence of the p
process. However, in our stratified spherically symmetric
models the accretion rate is rapidly reduced (and with this
the neutrino luminosities) after the onset of the explosion.
In a more realistic scenario considering convective turn-
over in the hot mantle, continued accretion is expected to
maintain a large neutrino luminosity beyond the onset of
the explosion and to further support the p process.
In order to understand the sensitivity of our results, one
must consider the dependence of the p process on the
conditions during the ejection of matter in supernova ex-
plosions. There are several essential parameters in addition
to the entropy s. One is the Y
e
value of the matter when
nuclei are formed. The larger the Y
e
value, the larger is the
proton abundance, producing a larger neutron abundance
for the same antineutrino flux during the p process. This
permits a more efficient bridging of beta-decay waiting
points by (n; p) reactions in the flow of proton captures to
heavier nuclei. The location (radius r) of matter during the
formation of nuclei and the ejection velocity also influence
the p process by determining the intensity and duration of
the antineutrino flux which the matter will experience.
Finally, the long-term evolution of the neutrino luminosi-
ties and energy spectra during the cooling phase of the
protoneutron star plays an important role. These factors are
poorly known due to existing uncertainties in the super-
nova explosion mechanism.
To test the dependence of the nucleosynthesis on these
parameters we have also carried out parametric calcula-
tions based on adiabatic expansions similar to those used in
Refs. [25,27] but for a constant realistic entropy per nu-
cleon s 50k
B
. This allows exploration of the sensitivity
of the nucleosynthesis without the need to perform full
radiation-hydrodynamical calculations. An example is
given in Fig. 3, which shows the dependence of the
p-nuclei abundances as a function of the Y
e
value of the
ejected matter. The different Y
e
values have been obtained
by varying the temperatures of the neutrino and antineu-
trino spectra assuming Fermi-Dirac distributions for both.
Close to Y
e
0:5 (and below) essentially no nuclei beyond
A 64 are produced. Nuclei heavier than A 64 are
produced only for Y
e
> 0:5, showing a very strong depen-
dence on Y
e
in the range 0.5– 0.6. A clear increase in the
production of the light p nuclei,
92;94
Mo and
96;98
Ru,is
observed as Y
e
gets larger. However, the abundances of
these nuclei are still a factor 10 smaller than the ones of
84
Sr. Similar results have been recently obtained by Pruet
et al. [28], in a study of the nucleosynthesis that occurs in
the early proton-rich neutrino wind. These authors suggest
that the production of
92
Mo is sensitive to the experimen-
tally unknown masses of nuclei around
92
Pd. Future ex-
perimental determinations of these masses will help to
decide if the solar system abundances of light p nuclei
can be due to the p process.
All core-collapse supernova explosions, independent of
existing model uncertainties, will eject hot, proton-rich
explosively processed matter subject to strong neutrino
irradiation. We argue that in all cases the p process will
operate in the innermost ejected layers producing neutron-
deficient nuclei above A 64. As the innermost ejecta,
this matter is most sensitive to the details of individual
explosions, thus their abundances will vary noticeably
from supernova to supernova (e.g., as a function of stellar
mass, rotation, etc.). The final amount of matter ejected
will also depend on the intensity of the fallback, but as
discussed in Ref. [11], mixing before fallback will always
40 45 50 55 60 65 70 75 80 85 90
Mass Number A
10
0
10
1
10
2
10
3
10
4
Y
i
/Y
i,
FIG. 2. The panel shows the isotopic abundances for
model B07 of Ref. [24] relative to solar abundances [29]. The
solid circles represent calculations where (anti)neutrino-
absorption reactions are included in the nucleosynthesis while
for the open circles neutrino interactions are neglected.
0.5 0.52 0.54 0.56 0.58 0.6
Y
e
10
2
10
3
10
4
10
5
10
6
10
7
10
8
Y
i
/Y
i,
74
Se
78
Kr
84
Sr
96
Ru
94
Mo
98
Ru
102
Pd
92
Mo
106
Cd
108
Cd
FIG. 3 (color online). Light p-nuclei abundances in compari-
son to solar abundances as a function of Y
e
. The Y
e
values given
are the ones obtained at a temperature of 3 GK that corresponds
to the moment when nuclei are just formed and the p process
starts to act.
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lead to the ejection of elements synthesized, even in the
innermost layers. Reference [11] explains the abundances
seen in hyper-metal-poor stars by the ejecta of faint or
weak core-collapse supernovae. Such faint supernova will
generally have small expansion velocities favoring an en-
hanced production of p elements, offering an explanation
for the presence of Sr in the star HE 1327-2326 [9]. Our
studies of the p process show that the elements between
Zn and Sr should be coproduced together with Sr. The
observation of these elements, which with the exception
of Ge and Rb are not detectable from the ground in optical
lines, but may be possible from space in the infrared or near
ultraviolet (e.g., the Hubble space and Spitzer space tele-
scopes), can provide support for the occurrence of the p
process at early times in the Galaxy and contribute valu-
able information about the conditions experienced by the
inner supernova ejecta in order to constrain current theo-
retical models of supernova explosions. Further studies are
required to fully understand the p process contribution to
the chemical evolution of the Galaxy. In this Letter, we
have discussed the innermost proton-rich supernova ejecta
before the emergence of the neutrino wind from the pro-
toneutron star. This neutrino wind will initially be proton
rich [23] but will turn neutron rich in its later phases
allowing for the synthesis of r-process nuclei [15,16,26].
The variations in the contribution of the p process (rep-
resented by Sr, Y, and Zr) and the r process (producing the
heaviest elements up to Th and U) [2,4] can shed light on
the connection of both of these processes and provide
information about the class of supernovae that produce
the heavy r-process nuclei.
C. F. and F. K. T. are supported by the Swiss National
Science Foundation (SNF). G. M. P. is supported by the
Spanish MEC and by the European Union ERDF under
Contracts No. AYA2002-04094-C03-02 and
No. AYA2003-06128. M. L. is supported by the SNF under
Grant No. PP002-106627/1. The research of E. B. has been
supported by DURSI of the Generalitat de Catalunya and
Spanish DGICYT grants. The research of W. R. H. has
been supported in part by the U.S. NSF under Contract
No. PHY-0244783 and by the U.S. DOE, through the
SciDAC Program. ORNL is managed by UT-Battelle,
LLC, for the U.S. DOE under Contract No. DE-AC05-
00OR22725.
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![FIG. 2. The panel shows the isotopic abundances for model B07 of Ref. [24] relative to solar abundances [29]. The solid circles represent calculations where (anti)neutrinoabsorption reactions are included in the nucleosynthesis while for the open circles neutrino interactions are neglected.](/figures/fig-2-the-panel-shows-the-isotopic-abundances-for-model-b07-1hlx89qk.webp)
![FIG. 1 (color online). Evolution of the abundances of neutrons, protons, alpha particles, and 56Ni in a nucleosynthesis trajectory resulting from model B07 of Ref. [24]. The abundance, Y, is defined as the number of nuclei of the species i present divided by the total number of nucleons which is conserved during the calculation. The solid (dashed) lines display the nucleosynthesis results which include (omit) neutrino and antineutrino absorption interactions after nuclei are formed. The abscissa measures the time since the onset of the supernova explosion.](/figures/fig-1-color-online-evolution-of-the-abundances-of-neutrons-23645hlm.webp)