arXiv:1102.4858v1 [nucl-th] 23 Feb 2011
11B and Constraints on Neutrino Oscillations and Spectra from
Sam M. Austin,1, 2, ∗Alexander Heger,3and Clarisse Tur1
1National Superconducting Cyclotron Laboratory,
1 Cyclotron, Michigan State University, East Lansing, MI 48824-1321
Joint Institute for Nuclear Astrophysics
2Department of Physics and Astronomy,
Michigan State University, East Lansing Michigan 48824
3School of Physics and Astronomy, University of Minnesota,
Twin Cities, Minneapolis, MN 55455-0149
Joint Institute for Nuclear Astrophysics†
(Dated: February 25, 2011)
We have studied the sensitivity to variations in the triple alpha and12C(α,γ)16O reaction rates, of
the yield of the neutrino process isotopes7Li,11B,19F,138La, and180Ta in core collapse supernovae.
Compared to solar abundances, less than 15% of7Li, about 25-80% of19F, and about half of138La is
produced in these stars. Over a range of ±2σ for each helium-burning rate,11B is overproduced and
the yield varies by an amount larger than the variation caused by the effects of neutrino oscillations.
The total11B yield, however, may eventually provide constraints on supernova neutrino spectra.
PACS numbers: 26.30.Jk, 26.50.+x, 14.60.Pq
About 1058neutrinos are emitted during a typical core collapse supernova explosion.
For some time it has been known (see  for a detailed history) that interactions of these
neutrinos with the stellar envelope can produce certain rare nuclei in abundances close to
those observed in nature. These nuclei, called here the neutrino nuclei, include7Li,11B,19F,
138La, and180Ta [1, 2].
It was pointed out  that the production of some of the180Ta and most of the138La by
the neutrino process was sensitive to the electron neutrino temperatures, and might serve to
probe the value of the neutrino oscillation parameter sin22θ13. Recently, [3–5] showed that
the yields of7Li and11B in supernova explosions are also sensitive to sin22θ13and to whether
the neutrino mass hierarchy is normal or inverted. In both cases, this sensitivity arises
because neutrino oscillations can change the neutrino spectra produced during core collapse
supernovae, increasing the average energies of the νeand ¯ νeand affecting the synthesis of the
neutrino nuclei. Since two of the main goals of neutrino physics  are to determine better
the value of sin22θ13and the nature of the mass hierarchy, the possibility that the observed
abundances of the neutrino nuclei might constrain these quantities is of great interest.
Their use for this purpose depends, however, on the robustness of the stellar yield pre-
dictions. Studies of the dependence of nucleosynthesis on the helium burning reaction rates
have shown [7, 8] that both the yields of the more abundant nuclides and stellar structure
are significantly affected. Since the neutrino nuclei result from neutrino induced spallation of
abundant progenitor nuclei, their production depends on the abundances of these nuclei and
on their location within the star, and thereby on the rates of the helium burning reactions.
In this paper, we examine the changes in the production of7Li,11B,19F,138La, and180Ta
caused by changes in the astrophysical helium burning rates within their uncertainty limits,
and compare the yield changes of7Li, and11B, with the predicted [3–5] effects of oscillations.
We then discuss how, and whether, the neutrino process nuclei can be used to constrain
the neutrino spectra from supernovae. We find that the constraints provided by neutrino
process nucleosynthesis are interesting but not yet definitive. Because of the great interest
in these issues it appears that a major effort to sharpen these constraints is warranted; a
discussion of important measurements and calculations is given below.
We used the KEPLER code [9–12] to model the evolution of 15, 20, and 25 solar mass
stars from central hydrogen burning up to core-collapse; a piston placed at the base of the
oxygen shell was then used to simulate the explosion. Following  we assumed a total
energy of 5 × 1052ergs per neutrino species, i.e. a total of 3 × 1053ergs energy release in
the supernova explosion. Mass loss processes were included. The neutrino spectra were
approximated by Fermi-Dirac distributions with a zero degeneracy parameter, a luminosity
exponentially decaying after onset of core collapse with a time-scale of 3 s and a constant
neutrino temperature: T = 4 MeV for νeand ¯ νe; T = 6 MeV for νµ, ¯ νµ, ντ,and ¯ ντ. For
further details, see [2, 7, 8, 13]. These choices are consistent with estimates of neutrino
emission intensity and time dependence from supernovae .
Initial stellar abundances were taken from both Anders & Grevesse  and from Lodders
, hereafter AG89 and L03. The L03 abundances for C, N, O, Ne are roughly 15%-
25% lower than those of AG89, whereas the abundances of heavier elements are roughly
15% higher. For calculations of neutrino process cross sections we used the results from
. Briefly, in that paper the charged and neutral current cross sections were first used to
calculate the excitation spectra of the product nuclei; experimental data and 0¯ hω shell-model
estimates were used to determine the Gamow-Teller response for12C and20Ne (leading to
11B and19F) and RPA estimates for the J ≤ 4 multipoles for all other transitions. The
SMOKER statistical model code , was then used there to follow the ensuing decays. The
γ process contributions to the yields are also included in our calculations, but are important
Isotope yields were stored at nine key points of stellar evolution [8, 13]. As anticipated,
7Li and11B were produced essentially only during the supernova stage; their yields are
shown in Fig. 1. Here an initial “A” (or “L”) label means that the calculations were done
for the AG89 (or L03) abundances, and a final “A” (or “C”) means that the12C(α,γ)16O
(or triple-alpha) rates were varied by ±2σ from their central values. These central values
were, resp., 1.2 times the rate recommended by Buchmann  with σ = 25% and that
recommended by Caughlan and Fowler  with σ = 12%. For the12C(α,γ)16O rate, the
central value is that commonly used in calculations with the KEPLER code [7, 19]; it is
consistent with recent measurements . The energy dependence obtained by Buchmann
was used for all calculations. The labels also give the stellar mass, or 3 STARS, the average
for the 15, 20, and 25 M⊙stars using a Scalo  Initial Mass Function (IMF) with a slope
of γ = −2.65. For normalization purposes we compare to the production factor for oxygen.
Since16O is made mainly in massive stars, a production factor ratio near one is consistent
with all (or most) of an isotope being made in a primary neutrino process (as are7Li,11B,
FIG. 1: Production factors of7Li and11B compared to those of16O for various reaction rates.
The left hand column shows the results when the triple-alpha reaction rate R3αis varied about
the central value of 1.0, the rate of ref. . The right-hand column shows the results when Rα,12
is varied about the central value of 1.2. The value for7Li has been multiplied by a factor of 10.
An example of the range of variation in11B yield predicted in  is shown as a band in the upper
right-hand panel. The dotted line at 0.4 is the production factor ratio that would give the solar
abundance of11B not made in the galactic cosmic rays. For more information see the text.
Examining first the results for average production in the three-star sample, and assuming
that this is a reasonable approximation of the total production process, we see that only
10%-15% of7Li is made in the neutrino process. This is not surprising, since there are
many processes, including the Big Bang, that make or destroy7Li and that are not fully
understood. On the other hand, for most values of the reaction rates11B is overproduced,
even if one ignores production by cosmic rays.
Fig. 2 shows the results for138La and180Ta. Here we show also results for the pre-SN
stage, the time when the contraction speed in the iron core reaches 1000 km sec−1, since
production during that stage is not negligible, especially for180Ta. A detailed examination,
however, shows that most of the138La and180Ta that is ejected in the SN is not what was
present in the pre-SN stage; that is mostly destroyed by the SN shock and most of what is
ejected was newly synthesized during the explosion [2, 11].
Since these two isotopes are secondary products (produced from pre-existing spallation
targets) a production ratio of about two for138La and180Ta (see the dotted line on Fig. 2)
would be necessary to reproduce the solar abundance. An additional complication is that
our models do not distinguish production in the short lived ground state from that in
the long-lived isomeric 9−state in180Ta; a better, but still approximate, treatment 
gives an isomer production of about 40% of the total production. It then appears that the
production of180Ta is roughly consistent with the solar abundance, given the uncertainties in
the production calculations, and that the production of138La corresponds to about half the
solar abundance.19F is a primary product, and it appears that 25%-75% of solar19F could
be made by the neutrino process. This complicates the determination of the importance of
other sources such as AGB stars and Wolf-Rayet winds.
We now consider whether a comparison of the observed abundances of7Li and11B to SN
model predictions can place constraints on the neutrino oscillation process, as was suggested
in Refs. [3–5]. These investigations were for a 16.2 M⊙star, using parameters almost identical
to those we have used, except that the explosion energy, Tνe, and T¯ νewere 1.0 Bethe, 3.2
MeV, and 5.0 MeV instead of 1.2 Bethe, 4.0 MeV and 4.0 MeV. The near equality of the
average neutrino energies should yield similar production for the two models in the absence
of neutrino oscillations.
In [3–5] neutrino oscillations produce significant increases in7Li production, up to 75%,
as sin22θ13increases from 10−6to 10−2for the normal neutrino hierarchy–the changes are
much smaller, around 15% for an inverted hierarchy. The changes for11B are small for
either hierarchy, around 20%. The number ratio N(7Li )/N(11B) is assumed to be less
susceptible then the absolute yields, to systematic uncertainties in the calculations and has