The type II supernova is considered as a candidate site for the production of
heavy elements. Since the supernova produces an intense neutrino flux, neutrino
scattering processes will impact element formation. We examine active-sterile
neutrino conversion in this environment and find that it may help to produce
the requisite neutron-to-seed ratio for synthesis of the r-process elements.Comment: 5 pages including 2 figures, to appear in the Proceedings of the
  Conference on the Intersections of Nuclear and Particle Physics 200

McLaughlin, G. C.

English

arXiv

G. C. McLaughlin

Crossref

arXiv:hep-ph/0008211v1  18 Aug 2000Active-Sterile Neutrino Transformationand r-Process NucleosynthesisG. C. McLaughlinTRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3Abstract. The type II supernova is considered as a candidate site for the productionof heavy elements. Since the supernova produces an intense neutrino flux, neutrinoscattering processes will impact element formation. We examine active-sterile neutrinoconversion in this environment and find that it may help to produce the requisiteneutron-to-seed ratio for synthesis of the r-process elements.The r-process of nucleosynthesis accounts for the most neutron rich of the heavyelements. The most likely environment for this type of synthesis is the late time(t > 10 s post-core bounce) supernova environment. Many studies have exploredthis ‘neutrino driven wind’ as a candidate environment and found it to be poten-tially viable [1,2]. However, to date, no model correctly reproduces the observedabundance pattern.In the neutrino driven wind, material in the form of free nucleons is ‘lifted’ off ofthe surface of the neutron star by energy deposited by neutrino interactions. Ana-lytic and semianalytic parameterizations of the thermodynamic and hydrodynamicconditions in the wind can be obtained [3,4]. Models of this type may be used toexplore the range of conditions within the context of the wind which will producethe solar system distribution of r-process elements. The key determinant of whethera given scenario will produce the r-process is the neutron to seed nucleus ratio atthe onset of the neutron capture phase. This ratio must be quite high (R > 100)in order to produce the very neutron-rich r-process elements. The factors whichdetermine the neutron-to-seed ratio are the entropy of the material, the hydrody-namic outflow timescale and the electron fraction, Ye = 1/(1 + n/p) where n/p isthe neutron-to-proton ratio. A study of many possible model parameters showsthat one must decrease the electron fraction, and/or increase the entropy and/ordecrease the hydrodynamic outflow timescale, relative to the conditions found intypical wind models, in order to produce the neutron-to-seed ratio necessary forthe r-process [5,6].Including the effects of neutrino interactions in general tends to make the requi-site conditions for r-process element production more extreme [7,8]. In particular,neutrino capture on free nucleons during alpha particle formation increases the elec-tron fraction [8]. This is the “alpha effect”. Other neutrino process are discussedin [2,9].There are three possible solutions to this problem. The first is that the supernovais the site of r-process synthesis, but it does not occur in the neutrino driven windas it is currently modeled. The second is that the r-process elements are madeat some other site such as neutron star-neutron star mergers. However, timescalearguments combined with isotopic abundance measurements and observations ofold halo star metallicity show that this site is unlikely to account for the entirer-process distribution [10,11].The third solution is the one that is investigated here: active-sterile (νe ↔ νs,ν̄e ↔ ν̄s) neutrino transformation. The νs in our study is defined as a particle whichmixes with the νe (and possibly also with νµ, and/or ντ ) but does not contributeto the width of the Z boson.If we neglect ν-ν forward scattering contributions to the weak potentials, thenthe equation which governs the evolution of the neutrinos as they pass though thematerial in the wind can be written as:ih̄∂∂rΨe(r)Ψs(r)=ϕe(r) (δm2/4E) sin 2θv(δm2/4E) sin 2θv −ϕe(r)Ψe(r)Ψs(r), (1)whereϕe(r) =14E(±2√2 GF[N−e (r)−N+e (r)−Nn(r)2]E − δm2 cos 2θv)(2)The upper sign is relevant for neutrino transformations; the lower one is for antineu-trinos. In these equations δm2 ≡ m22 − m21 is the vacuum mass-squared splitting,θv is the vacuum mixing angle, GF is the Fermi constant, and N−e (r), N+e (r), andNn(r) are the total proper number densities of electrons, positrons, and neutronsrespectively in the medium. Resonances can occur when the on-diagonal terms inthe wave equation are zero. The quantity in the brackets in Eq. 2 is proportionalto Ye − 1/3. Since the electron fraction can take on values between zero and one,the bracketed quantity in Eq. 2 can be either positive or negative. Therefore, for agiven choice of δm2, resonances may occur for neutrinos or antineutrinos dependingon the value of the electron fraction.In order to determine the survival probabilities of the neutrinos and antineutri-nos, we must know the electron fraction. In the neutrino driven wind, neutrinoand antineutrino capture are the most important reactions in determining the elec-tron fraction. However, near the surface of the protoneutron star there is also acontribution from electrons and positrons:νe + n ⇀↽ p + e−; ν̄e + p ⇀↽ n + e+. (3)Therefore, the problem involves a feedback mechanism. The neutrino capture ratesdetermine the electron fraction and the electron fraction determines the potentialwhich is used in the neutrino transformation equations. These equations thendetermine survival probabilities of the neutrinos, and therefore their capture rates.We note that we can not assume weak equilibrium, (very fast capture ratescompared with outflow rate) or weak freeze-out (very slow rates compared with theoutflow rate). The rates must be tracked numerically. A previous study took thelimit of weak equilibrium and found different behavior [12] than presented here.We perform calculations by tracking a mass element in the neutrino driven wind.We use the results of analytic models [4], where r ∝ exp(−t/τ) and ρ ∝ r−3where τ is the outflow timescale. Close to the surface, before the wind begins tooperate we use the density profile of Wilson and Mayle [13]. At each time stepwe calculate all thermodynamic quantities, calculate the weak rates and evolve theneutrino transformation equations forward. We assume, since the outflow timescaleis short, t ∼ τ <∼ 0.5 s, that each mass element will have the same evolution as theprevious one. Since we use a nuclear statistical equilibrium calculation, we cutour calculations off at the time when heavy nuclei begin to form. More detail iscontained in [14].A calculation for one mass element is shown in Fig. 1. The upper curve showsthe evolution for the case of no neutrino oscillations. The wind parameters wereτ = 0.3 s, s = 100. The solid line shows the actual electron fraction, while theFIGURE 1. The electron fraction is plotted against distance from the center of the neutron star.The upper line shows the evolution with no transformation. The lower line shows the evolutionof active-sterile mixing parameters of sin2 θ = 0.01 and δm2 = 20 eV2. The dotted line shows thevalue that the electron fraction would take on if weak equilibrium obtained.dotted line shows what the electron fraction would be if weak equilibrium obtained.The initial rise is due to Pauli unblocking of the electrons at the surface of theproto-neutron star. The lower curve shows the evolution of the electron fractionfor mixing parameters of δm2 = 20 eV2, sin2 2θv = 0.01. In the latter case thereis a rapid drop in the electron fraction when the neutrinos begin to transform.In fact, there are three neutrino transformations. Initially, the electron neutrinostransform to steriles. Later antineutrinos transform, and finally, when the densityfalls far enough the antineutrinos transform back. The first transformation of theantineutrinos is seen in the small bump in the equilibrium electron fraction. A small“alpha effect” can be see as the slight rise in both solid lines at large distance.The active-sterile transformation scenario successfully reproduces a low electronfraction which is beneficial to the r-process. We now consider a range of δm2, sin2 θparameters. A contour plot of the electron fraction is shown in Fig. 2. Inside thedashed contour shows the region where conditions are neutron-rich enough to befavorable for r-process nucleosynthesis. In the bottom left corner of the plot, thesolution is approaching the case without neutrino transformation.Although not shown here, we have studied a range of timescales for the neu-trino driven wind models, and seen that the qualitative features of this effect arereproduced [14].We have used several approximations in our calculations, which we are contin-uing to study. These include the importance of the neutrino-neutrino scatteringFIGURE 2. Contour plot of electron fraction as measured at the point where heavy nuclei beginto form. Neutrino driven wind parameters employed here are s/k = 100, τ = 0.3s. .background in the oscillation equations, the importance of nonradial paths andfeedback in the dense region near the proto-neutron star. The region where thelatter two are important is the shaded region in Fig. 2. These problems are beingstudied in [15].Conclusions: Meteoritic and observational evidence points to supernovae as thesource of the r-process elements, although a self-consistent model of the neutrinodriven wind which will produce the r-process elements is still elusive. In the nextfew years significant advances are expected in supernova modeling. If and whenpotential hydrodynamic solutions are exhausted and the caveats above have beenexplored, then the r-process may provide a signature for new neutrino physics.ACKNOWLEDGEMENTSThis work was done in collaboration with J. M. Fetter, A. B. Balantekin and G.M. Fuller.REFERENCES1. Woosley, S. E., Wilson, J. R., Mathews, G. J., Hoffman, R. D. and Meyer, B.S. 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