Using Helioseismology to Constrain Solar Models

Non-standard solar models to resolve the solar neutrino problem fail tests imposed by helioseismology, suggesting that such models are rather contrived, with resolution of the neutrino problem lying in the realm of particle physics. Using Helioseismology to Constrain Solar Models The energy radiated by the Sun derives Jørgen Christensen-Dalsgaard from the fusion of four hydrogen atoms into one helium atom via different paths. Teoretisk Astrofysik Center, Danmarks Grundforskningfond The reaction generates approximately 4.1 x Institut for Fysik og Astronomi, Aarhus Universitet 10-12 J (the precise amount depends on the energy lost as neutrinos) and since the PP-I PP-II PP-III Earth receives about 1360 Wm-2 from the Sun, the total flux of neutrinos must be 1H + 1H → 2D + e+ + ve 3He + 4He → 7Be + γ 7Be + 1H → 8B + γ around 7 x 1014 m-2s-1. The cross-section 2D + 1H → 3He + γ 7Be + e- → 7Li + ve 8Be → 8B + e+ + ve for neutrino absorption is so small that vir 3He + 3He → 4He + 21H 7Li + 1h → 4He + 4He 8Be → 4He + 4He tually all the neutrinos escape immediately from the Sun, in contrast to the radiative Fig. 1 — The most important hydrogen-burning reactions in the Sun, the so-called PP-I, PP-II energy which reaches the solar surface and PP-III chains. The initial reaction is the fusion of two hydrogen nuclei into a deuterium through a slow diffusive process since the nucleus ; charge and lepton number conservation demands emission of a positron and a neu mean-free path of a photon near the solar trino. This reaction controls the overall rate of energy production. The subsequent reaction path centre is only a few mm. Thus, the neutrinos depends on the branchings between the 3He + 3He and the 3He + 4He reactions, and between in principle provide direct information about the 7Be + e- and the 7Be + 1H reactions. The PP-III branch is very rare. Neutrinos produced in nuclear reactions in the solar core. the 1H + 1H reaction, the electron capture in 7Be, and the positron decay of 8B, have average Calculating an accurate estimate of the energies of 0.26 MeV, 1.06 MeV and 7.46 MeV, respectively. Neutrinos are also emitted by the neutrino detection rate is not trivial for it rare triple reaction 1H(1He-,ve)2D, and modest contributions to the energy generation and the relies on models that follow numerically the neutrino flux come from hydrogen fusion through the so-called CNO-cycle. Sun’s evolution during the conversion of hydrogen into helium (Fig. 1 gives the domi less than 0.02%. So the constraint that There have been several independent cal nant reaction paths). Results depend on the computed luminosity should fit the ob culations of neutrino capture rates, with re nuclear reaction rates and on the assumed served value essentially determines the sults depending on the assumed physics. All physics of matter, and involve simplifying number of low-energy neutrinos from the recent calculations give similar results (e.g., assumptions, the most important probably 1H(1H,e+ve)2D reaction. In contrast, the flux [1]). Fig. 2 compares neutrino event rates being to neglect hydrodynamic processes of high-energy neutrinos, especially that for measured experimentally using 37CI and that may result in a partial mixing. The out the 8B(,e+ve)8Be reaction, depends on the 71 Ga (see insert overleaf) with those for se come is called a “standard” solar model and branching ratios between the different lected standard models, computed with dif analogous calculations for other stars form chains which are in turn strongly tempera ferent equations of state, opacity tables, nu the basis for many areas of astrophysics. ture-dependent, with the fraction of the reac clear parameters, or ages. Although it is dif Clearly, any discrepancy between the ob tions that go through the PP-II and PP-III ficult to assign statistically meaningful error served and the predicted rates of solar neu chains increasing very rapidly with tempera bars, calculations where the relevant para trino detection casts doubt on this basis. ture; so therefore does the flux of high-ener meters were varied within reasonable limits The initial helium abundance, which can gy neutrinos. The table overleaf presents indicate that the error in the computed cap not be determined reliably from spectro rates for a standard model computed using ture rate is unlikely to exceed 2 SNU for scopic observations, is treated as a free representative and up-to-date values for the detection using 37CI and 10 SNU for the parameter, being adjusted until the com various variables. The number of detections 71 Ga experiment [3]. So the discrepancies puted luminosity agrees with observations. is conventionally given in Solar Neutrino between theory and experiment — collec The computations also involve a second a Units (SNU), where one SNU corresponds to tively called the solar neutrino problem — priori unknown parameter describing con 10-36 captures per target atom per second. discussed in the insert are highly significant. vective heat transport near the solar sur face; its value Is fixed by requiring the model to give the correct radius for the Sun. The rate of neutrino detection depends strongly on the neutrino energy. In standard solar models, about 85% of the energy production comes from the PP-I chain (see Fig. 1), with the PP-III chain contributing Jørgen Christensen-Dalsgaard has been an Asso ciate Professor in the Institute of Physics and Astro nomy, Aarhus University, DK-8000 Aarhus C, since 1984 and was appointed this year to be the Associate Director of the Theoretical Astrophysics Center, Aarhus. After graduating from Aarhus University in 1975, he received his PhD from Cambridge University in 1978 and then held postdoctoral positions at the Fig. 2 — Measured and computed neutrino event rates for the Kamiokande (left) and Ga (right) University of Liege, the National Center for Atmo experiments. The measured rates are indicated by error boxes and the large filled circles and spheric Research, Boulder, CO (USA), and NOR- DITA, Copenhagen. Professor Christensen-Dals squares show the calculated results of Table 1, where the filled squares include the effect of gaard participates in the Global Oscillations Network WIMPs simulated through a reduction in the core opacity. The crosses are based on other Group and is a Co-investigator on the SOI and GOLF standard models, differing in equation of state, opacity tables, nuclear parameters, or age. The instruments to be launched aboard SOHO. filled triangles pointing down and up are for partially and fully mixed models, respectively. Europhys. News 25(1994) 71 One cannot exclude a “boring" solution to increased, the temperature gradient, and Mixing might bring additional hydrogen to the neutrino problem involving modification hence the neutrino flux, is reduced. This can the solar core, allowing the solar luminosity of, for example, opacities and the branching be accomplished through an overall reduc to be generated at lower temperature and ratios in the PP chains. In particular, since tion of the opacity, e.g., by reducing the hence reducing the predicted neutrino cap the gallium experiments seem consistent abundance of elements heavier than H2 and ture rates. Fig. 1 also shows results for mo with the neutrinos from the reaction which He. Alternatively, the efficiency of energy dels with partial and complete mixing of the dominates the energy generation, one may transport can be increased by invoking other solar interior; only the latter gives a pre in principle be able to reduce the capture modes of transport. dicted rate for the 37Cl experiment in accor rate while maintaining the solar surface One suggestion is that the solar core con dance with observations. luminosity. Further measurements of the tains hypothetical weakly interacting mas relevant nuclear reactions, particularly the sive particles (WIMPs) which transport a Conclusions somewhat uncertain 7Be(1H,γ)8B reaction, significant fraction of the luminous output in In conclusion, some experimental results are required. The possibility of remaining the solar core. I have simulated their pre are disturbing, notably a measured flux experimental problems must also be taken sence through a localized reduction in the which is smaller than the predicted value, in into account [4]. opacity in the solar core to give the neutrino some cases by factors of 2-3. Whereas rates shown in the table and Fig. 2. It is evi initial experiments were only sensitive to Non-standard models dent that the 37CI and the 71 Ga capture high-energy neutrinos coming from rare Most attempts to make the predicted neu rates are consistent with the measurements. reactions that contribute little to the energy trino capture rate agree with observations Note, however, that for the 37CI experiment generation and have rates which depend Involve changes in the temperature distribu the contribution from 8B is reduced much very strongly on the temperature of the solar tion In the solar core to reduce the central more strongly than the contribution from core, it has been difficult to achieve better temperature, and hence the flux of high- 7Be. As a result, the predicted rate for the agreement via minor adjustments to the energy neutrinos, while retaining the total Kamiokande experiment which only sees model’s parameters given that the observed energy production. The temperature gra neutrinos from 8B is now too low. This is solar luminosity should be reproduced. Al dient in the solar interior must be sufficient a general problem in attempts to match though the discrepancy is less marked, the to ensure transport of the energy from the simultaneously the 37CI and Kamiokande observed detection rate is once again less core to the surface.

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