For more than thirty years standard' solar models and neutrino experiments on Earth have disagreed on the amount of neutrinos produced in the thermonuclear core of the Sun, with the former always predicting a flux in excess. A number of ingenious suggestions have been made to explain the discrepancy, either byexotic’ solar models or by invoking non-standard' neutrino properties (in the particle physics sense) which will explain why they are not detected. Among these, a non-zero mass of the neutrinos would allow oscillations between the electron neutrino e, generated by the thermonuclear reactions, and its siblings the muon and tau neutrinos or asterile neutrino’, undetectable by present instruments. Another interesting process could come from the neutrino having a magnetic moment that through interaction (precession) with the Sun’s magnetic field could change from having a left handed helicity to a right handed one, thus becoming ’sterile’ to detectors. Recently, evidence has been gathered in favour of these oscillation processes, based on the careful study of the high energy neutrinos (> 5 Mev) detected by the Sudbury National Observatory (SNO) (Ahmad et al. 2002, nucl-ex/0204008) and by the Super-Kamiokande experiments (Fukuda et al. 1998, Phys. Rev. Lett. 81, 1158).
There is thus hope that astrophysicists will soon be able to use the neutrinos fluxes measured on Earth to assess directly the conditions of the innermost region of the Sun where the neutrinos are emitted, and perhaps even detect its internal magnetic field. Meanwhile, astrophysicists are further motivated to improve the accuracy of their models of the solar interior, in order to sharpen their predictions of the neutrino fluxes and help particle physicists to disentangle between several neutrino oscillation solutions. For this they have access to a very powerful diagnostic tool, namely helioseismology. Helioseismology is the study of the acoustic waves observed on the surface of the Sun. The study of the wave propagation inside the Sun allows to explore its internal structure. At the surface of the Sun are observed motions of the order of one km per second with a period of approximately 5 minutes, which are interpreted as the superposition of many coherent acoustic modes, reflecting on the surface (fig. 1). The precise identification of the degree and order of each mode allows to deduce the penetration of the waves down to the internal regions. Thousands of modes have already been identified ! From this harvest of information, is deduced the radial extension of the external convective layer (approximately 190 000 km), the sound speed down to very deep areas (20 % of the Sun radius), and indications on the internal rotation of the Sun.
Figure 1. The permanent motions observed on the surface of the Sun is due to the combination of million different modes of oscillation. Each mode is characterized by the number of wave reflections at the surface of the sun. The figure on the left represents schematically one mode of oscillation, where regions of positive speed (towards the solar interior) are coloured in red by contrast with the blue regions, of negative speed. The cut of the Sun visualizes the central area, the sun core where the nuclear reactions and the production of electronic neutrinos proceed. The figure of right-hand side represents schematically how the modes of pressure (p) and the modes of gravity (g) propagate into the sun, as well as the various zones of the Sun : the core, radiative zone, convective zone. Figures drawn from the GONG web site Global Oscillation Network Group. The Sun is radially made up of several zones : outside a convective layer, where energy is transported by bubbles of matter hot when going up, and cold when falling down ; then a radiative layer, where energy is transported more efficiently by radiation. The transition between these two zones occurs at approximately 0.7 solar radius, and the transition is very abrupt. This transition is called the tachocline. Outside of this radius, the Sun rotates differentially, more quickly at the equator than at the poles. Below the tachocline, the Sun rotates practically like a solid body (fig 2).
Figure 2. Rotation frequency as a function of radius in the Sun. In the outerparts, the rotation frequency depends on the latitude, indicated here for each curve. The period of rotation is 24 days at the equator, and approximately 32 days towards the poles. Below the tachocline (0.7 solar radius), the Sun rotates almost like a solid body. Figure drawn from the GONG web site Global Oscillation Network Group. Helioseismology has reached an accuracy level where it now constrains the thermal and mechanical structure of the Sun very precisely. Through powerful inversion procedures similar to those employed by geophysicists in probing the Earth’s interior, it is possible to infer key variables such as sound speed, density, temperature and hydrogen content as a function of depth (the latter two requiring some extra assumptions on the microscopic properties of the solar plasma). In a paper which will appear soon in Astronomy & Astrophysics, a Franco-Indian team (A. S. Brun and J.-P. Zahn from Observatoire de Paris, H. M. Antia and K. Chitre from the Tata Institute of Fundamental Research, Mumbai) has computed solar models that are now in very good agreement with observations from the helioseismic space experiments (Golf, MDI, Virgo) on board the Solar and Heliospheric Observatory (SOHO), thus validating our current understanding of the solar internal structure.
Figure 3. Theoretical models compared with the seismic Sun. The relative differences in sound speed c and density rho between the Sun and the models are plotted versus the radial coordinate. The reference model Ref, built without internal mixing, displays the largest discrepancy (note the peak located in the tachocline, around r/Rsun = 0.65). The models improve substantially when tachocline mixing is taken in account, as illustrated by model Btz. Allowing for variations within their intrinsic errors of the main physical ingredients improve the models even further, as illustrated by models N0 and N in the central region of their sound speed profile and everywhere in their density profile.
Figure 3 displays the relative difference in sound speed c and density rho between the Sun and several models. One important achievement of helioseismology has been to demonstrate the existence of a thin transition region at the base of the solar convection zone (r 0.71 Rsun), where the rotation rate changes from latitude-dependent above, to almost uniform below, in the stable radiative interior. When mild mixing occurring in that so-called tachocline is accounted for, the overall agreement between the seismic Sun and the models is greatly improved. For instance, in Figure 3 the conspicuous peak seen in the sound speed profile in the tachocline of model Ref (without mixing) disappeared when mixing is included (cf. model Btz). As well, the predicted abundance of photospheric lithium 7 is in agreement with the observed one (that fragile element is transported in the tachocline to the level where it is destroyed through thermonuclear reactions). Further if one allows for variations within their intrinsic uncertainties of the main microscopic physical ingredients such as opacity, equation of state, nuclear reaction rates, microscopic diffusion, electron screening etc., the model agrees even better with the seismic Sun (compare for example models Btz and N). Using their most accurate solar model, Brun et al. have deduced the following updated solar neutrino fluxes for the 3 types of experiments (gallium, chlorine and water, in SNU, "Solar Neutrino Units") : 71Ga = 123.7 +/- 8.7 SNU, 37Cl = 6.41 +/- 0.86 SNU and Water = (4.48 +/- 0.71) * 106 cm-2 s-1. The latter flux can be compared directly with that derived from the SNO experiment, using the neutral current channel as well, which is equally sensitive to all neutrino flavours (Ahmad et al. 2002) ; the resulting Water (or 8B) flux, is found to be (5.09 +/- 0.62) * 106 cm-2 s-1, within the error bars of the solar neutrino prediction by Brun et al. Thanks to helioseismology, the solar models have thus improved nowadays to a point where they can be used to confirm and constrain the properties of the neutrinos.