Proc. Neutrino Astrophysics - MPP Theory Group

the outer convection zone. As for the depth of the convection zone, there are two other input
modifications that may lead to an increase: convective overshoot (see below) and element
diffusion.
d) Element Diffusion
Driven by the gradients of pressure, temperature, and composition, helium and the heavy
elements diffuse toward the solar center, while hydrogen diffuses upward. The process is
slow, with a characteristic time exceeding the Sun’s age by a factor 100 or more. Nevertheless
diffusion should be included into the standard solar model since it produces significant effects,
especially in view of the details that can be seen by helioseismology. The following table
summarizes some results [5]:
Diffusion Y0 YS rb/r⊙ Tc(10 6 ) K snu(Cl) snu(Ga)
— 0.268 0.268 0.726 15.56 7.0 126
He 0.270 0.239 0.710 15.70 8.1 130
He & heavy el. 0.278 0.247 0.712 15.84 9.3 137
The obvious effect of a decreased surface mass fraction YS of He is essentially in agreement with
the results of other authors, and with the helioseismological result (see above); the increase of
YS obtained if heavy element diffusion is included is due to the larger initial helium content,
Y0, which is required in this case for the luminosity adjustment. Also, the central temperature
rises: Helium diffusion changes the mean molecular weight, which must be compensated by a
higher temperature in order to maintain the hydrostatic equilibrium; heavy element diffusion
increases the opacity, which must be compensated by a steeper temperature gradient (and
hence larger Tc) to maintain the radiative transport of energy. Together with Tc, the neutrino
rates predicted for the chlorine and gallium experiments are increased, as listed in columns
6 and 7 of the table. It should be noted that the Tc effect found in other calculations is
somewhat smaller, cf. the contribution of Schlattl and Weiss to these proceedings. Also, the
effect of helium diffusion on the depth of the convection zone (column 4) is in contrast to the
result of Cox et al. [12].
The depth of the convection zone has been determined from helioseismology by several authors.
Below the convection zone the temperature gradient is determined by the requirement
of radiative energy transport; within the convection zone the gradient is nearly adiabatic because
of the large heat capacity and hence large effectivity of the convective transport. Thus,
a prominent transition occurs in dT/dr and, accordingly, in dc 2 /dr. As the sound speed c(r)
can be obtained from the p-mode frequencies, the transition can be located. Christensen-
Dalsgaard et al. [10] find rb/r⊙ = 0.713±0.003, a more recent study [7] yields an even smaller
uncertainty, 0.713 ± 0.001, with the claim that systematic errors are included! — The temperature
at the base of the convection zone slightly depends on the helium abundance; for
the value of YS quoted above a good estimate [10] is (2.22 ± 0.05) · 10 6 K.
Neutrinos
The standard model of the Sun predicts the flux of neutrinos, as a function of neutrino energy,
that should be observed on Earth. So far 5 detectors have been used for such observations:
One using chlorine, two using gallium and two using water. The detectors as well as the
observational results are reviewed elsewhere in these proceedings. Briefly the results are
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