## 2. Basic equations and the SSM-like approachThe basic equations of the neutrino fluxes in the standard solar models are the followings (see e.g. Heeger & Robertson, 1996): with a notation similar to that of Heeger & Robertson (1996):
the subscripts i = 1, 7 and 8 refer to
, and
and Now let us see how these equations may serve to solve the solar neutrino problems. There are three solar neutrino problems distinguished by Bahcall (1994, 1996, 1997): the first is related to the lower than expected neutrino fluxes, the second to the problem of missing beryllium neutrinos as relative to the boron neutrinos, and the third to the gallium detector data which do not allow a positive flux for the beryllium neutrinos in the frame of the standard solar model. It is possible to find a solution to all of the three neutrino problems if we are able to find positive values for all of the neutrino fluxes in the above presented equations. I point out, that the condition of this requirement can be formulated with the following inequality: Numerically, If we require a physical , with the numerical values of the detector sensitivity coefficients, this constraint will take the following form: In the obtained solutions the total neutrino flux is compatible
with the observed solar luminosity ,
but the reactions involved in the SSM (the To determine the terms I introduced the "a priori" knowledge on the pp,CNO chains, namely, their temperature dependence. This is a necessary step to subtract more detailed information from the neutrino detector data. In this way one can derive the temperature in the solar core as seen by the different type of neutrino detectors. I note that finding the temperature of the solar core as deduced from the observed neutrino fluxes does not involve the introduction of any solar model dependency, since the neutrino fluxes of the SSM pp,CNO reactions depend on temperature only through nuclear physics. Instead, it points out the still remaining solar model dependencies of the previous SSM calculations and allowing other types of chains, it removes a hypothetical limitation, and accepting the presence of explosive chains as well, it probably presents a better approach to the actual Sun. The calculations of the previous section suggested to complete the SuperKamiokande neutrino-equation with a new term where Similarly, the temperature-dependent gallium-equation will take the form: Now let us first determine the solutions of these equations in the
case . The obtained solutions
will be relevant to the SSM-like
solar core. Now we know that the Sun can have only one central
temperature From the observed values, it is easy to obtain , and . With these values, the chlorine neutrino-temperature from (11) , the gallium neutrino-temperature is from (12) and the SuperKamiokande neutrino-temperature is from (10) . The neutrino flux equations are highly sensitive to the value of the temperature. Assuming that the actual Sun follows a standard solar model but with a different central temperature, the above result shows that the different neutrino detectors see different temperatures. This result suggest that the different neutrino detectors show sensitivities different from the one expected from the standard solar model, i.e. some reactions produce neutrinos which is not taken into account into the standard solar model, and/or that they are sensitive to different types of non-pp,CNO runaway reactions. Let us explore the consequences of this conjecture. © European Southern Observatory (ESO) 1999 Online publication: August 13, 199 |