**AAS Meeting #193 - Austin, Texas, January 1999**

*Session 100. The Quiet and Active Sun*

Display, Saturday, January 9, 1999, 9:20am-4:00pm, Exhibit Hall 1
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## [100.05] MSW Time Variations of the Solar Neutrino flux

*L.M. Malyshkin, R.M. Kulsrud (Princeton University Observatory)*

We consider the possibility of MSW time variations of the
solar neutrino flux due to neutrino interference effects.
For two types of neutrinos there are two MSW neutrino
solutions, + and -. In vacuum these are the m_{1} and
m_{2} (m_{1}2) mass neutrino states. These two neutrino
states have propagation time delays relative to light, t_{+}
and t_{-}, due to nonzero rest masses. Let
\sigma_{t}\equiv\hbar/|t_{+}-t_{-}|. The energy difference of
the two states is \sigma_{a}={\cal E}\,a|t_{+}-t_{-}|/c, where
{\cal E} is the emitted neutrino energy, and a is the
acceleration of the emitting nucleus.

Two necessary criteria to observe neutrino flux time
variations are proposed. The first criterion,
\sigma{{\lower.5ex\;\buildrel{\mbox{\footnotesize<}}\over{\mbox{\footnotesize\sim}}\;}}\sigma_{t},
for the time variation not to be averaged to zero over the
detection energy width \sigma, should be satisfied. In the
case of the 0.862\,{\rm Mev} ^{7}Be solar neutrino line
this criterion gives us an upper estimate for m_{2}^{2}-m_{1}^{2},
the difference of neutrino mass squared, of ~
10^{-9}{\rm ev}^{2}. The second criterion,
\sigma_{a}{{\lower.5ex\;\buildrel{\mbox{\footnotesize<}}\over{\mbox{\footnotesize\sim}}\;}}\sigma_{t},
is necessary for collisional coherence to exist. This
criterion is equivalent to a plausible condition
a|t_{+}^{2}-t_{-}^{2}|{{\lower.5ex\;\buildrel{\mbox{\footnotesize<}}\over{\mbox{\footnotesize\sim}}\;}}
{{\!\,\lambda\!\!\!\!\!\stackrel{-}{\phantom{__}}\!\,}}.
Our criterion is stronger than collisional coherence
criteria formerly suggested, which are roughly equivalent to
the condition
a|t_{+}^{2}-t_{-}^{2}|{{\lower.5ex\;\buildrel{\mbox{\footnotesize<}}\over{\mbox{\footnotesize\sim}}\;}}
l, because the neutrino De Broglie wavelength
{{\!\,\lambda\!\!\!\!\!\stackrel{-}{\phantom{__}}\!\,}}
is much less than the interparticle distance in the solar
interior l.

Exact values for the detected neutrino flux and its
variations will be presented for both the case of a solar
neutrino line, and the case of a continuous neutrino
spectrum with a Gaussian shape of the energy response
function of the neutrino detection device.

The author(s) of this abstract have provided an email address
for comments about the abstract:
leonmal@astro.princeton.edu

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