  Recent analysis of the Homestake data indicates that the solar neutrino flux
contains a periodic variation that may be attributed to rotational modulation
occurring deep in the solar interior, either in the tachocline or in the
radiative zone. This paper presents an analysis of GALLEX data that yields
supporting evidence of this rotational modulation at the 0.1% significance
level. The depth of modulation inferred from the rotational signature is large
enough to explain the neutrino deficit. The Rieger 157-day periodicity, first
discovered in solar gamma-ray flares, is present also in Homestake data. A
related oscillation with period 52 days is found in the GALLEX data. The
relationship of these periods to the rotational period inferred from neutrino
data suggests that they are due to r-mode oscillations.
