  Unexplained annual variations in nuclear decay rates have been reported in
recent years by a number of groups. We show that data from these experiments
exhibit not only variations in time related to Earth-Sun distance, but also
periodicities attributable to solar rotation. Additionally, anomalous decay
rates coincident in time with a series of solar flares in December 2006 also
point to a solar influence on nuclear decay rates. This influence could arise
from some flavor of solar neutrinos, or through some other objects we call
"neutrellos" which behave in some ways like neutrinos. The indication that
neutrinos or neutrellos must interact weakly in the Sun implies that we may be
able to use data on time-varying nuclear decay rates to probe the interior of
the Sun, a technique which we may call "helioradiology".
