  We employ ring-diagram analysis to study the sub-surface thermal structure of
active regions. We present results using a large number of active regions over
the course of Solar Cycle 23. We present both traditional inversions of
ring-diagram frequency differences, with a total sample size of 264, and a
statistical study using Principal Component Analysis. We confirm earlier
results on smaller samples that sound speed and adiabatic index are changed
below regions of strong magnetic field. We find that sound speed is decreased
in the region between approximately r=0.99R_sun and r=0.995R_sun (depths of 3Mm
to 7Mm), and increased in the region between r=0.97R_sun and r=0.985R_sun
(depths of 11Mm to 21Mm). The adiabatic index is enhanced in the same deeper
layers that sound-speed enhancement is seen. A weak decrease in adiabatic index
is seen in the shallower layers in many active regions. We find that the
magnitudes of these perturbations depend on the strength of the surface
magnetic field, but we find a great deal of scatter in this relation, implying
other factors may be relevant.
