  We combine SAURON integral field data of a representative sample of local
early-type, red sequence galaxies with Spitzer/IRAC imaging in order to
investigate the presence of trace star formation in these systems. With the
Spitzer data, we identify galaxies hosting low-level star formation, as traced
by PAH emission, with measured star formation rates that compare well to those
estimated from other tracers. This star formation proceeds according to
established scaling relations with molecular gas content, in surface density
regimes characteristic of disk galaxies and circumnuclear starbursts. We find
that star formation in early-type galaxies happens exclusively in fast-rotating
systems and occurs in two distinct modes. In the first, star formation is a
diffuse process, corresponding to widespread young stellar populations and high
molecular gas content. The equal presence of co- and counter-rotating
components in these systems strongly implies an external origin for the
star-forming gas, and we argue that these star formation events may be the
final stages of (mostly minor) mergers that build up the bulges of red sequence
lenticulars. In the second mode of star formation, the process is concentrated
into well-defined disk or ring morphologies, outside of which the host galaxies
exhibit uniformly evolved stellar populations. This implies that these star
formation events represent rejuvenations within previously quiescent stellar
systems. Evidence for earlier star formation events similar to these in all
fast rotating early-type galaxies suggests that this mode of star formation may
be common to all such galaxies, with a duty cycle of roughly 1/10, and likely
contributes to the embedded, co-rotating inner stellar disks ubiquitous in this
population.
