  The Bullet Cluster is a massive galaxy cluster at z=0.297 undergoing a major
supersonic (Mach 3) merger event. Using Spitzer 24um images, IRAC data, optical
imaging, and optical spectroscopy, we present the global star formation rate
(SFR) of this unique cluster. Using a 90% spectroscopically complete sample of
37 non-AGN MIPS confirmed cluster members out to R<1.7 Mpc, and the Rieke et
al. (2009) relation to convert from 24um flux to SFR, we calculate an
integrated obscured SFR of 267 Msolar/yr and a specific star formation rate of
28 Msolar/yr per 10^14 Msolar. The cluster mass normalized integrated SFR of
the Bullet Cluster is among the highest in a sample of eight other clusters and
cluster mergers from the literature. Five LIRGs and one ULIRG contribute 30%
and 40% of the total SFR of the cluster, respectively. To investigate the
origin of the elevated specific SFR, we compare the infrared luminosity
function (IR LF) of the Bullet Cluster to those of Coma (evolved to z=0.297)
and CL1358+62. The Bullet Cluster IR LF exhibits an excess of sources compared
to the IR LFs of the other massive clusters. A Schechter function fit of the
Bullet Cluster IR LF yields L*=44.68+/-0.11 ergs/s, which is ~0.25 and 0.35 dex
brighter than L* of evolved Coma and CL1358+62, respectively. The elevated IR
LF of the Bullet Cluster relative to other clusters can be explained if we
attribute the "excess" star-forming IR galaxies to a population associated with
the infalling group that have not yet been transformed into quiescent galaxies.
In this case, the timescale required for quenching star formation in the
cluster environment must be longer than the timescale since the group's
accretion -- a few hundred million years. We suggest that "strangulation" is
likely to be an important process in the evolution of star formation in
clusters.
