Reversal of Fortune: Confirmation of an Increasing Star Formation-Density Relation in a Cluster at z=1.62

We measure the rest-frame colors (dust-corrected), infrared luminosities, star formation rates, and stellar masses of 92 galaxies in a Spitzer-selected cluster at z=1.62. By fitting spectral energy distributions (SEDs) to 10-band photometry (0.4 micron < lambda(obs) <8 micron) and measuring 24 micron fluxes for the 12 spectroscopically confirmed and 80 photometrically selected members, we discover an exceptionally high level of star formation in the cluster core of ~1700 Msun/yr per Mpc^2. The cluster galaxies define a strong blue sequence in (U-V) color and span a range in color. We identify 17 members with L(IR)>10^(11) Lsun, and these IR luminous members follow the same trend of increasing star formation with stellar mass that is observed in the field at z~2. Using rates derived from both the 24 micron imaging and SED fitting, we find that the relative fraction of star-forming members triples from the lowest to highest galaxy density regions, e.g. the IR luminous fraction increases from ~8% at Sigma~10 gal per Mpc^2 to ~25% at Sigma>100 gal per Mpc^2. The observed increase is a reversal of the well-documented trend at z<1 and signals that we have reached the epoch when massive cluster galaxies are still forming a substantial fraction of their stars.