We report the detection of the Paschen-alpha emission line in the z=2.515 galaxy SMM J163554.2+661225 using Spitzer spectroscopy. SMM J163554.2+661225 is a sub-millimeter-selected infrared (IR)-luminous galaxy maintaining a high star-formation rate (SFR), with no evidence of an AGN from optical or infrared spectroscopy, nor X-ray emission. This galaxy is lensed gravitationally by the cluster Abell 2218, making it accessible to Spitzer spectroscopy. Correcting for nebular extinction derived from the H-alpha and Pa-alpha lines, the dust-corrected luminosity is L(Pa-alpha) = (2.57+/-0.43) x 10^43 erg s^-1, which corresponds to an ionization rate, Q = (1.6+/-0.3) x 10^55 photons s^-1. The instantaneous SFR is 171+/-28 solar masses per year, assuming a Salpeter-like initial mass function. The total IR luminosity derived using 70, 450, and 850 micron data is L(IR) = (5-10) x 10^11 solar luminosities, corrected for gravitational lensing. This corresponds to a SFR=90-180 solar masses per year, where the upper range is consistent with that derived from the Paschen-alpha luminosity. While the L(8 micron) / L(Pa-alpha) ratio is consistent with the extrapolated relation observed in local galaxies and star-forming regions, the rest-frame 24 micron luminosity is significantly lower with respect to local galaxies of comparable Paschen-alpha luminosity. Thus, SMM J163554.2+661225 arguably lacks a warmer dust component (T ~ 70 K), which is associated with deeply embedded star formation, and which contrasts with local galaxies with comparable SFRs. Rather, the starburst is consistent with star-forming local galaxies with intrinsic luminosities, L(IR) ~ 10^10 solar luminosities, but scaled-up by a factor of 10-100.
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