We present the results of a Spitzer Infrared Spectrograph (IRS) survey of 24um-selected luminous infrared galaxies (LIRGs, L_IR > 10^11 L_sun) in the rich cluster Cl0024+16 at z=0.4. Optically, these LIRGs resemble unremarkable spiral galaxies with e(a)/e(c) spectral classifications and [Oii]-derived star formation rates (SFRs) of <2 M_sun/yr, generally indistinguishable from the quiescent star forming population in the cluster. Our IRS spectra show that the majority of the 24um-detected galaxies exhibit polycyclic aromatic hydrocarbon (PAH) emission with implied SFRs ~30-60 M_sun/yr, with only one (<10%) of the sample displaying unambiguous evidence of an active galactic nucleus in the mid-infrared. This confirms the presence of a large population of obscured starburst galaxies in distant clusters, which comprise the bulk of the star formation occurring in these environments at z~0.5. We suggest that, although several mechanisms could be at play, these dusty starbursts could be the signature of an important evolutionary transition converting gas-rich spiral galaxies in distant clusters into the passive, bulge-dominated lenticular galaxies that become increasingly abundant in the cores of rich clusters in the ~4Gyr to the present day.
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