To investigate what drives the reversal of the morphology-density relation at intermediate/high redshift, we present a multi-wavelength analysis of 27 dusty starburst galaxies in the massive cluster Cl 0024+17 at z = 0.4. We combine H-alpha dynamical maps from the VLT/FLAMES multi-IFU system with far-infrared imaging using Herschel SPIRE and millimetre spectroscopy from IRAM/NOEMA, in order to measure the dynamics, star formation rates and gas masses of this sample. Most galaxies appear to be rotationally supported, with a median ratio of rotational support to line-of-sight velocity dispersion v/sigma ~ 5 +/- 2, and specific angular momentum lambda_R = 0.83 +/- 0.06 - comparable to field spirals of a similar mass at this redshift. The star formation rates of 3 - 26 M_solar/yr and average 12 CO derived gas mass of 1 x 10^10 M_solar suggest gas depletion timescales of ~ 1Gyr (~ 0.25 of the cluster crossing time). We derive characteristic dust temperatures (mean T_dust = 26 +/- 1 K) consistent with local galaxies of similar far-infrared luminosity, suggesting that the low density gas is yet to be stripped. Taken together, these results suggest that these starbursts have only recently accreted from the field, with star formation rates likely enhanced due to the effects of ram pressure. In order to make the transition to cluster S0s these galaxies must lose ~ 40% of their specific angular momentum. We suggest this must occur > 1 Gyr later, after the molecular gas has been depleted and/or stripped, via multiple tidal interactions with other cluster members.
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