We present an infrared study of a z=0.872 cluster, SpARCS J161314+564930, with the primary aim of distinguishing the dynamical histories of spectroscopically confirmed star-forming members to assess the role of cluster environment. We utilize deep MIPS imaging and a mass-limited sample of 85 spectroscopic members to identify 16 24um-bright sources within the cluster, and measure their 24um star formation rates (SFRs) down to ~6 Msolar/year. Based on their line-of-sight velocities and stellar ages, MIPS cluster members appear to be an infalling population that was recently accreted from the field with minimal environmental dependency on their star formation. However, we identify a double-sequenced distribution of star-forming galaxies amongst the members, with one branch exhibiting declining specific SFRs with mass. The members along this sub-main sequence contain spectral features suggestive of passive galaxies. Using caustic diagrams, we kinematically identify these galaxies as a virialized and/or backsplash population. Moreover, we find a mix of dynamical histories at all projected radii, indicating that standard definitions of environment (i.e., radius and density) are contaminated with recently accreted interlopers, which could contribute to a lack of environmental trends for star-forming galaxies. A cleaner narrative of their dynamical past begins to unfold when using a proxy for accretion histories through profiles of constant (r/r_200)x(Delta v/sigma_v); galaxies accreted at earlier times possess lower values of (r/r_200)x(Delta v/sigma_v) with minimal contamination from the distinct infalling population. Therefore, adopting a time-averaged definition for density (as traced by accretion histories) rather than an instantaneous density yields a depressed specific SFR within the dynamical cluster core.
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