We investigate the optical and Wide-field Survey Explorer (WISE) colors of E+A identified post-starburst galaxies, including a deep analysis on 190 post-starbursts detected in the 2{mu}m All Sky Survey Extended Source Catalog. The post-starburst galaxies appear in both the optical green valley and the WISE Infrared Transition Zone (IRTZ). Furthermore, we find that post-starbursts occupy a distinct region [3.4]-[4.6] vs. [4.6]-[12] WISE colors, enabling the identification of this class of transitioning galaxies through the use of broad-band photometric criteria alone. We have investigated possible causes for the WISE colors of post-starbursts by constructing a composite spectral energy distribution (SED), finding that mid-infrared (4-12{mu}m) properties of post-starbursts are consistent with either 11.3{mu}m polycyclic aromatic hydrocarbon emission, or Thermally Pulsating Asymptotic Giant Branch (TP-AGB) and post-AGB stars. The composite SED of extended post- starburst galaxies with 22{mu}m emission detected with signal to noise >3 requires a hot dust component to produce their observed rising mid-infrared SED between 12 and 22{mu}m. The composite SED of WISE 22{mu}m non-detections (S/N<3), created by stacking 22{mu}m images, is also flat, requiring a hot dust component. The most likely source of this mid-infrared emission of these E+A galaxies is a buried active galactic nucleus. The inferred upper limit to the Eddington ratios of post-starbursts are 1e-2 to 1e-4, with an average of 1e-3. This suggests that AGNs are not radiatively dominant in these systems. This could mean that including selections able to identify active galactic nuclei as part of a search for transitioning and post-starburst galaxies would create a more complete census of the transition pathways taken as a galaxy quenches its star formation.
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