We study protostellar envelope and outflow evolution using Hubble Space Telescope NICMOS or WFC3 images of 304 protostars in the Orion Molecular clouds. These near-IR images resolve structures in the envelopes delineated by the scattered light of the central protostars with 80 AU resolution and they complement the 1.2-870 micron spectral energy distributions obtained with the Herschel Orion Protostar Survey program (HOPS). Based on their 1.60 micron morphologies, we classify the protostars into five categories: non-detections, point sources without nebulosity, bipolar cavity sources, unipolar cavity sources, and irregulars. We find point sources without associated nebulosity are the most numerous, and show through monochromatic Monte Carlo radiative transfer modeling that this morphology occurs when protostars are observed at low inclinations or have low envelope densities. We also find that the morphology is correlated with the SED-determined evolutionary class with Class 0 protostars more likely to be non-detections, Class I protostars to show cavities and flat-spectrum protostars to be point sources. Using an edge detection algorithm to trace the projected edges of the cavities, we fit power-laws to the resulting cavity shapes, thereby measuring the cavity half-opening angles and power-law exponents. We find no evidence for the growth of outflow cavities as protostars evolve through the Class I protostar phase, in contradiction with previous studies of smaller samples. We conclude that the decline of mass infall with time cannot be explained by the progressive clearing of envelopes by growing outflow cavities. Furthermore, the low star formation efficiency inferred for molecular cores cannot be explained by envelope clearing alone.
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