We present a study of hierarchical structure in the Perseus molecular cloud, from the scale of the entire cloud ($gtrsim$10 pc) to smaller clumps ($sim$1 pc), cores ($sim$0.05-0.1 pc), envelopes ($sim$300-3000 AU) and protostellar objects ($sim$15 AU). We use new observations from the Submillimeter Array (SMA) large project Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES) to probe the envelopes, and recent single-dish and interferometric observations from the literature for the remaining scales. This is the first study to analyze hierarchical structure over five scales in the same cloud complex. We compare the number of fragments with the number of Jeans masses in each scale to calculate the Jeans efficiency, or the ratio of observed to expected number of fragments. The velocity dispersion is assumed to arise either from purely thermal motions, or from combined thermal and non-thermal motions inferred from observed spectral line widths. For each scale, thermal Jeans fragmentation predicts more fragments than observed, corresponding to inefficient thermal Jeans fragmentation. For the smallest scale, thermal plus non-thermal Jeans fragmentation also predicts too many protostellar objects. However at each of the larger scales thermal plus non-thermal Jeans fragmentation predicts fewer than one fragment, corresponding to no fragmentation into envelopes, cores, and clumps. Over all scales, the results are inconsistent with complete Jeans fragmentation based on either thermal or thermal plus non-thermal motions. They are more nearly consistent with inefficient thermal Jeans fragmentation, where the thermal Jeans efficiency increases from the largest to the smallest scale.
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