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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$1pc), cores ($\sim$0.05-0.1 pc), envelopes ($\sim$300-3000 AU) and protostellarobjects ($\sim$15 AU). We use new observations from the Submillimeter Array(SMA) large project "Mass Assembly of Stellar Systems and their Evolution withthe SMA (MASSES)" to probe the envelopes, and recent single-dish andinterferometric observations from the literature for the remaining scales. Thisis the first study to analyze hierarchical structure over five scales in thesame cloud complex. We compare the number of fragments with the number of Jeansmasses in each scale to calculate the Jeans efficiency, or the ratio ofobserved to expected number of fragments. The velocity dispersion is assumed toarise either from purely thermal motions, or from combined thermal andnon-thermal motions inferred from observed spectral line widths. For eachscale, thermal Jeans fragmentation predicts more fragments than observed,corresponding to inefficient thermal Jeans fragmentation. For the smallestscale, thermal plus non-thermal Jeans fragmentation also predicts too manyprotostellar objects. However at each of the larger scales thermal plusnon-thermal Jeans fragmentation predicts fewer than one fragment, correspondingto no fragmentation into envelopes, cores, and clumps. Over all scales, theresults are inconsistent with complete Jeans fragmentation based on eitherthermal or thermal plus non-thermal motions. They are more nearly consistentwith inefficient thermal Jeans fragmentation, where the thermal Jeansefficiency increases from the largest to the smallest scale.

Hierarchical fragmentation in the Perseus molecular cloud: From the cloud scale to protostellar objects