Dust Grains Cannot Grow to Millimeter Sizes in Protostellar Envelopes

A big question in the field of star and planet formation is the time at which substantial dust grain growth occurs. The observed properties of dust emission across different wavelength ranges have been used as an indication that millimeter-sized grains are already present in the envelopes of young protostars. However, this interpretation is in tension with results from coagulation simulations, which are not able to produce such large grains in these conditions. In this work, we show analytically that the production of millimeter-sized grains in protostellar envelopes is impossible under the standard assumptions about the coagulation process. We discuss several possibilities that may serve to explain the observed dust emission in the absence of in situ grain growth to millimeter sizes.