The Millimeter Continuum Size-Frequency Relationship in the UZ Tau E Disk

We present high spatial resolution observations of the continuum emission from the young multiple star system UZ Tau at frequencies from 6 to 340 GHz. To quantify the spatial variation of dust emission in the UZ Tau E circumbinary disk, the observed interferometric visibilities are modeled with a simple parametric prescription for the radial surface brightnesses at each frequency. We find evidence that the spectrum steepens with radius in the disk, manifested as a positive correlation between the observing frequency and the radius that encircles a fixed fraction of the emission (R-eff proportional to nu(0.34 +/- 0.08)). The origins of this size-frequency relation are explored in the context of a theoretical framework for the growth and migration of disk solids. While that framework can reproduce a similar size-frequency relation, it predicts a steeper spectrum than that observed. Moreover, it comes closest to matching the data only on timescales much shorter (<= 1 Myr) than the putative UZ Tau age (similar to 2-3 Myr). These discrepancies are direct consequences of the rapid radial drift rates predicted by models of dust evolution in a smooth gas disk. One way to mitigate that efficiency problem is to invoke small-scale gas pressure modulations that locally concentrate drifting solids. If such particle traps reach high-continuum optical depths at 30-340 GHz with a similar to 30%-60%. filling fraction in the inner disk (r less than or similar to 20 au), they can also explain the observed spatial gradient in the UZ Tau E disk spectrum.S.A. acknowledges support for this work from NASA Origins of Solar Systems grant NNX12AJ04G. T.B. acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement No. 714769. J.M.C. acknowledges support from the National Aeronautics and Space Administration under grant No. 15XRP15_20140 issued through the Exoplanets Research Program. Part of this research (by J.L.) was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. This work (by L.T.) was partly supported by the Italian Ministero dell'Istruzione, Universita e Ricerca through the grant Progetti Premiali 2012-iALMA (CUP C52I13000140001), and by the Deutsche Forschungs-gemeinschaft (DFG, German Research Foundation)-Ref no. FOR 2634/1 TE 1024/1-1. CARMA development and operations were supported by the National Science Foundation under a cooperative agreement and by the CARMA partner universities. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. The VLA is run by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc