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

TL;DR

This study investigates the size-frequency relationship of dust emission in the UZ Tau E disk, revealing a radial spectral steepening and exploring dust growth and migration models, highlighting discrepancies and potential particle trapping effects.

Contribution

It provides high-resolution multi-frequency observations of UZ Tau E's disk and analyzes the size-frequency relation, testing dust evolution models against observed data.

Findings

Size of emission region increases with frequency as R_eff ∝ ν^{0.34}

Dust evolution models predict steeper spectra than observed

Particle traps with high optical depth can explain the spectral gradient

Abstract

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 ($R_{eff} \propto \nu^{0.34 \pm 0.08}$). 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 is observed. Moreover, it comes closest to matching the data only on timescales much shorter ($\le 1$ Myr) than the putative UZ Tau age (~2-3 Myr). These discrepancies are the 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 ~30-60% filling fraction in the inner disk ($r \lesssim20$ au), they can also explain the observed spatial gradient in the UZ Tau E disk spectrum.