Measuring Turbulence in a Protoplanetary Disk with COKevin Flaherty (Wesleyan University), A. Meredith Hughes (Wesleyan University), Katherine Rosenfeld (CfA), Sean Andrews (CfA),

Eugene Chiang (UC Berkeley), Skylar Kerzner (UC Berkeley), David Wilner (CfA)

Turbulence and Planet FormationTurbulence is expected to be prevalent within protoplanetary disks, serving as a main driver for angular momentum transport and accretion through the disk (e.g. Turner et al. 2014). These random motions can also have an impact on planet formation.- Large turbulent motions could increase the erosive collisions of

planetesimals (Ida et al. 2008) and increase the relative velocities of sub-micron sized particles enough that they fragment rather than stick (Poppe et al. 2000, Gundlach et al. 2011)

- Low levels of turbulence allow small dust grains to settle to the midplane where they can aggregate into larger particles (Ciesla et al. 2007)

- Turbulence could counteract the inward motion of small planets associated with Type I migration (Laughlin et al. 2004)

Using molecular lines to constrain turbulenceMolecular emission lines trace the dynamics of the cold outer disk and can be used to search for turbulent motion.

- Using high resolution SMA CO 3-2 data, Hughes et al. 2011 tentatively measure 300m/s turbulence (~40%cs) in HD 163296, and an upper limit (<40m/sec) in TW Hya

- Using CS instead of CO Guilloteau et al. 2012 measure 0.11 km/s (~50%cs) in DM Tau

These studies provide tantalizing evidence for turbulence within the disk, and newer data, especially from ALMA, may allow for tighter constraints on the strength of the turbulence.Here we take advantage of science verification ALMA data of CO 3-2, CO 2-1, 13CO 2-1 and C18O 2-1 within HD 163296. For the first time we combine all four CO lines into a statistical robust measure of turbulence in HD 163296.

HD 163296

Results:

References: Ciesla et al. 2007 ApJ 654 159, Foreman-Mackey et al. 2013 PASP 125 306, Guilloteau et al. 2012 A&A 548 70, Gundlach et al. 2011 Icarus 214 717, Hughes et al. 2011 ApJ 727 85, Laughlin et al. 2004 ApJ 608 489 , Poppe et al. 2000 ApJ 533 454, Rosenfeld et al. 2013 ApJ 774 16, Simon et al. 2015 ApJ accepted, Turner et al. 2014 PPVI

Using the disk models of Rosenfeld et al. (2013), along with an affine-invariant MCMC code (Foreman-Mackey et al. 2013) we seek to find the best fit model parameters (three describing the density structure, three describing the temperature structure plus turbulence and inclination) along with their uncertainties, and any degeneracies, while accounting for both statistical and systematic uncertainties using all four CO emission lines.

Near side of the disk

Far side of the disk

CO 3-2

(Top): CO 3-2 channel maps comparing the best fit model (black contours) with the data (colored contours). Contours are in units of 0.14Jy/beam(Bottom): Channel maps derived from visibility residuals (red/black contours).

CO 3-2 constrains turbulence to <3% of the sound speed

CO 3-2 τ=1 surface

Optically thick lines (CO 3-2, CO 2-1) trace the upper reaches of the molecular layer, while more optically thin tracers (13CO, C18O) penetrate deeper into the disk. Fitting all four lines simultaneously allows us to constrain the structure and turbulence throughout the disk.

Recent ALMA CO measurements (~0.7” resolution, 100-300m/s channel widths) of HD 163296 (~2.3 Msun, 122 pc away, ~3 Myr old) are able to spatially resolve the front and back side of the disk. The lack of CO emission between these layers is direct evidence of a cold midplane (Rosenfeld et al. 2013) and can be used to constrain thermal structure, a key degeneracy with turbulence.

Taking advantage of the more robust constraint on disk structure from the simultaneous fitting of all four emission lines (left panels) we find a low level of turbulence (vturb<0.16cs), consistent with the CO 3-2 fit.

Our limit on turbulence from CO 3-2 implies α<1e-3, suggesting that MRI is less efficient in the outer disk than previously thought. We measure weak turbulence despite the strong accretion rate onto the star (5e-7 M☉/yr), suggesting that either the turbulence increases strongly toward the inner disk, or that angular momentum is removed by a process that does not drive strong turbulence.

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While simulations (e.g. Simon et al. 2015) predict vturb~0.3-0.5cs in the upper layers of the disk, we find that the CO 3-2 data (black solid line) are best fit by models with vturb<0.03cs (red-dotted line). Fitting the data with turbulence fixed at the spectral resolution (vturb=0.1km/s~0.15cs), while allowing the other model parameters to vary, produces a significantly worse fit (blue-dashed line), confirming the low level of turbulence and our ability to push below the spectral resolution. The change in peak-to-trough ratio between the high/low turbulence models is similar to that predicted by Simon et al. 2015 based on simulated observations of numerical MRI models.

CO 3-2 CO 2-1

13CO 2-1 C18O 2-1

modeldata