0.05 | $10^{-4}$ | 3.3$\times 10^{-5}$ | 0.09 | 0.69 | 0.46 | 0.21 | 0.16 | 0.13 | 0.12 | 0.12 | 0.81 | 0.75 | 0.64 | 0.32 | 0.19
0.05 | $10^{-4}$ | 1$\times 10^{-4}$ | 0.24 | 0.80 | 0.61 | 0.48 | 0.25 | 0.24 | 0.22 | 0.21 | 1.00 | 0.87 | 0.76 | 0.57 | 0.26
0.05 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 0.32 | 0.82 | 0.57 | 0.98 | 0.30 | 0.29 | 0.29 | 0.27 | 1.00 | 0.92 | 0.77 | 0.55 | 0.48
0.05 | $10^{-4}$ | 1$\times 10^{-3}$ | 0.42 | 0.56 | 0.56 | 0.55 | 0.42 | 0.40 | 0.38 | 0.37 | 1.00 | 0.56 | 0.56 | 0.56 | 0.54
0.05 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 0.55 | 0.75 | 0.60 | 0.97 | 0.53 | 0.50 | 0.49 | 0.48 | 1.00 | 1.00 | 0.72 | 0.58 | 0.98
0.05 | $10^{-3}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.13 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00
0.05 | $10^{-3}$ | 1$\times 10^{-4}$ | 0.20 | 0.77 | 0.52 | 0.27 | 0.20 | 0.18 | 0.17 | 0.16 | 1.00 | 0.89 | 0.72 | 0.47 | 0.24
0.05 | $10^{-3}$ | 3.3$\times 10^{-4}$ | 0.27 | 0.77 | 0.54 | 0.38 | 0.30 | 0.27 | 0.26 | 0.24 | 1.00 | 0.96 | 0.72 | 0.51 | 0.34
0.05 | $10^{-3}$ | 1$\times 10^{-3}$ | 0.37 | 0.73 | 0.56 | 0.44 | 0.38 | 0.36 | 0.34 | 0.32 | 1.00 | 0.84 | 0.68 | 0.54 | 0.41
0.05 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 0.57 | 0.94 | 0.62 | 0.54 | 0.50 | 0.47 | 0.46 | 0.45 | 0.99 | 0.98 | 0.94 | 0.62 | 0.53
0.05 | $10^{-2}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.05 | $10^{-2}$ | 1$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.05 | $10^{-2}$ | 3.3$\times 10^{-4}$ | 0.21 | 0.39 | 0.26 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.52 | 0.37 | 0.25 | 0.19
0.05 | $10^{-2}$ | 1$\times 10^{-3}$ | 0.30 | 1.00 | 0.62 | 0.38 | 0.33 | 0.33 | 0.31 | 0.30 | 1.00 | 1.00 | 0.98 | 0.58 | 0.35
0.05 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 0.43 | 1.00 | 0.74 | 0.61 | 0.53 | 0.46 | 0.44 | 0.42 | 1.00 | 1.00 | 1.00 | 0.75 | 0.60
0.07 | $10^{-4}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10
0.07 | $10^{-4}$ | 1$\times 10^{-4}$ | 0.14 | 0.78 | 0.68 | 0.36 | 0.25 | 0.18 | 0.15 | 0.14 | 0.96 | 0.82 | 0.73 | 0.61 | 0.32
0.07 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 0.33 | 1.00 | 0.75 | 0.63 | 0.36 | 0.33 | 0.31 | 0.30 | 1.00 | 1.00 | 0.81 | 0.68 | 0.36
0.07 | $10^{-4}$ | 1$\times 10^{-3}$ | 0.42 | 0.79 | 0.76 | 0.48 | 0.44 | 0.41 | 0.39 | 0.37 | 1.00 | 0.82 | 0.77 | 0.64 | 0.44
0.07 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 0.56 | 1.00 | 1.00 | 0.84 | 0.58 | 0.52 | 0.50 | 0.48 | 1.00 | 1.00 | 1.00 | 0.63 | 0.82
0.07 | $10^{-3}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.07 | $10^{-3}$ | 1$\times 10^{-4}$ | 0.00 | 0.00 | 0.18 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.14
0.07 | $10^{-3}$ | 3.3$\times 10^{-4}$ | 0.28 | 0.97 | 0.70 | 0.43 | 0.32 | 0.29 | 0.27 | 0.26 | 1.00 | 1.00 | 0.78 | 0.63 | 0.38
0.07 | $10^{-3}$ | 1$\times 10^{-3}$ | 0.36 | 0.82 | 0.71 | 0.53 | 0.43 | 0.37 | 0.35 | 0.33 | 1.00 | 1.00 | 0.78 | 0.66 | 0.49
0.07 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 0.52 | 0.97 | 0.90 | 0.68 | 0.57 | 0.52 | 0.48 | 0.47 | 1.00 | 1.00 | 0.97 | 0.88 | 0.65
0.07 | $10^{-2}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.07 | $10^{-2}$ | 1$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.07 | $10^{-2}$ | 3.3$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.07 | $10^{-2}$ | 1$\times 10^{-3}$ | 0.28 | 0.52 | 0.37 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.65 | 0.48 | 0.35 | 0.13
0.07 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 0.40 | 1.00 | 0.97 | 0.58 | 0.46 | 0.43 | 0.41 | 0.41 | 1.00 | 1.00 | 1.00 | 0.99 | 0.53
0.10 | $10^{-4}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.10 | $10^{-4}$ | 1$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.12 | 0.11 | 0.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10
0.10 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 0.21 | 0.83 | 0.79 | 0.55 | 0.43 | 0.32 | 0.22 | 0.19 | 1.00 | 0.89 | 0.80 | 0.71 | 0.48
0.10 | $10^{-4}$ | 1$\times 10^{-3}$ | 0.41 | 1.00 | 0.81 | 0.75 | 0.50 | 0.44 | 0.42 | 0.40 | 1.00 | 1.00 | 0.84 | 0.78 | 0.51
0.10 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 0.53 | 0.86 | 0.84 | 0.72 | 0.70 | 0.54 | 0.48 | 0.29 | 0.75 | 0.88 | 0.86 | 0.72 | 0.71
0.10 | $10^{-3}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.10 | $10^{-3}$ | 1$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.10 | $10^{-3}$ | 3.3$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.18 | 0.15 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15
0.10 | $10^{-3}$ | 1$\times 10^{-3}$ | 0.38 | 1.00 | 0.82 | 0.65 | 0.46 | 0.40 | 0.39 | 0.36 | 1.00 | 1.00 | 1.00 | 0.76 | 0.56
0.10 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 0.49 | 1.00 | 0.98 | 0.74 | 0.59 | 0.52 | 0.49 | 0.47 | 1.00 | 1.00 | 1.00 | 0.81 | 0.68
0.10 | $10^{-2}$ | 3.3$\times 10^{-5}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.10 | $10^{-2}$ | 1$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00
0.10 | $10^{-2}$ | 3.3$\times 10^{-4}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
0.10 | $10^{-2}$ | 1$\times 10^{-3}$ | 0.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 | 0.00 | 0.00 | 0.00
0.10 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 0.38 | 0.72 | 0.49 | 0.40 | 0.15 | 0.16 | 0.00 | 0.00 | 1.00 | 0.88 | 0.69 | 0.47 | 0.38
Kernel | $\sigma$ | $=0.025r_{p}$ |  |  |  |  |  |  |  |  |  |  |  |  |
0.05 | $10^{-4}$ | 3.3$\times 10^{-5}$ | 0.09 | – | – | – | – | 0.13 | 0.12 | 0.12 | – | – | – | – | –
0.05 | $10^{-3}$ | 3.3$\times 10^{-5}$ | 0.00 | – | 0.13 | 0.11 | 0.11 | 0.09 | 0.08 | – | – | – | – | 0.13 | 0.11
0.05 | $10^{-2}$ | 3.3$\times 10^{-4}$ | 0.21 | – | – | – | 0.20 | – | 0.11 | 0.13 | – | – | – | – | –
0.07 | $10^{-4}$ | 3.3$\times 10^{-5}$ | 0.00 | – | – | 0.10 | 0.09 | 0.08 | 0.09 | 0.09 | – | – | – | 0.08 | 0.09
0.07 | $10^{-3}$ | 1$\times 10^{-4}$ | 0.00 | – | – | 0.15 | 0.14 | 0.12 | 0.13 | – | – | – | – | 0.17 | 0.14
0.07 | $10^{-2}$ | 1$\times 10^{-3}$ | 0.28 | – | – | – | 0.09 | 0.10 | 0.09 | 0.08 | – | – | – | – | 0.12
0.10 | $10^{-4}$ | 3.3$\times 10^{-5}$ | 0.00 | – | – | 0.07 | 0.08 | 0.08 | 0.08 | 0.08 | – | – | – | – | 0.07
0.10 | $10^{-4}$ | 1$\times 10^{-4}$ | 0.00 | – | – | 0.10 | 0.12 | 0.12 | 0.11 | 0.12 | – | – | – | 0.09 | 0.10
0.10 | $10^{-3}$ | 3.3$\times 10^{-4}$ | 0.00 | – | – | – | – | – | 0.15 | 0.11 | – | – | – | 0.16 | –
0.10 | $10^{-2}$ | 1$\times 10^{-3}$ | 0.11 | – | – | – | 0.12 | 0.08 | 0.11 | – | – | – | – | – | –
0.10 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 0.38 | – | – | – | – | – | 0.40 | 0.13 | – | – | – | – | –
Common | Gaps | Separated | by | Horseshoe | $\frac{\Delta_{1}}{\Delta_{2}}$ |  |  |  |  |  |  |  |  |  |
0.05 | $10^{-4}$ | 1$\times 10^{-4}$ | 0.24 | – | – | $\frac{0.28}{0.10}$ | – | – | – | – | – | – | – | – | –
0.05 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 0.32 | – | – | $\frac{0.32}{0.13}$ | – | – | – | – | – | – | – | – | $\frac{0.29}{0.07}$
0.05 | $10^{-4}$ | 1$\times 10^{-3}$ | 0.42 | $\frac{0.10}{0.19}$ | $\frac{0.11}{0.20}$ | $\frac{0.10}{0.19}$ | $\frac{0.25}{0.15}$ | $\frac{0.26}{0.15}$ | – | – | – | $\frac{0.09}{0.17}$ | $\frac{0.10}{0.19}$ | $\frac{0.11}{0.20}$ | $\frac{0.10}{0.18}$
0.05 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 0.55 | – | – | $\frac{0.56}{0.81}$ | – | – | – | – | – | – | – | – | $\frac{0.54}{0.86}$
0.05 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 0.57 | $\frac{0.07}{0.93}$ | – | – | – | – | – | – | $\frac{0.09}{0.99}$ | $\frac{0.09}{0.97}$ | $\frac{0.07}{0.93}$ | – | –
0.07 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 0.33 | – | – | $\frac{0.41}{0.19}$ | – | – | – | – | – | – | – | – | –
0.07 | $10^{-4}$ | 1$\times 10^{-3}$ | 0.42 | – | – | – | $\frac{0.27}{0.19}$ | – | – | – | – | – | – | $\frac{0.51}{0.19}$ | $\frac{0.25}{0.17}$
0.07 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 0.56 | – | – | $\frac{0.61}{0.39}$ | – | – | – | – | – | – | – | – | $\frac{0.59}{0.27}$
0.07 | $10^{-3}$ | 3.3$\times 10^{-4}$ | 0.28 | $\frac{0.88}{0.74}$ | – | – | – | – | – | – | – | – | – | – | –
0.07 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 0.40 | – | $\frac{0.82}{0.62}$ | – | – | – | – | – | – | – | – | $\frac{0.81}{0.88}$ | –
0.10 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 0.21 | – | – | – | – | – | – | – | – | – | – | $\frac{0.62}{0.18}$ | –
0.10 | $10^{-4}$ | 1$\times 10^{-3}$ | 0.41 | – | – | $\frac{0.57}{0.18}$ | – | – | – | – | – | – | – | $\frac{0.58}{0.30}$ | $\frac{0.27}{0.30}$
0.10 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 0.53 | $\frac{0.16}{0.65}$ | $\frac{0.19}{0.66}$ | $\frac{0.19}{0.63}$ | $\frac{0.16}{0.39}$ | $\frac{0.35}{0.13}$ | $\frac{0.33}{0.02}$ | – | $\frac{0.14}{0.67}$ | $\frac{0.15}{0.65}$ | $\frac{0.16}{0.65}$ | $\frac{0.17}{0.64}$ | $\frac{0.16}{0.42}$
0.10 | $10^{-3}$ | 1$\times 10^{-3}$ | 0.38 | – | – | – | – | – | $\frac{0.18}{0.18}$ | $\frac{0.17}{0.15}$ | – | – | – | – | –
0.10 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 0.49 | – | $\frac{0.85}{0.64}$ | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-2}$ | 1$\times 10^{-4}$ | 0.00 | – | – | – | – | – | – | – | $\frac{0.12}{0.12}$ | – | – | – | –

Note. — A summary of the gap widths of the gas surface density profile, and
dust emission profile under dust size distribution DSD1 and DSD2. (1) aspect
ratio $h/r$ (2) $\alpha$ viscosity (3) planet-stellar mass ratio $q$ (4) The
width of the gas surface density (5-11) The gap width of the dust emission
under DSD1, with initial gas surface density $\Sigma_{g,0}$ = 0.1, 0.3, 1, 3,
10, 30, 100 $\mathrm{g\,cm^{-2}}$ ($St_{max}$ = 1.57 $\times$ $10^{-1}$, 5.23
$\times$ $10^{-2}$, 1.57 $\times$ $10^{-2}$, 5.23 $\times$ $10^{-3}$, 1.57
$\times$ $10^{-3}$, 5.23 $\times$ $10^{-4}$, 1.57 $\times$ $10^{-4}$) (12-16)
The gap width of the dust emission under DSD2, with initial gas surface
density $\Sigma_{g,0}$ = 1, 3, 10, 30, 100 $\mathrm{g\,cm^{-2}}$ ($St_{max}$ =
1.57, 5.32 $\times$ $10^{-1}$, 1.57 $\times$ $10^{-1}$, 5.23 $\times$
$10^{-2}$, 1.57 $\times$ $10^{-2}$) While the gap widths $\Delta_{g}$ are
found from unconvolved gas surface density profile, the rest of $\Delta_{d}$
are found from smoothed dust continuum intensity. The convolution beam for
dust emission $\sigma$ = 0.06 $r_{p}$ for the top rows; $\sigma$ = 0.025
$r_{p}$ for 11 rows horizontal single and double lines. Bottom rows under the
double lines are the gaps with the horseshoe that separates them into two
gaps. The value on top the bar shows the width of the inner gap
($\Delta_{1}$), whereas the value under the bar shows the width of the out gap
($\Delta_{2}$).

Table 5: Gap Depths $\big{(}log_{10}(\delta-1)\big{)}$ for the Gas, DSD1 and
DSD2

h/r | $\alpha$ | $q$ | $\delta_{g}-1$ | $\delta_{d,0p1}-1$ | $\delta_{d,0p3}-1$ | $\delta_{d,1}-1$ | $\delta_{d,3}-1$ | $\delta_{d,10}-1$ | $\delta_{d,30}-1$ | $\delta_{d,100}-1$ | $\delta_{d,1}-1$ | $\delta_{d,3}-1$ | $\delta_{d,10}-1$ | $\delta_{d,30}-1$ | $\delta_{d,100}-1$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | $(M_{p}/M_{*})$ | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$) | ($log_{10}$)
0.05 | $10^{-4}$ | 3.3$\times 10^{-5}$ | -1.03 | 1.94 | 1.25 | 0.62 | 0.24 | -0.03 | -0.21 | -0.41 | 3.66 | 2.93 | 2.10 | 1.25 | 0.50
0.05 | $10^{-4}$ | 1$\times 10^{-4}$ | 0.34 | 1.66 | 1.05 | 0.57 | 0.39 | 0.29 | 0.23 | 0.10 | 3.67 | 2.62 | 1.60 | 0.87 | 0.32
0.05 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 1.15 | 1.56 | 1.12 | 0.82 | 0.64 | 0.57 | 0.53 | 0.53 | 2.70 | 2.10 | 1.54 | 0.93 | 0.54
0.05 | $10^{-4}$ | 1$\times 10^{-3}$ | 3.43 | 3.12 | 2.56 | 2.14 | 1.90 | 1.72 | 1.65 | 1.56 | 3.66 | 3.47 | 3.13 | 2.64 | 2.05
0.05 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 2.05 | 4.55 | 3.90 | 3.20 | 2.67 | 2.26 | 1.93 | 1.73 | 8.75 | 8.00 | 6.93 | 5.75 | 4.10
0.05 | $10^{-3}$ | 3.3$\times 10^{-5}$ | – | – | -0.55 | -0.73 | – | – | – | – | – | – | -0.77 | -0.61 | -0.81
0.05 | $10^{-3}$ | 1$\times 10^{-4}$ | -0.27 | 2.24 | 1.46 | 0.72 | 0.24 | 0.01 | -0.10 | -0.26 | 4.94 | 3.83 | 2.55 | 1.46 | 0.57
0.05 | $10^{-3}$ | 3.3$\times 10^{-4}$ | 0.81 | 3.03 | 2.26 | 1.59 | 1.17 | 0.82 | 0.51 | 0.37 | 6.67 | 5.69 | 4.37 | 3.03 | 1.84
0.05 | $10^{-3}$ | 1$\times 10^{-3}$ | 2.35 | 2.54 | 3.08 | 2.86 | 2.49 | 2.17 | 1.89 | 1.49 | 3.40 | 3.08 | 2.72 | 3.23 | 3.78
0.05 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 1.96 | 3.52 | 2.95 | 2.43 | 2.10 | 1.78 | 1.48 | 1.34 | – | – | 5.44 | 4.22 | 3.13
0.05 | $10^{-2}$ | 3.3$\times 10^{-5}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.05 | $10^{-2}$ | 1$\times 10^{-4}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.05 | $10^{-2}$ | 3.3$\times 10^{-4}$ | -0.32 | 0.81 | 0.16 | -0.25 | -0.72 | – | -0.72 | – | 1.45 | 1.20 | 0.75 | 0.11 | -0.41
0.05 | $10^{-2}$ | 1$\times 10^{-3}$ | 0.64 | 1.88 | 1.24 | 0.59 | 0.24 | 0.04 | -0.01 | -0.10 | – | 3.37 | 2.22 | 1.27 | 0.44
0.05 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 2.69 | 3.05 | 2.50 | 2.01 | 1.69 | 1.35 | 1.05 | 0.74 | 4.87 | 4.12 | 5.00 | 3.85 | 2.60
0.07 | $10^{-4}$ | 3.3$\times 10^{-5}$ | – | – | – | -0.49 | -0.55 | -0.58 | -0.65 | – | – | – | – | – | -0.61
0.07 | $10^{-4}$ | 1$\times 10^{-4}$ | -0.69 | 2.31 | 1.92 | 1.08 | 0.51 | 0.15 | -0.04 | -0.28 | 4.06 | 3.26 | 2.41 | 1.73 | 0.88
0.07 | $10^{-4}$ | 3.3$\times 10^{-4}$ | 0.59 | 2.13 | 1.88 | 1.32 | 0.93 | 0.60 | 0.39 | 0.25 | 3.09 | 2.32 | 1.94 | 1.54 | 1.03
0.07 | $10^{-4}$ | 1$\times 10^{-3}$ | 1.86 | 3.34 | 2.93 | 2.20 | 1.81 | 1.51 | 1.29 | 1.02 | 4.57 | 3.89 | 3.44 | 2.92 | 2.20
0.07 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 2.60 | 5.10 | 4.63 | 3.79 | 3.24 | 2.75 | 2.42 | 2.04 | 9.89 | 9.11 | 8.10 | 7.02 | 5.69
0.07 | $10^{-3}$ | 3.3$\times 10^{-5}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.07 | $10^{-3}$ | 1$\times 10^{-4}$ | – | – | -0.47 | -0.39 | -0.63 | -0.65 | – | – | – | – | -0.56 | -0.55 | -0.54
0.07 | $10^{-3}$ | 3.3$\times 10^{-4}$ | 0.03 | 2.85 | 2.29 | 1.38 | 0.83 | 0.48 | 0.28 | 0.09 | 6.25 | 5.40 | 3.86 | 2.53 | 1.33
0.07 | $10^{-3}$ | 1$\times 10^{-3}$ | 1.04 | 3.50 | 2.96 | 2.12 | 1.64 | 1.26 | 0.93 | 0.72 | 7.71 | 6.91 | 5.78 | 4.49 | 2.86
0.07 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 2.38 | 4.86 | 4.36 | 3.58 | 3.12 | 2.78 | 2.48 | 2.11 | 4.69 | – | 7.61 | 6.49 | 4.89
0.07 | $10^{-2}$ | 3.3$\times 10^{-5}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.07 | $10^{-2}$ | 1$\times 10^{-4}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.07 | $10^{-2}$ | 3.3$\times 10^{-4}$ | – | – | – | – | – | – | – | – | -0.45 | – | – | – | –
0.07 | $10^{-2}$ | 1$\times 10^{-3}$ | -0.09 | 0.84 | 0.18 | -0.37 | -0.71 | – | – | – | 1.84 | 1.46 | 0.79 | 0.10 | -0.49
0.07 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 1.08 | 2.09 | 1.63 | 1.01 | 0.58 | 0.28 | 0.16 | 0.11 | – | – | 2.99 | 1.84 | 0.87
0.10 | $10^{-4}$ | 3.3$\times 10^{-5}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-4}$ | 1$\times 10^{-4}$ | – | – | – | -0.63 | -0.29 | -0.25 | -0.38 | -0.57 | – | – | – | – | -0.80
0.10 | $10^{-4}$ | 3.3$\times 10^{-4}$ | -0.33 | 2.51 | 2.23 | 1.49 | 0.73 | 0.26 | 0.00 | -0.27 | 4.10 | 3.50 | 3.00 | 2.20 | 1.15
0.10 | $10^{-4}$ | 1$\times 10^{-3}$ | 0.79 | 2.75 | 2.42 | 1.76 | 1.18 | 0.71 | 0.45 | 0.21 | 4.55 | 3.74 | 3.13 | 2.40 | 1.46
0.10 | $10^{-4}$ | 3.3$\times 10^{-3}$ | 1.84 | 3.71 | 3.08 | 2.81 | 2.36 | 1.87 | 1.52 | 1.14 | 5.84 | 4.47 | 3.77 | 3.37 | 4.29
0.10 | $10^{-3}$ | 3.3$\times 10^{-5}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-3}$ | 1$\times 10^{-4}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-3}$ | 3.3$\times 10^{-4}$ | – | – | – | -0.41 | -0.58 | -0.57 | -0.62 | – | – | – | – | -0.67 | -0.67
0.10 | $10^{-3}$ | 1$\times 10^{-3}$ | 0.17 | 2.54 | 2.10 | 1.33 | 0.59 | 0.08 | -0.18 | -0.34 | – | 5.06 | 3.52 | 2.29 | 1.14
0.10 | $10^{-3}$ | 3.3$\times 10^{-3}$ | 1.33 | 3.19 | 2.74 | 2.04 | 1.40 | 0.97 | 0.63 | 0.26 | – | 6.64 | 5.63 | 4.52 | 2.92
0.10 | $10^{-2}$ | 3.3$\times 10^{-5}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-2}$ | 1$\times 10^{-4}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-2}$ | 3.3$\times 10^{-4}$ | – | – | – | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-2}$ | 1$\times 10^{-3}$ | -1.45 | – | – | – | – | – | – | – | – | – | – | – | –
0.10 | $10^{-2}$ | 3.3$\times 10^{-3}$ | 0.17 | 1.24 | 0.55 | -0.07 | -0.61 | -0.62 | -0.62 | -0.64 | 2.87 | 2.14 | 1.30 | 0.48 | -0.25

Note. — A summary of the gap depths of the gas surface density profiles and
dust emission profiles under dust size distribution DSD1 and DSD2. The layout
is similar to Table 4, except that the depths are listed in
$log_{10}(\delta-1)$ and only $\sigma$ = 0.06 $r_{p}$ kernel is applied to
find the depths.

## References

  * ALMA Partnership et al. (2015) ALMA Partnership, Brogan, C. L., Pérez, L. M., et al. 2015, ApJ, 808, L3, doi: 10.1088/2041-8205/808/1/L3
  * Andrews et al. (2018) Andrews, S. M., Huang, J., & et al. 2018, ApJ
  * Andrews et al. (2016) Andrews, S. M., Wilner, D. J., Zhu, Z., et al. 2016, ApJ, 820, L40, doi: 10.3847/2041-8205/820/2/L40
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Ataiee et al. (2013) Ataiee, S., Pinilla, P., Zsom, A., et al. 2013, A&A, 553, L3, doi: 10.1051/0004-6361/201321125
  * Avenhaus et al. (2018) Avenhaus, H., Quanz, S. P., Garufi, A., et al. 2018, ApJ, 863, 44, doi: 10.3847/1538-4357/aab846
  * Bae et al. (2018) Bae, J., Pinilla, P., & Birnstiel, T. 2018, ApJ, 864, L26, doi: 10.3847/2041-8213/aadd51
  * Bae & Zhu (2018a) Bae, J., & Zhu, Z. 2018a, ApJ, 859, 118, doi: 10.3847/1538-4357/aabf8c
  * Bae & Zhu (2018b) —. 2018b, ApJ, 859, 119, doi: 10.3847/1538-4357/aabf93
  * Bae et al. (2016) Bae, J., Zhu, Z., & Hartmann, L. 2016, ApJ, 819, 134, doi: 10.3847/0004-637X/819/2/134
  * Bae et al. (2017) —. 2017, ApJ, 850, 201, doi: 10.3847/1538-4357/aa9705
  * Bai (2017) Bai, X.-N. 2017, ApJ, 845, 75, doi: 10.3847/1538-4357/aa7dda
  * Baruteau & Masset (2008a) Baruteau, C., & Masset, F. 2008a, ApJ, 672, 1054, doi: 10.1086/523667
  * Baruteau & Masset (2008b) —. 2008b, ApJ, 678, 483, doi: 10.1086/529487
  * Baruteau & Zhu (2016) Baruteau, C., & Zhu, Z. 2016, MNRAS, 458, 3927, doi: 10.1093/mnras/stv2527
  * Baruteau et al. (2014) Baruteau, C., Crida, A., Paardekooper, S.-J., et al. 2014, Protostars and Planets VI, 667, doi: 10.2458/azu_uapress_9780816531240-ch029
  * Benisty et al. (2018) Benisty, M., Juhasz, A., Facchini, S., et al. 2018, ArXiv e-prints.  https://arxiv.org/abs/1809.01082
  * Birnstiel et al. (2012) Birnstiel, T., Klahr, H., & Ercolano, B. 2012, A&A, 539, A148, doi: 10.1051/0004-6361/201118136
  * Birnstiel et al. (2018) Birnstiel et al., T. 2018, ApJ
  * Bowler & Nielsen (2018) Bowler, B. P., & Nielsen, E. L. 2018, ArXiv e-prints.  https://arxiv.org/abs/1802.10132
  * Casassus et al. (2013) Casassus, S., van der Plas, G., M, S. P., et al. 2013, Nature, 493, 191, doi: 10.1038/nature11769
  * Chabrier et al. (2014) Chabrier, G., Johansen, A., Janson, M., & Rafikov, R. 2014, Protostars and Planets VI, 619, doi: 10.2458/azu_uapress_9780816531240-ch027
  * Charnoz et al. (2011) Charnoz, S., Fouchet, L., Aleon, J., & Moreira, M. 2011, ApJ, 737, 33, doi: 10.1088/0004-637X/737/1/33
  * Cieza et al. (2017) Cieza, L. A., Casassus, S., Pérez, S., et al. 2017, ApJ, 851, L23, doi: 10.3847/2041-8213/aa9b7b
  * Clanton & Gaudi (2014) Clanton, C., & Gaudi, B. S. 2014, ApJ, 791, 91, doi: 10.1088/0004-637X/791/2/91
  * Crnkovic-Rubsamen et al. (2015) Crnkovic-Rubsamen, I., Zhu, Z., & Stone, J. M. 2015, MNRAS, 450, 4285, doi: 10.1093/mnras/stv828
  * D’Alessio et al. (2001) D’Alessio, P., Calvet, N., & Hartmann, L. 2001, ApJ, 553, 321, doi: 10.1086/320655
  * D’Alessio et al. (1998) D’Alessio, P., Canto, J., Calvet, N., & Lizano, S. 1998, ApJ, 500, 411, doi: 10.1086/305702
  * D’Antona & Mazzitelli (1994) D’Antona, F., & Mazzitelli, I. 1994, ApJS, 90, 467, doi: 10.1086/191867
  * Davies et al. (2014) Davies, M. B., Adams, F. C., Armitage, P., et al. 2014, Protostars and Planets VI, 787, doi: 10.2458/azu_uapress_9780816531240-ch034
  * Dipierro et al. (2015) Dipierro, G., Pinilla, P., Lodato, G., & Testi, L. 2015, ArXiv e-prints.  https://arxiv.org/abs/1504.08099
  * Dipierro et al. (2018) Dipierro, G., Ricci, L., Pérez, L., et al. 2018, MNRAS, 475, 5296, doi: 10.1093/mnras/sty181
  * Dodson-Robinson & Salyk (2011) Dodson-Robinson, S. E., & Salyk, C. 2011, ApJ, 738, 131, doi: 10.1088/0004-637X/738/2/131
  * Donati et al. (2016) Donati, J. F., Moutou, C., Malo, L., et al. 2016, Nature, 534, 662, doi: 10.1038/nature18305
  * Dong & Fung (2017) Dong, R., & Fung, J. 2017, ApJ, 835, 146, doi: 10.3847/1538-4357/835/2/146
  * Dong et al. (2017) Dong, R., Li, S., Chiang, E., & Li, H. 2017, ApJ, 843, 127, doi: 10.3847/1538-4357/aa72f2
  * Dong et al. (2018a) —. 2018a, ArXiv e-prints.  https://arxiv.org/abs/1808.06613
  * Dong et al. (2018b) —. 2018b, ArXiv e-prints.  https://arxiv.org/abs/1808.06613
  * Dong et al. (2011) Dong, R., Rafikov, R. R., & Stone, J. M. 2011, ApJ, 741, 57, doi: 10.1088/0004-637X/741/1/57
  * Dong et al. (2015) Dong, R., Zhu, Z., Rafikov, R. R., & Stone, J. M. 2015, ApJ, 809, L5, doi: 10.1088/2041-8205/809/1/L5
  * Duffell & MacFadyen (2012) Duffell, P. C., & MacFadyen, A. I. 2012, ApJ, 755, 7, doi: 10.1088/0004-637X/755/1/7
  * Dullemond et al. (2018) Dullemond et al., C. P. 2018, ApJ
  * Espaillat et al. (2014) Espaillat, C., Muzerolle, J., Najita, J., et al. 2014, Protostars and Planets VI, 497, doi: 10.2458/azu_uapress_9780816531240-ch022
  * Fedele et al. (2018) Fedele, D., Tazzari, M., Booth, R., et al. 2018, A&A, 610, A24, doi: 10.1051/0004-6361/201731978
  * Flaherty et al. (2018) Flaherty, K. M., Hughes, A. M., Teague, R., et al. 2018, ApJ, 856, 117, doi: 10.3847/1538-4357/aab615
  * Flock et al. (2015) Flock, M., Ruge, J. P., Dzyurkevich, N., et al. 2015, A&A, 574, A68, doi: 10.1051/0004-6361/201424693
  * Fu et al. (2014) Fu, W., Li, H., Lubow, S., Li, S., & Liang, E. 2014, ApJ, 795, L39, doi: 10.1088/2041-8205/795/2/L39
  * Fuente et al. (2017) Fuente, A., Baruteau, C., Neri, R., et al. 2017, ApJ, 846, L3, doi: 10.3847/2041-8213/aa8558
  * Fung & Dong (2015) Fung, J., & Dong, R. 2015, ApJ, 815, L21, doi: 10.1088/2041-8205/815/2/L21
  * Fung et al. (2014) Fung, J., Shi, J.-M., & Chiang, E. 2014, ApJ, 782, 88, doi: 10.1088/0004-637X/782/2/88
  * Garufi et al. (2017) Garufi, A., Benisty, M., Stolker, T., et al. 2017, The Messenger, 169, 32, doi: 10.18727/0722-6691/5036
  * Goldreich & Tremaine (1980) Goldreich, P., & Tremaine, S. 1980, ApJ, 241, 425, doi: 10.1086/158356
  * Gonzalez et al. (2012) Gonzalez, J.-F., Pinte, C., Maddison, S. T., Ménard, F., & Fouchet, L. 2012, A&A, 547, A58, doi: 10.1051/0004-6361/201218806
  * Goodman & Rafikov (2001) Goodman, J., & Rafikov, R. R. 2001, ApJ, 552, 793, doi: 10.1086/320572
  * Guzmán et al. (2018) Guzmán et al., V. V. 2018, ApJ
  * Hammer et al. (2017) Hammer, M., Kratter, K. M., & Lin, M.-K. 2017, MNRAS, 466, 3533, doi: 10.1093/mnras/stw3000
  * Hartmann et al. (1998) Hartmann, L., Calvet, N., Gullbring, E., & D’Alessio, P. 1998, ApJ, 495, 385, doi: 10.1086/305277
  * Huang et al. (2018a) Huang, J., Andrews, S. M., & et al. 2018a, ApJ
  * Huang et al. (2018b) —. 2018b, ApJ
  * Hull et al. (2018) Hull, C. L. H., Yang, H., Li, Z.-Y., et al. 2018, ApJ, 860, 82, doi: 10.3847/1538-4357/aabfeb
  * Hunter (2007) Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90
  * Isella & Turner (2018) Isella, A., & Turner, N. J. 2018, ApJ, 860, 27, doi: 10.3847/1538-4357/aabb07
  * Isella et al. (2016) Isella, A., Guidi, G., Testi, L., et al. 2016, Phys. Rev. Lett., 117, 251101
  * Isella et al. (2018) Isella et al., A. 2018, ApJ
  * Jin et al. (2016) Jin, S., Li, S., Isella, A., Li, H., & Ji, J. 2016, ApJ, 818, 76, doi: 10.3847/0004-637X/818/1/76
  * Johansen et al. (2014) Johansen, A., Blum, J., Tanaka, H., et al. 2014, in Protostars & Planets VI, eds. H. Beuther, R. Klessen, C. Dullemond, & Th. Henning (Univ. Arizona Press: Tucson), in press.  https://arxiv.org/abs/1402.1344
  * Johns-Krull et al. (2016) Johns-Krull, C. M., McLane, J. N., Prato, L., et al. 2016, ApJ, 826, 206, doi: 10.3847/0004-637X/826/2/206
  * Jones et al. (2001–) Jones, E., Oliphant, T., Peterson, P., et al. 2001–, SciPy: Open source scientific tools for Python.  http://www.scipy.org/
  * Kanagawa et al. (2015) Kanagawa, K. D., Muto, T., Tanaka, H., et al. 2015, ApJ, 806, L15, doi: 10.1088/2041-8205/806/1/L15
  * Kanagawa et al. (2016) —. 2016, PASJ, 68, 43, doi: 10.1093/pasj/psw037
  * Kataoka et al. (2017) Kataoka, A., Tsukagoshi, T., Pohl, A., et al. 2017, ApJ, 844, L5, doi: 10.3847/2041-8213/aa7e33
  * Keppler et al. (2018) Keppler, M., Benisty, M., Müller, A., et al. 2018, A&A, 617, A44, doi: 10.1051/0004-6361/201832957
  * Kley & Dirksen (2006) Kley, W., & Dirksen, G. 2006, A&A, 447, 369, doi: 10.1051/0004-6361:20053914
  * Kley & Nelson (2012) Kley, W., & Nelson, R. P. 2012, ARA&A, 50, 211, doi: 10.1146/annurev-astro-081811-125523
  * Kurtovic et al. (2018) Kurtovic, N., Pérez, L. M., & et al. 2018, ApJ
  * Liu et al. (2018) Liu, S.-F., Jin, S., Li, S., Isella, A., & Li, H. 2018, ApJ, 857, 87, doi: 10.3847/1538-4357/aab718
  * Lubow (1991a) Lubow, S. H. 1991a, ApJ, 381, 259, doi: 10.1086/170647
  * Lubow (1991b) —. 1991b, ApJ, 381, 268, doi: 10.1086/170648
  * Lyra et al. (2009) Lyra, W., Johansen, A., Klahr, H., & Piskunov, N. 2009, A&A, 493, 1125, doi: 10.1051/0004-6361:200810797
  * Lyra & Lin (2013) Lyra, W., & Lin, M.-K. 2013, ApJ, 775, 17, doi: 10.1088/0004-637X/775/1/17
  * Marois et al. (2010) Marois, C., Zuckerman, B., Konopacky, Q. M., Macintosh, B., & Barman, T. 2010, Nature, 468, 1080, doi: 10.1038/nature09684
  * Masset (2000) Masset, F. 2000, A&AS, 141, 165, doi: 10.1051/aas:2000116
  * Masset (2002) Masset, F. S. 2002, A&A, 387, 605, doi: 10.1051/0004-6361:20020240
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * Meru et al. (2017) Meru, F., Juhász, A., Ilee, J. D., et al. 2017, ApJ, 839, L24, doi: 10.3847/2041-8213/aa6837
  * Meshkat et al. (2017) Meshkat, T., Mawet, D., Bryan, M. L., et al. 2017, AJ, 154, 245, doi: 10.3847/1538-3881/aa8e9a
  * Müller et al. (2012) Müller, T. W. A., Kley, W., & Meru, F. 2012, A&A, 541, A123, doi: 10.1051/0004-6361/201118737
  * Muto et al. (2010) Muto, T., Suzuki, T. K., & Inutsuka, S.-i. 2010, ApJ, 724, 448, doi: 10.1088/0004-637X/724/1/448
  * Okuzumi et al. (2016) Okuzumi, S., Momose, M., Sirono, S.-i., Kobayashi, H., & Tanaka, H. 2016, ApJ, 821, 82, doi: 10.3847/0004-637X/821/2/82
  * Paardekooper & Mellema (2006) Paardekooper, S.-J., & Mellema, G. 2006, A&A, 453, 1129, doi: 10.1051/0004-6361:20054449
  * Pérez et al. (2015) Pérez, L. M., Chandler, C. J., Isella, A., et al. 2015, ApJ, 813, 41, doi: 10.1088/0004-637X/813/1/41
  * Pérez et al. (2016) Pérez, L. M., Carpenter, J. M., Andrews, S. M., et al. 2016, Science, 353, 1519, doi: 10.1126/science.aaf8296
  * Perez et al. (2015) Perez, S., Casassus, S., Ménard, F., et al. 2015, ApJ, 798, 85, doi: 10.1088/0004-637X/798/2/85
  * Pérez et al. (2018) Pérez et al., L. 2018, ApJ
  * Picogna & Kley (2015) Picogna, G., & Kley, W. 2015, A&A, 584, A110, doi: 10.1051/0004-6361/201526921
  * Pinilla et al. (2012) Pinilla, P., Birnstiel, T., Ricci, L., et al. 2012, A&A, 538, A114, doi: 10.1051/0004-6361/201118204
  * Pinilla et al. (2016) Pinilla, P., Flock, M., Ovelar, M. d. J., & Birnstiel, T. 2016, A&A, 596, A81, doi: 10.1051/0004-6361/201628441
  * Pinte et al. (2016) Pinte, C., Dent, W. R. F., Ménard, F., et al. 2016, ApJ, 816, 25, doi: 10.3847/0004-637X/816/1/25
  * Pinte et al. (2018) Pinte, C., Price, D. J., Ménard, F., et al. 2018, ApJ, 860, L13, doi: 10.3847/2041-8213/aac6dc
  * Ragusa et al. (2018) Ragusa, E., Rosotti, G., Teyssandier, J., et al. 2018, MNRAS, 474, 4460, doi: 10.1093/mnras/stx3094
  * Raymond et al. (2014) Raymond, S. N., Kokubo, E., Morbidelli, A., Morishima, R., & Walsh, K. J. 2014, Protostars and Planets VI, 595, doi: 10.2458/azu_uapress_9780816531240-ch026
  * Ricci et al. (2018) Ricci, L., Liu, S.-F., Isella, A., & Li, H. 2018, ApJ, 853, 110, doi: 10.3847/1538-4357/aaa546
  * Ricci et al. (2010a) Ricci, L., Testi, L., Natta, A., & Brooks, K. J. 2010a, A&A, 521, A66, doi: 10.1051/0004-6361/201015039
  * Ricci et al. (2010b) Ricci, L., Testi, L., Natta, A., et al. 2010b, A&A, 512, A15, doi: 10.1051/0004-6361/200913403
  * Rosotti et al. (2016) Rosotti, G. P., Juhasz, A., Booth, R. A., & Clarke, C. J. 2016, MNRAS, 459, 2790, doi: 10.1093/mnras/stw691
  * Ruge et al. (2016) Ruge, J. P., Flock, M., Wolf, S., et al. 2016, A&A, 590, A17, doi: 10.1051/0004-6361/201526616
  * Sallum et al. (2015) Sallum, S., Follette, K. B., Eisner, J. A., et al. 2015, Nature, 527, 342, doi: 10.1038/nature15761
  * Stone & Norman (1992) Stone, J. M., & Norman, M. L. 1992, ApJS, 80, 753, doi: 10.1086/191680
  * Suriano et al. (2018) Suriano, S. S., Li, Z.-Y., Krasnopolsky, R., & Shang, H. 2018, MNRAS, 477, 1239, doi: 10.1093/mnras/sty717
  * Takahashi & Inutsuka (2014) Takahashi, S. Z., & Inutsuka, S.-i. 2014, ApJ, 794, 55, doi: 10.1088/0004-637X/794/1/55
  * Tanaka et al. (2002) Tanaka, H., Takeuchi, T., & Ward, W. R. 2002, ApJ, 565, 1257, doi: 10.1086/324713
  * Teague et al. (2018) Teague, R., Bae, J., Bergin, E. A., Birnstiel, T., & Foreman-Mackey, D. 2018, ApJ, 860, L12, doi: 10.3847/2041-8213/aac6d7
  * Teyssandier & Ogilvie (2017) Teyssandier, J., & Ogilvie, G. I. 2017, MNRAS, 467, 4577, doi: 10.1093/mnras/stx426
  * Turner et al. (2014) Turner, N. J., Fromang, S., Gammie, C., et al. 2014, Protostars and Planets VI, 411, doi: 10.2458/azu_uapress_9780816531240-ch018
  * van der Marel et al. (2013) van der Marel, N., van Dishoeck, E. F., Bruderer, S., et al. 2013, Science, 340, 1199, doi: 10.1126/science.1236770
  * Van Der Walt et al. (2011) Van Der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, ArXiv e-prints.  https://arxiv.org/abs/1102.1523
  * Vigan et al. (2017) Vigan, A., Bonavita, M., Biller, B., et al. 2017, A&A, 603, A3, doi: 10.1051/0004-6361/201630133
  * Wolf & D’Angelo (2005) Wolf, S., & D’Angelo, G. 2005, ApJ, 619, 1114, doi: 10.1086/426662
  * Yang et al. (2018) Yang, C.-C., Mac Low, M.-M., & Johansen, A. 2018, ApJ, 868, 27, doi: 10.3847/1538-4357/aae7d4
  * Youdin & Goodman (2005) Youdin, A. N., & Goodman, J. 2005, ApJ, 620, 459, doi: 10.1086/426895
  * Youdin & Lithwick (2007) Youdin, A. N., & Lithwick, Y. 2007, Icarus, 192, 588, doi: 10.1016/j.icarus.2007.07.012
  * Yu et al. (2017) Yu, L., Donati, J.-F., Hébrard, E. M., et al. 2017, MNRAS, 467, 1342, doi: 10.1093/mnras/stx009
  * Zhang et al. (2015) Zhang, K., Blake, G. A., & Bergin, E. A. 2015, ApJ, 806, L7, doi: 10.1088/2041-8205/806/1/L7
  * Zhu et al. (2018) Zhu, Z., Andrews, S. M., & Isella, A. 2018, MNRAS, 479, 1850, doi: 10.1093/mnras/sty1503
  * Zhu et al. (2015a) Zhu, Z., Dong, R., Stone, J. M., & Rafikov, R. R. 2015a, ApJ, 813, 88, doi: 10.1088/0004-637X/813/2/88
  * Zhu et al. (2012) Zhu, Z., Nelson, R. P., Dong, R., Espaillat, C., & Hartmann, L. 2012, ApJ, 755, 6, doi: 10.1088/0004-637X/755/1/6
  * Zhu et al. (2011) Zhu, Z., Nelson, R. P., Hartmann, L., Espaillat, C., & Calvet, N. 2011, ApJ, 729, 47, doi: 10.1088/0004-637X/729/1/47
  * Zhu et al. (2015b) Zhu, Z., Stone, J. M., & Bai, X.-N. 2015b, ApJ, 801, 81, doi: 10.1088/0004-637X/801/2/81
  * Zhu et al. (2013) Zhu, Z., Stone, J. M., & Rafikov, R. R. 2013, ApJ, 768, 143, doi: 10.1088/0004-637X/768/2/143
  * Zhu et al. (2014) Zhu, Z., Stone, J. M., Rafikov, R. R., & Bai, X.-n. 2014, ApJ, 785, 122, doi: 10.1088/0004-637X/785/2/122