The Synthetic ALMA Multiband Analysisof the dust properties of the TW Hya protoplanetary disks
1123Seongjoong Kim , Nomura Hideko , Takashi Tsukagoshi , Ryohei Kawabe , Takayuki Muto

41Department of Earth and Planetary Sciences, Tokyo Institute of Technoloty, Tokyo 152-0027, Japan
2College of Science, Ibaraki University, Bunkyo 2-1-1, Mito, Ibaraki 310-8512, Japan
3National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, JapanTW Hya protoplanetary disk(S. Andrew)

4Division of Liberal Arts, Kogakuin University, 1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677, JapanAbstract
TW Hya is one of the well studied protoplanetary disks (PPDs) with its proximity. Recently, high spatial resolution ALMA observations have revealed clear gap
structures and the radial profiles of dust properties of the disk (e.g., Andrews et al. 2016, Tsukagoshi et al. 2016). Multi-band observations of dust continuum emission isuseful to constrain the radial profiles of dust temperature and dust opacity which help us to understand physical and chemical properties, such as dust evolution as well
as locations of snowlines, in the disk. In this work, we have performed the sensitivity analysis of the synthetic ALMA observations to find the best set of ALMA multiband observation for constraining dust properties of TW Hya PPD. First, we derived radial profiles of dust temperature Td, optical depth 𝛕𝞶, and opacity power-law
index β with the assumption of 𝞳𝞶∝𝞶β using the existing ALMA Band 4, 6 and 7 high spatial resolution data. However, this dataset was too sensitive to the errors inobserved intensity so that only 10% errors make it difficult to make constraint on Td, 𝛕𝞶, and β. Thus, we have performed Synthetic ALMA Multi-band Analysis in order
to find the best ALMA band set. Our result suggests the best set is ALMA Band [10,7,3] and there are two conditions for good constraint on Td, 𝛕𝞶, and β; (1) thecombination of one band from Band 9 or 10 and one band from Band 3 or 4 and (2) enough frequency intervals between the selected bands.

1. Motivation

2. The Synthetic ALMA Multiband Analysis- Estimation of Td, 𝛕𝞶 and β from ALMA Band 7, 6, and 4 data with the assumptions,1) Calculation of I𝞶, model,2) Sensitivity Analysis
Finding possible range of Td,syn, 𝛕𝞶,syn, and,βsyn within ±10% error of I𝞶, model

Temperature[K]Td,model (R) = 26K (R/10AU)-0.4
𝛕𝞶,model(R) & βmodel(R) from ALMA Band 4&6

A large bump around 30 AU by highsensitivity against the observational error

Sensitivity Analysis

Band 4+6 - Tsukagoshi+2016
Band 7 - Andrews+2016

I𝞶3, synI𝞶, model

What is the best set of 3 ALMAbands giving us a good constrainton Td, 𝛕𝞶 and β?

I𝞶2, synI𝞶1, syn𝞶1

𝞶2

𝞶3

𝞶

3. Results

Td,syn- For all possible 3-band combination of ALMA Band [3,4,5,6,7,8,9,10],
the Best result is [10,7,3] combination.
- 2 conditions for good constraint on Td, 𝛕𝞶 and βIB7(1) One band from Band 9 or 10 + One band from Band 3 or 4ex) [10,7,3], [10,8,3], [9,7,3], [9,8,3] ≫ [7,6,4](2) Enough frequency intervals between the selected bandsex) [10,7,3] > [10,8,3] > [9,7,3] > [9,8,3]

Bump byhigh sensitivity

are translated from the range of ±10% error of I𝞶,model.

5. Application to [9,6,4] data

𝛕112GHzTd,syn [K]Figure 1. [Top] Td radial profile estimation by ALMA
multi-band data (Band 4+6 and 7). [Bottom] Thesensitivity map of Td for ±10% Intensity errors of IB4+6and IB7 at 30 AU.

β
Figure 4. Blackbody curves at the temperature of 10, 15,20, 25, and 30 K. Gray shaded regions present thecoverage of ALMA Band 3 to 10.

- Reasons of 2 conditions for good constraint on Td, 𝛕𝞶 and β(1) Band 9 & 10: Deviated from Rayleigh-Jeans limit⇒ more degree of freedom to fit Td and 𝛕𝞶(2) Band 3 & 4: Optically thin band
⇒ Information of 𝛕𝞶(3) Enough frequency intervals between the selected bands⇒ Enough Δ𝞶 reduces the error of SED slope fitting caused by theobservational error❖ Reference
1. Andrews, S. M., Steinfelds, E., Zolman, N. et al.2016, ApJL, 820, L40
2. Tsukagoshi, T., Nomura, H., Muto, T. et al. 2016, ApJL, 829, L35
3. Schwarz. K. R., Bergin, E. A., Cleeves, L. I. et al 2016, ApJ, 823, 91S

Figure 3. The possible range of Td,syn (TopLeft), 𝛕𝞶,syn (Top-Right) and βsyn (BottomLeft) obtained by ALMA Band set [7,6,4],[9,8,3], [9,7,3], [10,8,3], and [10,7,3]. The
possible range of each parameter of each bandset is represented by different color-shadedregion. Td,model=26K(R/10AU)-0.4 and 𝛕𝞶,modeland βmodel are shown by white line in eachpanel.

Temperature[K]4. Discussion

ββsynFigure 2. Schematic figure of Synthetic ALMA Multiband Analysis. The possible range of Td,syn, 𝛕𝞶,syn, and βsyn𝛕𝞶TdIB4+6

𝛕𝞶,synBand 4+6 - Tsukagoshi+2016
Band 9 - Schwarz+2016

Figure 5. Estimated Td (Green diamond) using ALMA Band
[9,6,4] combination. Compared to Band [7,6,4] (Black point), it
has relatively smooth profile around 30 AU. However,smoothed Band [7,6,4] result (Magenta square) indicates it issmoothing effect.

- We apply the same analysis to Band [9,6,4] data confirming the consistency of theSynthetic ALMA Multiband Analysis.
✓ Band [9,6,4] vs Band [7,6,4]: [9,6,4] doesn’t show any bump around 30 AU⇒ It looks consistent with our analysis✓ Smoothed Band [7,6,4] vs Band [7,6,4]: Beam~ 0.4ʺ× 0.2ʺ vs ~ 0.088ʺ× 0.061ʺ
⇒ The bump around 30 AU is smoothed out by large beam of Band 9

6. Summary
Synthetic ALMA Multiband Analysis to constrain Td, 𝛕𝞶 and β accurately.
• The best set of ALMA bands is [10, 7, 3]• 2 conditions for good constraint
1. One band from Band 9 or 10 & One band from Band 3 or 4
2. Enough frequency intervals between selected bands