The synthetic ALMA multiband analysis of dust properties of the TW - - PowerPoint PPT Presentation

30 Oct. 2018 Cosmic Dust and Magnetism 2018

The synthetic ALMA multiband analysis of dust properties of the TW Hya protoplanetary disk

Seongjoong Kim1, Hideko Nomura1, 
 Takashi Tsukagoshi2, Ryohei Kawabe2, Takayuki Muto3

1 Tokyo Institute of Technology,
 2 National Astronomical Observatory of Japan, 3 Kogakuin University

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(Kim et al. submitted)

30 Oct. 2018 Cosmic Dust and Magnetism 2018

Introduction: Protoplanetary disks

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Dust properties in disks: Key information to understand Planet formation process

Testi+2014 Ormel+2010

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Introduction: TW Hya

• The origin of gaps/rings in the TW

Hya disk?

✓ Planet-disk interaction?


(Kanagawa et al. 2016, Dong et al. 2017, Bae et al. 2017, Fedele et al. 2018)

✓ Magneto-Rotational Instability? 


(Flock et al. 2015)

✓ Secular Gravitational instability? 


(Youdin 2011; Takahashi & Inutsuka 2014)

✓ Growth and destruction of dust

grains near snowlines? 


(Zhang et al. 2015, Okuzumi et al. 2016)

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Andrews et al. 2016 ALMA Band 7 dust continuum
 (𝞵~0.87mm)

• Which model is the best explanation?

⇒ Radial distribution of dust properties!!

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Previous Work

• 𝛖190GHz and 𝞬 radial profile derived from
• To solve equations, Adding an assumption

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Tsukagoshi et al. 2016

✓ Assumptions:

• 1. Dust opacity 𝞴𝞷∝𝞷𝞬
• 2. Vertically homogeneous disk

✓ Equations for I𝞷 & Dust properties:

• 1. I𝞷(r) = B𝞷(Td(r)) (1-exp(-𝛖𝞷(r)))
• 2. 𝛖𝞷(r) = 𝛖0(r) (𝞷/𝞷0)𝞬(r)

✓ Observations: Intensities at 
 ALMA Band 4 (𝞵~2mm) & 6 (𝞵~1.3mm) Td,model(r)=26K(r/10AU)-0.4

𝛖190GHz

𝞬 (𝞴𝞷∝𝞷𝞬)

30 Oct. 2018 Cosmic Dust and Magnetism 2018

Previous Work

• 𝛖190GHz and 𝞬 radial profile derived from
• To solve equations, Adding an assumption

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Tsukagoshi et al. 2016

✓ Assumptions:

• 1. Dust opacity 𝞴𝞷∝𝞷𝞬
• 2. Vertically homogeneous disk

✓ Equations for I𝞷 & Dust properties:

• 1. I𝞷(r) = B𝞷(Td(r)) (1-exp(-𝛖𝞷(r)))
• 2. 𝛖𝞷(r) = 𝛖0(r) (𝞷/𝞷0)𝞬(r)

✓ Observations: Intensities at 
 ALMA Band 4 (𝞵~2mm) & 6 (𝞵~1.3mm) Td,model(r)=26K(r/10AU)-0.4

𝛖190GHz

𝞬 (𝞴𝞷∝𝞷𝞬)

• Adding one more observational data to

drop the Td assumption!!

• Which three ALMA bands are the best?


⇒ Synthetic multiband analysis

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The synthetic multiband analysis: Methodology

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I𝞷1, syn I𝞷2, syn I𝞷3, syn Td,syn βsyn 𝛖𝞷,syn

(100%-x)I𝞷,model ≤ I𝞷,syn ≤ (100%+x)I𝞷,model
 where x=10-20%

𝞷 I𝞷, model 𝞷1 𝞷2 𝞷3 1) Td,model(r)=26K(r/10AU)-0.4 2) 𝛖model(r) and 𝞬model(r)

• 1. Calculate Model intensities
• 2. Extract I𝞷,syn within I𝞷,model ± observational errors:
• 3. Derive the constraint ranges of the synthetic dust properties
• Using the same equations & assumptions in the previous work,

Pick [𝞷1,𝞷2,𝞷3] among Band [3,4,5,6,7,8,9,10]

30 Oct. 2018 Cosmic Dust and Magnetism 2018

The synthetic multiband analysis: Results

• Good band sets are [10,6,3] (green),

[10,7,3] (red), [9,6,3] (blue), [9,7,3] (purple)

• 2 conditions for good band set

i. Band 9 or 10 is included ii. Enough frequency intervals between the bands

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10 20 30 40 50 Radius [AU] 10 1 0.1 0.01 𝛖B3 10 20 30 40 50 Radius [AU] 10 20 30 40 50 60 Td [K] 1.5 0.5

• 0.5

𝞬

𝛖112GHz(r)

𝞬(r) (𝞴𝞷∝𝞷𝞬)

Td(r)

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✓ Combination of optically thick and thin band

• Higher 𝛖𝞷 ➔ I(r)≅B𝞷(Td(r)) ➔ Good Td constraints
• lower 𝛖𝞷 ➔ I(r)≅B𝞷(Td(r))𝛖𝞷 ➔ Good 𝛖𝞷 constraints

✓ higher 𝞬 ➔ 𝛖𝞷↑ at high 𝞷 & 𝛖𝞷↓ at low 𝞷 ✓ Low Td at high 𝞷
 → Deviation from Rayleigh-
 Jeans limit↑
 → Better constraint on Td ✓ Enough 𝞷 interval 
 → accurate 𝜷 constraint

The synthetic multiband analysis: Interpretations

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Blackbody curves at different Td

I𝞷∝𝞷2 BB

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Application to archival data

• Is the synthetic multiband analysis consistent with the data?
• Band 4 & 6 (Tsukagoshi+2016): ∼0.088”×0.062”, 1σ∼29𝜈Jy/beam
• Band 7 (Andrews+2016): ∼0.024”×0.018”, 1σ∼35𝜈Jy/beam
• Band 9 (Schwarz+2016):∼0.432”×0.251”, 1σ∼10mJy/beam

⇒ High-resolution set [7,6,4] & low-resolution set [9,6,4]

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B4+6 B7 B9 𝞵~1.5 mm 𝞵~0.87 mm 𝞵~0.45 mm

30 Oct. 2018 Cosmic Dust and Magnetism 2018

Application to archival data: Td

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High-resolution Band [7,6,4] set 
 (75 mas ~ 4.5 AU) Low-resolution Band [9,6,4] set (340 mas ~ 20 AU) 10 20 30 40 50 60 Td [K]

10 20 30 40 50 Radius [AU]

✓ Td,model(r) is well reproduced by [9,6,4], but not by [7,6,4]. ✓ Constraint ranges: Too broad for both

10 20 30 40 50 60 Td [K]

10 20 30 40 50 Radius [AU]

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Application to archival data: 𝛖B4 and 𝞬

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1.5 0.5

• 0.5

𝞬 10 1 0.1 0.01 𝛖B4 10 20 30 40 50 Radius [AU]

✓ 𝛖B4(r) & 𝞬(r) are well reproduced by [9,6,4], but not by [7,6,4]. ✓ Constraint ranges: [9,6,4] gives better constraints than [7,6,4]

High-resolution Band [7,6,4] set 
 (75 mas ~ 4.5 AU) Low-resolution Band [9,6,4] set (340 mas ~ 20 AU) 1.5 0.5

• 0.5

𝞬 10 1 0.1 0.01 𝛖B4 10 20 30 40 50 Radius [AU]

30 Oct. 2018 Cosmic Dust and Magnetism 2018

Summary

• The synthetic multiband analysis for finding the best ALMA band

set providing good constraints on the radial profiles of Td, 𝛖𝞷, and 𝞬.

• We find two conditions for the best ALMA bands sets

1) Band 9/10 is included in the band sets 2) Enough frequency intervals between the bands ⇒ The combination of optically thick and thin band is needed

• Td(r), 𝛖𝞷(r), and 𝞬(r) derived from [9,6,4] set reproduce the model

well, but those derived from [7,6,4] set do not.
 ⇒ Consistent with the synthetic analysis results

• High-resolution Band 9 data will help to understand the origin of

the ring/gap structure in the disk.

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