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

The synthetic ALMA multiband analysis of dust properties of the TW Hya protoplanetary disk (Kim et al. submitted) Seongjoong Kim 1 , Hideko Nomura 1 , 
 Takashi Tsukagoshi 2 , Ryohei Kawabe 2 , Takayuki Muto 3 1 Tokyo Institute of Technology, 
 2 National Astronomical Observatory of Japan, 3 Kogakuin University � 1 30 Oct. 2018 Cosmic Dust and Magnetism 2018

Introduction: Protoplanetary disks Ormel+2010 Testi+2014 Dust properties in disks: Key information to understand Planet formation process � 2 30 Oct. 2018 Cosmic Dust and Magnetism 2018

Introduction: TW Hya • The origin of gaps/rings in the TW Hya disk? ALMA Band 7 dust continuum 
 ✓ Planet-disk interaction? 
 ( 𝞵 ~0.87mm) (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? 
 Andrews et al. 2016 (Zhang et al. 2015, Okuzumi et al. 2016) • Which model is the best explanation? ⇒ Radial distribution of dust properties!! � 3 30 Oct. 2018 Cosmic Dust and Magnetism 2018

Previous Work • 𝛖 190GHz and 𝞬 radial profile derived from ✓ Assumptions: 1. Dust opacity 𝞴 𝞷 ∝ 𝞷 𝞬 2. Vertically homogeneous disk ✓ Equations for I 𝞷 & Dust properties: 1. I 𝞷 (r) = B 𝞷 (T d (r)) (1-exp(- 𝛖 𝞷 (r))) 2. 𝛖 𝞷 (r) = 𝛖 0 (r) ( 𝞷 / 𝞷 0 ) 𝞬 (r) 𝛖 190GHz ✓ Observations: Intensities at 
 𝞬 ( 𝞴 𝞷 ∝ 𝞷 𝞬 ) ALMA Band 4 ( 𝞵 ~ 2mm) & 6 ( 𝞵 ~ 1.3mm) • To solve equations, Adding an assumption T d,model (r)=26K(r/10AU) -0.4 Tsukagoshi et al. 2016 � 4 30 Oct. 2018 Cosmic Dust and Magnetism 2018

Previous Work • 𝛖 190GHz and 𝞬 radial profile derived from ✓ Assumptions: 1. Dust opacity 𝞴 𝞷 ∝ 𝞷 𝞬 2. Vertically homogeneous disk • Adding one more observational data to ✓ Equations for I 𝞷 & Dust properties: drop the T d assumption!! 1. I 𝞷 (r) = B 𝞷 (T d (r)) (1-exp(- 𝛖 𝞷 (r))) • Which three ALMA bands are the best? 
 2. 𝛖 𝞷 (r) = 𝛖 0 (r) ( 𝞷 / 𝞷 0 ) 𝞬 (r) 𝛖 190GHz ⇒ Synthetic multiband analysis ✓ Observations: Intensities at 
 𝞬 ( 𝞴 𝞷 ∝ 𝞷 𝞬 ) ALMA Band 4 ( 𝞵 ~ 2mm) & 6 ( 𝞵 ~ 1.3mm) • To solve equations, Adding an assumption T d,model (r)=26K(r/10AU) -0.4 Tsukagoshi et al. 2016 � 5 30 Oct. 2018 Cosmic Dust and Magnetism 2018

The synthetic multiband analysis: Methodology • Using the same equations & assumptions in the previous work, 1. Calculate Model intensities Pick [ 𝞷 1 , 𝞷 2 , 𝞷 3 ] among I 𝞷 , model Band [3,4,5,6,7,8,9,10] 1) T d,model (r)=26K(r/10AU) -0.4 2) 𝛖 model (r) and 𝞬 model (r) 𝞷 𝞷 1 𝞷 2 𝞷 3 2. Extract I 𝞷 ,syn within I 𝞷 ,model ± observational errors: (100%-x)I 𝞷 ,model ≤ I 𝞷 ,syn ≤ (100%+x)I 𝞷 ,model 
 I 𝞷 3, syn T d,syn where x=10-20% β syn I 𝞷 2, syn 𝛖𝞷 ,syn I 𝞷 1, syn 3. Derive the constraint ranges of the synthetic dust properties � 6 30 Oct. 2018 Cosmic Dust and Magnetism 2018

The synthetic multiband analysis: Results 60 10 50 1 40 T d [K] 𝛖 B3 30 0.1 20 𝛖 112GHz (r) T d (r) 0.01 10 0 10 20 30 40 50 Radius [AU] • Good band sets are [10,6,3] (green), 1.5 [10,7,3] (red), [9,6,3] (blue), [9,7,3] (purple) 𝞬 • 2 conditions for good band set 0.5 i. Band 9 or 10 is included -0.5 ii. Enough frequency intervals 𝞬 (r) ( 𝞴 𝞷 ∝ 𝞷 𝞬 ) between the bands 0 10 20 30 40 50 Radius [AU] � 7 30 Oct. 2018 Cosmic Dust and Magnetism 2018

The synthetic multiband analysis: Interpretations ✓ Combination of optically thick and thin band ‣ Higher 𝛖 𝞷 ➔ I(r) ≅ B 𝞷 (T d (r)) ➔ Good T d constraints ‣ lower 𝛖 𝞷 ➔ I(r) ≅ B 𝞷 (T d (r)) 𝛖 𝞷 ➔ Good 𝛖 𝞷 constraints ✓ higher 𝞬 ➔ 𝛖 𝞷 ↑ at high 𝞷 & 𝛖 𝞷 ↓ at low 𝞷 Blackbody curves at di ff erent T d ✓ Low T d at high 𝞷 
 → Deviation from Rayleigh- 
 I 𝞷 ∝ 𝞷 2 Jeans limit ↑ 
 → Better constraint on T d ✓ Enough 𝞷 interval 
 BB → accurate 𝜷 constraint � 8 30 Oct. 2018 Cosmic Dust and Magnetism 2018

Application to archival data • Is the synthetic multiband analysis consistent with the data? Band 4 & 6 (Tsukagoshi+2016): ∼ 0.088” × 0.062”, 1 σ ∼ 29 𝜈 Jy/beam ‣ Band 7 (Andrews+2016): ∼ 0.024” × 0.018”, 1 σ ∼ 35 𝜈 Jy/beam ‣ Band 9 (Schwarz+2016): ∼ 0.432” × 0.251”, 1 σ ∼ 10mJy/beam ‣ ⇒ High-resolution set [7,6,4] & low-resolution set [9,6,4] 𝞵 ~0.87 mm 𝞵 ~1.5 mm 𝞵 ~0.45 mm B4+6 B7 B9 � 9 30 Oct. 2018 Cosmic Dust and Magnetism 2018

Application to archival data: T d High-resolution Band [7,6,4] set 
 Low-resolution Band [9,6,4] set (75 mas ~ 4.5 AU) (340 mas ~ 20 AU) 60 60 50 50 40 40 T d [K] T d [K] 30 30 20 20 10 10 20 30 40 10 50 20 30 40 0 10 50 0 Radius [AU] Radius [AU] ✓ T d,model (r) is well reproduced by [9,6,4] , but not by [7,6,4] . ✓ Constraint ranges: Too broad for both � 10 30 Oct. 2018 Cosmic Dust and Magnetism 2018

Application to archival data: 𝛖 B4 and 𝞬 High-resolution Band [7,6,4] set 
 Low-resolution Band [9,6,4] set (75 mas ~ 4.5 AU) (340 mas ~ 20 AU) 10 10 1 1 𝛖 B4 𝛖 B4 0.1 0.1 0.01 0.01 1.5 1.5 𝞬 𝞬 0.5 0.5 -0.5 -0.5 0 10 20 30 40 50 0 10 20 30 40 50 Radius [AU] Radius [AU] ✓ 𝛖 B4 (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] � 11 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 T d , 𝛖 𝞷 , 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 • T d (r), 𝛖 𝞷 (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. � 12 30 Oct. 2018 Cosmic Dust and Magnetism 2018