1. Surface Density Structure in Outer Region of Protoplanetary Disk Jul. 24th 2014 Nobeyama UM Eiji Akiyama (NAOJ) Munetake Momose, Yoshimi Kitamura, Takashi Tsukagosh, Shota Shimada, Masahiko Hayashi, Shin Koyamatsu

2. Importance of Outer Region of the Disk How is disk gas cleared ? How can planets form at a distant from a central star ? Kalas et al. 2009 Fomalhaut r = 119 AU

3. Power Law Disk Model Power law description in surface density was introduced in the minimum mass solar nebula. (e.g. Kusaka et al. 1970, Weidenschilling 1977, Hayashi et al. 1985)

4. Discrepancy between Dust & Gas Emission Discrepancy in disk size has emerged between the extent of the dust continuum and molecular gas emission. Dust continuum: smaller size Gas emission: larger size Examples ・ AB Aur (Pietu et al. 2005) Continuum (2.8, 1.4mm): 350±30 AU 12 CO(J=2-1): 1050±10 AU ・ HD 163296 (Isella et al. 2007) Continuum (0.87-7mm) : 200±15 AU 12 CO(J=3-2) etc: 540±40 AU Is the power law description really appropriate ?

5. Similarity Solution Disk Model  Surface density is based on the theory of viscous evolution ( Lynden-Bell & Pringle 1974, Hartmann et al. 1998)  Radial temperature distribution Same as power-law disk model power-law similarity x[AU] y[AU] x[AU] log n H2 [1/cc] Log r [AU] Log Σ(r) [g cm -2 ] r out power-law similarity distance where Σ(r) starts decreasing exponentially normalized surface density C2C2

6. Examples of Similarity Solution velocity [km s -1 ] HD163296 R.A. Dec. 2 4 6 8 2 4 6 8 2 4 6 8 Power Similarity Hughes et al. 2008 ALMA SV band7 color: CO(3-2) contour: continuum 10 100 1000 r [AU] CO(3-2) continuum r c = 125 AU de Gregorio-Monsalvo et al. 2013 10 - 2 10 - 3 10 - 4 10 - 1 10 -2 10 -3 10 -0 CO(3-2) [Jy/beam] continuum [Jy/beam] 10 8 6 4 2 Vel. [km/s] CO(3-2) 2 0 4 6 2 4 6 offset [arcsec]

7. Gallery of Protoplanetary Disks (Radio) Andrews et al. 2011 Mathew et al. 2012 Brown et al. 2012 Cieza et al. 2012 Isella et al. 2010

8. Object Details distance [pc]SP typeM * [M ☉ ]M disk [M ☉ ]inclination [deg.] 140A2/32.30.02938 MWC 480 is bright Herbig Ae star with primordial disk. Many people have observed and basic properties are well known. No complex structures → easy to analyze the structure Kusakabe et al. 2012 Acke & van den Ancker 2004 No complex structures log λ[μm] log λF λ [erg cm -2 s -1 μm] H-band Subaru

9. Observation Details Telescope Reciever NRO45, ASTE BEARS, T100H/V, CATS345 Lines 12 CO(1-0), 13 CO(1-0), C 18 O(1-0), 12 CO(3-2), 13 CO(3-2) Frequency109 – 115 GHz, 330 – 345 GHz Spatial res.~ 15” (~2100 AU), ~ 23”(~3200 AU) Velocity res.~ 0.055 – 0.1 km/s Integ. time4.2h (2.0h on source) System temp.140 -350 K

10. Model Parameters ・ Fixed parameters ： The results obtained by other observations applied ・ Free parameters ： Best fit parameters are searched ・ X （ 12 CO) = 10000 ・ Local Thermal Equilibrium (LTE) ・ X （ 12 CO) / X （ 13 CO) = 60 ・ Hydrostatic Equilibrium ・ X （ 13 CO) / X （ C 18 O) = 5 ・ Outer radius ： r out (C 2 ) ・ Temperature ： T 100 ・ Surface density ： Σ 100 (C 1 ) distance [pc] M * [M ☉ ] inclination [deg.] pq HD1632961402.3381.00.5

11. Model Fit Results Similarity solution shows better fit in multi-CO line observation → It supports viscous evolution Akiyama et al. 2013

12. Observation Details Lines 12 CO(2-1), 13 CO(2-1), C 18 O(2-1) Frequency219 – 230 GHz Spatial res.~ 0.68” x ~ 0.55” FoV~ 27” Proj. baseline16 – 400 m Velocity res.0.3 – 0.66 km/s Integ. time4.2h (2.0h on source) System temp.60 -180 K (0.8mm water vapor) ALMA SV band 6

13. Results (ALMA SV band 6) 12 CO(2-1) 13 CO(2-1) C 18 O(2-1) 0th1st2nd Akiyama et al. submitted

14. Results (ALMA SV band 6) 12 CO(2-1) 13 CO(2-1) C 18 O(2-1) 0th1st2nd Akiyama et al. submitted Vlsr [km s-1]Flux Density [Jy] 12CO(2-1)13CO(2-1)C18O(2-1)

15. Successful Example of SS Model 1 Akiyama et al. submitted CO (2-1) 13 CO (2-1)C 18 O (2-1) PL SS 700

16. Successful Example of SS Model 2 r out = 700AU, p=1.0, θ=45° T 100 [K] Σ 100 [gm s -1 ] 12 CO(J =3-2) 13 CO(J =3-2) 12 CO(J =1-0) 13 CO(J =1-0) 0.001 12 CO(J =3-2) 13 CO(J =1-0) 13 CO(J =3-2) 40 30 20 10 0 0 0.15 0.3 12 CO(J =1-0) 1.5 3 0 -10 0 10 20 30 Tmb [K] 3 1.5 0 -1.5 Tmb [K] 40 -0.15 0 0.15 0.3 20 15 10 5 0 -5 20 15 10 5 0 -5 -10 0 2 4 6 8 10 12 Vlsr [km s-1]

17. Summary 1.MWC 480 was selected for its simple disk structure. 2.Similarity solution model is based on the viscous evolution. → Surface density tapers off gradually with distance. 3.Similarity solution reproduces the observation ・ Verified by NRO45/ASTE (single dish) and ALMA SV (interferometry) and data. ・ Similarity solution model is more suitable than power law for describing disks. → The disk evolves via viscous diffusion