Growth and Transport Processes in Protoplanetary Disks

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1 Growth and Transport Processes in Protoplanetary Disks Til Birnstiel Harvard-Smithsonian Center for Astrophysics Transformational Science With ALMA: From Dust To Rocks To Planets Waikoloa Village, Hawaii

2 Introduction

3 Dusty Disks Rich in small dust grains Lifetimes of ~ 3 Myrs Evolving viscously

4 Dust Physics coagulation Vertical Evolution turbulent mixing, settling, dead zones, fragmentation & cratering &... Radial (& Azimuthal) Evolution particle drift, mixing, gas drag, meridional flows, turbulent concentration, pressure traps, photophoresis,... Dust Size Evolution sticking, bouncing, fragmentation, compaction, erosion, evaporation, condensation,...

5 Outline Transport Mechanisms Drag Forces Radial Drift Settling & Mixing Growth Mechanisms Impact Velocities Collisional Outcomes Global Dust Evolution Grain Sizes Dust Surface Densities Transition Disks more historical: Dominik, PP V, 2007

6 Transport Mechanisms

7 Drag Force stop v 9v mv F drag ; St stop orb» a s g 2 (Stokes number) St << 1 i.e. fric orb St ~ 1 i.e. fric ' orb St >> 1 i.e. fric orb e.g., Whipple (1972)

8 Drag Force stop v 9v mv F drag ; St stop orb» a s g 2 (Stokes number) St << 1 i.e. fric orb St ~ 1 i.e. fric ' orb St >> 1 i.e. fric orb e.g., Whipple (1972)

9 Drag Force stop v 9v mv F drag ; St stop orb» a s g 2 (Stokes number) St << 1 i.e. fric orb St ~ 1 i.e. fric ' orb St >> 1 i.e. fric orb e.g., Whipple (1972)

10 Drag Force stop v 9v mv F drag ; St stop orb» a s g 2 (Stokes number) St << 1 i.e. fric orb St ~ 1 i.e. fric ' orb St >> 1 i.e. fric orb e.g., Whipple (1972)

11 Vertical Settling Gravity Centrif.

12 Vertical Settling Drag Gravity Vertical Settling u z d z k St

13 Vertical Settling Turbulent Mixing t mix z2 D

14 Vertical Settling Vertical Settling Turbulent Mixing H dust c St H gas gas large dust small dust e.g., Dubrulle et al. (1995)

15 Radial Drift Dust:! towards Keplerian Gas:! sub-keplerian Result:!headwind Gravity v K Centrif. Angular Momentum Transfer from dust to gas Orbital Decay Gravity Centrif. Pressure e.g., Weidenschilling (1977) Nakagawa et al. (1986)

16 Radial Drift Drift towards pressure maximum u r 1 St ` St 1 c 2 s dlnp u k dlnr ~50 m/s inward!

17 Summary: Transport Dust is dragged along with gas... mixed by turbulence Dust drifts up the pressure gradient: sedimentation to mid-plane radial drift All depends on particle size!

18 Growth Mechanisms Velocities, Outcomes, Codes, & Size Evolution

Relative Velocities Radial Drift Vertical Settling Radial Drift Ve rtic al Settli ng 10 3 m/s 35 10 3 m/s 35 10 2 30 10 2 30 10 1 25 10 1 25 a[cm] 10 0 10 1 20 15 a[cm] 10 0 10 1 20 15 10 2 10 10 2

19 Relative Velocities Radial Drift Vertical Settling Radial Drift Ve rtic al Settli ng 10 3 m/s m/s a[cm] a[cm] grain size a[cm] Turbluent Motion a[cm] Turbulent Motion 10 3 m/s Azimuthal Azimuthal Drift m/s a[cm] a[cm] a[cm] grain size a[cm] Trend: impact velocity increases with grain size!

20 Movies courtesy of J. Blum and collaborators, see e.g. Blum & Wurm 2008, Güttler et al Collisional Outcomes Sticking Fragmentation Bouncing Mass Transfer

21 Numerical Challenges Large parameter space Dynamical Range Mass: orders of magnitude Particle Number: Collision times (0.1 year) vs. disk life time (3 x 10 6 years) already 0D models can take hours

22 Coagulation Coagulation mass distribution Gains Losses particle size Fragmentation

23 Monte Carlo Methods Examples: Gillespie 1975 Ormel et al. 2007,... Zsom et al. 2008,... Pros: Easy to code Easy to add properties: porosity, charges, velocity distribution,... Cons: low dynamic range, small mass fractions neglected slow for non-local simulations or high collisions frequency

Grid Based Methods Examples: @f(m) @t Z 1 = + 1 2 0 f(m 0 ) f(m m 0 ) Z 1 K(m 0,m m 0 ) dm 0 f(m 0 ) f(m) K(m, m 0 ) dm 0 0 + 1 ZZ 1 f(m 0 ) f(m

2005 Brauer et al. 2008,... Birnstiel et al. 2009,.

24 Grid Based Z 1 = f(m 0 ) f(m m 0 ) Z 1 K(m 0,m m 0 ) dm 0 f(m 0 ) f(m) K(m, m 0 ) dm ZZ 1 f(m 0 ) f(m 00 ) L(m 0,m 00 ) 2 0 Z 1 S(m, m 0,m 00 ) dm 0 dm 00 f(m 0 ) f(m) L(m, m 0 ) dm 0 0 Weidenschilling 1980,... Nakagawa et al Dullemond et al Brauer et al. 2008,... Birnstiel et al. 2009,... Okuzumi et al. 2009,... Pros: high dynamic range implicit integration possible fast for multi dimensional simulations Cons: porosity, charges, velocity distribution: only mean values diffusive method, problem with low number statistics

25 Bouncing Barrier Zsom et al. 2010

Fractal Growth 10 OKUZUM a m m cm 10 4 10 2 10 0 10 2 10 4 10 6 10 0 increasing t 5 AU Ρint m m g cm 3 10 2 10 4 10 6 E imp E roll 965 yr a Λ mfp t s 1 2046 yr 2256 yr t s t Η 2122 yr 10 10 10 5 10 0

26 Fractal Growth 10 OKUZUM a m m cm increasing t 5 AU Ρint m m g cm E imp E roll 965 yr a Λ mfp t s yr 2256 yr t s t Η 2122 yr weighted average mass m m g Fractal particles could break through the drift barrier Assumption: icy particles fragment 35 m/s & no significant compaction occurs Note: extremely low internal density Okuzumi et al. 2012

27 Growth Barriers mass distribution Brownian motion Bouncing Turbulent motion grain size [cm] grow» 1 e.g. Birnstiel et al. (2011)

28 Compact Growth take two grain sizes - calculate impact velocity - derive outcome Fragmentation Erosion Mass Transfer Bouncing Sticking Windmark, Birnstiel et al. 2012a

29 Compact Growth Surface density [g cm -2 ] grain mass [g] Windmark, Birnstiel et al. 2012b see also: Garaud et al., 2013

30 Summary: Growth Dust is sticking... fragmenting... bouncing... cratering... porous Several Barriers to Growth charging, bouncing, fragmentation,... most can be overcome!

31 Global Dust Evolution I. Grain Sizes and Surface Densities

32 Rules of Thumb Rule 1: the larger the grain,... a)... the larger its inward drift velocity b)... the larger the collision velocity Rule 2: grow» 1 Rule 3: particles drift to higher pressure

33 Dust Evolution in a Nutshell Rule 1: the larger the grain, the larger its inward drift velocity... the larger the turbulent collision velocity Grain size cm v Õ µm 1 AU 100 AU Distance from Star

34 Dust Evolution in a Nutshell Rule 2: lower dust-to-gas ratio = slower growth Grain size cm d/g = 0.01 µm 1 AU 100 AU Distance from Star

35 Dust Evolution in a Nutshell Rule 2: lower dust-to-gas ratio = slower growth Grain size cm d/g = 0.01 µm 1 AU 100 AU Distance from Star

36 Dust Evolution in a Nutshell Rule 2: lower dust-to-gas ratio = slower growth Grain size cm d/g = 0.01 µm 1 AU 100 AU Distance from Star

37 Dust Evolution in a Nutshell Rule 2: lower dust-to-gas ratio = slower growth Grain size cm d/g = 0.01 µm 1 AU 100 AU Distance from Star

38 Dust Evolution in a Nutshell Rule 2: lower dust-to-gas ratio = slower growth d/g = 0.01 Grain size cm d/g = d/g = µm 1 AU 100 AU Distance from Star

39 Size Barriers a frag» 0.06 g s u 2 f c 2 s a drift» dust Vk 2 s c 2 s 1 See talks on observations by Luca Ricci & Laura Pérez e.g., Birnstiel et al. 2012a

40 Just Grain Growth Turbulent Motion & Differential Motion Brownian Motion Growth

41 Just Grain Growth Growth time scale typicaly ~! -1 Growth is fastest in inner regions

42 Just Grain Growth

43 Grain Growth & Drift

44 Growth & Drift & Fragmentation

45 Surface Density Knowing aprq Calculate vprq 9M9 d prq rvprq9const. d prq

46 Surface Density From basic principles (Birnstiel et al. 2012): drift / q gas r 2 k / r 3 4 frag / t k v 2 frag / r 3 2 Note Not directly dependent on the (uncertain) drift rate, the relative importance is what counts!

47 Surface Density From basic principles (Birnstiel et al. 2012): drift / frag / r 3 4 r 3 2 outer or old disk inner disk: MMSN

48 Surface Density From basic principles (Birnstiel et al. 2012): drift / frag / r 3 4 r 3 2 outer or old disk inner disk: MMSN Weidenschilling 77, Hayashi 81: r -1.5 Chiang & Laughlin 13: r -1.6

49 Surface Density From basic principles (Birnstiel et al. 2012): drift / frag / r 3 4 r 3 2 outer or old disk inner disk: MMSN Andrews et al Weidenschilling 77, Hayashi 81: r -1.5 Chiang & Laughlin 13: r -1.6

50 Surface Density drift / q gas r 2 k / r 3 4 / / 3 Best Fit for Gas Theoretical Expectation Best Fit for Dust Birnstiel et al Andrews et al. 2012

51 Issue of Timescales drift» r» 1 v d St ˆH r 2 orbits Particles drift inward in a few 100 orbits! Possible Solution Pressure Bumps u r 1 St ` St 1 c 2 s dlnp u k dlnr See Talk by Luca Ricci e.g. Klahr & Henning 1997 Kretke & Lin 2007 Brauer

52 Global Dust Evolution II. Transition Disks

53 SED energy flux wave length in µm

54 SED energy flux wave length in µm

2011 Properties of Transition Disks Espaillat et al.

55 wide range of accretion rates * for mm-bright disks. See Andrews et al Properties of Transition Disks Espaillat et al SR 21, Brown et al not all TDs have a TD-like SED transition disk fraction*: > 1/3 obs. median hole size: 35 AU

56 Photoevaporation Owen et al see also Owen & Clarke 2012 " Talk:! B. Ercolano " Poster:" G. Rosotti

57 Grain Growth? Model Image Dust Model Model SED " = 10-5 grain size [cm] Observation R [AU] # [µm] Birnstiel, Andrews, Ercolano 2012 Brown et al. 2009

58 Planets & Instabilities Pinilla, Birnstiel et al Ataiee et al., arxiv: Gas surface density Gas surface density see also: Goldreich et al. H. Li et al., F. Masset et al., A. Crida et al., W. Lyra et al.,...

Planets & Instabilities trapping no trapping Ataiee et al., arxiv:1304.

59 Planets & Instabilities trapping no trapping Ataiee et al., arxiv: see also: H. Li et al., F. Masset et al., A. Crida et al., G. Lesur et al., W. Lyra et al.,...

60 Dust Filtration Pinilla, Birnstiel et al see also: Rice et al Zhu et al. 2012

61 Planets & Instabilities simulated CARMA image Pinilla, Birnstiel et al. 2012

62 Planets & Instabilities Williams & Cieza 2011 Pinilla, Birnstiel et al. 2012

63 Asymmetries Birnstiel et al Collaboration with Li & Li Talks: N. v. d. Marel" S. Wolf" " A. Isella S. Casassus" " F. Ménard" S. Maddison

64 Asymmetries Birnstiel et al Collaboration with Li & Li Talks: N. v. d. Marel" S. Wolf" " A. Isella S. Casassus" " F. Ménard" S. Maddison

65 Asymmetries Birnstiel et al Collaboration with Li & Li Talks: N. v. d. Marel" S. Wolf" " A. Isella S. Casassus" " F. Ménard" S. Maddison

Asymmetries Acknowledgements. We thank Ewine van Dishoeck, Simon Bruderer, Nienke Fig. 3. ALMA simulated images at 345 GHz with an observation time of 2 h. The total flux of the source is 0.

66 Asymmetries Acknowledgements. We thank Ewine van Dishoeck, Simon Bruderer, Nienke Fig. 3. ALMA simulated images at 345 GHz with an observation time of 2 h. The total flux of the source is 0.13 Jy and the contour lines are at 2, 4, 6, and 8 times the rms of 0.22 mjy. Birnstiel et al Fig. 4. Spectral index mm using simulated images at bands 7 and 9. The antenna configuration was chosen such that the angular resolution is similar for both bands ( , 22 AU at 140 pc). and resolve regions where the dust is trapped creating a strong azimuthal intensity variation. The spectral slope mm of the spectral energy distribution F / is directly related to the dust opacity index at these long wavelengths (e.g., Testi et al. 2003), and it is interpreted in terms of the grain size ( mm. 3 implies mm sized grains). With the simulated images in Fig. 3, we compute the mm map (Fig. 4), considering an antenna configuration that provides a wavelengths and also in lopsided banana-shaped structures in resolved (sub-)mm images. Finding the size range where the bifurcation between concentration and di usion happens would put constraints on the turbulence strength and the local gas density of the disk. van der Marel, Geo rey Mathews, Hui Li, and the referee for useful comments. References Alexander, R. D., & Armitage, P. J. 2007, MNRAS, 375, 500 Andrews, S. M., Wilner, D. J., Espaillat, C., et al. 2011, ApJ, 732, 42 Barge, P., & Sommeria, J. 1995, A&A, 295, L1 Birnstiel, T., Dullemond, C. P., & Brauer, F. 2010, A&A, 513, A79 Birnstiel, T., Klahr, H., & Ercolano, B. 2012, A&A, 539, A148 Blum, J., & Wurm, G. 2008, ARA&A, 46, 21 Brauer, F., Dullemond, C. P., Johansen, A., et al. 2007, A&A, 469, 1169 Brauer, F., Henning, T., & Dullemond, C. P. 2008, A&A, 487, L1 Brown, J. M., Blake, G. A., Qi, C., Dullemond, C. P., & Wilner, D. J. 2008, ApJ, 675, L109 Brown, J. M., Blake, G. A., Qi, C., et al. 2009, ApJ, 704, 496 Cuzzi, J. N., & Hogan, R. C. 2003, Icarus, 164, 127 Cuzzi, J. N., Hogan, R. C., & Shari, K. 2008, ApJ, 687, 1432 Dzyurkevich, N., Flock, M., Turner, N. J., Klahr, H., & Henning, T. 2010, A&A, 515, A70 Garaud, P. 2007, ApJ, 671, 2091 Goldreich, P., & Ward, W. R. 1973, ApJ, 183, 1051 Hughes, A. M., Andrews, S. M., Espaillat, C., et al. 2009, ApJ, 698, 131 Isella, A., Natta, A., Wilner, D., Carpenter, J. M., & Testi, L. 2010, ApJ, 725, 1735 Johansen, A., & Klahr, H. 2005, ApJ, 634, 1353 Johansen, A., Oishi, J. S., Low, M.-M. M., et al. 2007, Nature, 448, 1022 Johansen, A., Youdin, A., & Klahr, H. 2009, ApJ, 697, 1269 Klahr, H. H., & Henning, T. 1997, Icarus, 128, 213 Kretke, K. A., & Lin, D. N. C. 2007, ApJ, 664, L55 Talks: N. v. d. Marel" S. Wolf" " A. Isella L43 S. Casassus" " F. Ménard" S. Maddison Collaboration with Li & Li Lyra, W., Johansen, A., Klahr, H., & Piskunov, N. 2009, A&A, 493, 1125 Mayama, S., Hashimoto, J., Muto, T., et al. 2012, ApJ, 760, L26 Meheut, H., Keppens, R., Casse, F., & Benz, W. 2012, A&A, 542, A9 Nakagawa, Y., Sekiya, M., & Hayashi, C. 1986, Icarus, 67, 375 Natta, A., Testi, L., Neri, R., Shepherd, D. S., & Wilner, D. J. 2004, A&A, 416, 179 Okuzumi, S., Tanaka, H., Kobayashi, H., & Wada, K. 2012, ApJ, 752, 106 Piétu, V., Dutrey, A., Guilloteau, S., Chapillon, E., & Pety, J. 2006, A&A, 460, Pinilla, P., Benisty, M., & Birnstiel, T. 2012a, A&A, 545, A81 Pinilla, P., Birnstiel, T., Ricci, L., et al. 2012b, A&A, 538, A114 Regály, Z., Juhász, A., Sándor, Z., & Dullemond, C. P. 2012, MNRAS, 419, 1701 Ricci, L., Testi, L., Natta, A., & Brooks, K. J. 2010a, A&A, 521, A66 Ricci, L., Testi, L., Natta, A., et al. 2010b, A&A, 512, A15 Rice, W. K. M., Armitage, P. J., Wood, K., & Lodato, G. 2006, MNRAS, 373,

67 radial drift problem supported by some observations not supported by others L. Riccis Talk time scale problem? missing physics? analytical grain sizes a(r) Summary larger grains in the inner regions different physical cases: drift vs. fragmentation observationally testable L. Pérez Talk analytical surface densities $ dust (r) $ dust $ gas! inner regions: MMSN/MMEN outer regions: L. Pérez Talk Dust Filtration potentially explains features of transition disks Watch out for ALMA Thanks for your attention!

Astro2020 Science White Paper Dust growth and dust trapping in protoplanetary disks with the ngvla

Astro2020 Science White Paper Dust growth and dust trapping in protoplanetary disks with the ngvla Thematic Areas: Star and Planet Formation Principal Author: Name: Nienke van der Marel Institution: Herzberg