The Streaming Instability in the Dead Zone of a Protoplanetary Disk

Chao-Chin Yang (���) Department of Physics and Astronomy

University of Nevada, Las VegasMordecai-Mark Mac Low (AMNH), Anders Johansen (Lund)

ApJ, to be submitted

The Streaming Instability in the Dead Zone of a Protoplanetary Disk

Chao-Chin Yang (���) Department of Physics and Astronomy

University of Nevada, Las VegasMordecai-Mark Mac Low (AMNH), Anders Johansen (Lund)

ApJ, to be submitted

Driving the formation of planetesimals by

Disk Magnetohydrodynamics & Turbulence

Arm

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Disk Magnetohydrodynamics & Turbulence

Arm

itage

(201

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16)

Dead zone is UNDEAD, still turbulent!!

Disk Magnetohydrodynamics & Turbulence• Dominant forcing on

• Large objects: stochastic gravity

• Small particles: drag • Dividing size ~ 100 m

(Oishi, Mac Low, Menou 2007; Nelson & Gressel 2010)

• In either case, random walks and diffusion in phase space result.

Yang, Mac Low, & Menou (2009)

Carballido, Fromang, & Papaloizou (2006)

Stochastic Gravitational Forcing on Large Objects

e0 > 0e0 = 0

Yang, Mac Low, & Menou (2009, 2012)

Moving on to pebbles in MHD turbulence…

Arm

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(201

1)Ba

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16)

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

αSS(z)

Dead zone 32H−1

Dead zone 16H−1

Ideal MHD 16H−1

Sedimentation of Small Particles in Turbulence

⌧s = 0.1

Yang, Mac Low, & Johansen, in prep.

⌫t = ↵SScsHg<latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit>

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

αSS(z)

Dead zone 32H−1

Dead zone 16H−1

Ideal MHD 16H−1

Sedimentation of Small Particles in Turbulence

⌧s = 0.1

Yang, Mac Low, & Johansen, in prep.

⌫t = ↵SScsHg<latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit>

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0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

αSS(z)

Dead zone 32H−1

Dead zone 16H−1

Ideal MHD 16H−1

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

⟨ρgu2⟩ z/ρ

0c2 s

Dead zone 32H−1

Dead zone 16H−1

Ideal MHD 16H−1

Sedimentation of Small Particles in Turbulence

⌧s = 0.1

Yang, Mac Low, & Johansen, in prep.

⌫t = ↵SScsHg<latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">AAACCXicdVBNS8NAEN34WetX1KOX1SJ4CklraXsQil56rNTYQlPCZrttl242YXcjlNCzF/+KFw8qXv0H3vw3btoKKvpg4PHeDDPzgphRqWz7w1haXlldW89t5De3tnd2zb39GxklAhMXRywSnQBJwignrqKKkU4sCAoDRtrB+DLz27dESBrxazWJSS9EQ04HFCOlJd888njiK3gOPcTiEfK9EKmRCNNWa4p9CRv+0DcLtuUUK5WyA22rVqtVyqU5sUtV6Fj2DAWwQNM3371+hJOQcIUZkrLr2LHqpUgoihmZ5r1EkhjhMRqSrqYchUT20tkrU3iilT4cREIXV3Cmfp9IUSjlJAx0Z3ap/O1l4l9eN1GDai+lPE4U4Xi+aJAwqCKY5QL7VBCs2EQThAXVt0I8QgJhpdPL6xC+PoX/E7do1Szn6qxQv1ikkQOH4BicAgdUQB00QBO4AIM78ACewLNxbzwaL8brvHXJWMwcgB8w3j4Bhk2aZg==</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit>

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Hg6=

r↵SS

⌧s + ↵SS<latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">AAACOnicdVBNT9tAEF2HtkCgJcCRy6pRJSQky+ZDSW4ILhz5aEqkOLLGm3Wyynrt7I6RIsv/iwt/glsvvXAAxJUfwOajUlvRJ+3q6b0ZzcyLMikMet5Pp7L04eOn5ZXV6tr65y8btc2tHybNNeNtlspUdyIwXArF2yhQ8k6mOSSR5NfR6HTqX99wbUSqvuMk470EBkrEggFaKaxdBrEGVpyFWWm/QUkDxcfVwIw1FnMrAJkNIQwSwKFOiqursiwChDw0dI++Y5Zhre65/n6jceRTz221Wo2jgznxDprUd70Z6mSB87B2H/RTlidcIZNgTNf3MuwVoFEwyctqkBueARvBgHctVZBw0ytmt5f0m1X6NE61fQrpTP2zo4DEmEkS2crpkuZfbyq+53VzjJu9QqgsR67YfFCcS4opnQZJ+0JzhnJiCTAt7K6UDcEmhjbuqg3h96X0/6S977Zc/+KwfnyySGOF7JCvZJf4pEGOyRk5J23CyC35RR7Jk3PnPDjPzsu8tOIserbJX3Be3wBc8LBi</latexit><latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">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</latexit><latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">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</latexit><latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">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</latexit>

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

αSS(z)

Dead zone 32H−1

Dead zone 16H−1

Ideal MHD 16H−1

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

⟨ρgu2⟩ z/ρ

0c2 s

Dead zone 32H−1

Dead zone 16H−1

Ideal MHD 16H−1

Sedimentation of Small Particles in Turbulence

The α accretion (shear stress) is not equivalent to vertical mixing of solids.

⌧s = 0.1

Yang, Mac Low, & Johansen, in prep.

⌫t = ↵SScsHg<latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit>

Hp

Hg6=

r↵SS

⌧s + ↵SS<latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">AAACOnicdVBNT9tAEF2HtkCgJcCRy6pRJSQky+ZDSW4ILhz5aEqkOLLGm3Wyynrt7I6RIsv/iwt/glsvvXAAxJUfwOajUlvRJ+3q6b0ZzcyLMikMet5Pp7L04eOn5ZXV6tr65y8btc2tHybNNeNtlspUdyIwXArF2yhQ8k6mOSSR5NfR6HTqX99wbUSqvuMk470EBkrEggFaKaxdBrEGVpyFWWm/QUkDxcfVwIw1FnMrAJkNIQwSwKFOiqursiwChDw0dI++Y5Zhre65/n6jceRTz221Wo2jgznxDprUd70Z6mSB87B2H/RTlidcIZNgTNf3MuwVoFEwyctqkBueARvBgHctVZBw0ytmt5f0m1X6NE61fQrpTP2zo4DEmEkS2crpkuZfbyq+53VzjJu9QqgsR67YfFCcS4opnQZJ+0JzhnJiCTAt7K6UDcEmhjbuqg3h96X0/6S977Zc/+KwfnyySGOF7JCvZJf4pEGOyRk5J23CyC35RR7Jk3PnPDjPzsu8tOIserbJX3Be3wBc8LBi</latexit><latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">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</latexit><latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">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</latexit><latexit sha1_base64="2N/tdtv1ET0f/4haJ6KQRHR3KqQ=">AAACOnicdVBNT9tAEF2HtkCgJcCRy6pRJSQky+ZDSW4ILhz5aEqkOLLGm3Wyynrt7I6RIsv/iwt/glsvvXAAxJUfwOajUlvRJ+3q6b0ZzcyLMikMet5Pp7L04eOn5ZXV6tr65y8btc2tHybNNeNtlspUdyIwXArF2yhQ8k6mOSSR5NfR6HTqX99wbUSqvuMk470EBkrEggFaKaxdBrEGVpyFWWm/QUkDxcfVwIw1FnMrAJkNIQwSwKFOiqursiwChDw0dI++Y5Zhre65/n6jceRTz221Wo2jgznxDprUd70Z6mSB87B2H/RTlidcIZNgTNf3MuwVoFEwyctqkBueARvBgHctVZBw0ytmt5f0m1X6NE61fQrpTP2zo4DEmEkS2crpkuZfbyq+53VzjJu9QqgsR67YfFCcS4opnQZJ+0JzhnJiCTAt7K6UDcEmhjbuqg3h96X0/6S977Zc/+KwfnyySGOF7JCvZJf4pEGOyRk5J23CyC35RR7Jk3PnPDjPzsu8tOIserbJX3Be3wBc8LBi</latexit>

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

Sedimentation of Small Particles in Turbulence

⌧s = 0.1

Yang, Mac Low, & Johansen, in prep.

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

αg,i(z)=

Dg,i(z)/c sH

g

αg,x

αg,y

αg,z

Ideal MHD 16H−1g

Dead zone 16H−1g

Dead zone 32H−1g

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

g

Ideal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

Sedimentation of Small Particles in Turbulence

⌧s = 0.1

Yang, Mac Low, & Johansen, in prep.

−4 −2 0 2 4z/Hg

10−4

10−3

10−2

10−1

100

αg,i(z)=

Dg,i(z)/c sH

g

αg,x

αg,y

αg,z

Ideal MHD 16H−1g

Dead zone 16H−1g

Dead zone 32H−1g

Hp

Hg'

r↵g,z

⌧s + ↵g,z<latexit sha1_base64="fMGsZzmF8SBdV4cDZcwWLup0SBs=">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</latexit><latexit sha1_base64="fMGsZzmF8SBdV4cDZcwWLup0SBs=">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</latexit><latexit sha1_base64="fMGsZzmF8SBdV4cDZcwWLup0SBs=">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</latexit><latexit sha1_base64="fMGsZzmF8SBdV4cDZcwWLup0SBs=">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</latexit>

How about disk-wind models?

Bai (2015)

Zhu et al. (2015)

⌧s,B = 0.07

⌧s,C = 0.7<latexit sha1_base64="kDujhcuYttpgmmqdD4q2txjd+2s=">AAACDnicdZDNSsNAFIUn/tb4F3XpZrBYXEhJRKguhNJuXFYwttCEMJlO2qGTSZiZCCX0Ddz4Km5cqLh17c63cdpGUbEXBg7fuZc794Qpo1LZ9oexsLi0vLJaWjPXNza3tq2d3RuZZAITFycsEZ0QScIoJ66iipFOKgiKQ0ba4bA58du3REia8Gs1Sokfoz6nEcVIaRRYFU+hLMjlcWMMKxfQrto1zzO/YLOAtcAqa2ta0JkryqCoVmC9e70EZzHhCjMkZdexU+XnSCiKGRmbXiZJivAQ9UlXS45iIv18es8YHmrSg1Ei9OMKTunPiRzFUo7iUHfGSA3kX28C//O6mYrO/JzyNFOE49miKGNQJXASDuxRQbBiIy0QFlT/FeIBEggrHaGpQ5h/+7dwT6rnVefqtFxvFGmUwD44AEfAATVQB5egBVyAwR14AE/g2bg3Ho0X43XWumAUM3vgVxlvnyURmRw=</latexit><latexit sha1_base64="kDujhcuYttpgmmqdD4q2txjd+2s=">AAACDnicdZDNSsNAFIUn/tb4F3XpZrBYXEhJRKguhNJuXFYwttCEMJlO2qGTSZiZCCX0Ddz4Km5cqLh17c63cdpGUbEXBg7fuZc794Qpo1LZ9oexsLi0vLJaWjPXNza3tq2d3RuZZAITFycsEZ0QScIoJ66iipFOKgiKQ0ba4bA58du3REia8Gs1Sokfoz6nEcVIaRRYFU+hLMjlcWMMKxfQrto1zzO/YLOAtcAqa2ta0JkryqCoVmC9e70EZzHhCjMkZdexU+XnSCiKGRmbXiZJivAQ9UlXS45iIv18es8YHmrSg1Ei9OMKTunPiRzFUo7iUHfGSA3kX28C//O6mYrO/JzyNFOE49miKGNQJXASDuxRQbBiIy0QFlT/FeIBEggrHaGpQ5h/+7dwT6rnVefqtFxvFGmUwD44AEfAATVQB5egBVyAwR14AE/g2bg3Ho0X43XWumAUM3vgVxlvnyURmRw=</latexit><latexit sha1_base64="kDujhcuYttpgmmqdD4q2txjd+2s=">AAACDnicdZDNSsNAFIUn/tb4F3XpZrBYXEhJRKguhNJuXFYwttCEMJlO2qGTSZiZCCX0Ddz4Km5cqLh17c63cdpGUbEXBg7fuZc794Qpo1LZ9oexsLi0vLJaWjPXNza3tq2d3RuZZAITFycsEZ0QScIoJ66iipFOKgiKQ0ba4bA58du3REia8Gs1Sokfoz6nEcVIaRRYFU+hLMjlcWMMKxfQrto1zzO/YLOAtcAqa2ta0JkryqCoVmC9e70EZzHhCjMkZdexU+XnSCiKGRmbXiZJivAQ9UlXS45iIv18es8YHmrSg1Ei9OMKTunPiRzFUo7iUHfGSA3kX28C//O6mYrO/JzyNFOE49miKGNQJXASDuxRQbBiIy0QFlT/FeIBEggrHaGpQ5h/+7dwT6rnVefqtFxvFGmUwD44AEfAATVQB5egBVyAwR14AE/g2bg3Ho0X43XWumAUM3vgVxlvnyURmRw=</latexit><latexit sha1_base64="kDujhcuYttpgmmqdD4q2txjd+2s=">AAACDnicdZDNSsNAFIUn/tb4F3XpZrBYXEhJRKguhNJuXFYwttCEMJlO2qGTSZiZCCX0Ddz4Km5cqLh17c63cdpGUbEXBg7fuZc794Qpo1LZ9oexsLi0vLJaWjPXNza3tq2d3RuZZAITFycsEZ0QScIoJ66iipFOKgiKQ0ba4bA58du3REia8Gs1Sokfoz6nEcVIaRRYFU+hLMjlcWMMKxfQrto1zzO/YLOAtcAqa2ta0JkryqCoVmC9e70EZzHhCjMkZdexU+XnSCiKGRmbXiZJivAQ9UlXS45iIv18es8YHmrSg1Ei9OMKTunPiRzFUo7iUHfGSA3kX28C//O6mYrO/JzyNFOE49miKGNQJXASDuxRQbBiIy0QFlT/FeIBEggrHaGpQ5h/+7dwT6rnVefqtFxvFGmUwD44AEfAATVQB5egBVyAwR14AE/g2bg3Ho0X43XWumAUM3vgVxlvnyURmRw=</latexit>

The Streaming Instability (Youdin & Goodman 2005; Johansen & Youdin 2007)

!

R

StrongerWeakerHeadwind:

Radial drift:

Slower Faster

Drag force: Weaker Stronger

Radial Particle Concentration in Turbulence

⌧s = 0.1

Yang

, Mac

Low

, & J

ohan

sen,

in p

rep.

�2 0 2x/Hg

0

20

40

60

80

100

t/P

no back reaction

�2 0 2x/Hg

Z = 0.01

�2 0 2x/Hg

Z = 0.02

�2 0 2x/Hg

Z = 0.04

�2 0 2x/Hg

Z = 0.08

10�1

100

101

h⌃pi/

Z⌃

g,0

Particle Dynamics in Stratified Magneto-rotational Turbulence4Hg ⇥ 8Hg ⇥ 8Hg — 16 H�1

g — �0 = 104 — ⇧ = 0.05 — ⌧s = 0.1

Radial Particle Concentration in Turbulence

⌧s = 0.1

Yang

, Mac

Low

, & J

ohan

sen,

in p

rep.

�2 0 2x/Hg

0

20

40

60

80

100

t/P

no back reaction

�2 0 2x/Hg

Z = 0.01

�2 0 2x/Hg

Z = 0.02

�2 0 2x/Hg

Z = 0.04

�2 0 2x/Hg

Z = 0.08

10�1

100

101

h⌃pi/

Z⌃

g,0

Particle Dynamics in Stratified Magneto-rotational Turbulence4Hg ⇥ 8Hg ⇥ 8Hg — 16 H�1

g — �0 = 104 — ⇧ = 0.05 — ⌧s = 0.1

�2 0 2x/Hg

0

20

40

60

80

100

t/P

no back reaction

�2 0 2x/Hg

Z = 0.01

�2 0 2x/Hg

Z = 0.02

�2 0 2x/Hg

Z = 0.04

�2 0 2x/Hg

Z = 0.08

10�1

100

101

h⌃pi/

Z⌃

g,0

Particle Dynamics in Ohmic Dead Zone4Hg ⇥ 8Hg ⇥ 8Hg — 16 H�1

g — �0 = 104 — ReM = 1 — ⇧ = 0.05 — ⌧s = 0.1

Radial Particle Concentration in Turbulence

⌧s = 0.1

Yang

, Mac

Low

, & J

ohan

sen,

in p

rep.

�2 0 2x/Hg

0

20

40

60

80

100

t/P

no back reaction

�2 0 2x/Hg

Z = 0.01

�2 0 2x/Hg

Z = 0.02

�2 0 2x/Hg

Z = 0.04

�2 0 2x/Hg

Z = 0.08

10�1

100

101

h⌃pi/

Z⌃

g,0

Particle Dynamics in Stratified Magneto-rotational Turbulence4Hg ⇥ 8Hg ⇥ 8Hg — 16 H�1

g — �0 = 104 — ⇧ = 0.05 — ⌧s = 0.1

�2 0 2x/Hg

0

20

40

60

80

100

t/P

no back reaction

�2 0 2x/Hg

Z = 0.01

�2 0 2x/Hg

Z = 0.02

�2 0 2x/Hg

Z = 0.04

�2 0 2x/Hg

Z = 0.08

10�1

100

101

h⌃pi/

Z⌃

g,0

Particle Dynamics in Ohmic Dead Zone4Hg ⇥ 8Hg ⇥ 8Hg — 16 H�1

g — �0 = 104 — ReM = 1 — ⇧ = 0.05 — ⌧s = 0.1

�2 0 2x/Hg

0

20

40

60

80

100

t/P

no back reaction

�2 0 2x/Hg

Z = 0.01

�2 0 2x/Hg

Z = 0.02

�2 0 2x/Hg

Z = 0.04

10�1

100

101

h⌃pi/

Z⌃

g,0

Particle Dynamics in Ohmic Dead Zone4Hg ⇥ 8Hg ⇥ 8Hg — 32 H�1

g — �0 = 104 — ReM = 1 — ⇧ = 0.05 — ⌧s = 0.1

Critical solid abundance

Yang, Johansen, & Carrera (2017)

For laminar disks

For τs = 0.1 in MHD turbulence Z ≳ 2%

Hp(laminar) ≪ Hp(MHD)

0 20 40 60 80 100t/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Hp/H

gIdeal MHD 16H−1

Dead zone 16H−1

Dead zone 32H−1

Yang, Mac Low, & Johansen, in prep.

Laminar

Summary

• Shear stress vs. turbulent diffusion • Ideal MHD: αSS ~ αg,x ~ αg,y ~ αg,z • Dead zone: αSS < αg,x ~ αg,y < αg,z

• Conditions for strong concentration of solids • Not sensitive to sedimentation • Sensitive to solid abundance and radial

diffusion