the streaming instability in the dead zone of a ... · dead zone 16h−1 dead zone 32h−1 −4...
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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
itage
(201
1)Ba
i (20
16)
Disk Magnetohydrodynamics & Turbulence
Arm
itage
(201
1)Ba
i (20
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
itage
(201
1)Ba
i (20
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=">AAACCXicdVBNS8NAEN34WetX1KOX1SJ4CklraXsQil56rNTYQlPCZrttl242YXcjlNCzF/+KFw8qXv0H3vw3btoKKvpg4PHeDDPzgphRqWz7w1haXlldW89t5De3tnd2zb39GxklAhMXRywSnQBJwignrqKKkU4sCAoDRtrB+DLz27dESBrxazWJSS9EQ04HFCOlJd888njiK3gOPcTiEfK9EKmRCNNWa4p9CRv+0DcLtuUUK5WyA22rVqtVyqU5sUtV6Fj2DAWwQNM3371+hJOQcIUZkrLr2LHqpUgoihmZ5r1EkhjhMRqSrqYchUT20tkrU3iilT4cREIXV3Cmfp9IUSjlJAx0Z3ap/O1l4l9eN1GDai+lPE4U4Xi+aJAwqCKY5QL7VBCs2EQThAXVt0I8QgJhpdPL6xC+PoX/E7do1Szn6qxQv1ikkQOH4BicAgdUQB00QBO4AIM78ACewLNxbzwaL8brvHXJWMwcgB8w3j4Bhk2aZg==</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>
Hp
Hg6=
r↵SS
⌧s + ↵SS<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><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
⌧s = 0.1
Yang, Mac Low, & Johansen, in prep.
⌫t = ↵SScsHg<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><latexit sha1_base64="UYZ9fR1NzhZrM494sAZ0RBshLXM=">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</latexit>
Hp
Hg6=
r↵SS
⌧s + ↵SS<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><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=">AAACCXicdVBNS8NAEN34WetX1KOX1SJ4CklraXsQil56rNTYQlPCZrttl242YXcjlNCzF/+KFw8qXv0H3vw3btoKKvpg4PHeDDPzgphRqWz7w1haXlldW89t5De3tnd2zb39GxklAhMXRywSnQBJwignrqKKkU4sCAoDRtrB+DLz27dESBrxazWJSS9EQ04HFCOlJd888njiK3gOPcTiEfK9EKmRCNNWa4p9CRv+0DcLtuUUK5WyA22rVqtVyqU5sUtV6Fj2DAWwQNM3371+hJOQcIUZkrLr2LHqpUgoihmZ5r1EkhjhMRqSrqYchUT20tkrU3iilT4cREIXV3Cmfp9IUSjlJAx0Z3ap/O1l4l9eN1GDai+lPE4U4Xi+aJAwqCKY5QL7VBCs2EQThAXVt0I8QgJhpdPL6xC+PoX/E7do1Szn6qxQv1ikkQOH4BicAgdUQB00QBO4AIM78ACewLNxbzwaL8brvHXJWMwcgB8w3j4Bhk2aZg==</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=">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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><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
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
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