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Magneto-rotational instabilityMagneto-rotational instability
Axel Brandenburg
(Nordita, Copenhagen)
2
Discs and disc viscosityDiscs and disc viscosity
• Magnetorotational instability (MRI)– how does it work?– simulations and experiments
• Vertical stratification and radiation– Heating near disc surface
• Star/disc coupling and outflows– Field lines open up, enhanced outflow
3
Alfven and slow magnetosonic wavesAlfven and slow magnetosonic waves
xyzy
xzx
yzxx
xzyx
bquBb
uBb
bBuqu
bBuu
'0
'0
'0
'0
2
2
02222 22A
2A
22A
24 qq
kvAA
Vertical field B0
Dispersion relation
Alfven frequency:
qrr )(
4
Alfven and slow magnetosonic wavesAlfven and slow magnetosonic waves
Alfven
slowmagnetosonic
qrr )(
5
March 23, 1965: Gemini 3March 23, 1965: Gemini 3
Gus Grissom & John Young: docking with Agena space craft
jiii Kr
GM
i
rrrr 3
6
Analogy with tidal disruption, etc.Analogy with tidal disruption, etc.
22K
22A 2 q
232 p
Space craft experiment
MRI (Balbus & Hawley 1991)
Tidal disruption of a star
7
Shearing sheet analysisShearing sheet analysis
yxx ktktk )( 23
0 linear analysis: variable wave number
Lqq
)(tRayleigh quotient
with Boris Dintrans (Toulouse)
43
8
Comparison withComparison withinviscidinviscid simulations simulations
Lqq
)(t
2/1qq
Only reliable till t<18
9
Shearing sheet simulationsShearing sheet simulationsDynamo makes its own turbulence
Hyperviscosity 1283
10
High resolution direct simulationHigh resolution direct simulation
5123 resolution
singular!
11
Simulations with stratificationSimulations with stratification
cyclic B-fieldalpha-Omega dynamo?negative alpha
12
Vertical stratificationVertical stratification
Brandenburg et al. (1996)
const turb ss cHc
HczHc ss )(turb z-dependence of
13
Heating near disc boundaryHeating near disc boundary
Turner (2004)
radp
radp
gasp
2
2...J
u
t
Tcv
022 / Bu
weak z-dependence of energy density
0/ BJ where
14
Dan Lathrop’s new MRI experimentDan Lathrop’s new MRI experiment
15
Dan Lathrop’s new MRI experimentDan Lathrop’s new MRI experiment
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Preliminary simulationsPreliminary simulations
1000 G(Ha=73)
2000 G(Ha=146)
500 G(Ha=37)
= 48 Hz (Ri2/ = 375)
17
Pencil CodePencil Code
• Started in Sept. 2001 with Wolfgang Dobler
• High order (6th order in space, 3rd order in time)
• Cache & memory efficient
• MPI, can run PacxMPI (across countries!)
• Maintained/developed by many people (CVS!)
• Automatic validation (over night or any time)
• Max resolution so far 10243
18
256 processor run at 1024256 processor run at 102433
19
Wallclock time versus processor #
20
CVS maintainedCVS maintained
• pserver (password protected)– Public (check-out only), private (ci/co, 20 people)
• Set of 12 test problems
• Nightly auto-test (different machines, web)
• Before check-in: run auto-test yourself
• Mpi and nompi dummy module for single processor machine (or use lam-mpi on laptops)
21
Pencil Code check insPencil Code check ins
22
Transfer equation & parTransfer equation & paraallelizationllelization
Analytic Solution:
Ray direction
Intrinsic Calculation
Processors
SII
d
d
23
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Communication
Processors
24
The Transfer Equation & The Transfer Equation & ParallelizationParallelization
Analytic Solution:
Ray direction
Processors
Intrinsic Calculation
25
Current implementationCurrent implementation
• Plasma composed of H and He
• Only hydrogen ionization
• Only H- opacity, calculated analytically
No need for look-up tables
• Ray directions determined by grid geometry
No interpolation is needed
26
Disc and outflow (YSOs)Disc and outflow (YSOs)
Disc temperature relative to halo is free parameter:Here about 3000K
Cooler disc: more vigorous evolution
von Rekowskii et al 2003 (A&A)
27
Unsteady outflowUnsteady outflow
transport from disc into the wind
BN/KL region in Orion:Greenhill et al (1998)
28
Application: magnetic Application: magnetic contamination of galaxy clustercontamination of galaxy cluster
10,000 galaxies for 1 Gyr, 1044 erg/s each
G182
tV
cMN
F
FB sw
kin
poyntrms
Similar figure also for outflows from protostellar disc
29
Further experiments: interaction with magnetosphereFurther experiments: interaction with magnetosphereAlternating fieldline uploading and downloadingAlternating fieldline uploading and downloading
Star connected with the disc Star disconnected from disc
Simil ar beh avior fo und b y G
oo dso n & W
ingl ee (19 99)vo
n R
ekow
skii
& B
rand
enbu
rg 2
004
(A&
A)
30
Similar behavior found by Goodson & WingleeSimilar behavior found by Goodson & Winglee
cf. field line opening: Uzdensky (2002), Pudritz & Matt (2004)
31
Open questionsOpen questions
• Radiation transfer with scattering
• where
• QPOs (vertical disc oscillation?)– In resonance with vert/rad epicycle freq?
• Viscous instability
BJS 1 /
0/ M