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

qq

Lqq

)(tRayleigh quotient

with Boris Dintrans (Toulouse)

43

8

Comparison withComparison withinviscidinviscid simulations simulations

qq

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

16

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