Magneto-hydrodynamic turbulence: from the ISM to discs Axel Brandenburg (Nordita, Copenhagen)...

Magneto-hydrodynamic Magneto-hydrodynamic turbulence: from the ISM to discsturbulence: from the ISM to discs

Axel BrandenburgAxel Brandenburg (Nordita, Copenhagen) (Nordita, Copenhagen)Collaborators:Collaborators:

Nils Erland HaugenNils Erland Haugen (Univ. Trondheim) (Univ. Trondheim)

Wolfgang DoblerWolfgang Dobler (Freiburg (Freiburg Calgary) Calgary)

Tarek YousefTarek Yousef (Univ. Trondheim) (Univ. Trondheim)

Antony MeeAntony Mee (Univ. Newcastle) (Univ. Newcastle)

Brandenburg: MHD turbulence 2

Sources of turbulenceSources of turbulence

• Gravitational and thermal energy– Turbulence mediated by instabilities

• convection

• MRI (magneto-rotational, Balbus-Hawley)

• Explicit driving by SN explosions– localized thermal (perhaps kinetic) sources


Conversion between different energy formsConversion between different energy forms

Thermal energy

Magnetic energy

Kinetic energy

Potential energy

u

BJu

/2J

22 S

pu

Examples:thermal convectionmagnetic buoyancymagnetorotational inst.


Galactic discs: supernova-driven turbulence

Microgauss fields: Korpi et al (1999, ApJ)221

02 2/ uB


Huge range of length scalesHuge range of length scales

• Driving mechanism:– SN explosions– parsec scale

• Dissipation scale– 108 cm (interstellar scintillation)

• What is the scale of B-field

• Linear theory: smallest scale!Korpi et al. (1999), Sarson et al. (2003)Korpi et al. (1999), Sarson et al. (2003)

no dynamo here…


Important questionsImportant questions• Is there a dynamo? (Or is resolution too poor?)• Is the turbulent B-field a small scale feature?• How important is compressibility?

– Does the turbulence become “acoustic” (ie potential)?

• PPM, hyperviscosity, shock viscosity, etc– Can they screw things up?

• Bottleneck effect (real or artifact?)

• Does the actual Prandtl number matter?– We are never able to do the real thing

Fundamental questions more idealized simulations


11stst problem: small scale dynamo problem: small scale dynamo• According to linear theory, field would be

regenerated at the resistive scale

Schekochihin et al (2003)Schekochihin et al (2003)

(Kazantsev 1968)


Forced turbulence: B-field Forced turbulence: B-field dynamo-generateddynamo-generated

magnetic peak: resistive scale?magnetic peak: resistive scale?

Maron & Cowley (2001)Maron & Cowley (2001)

Kin. spectrum

Magn.spectrum


Peaked at resistive scale!?Peaked at resistive scale!?(nonhelical case)


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 currently 10243


Kazantsev spectrum (kinematic)Kazantsev spectrum (kinematic)

Kazantsev spectrum Kazantsev spectrum confirmed (even for confirmed (even for =1) =1)

Spectrum remains highly Spectrum remains highly time-dependenttime-dependent

Opposite limit, no scale separation, forcing at kf=1-2


256 processor run at 1024256 processor run at 102433

1st Result: not peaked at resistive scale -- Kolmogov scaling!

Haugen et al. (2003, A

pJ 597, L141)

-3/2slope?


22ndnd problem: deviations from Kolmogorov? problem: deviations from Kolmogorov?

Porter, Pouquet, & Woodward (1998) using PPM, 10243 meshpoints

Kaneda et al. (2003) on the Earth simulator, 40963 meshpoints

(dashed: Pencil-Code with 10243 )

compensated spectrum


Bottleneck effect: Bottleneck effect: 1D vs 3D spectra1D vs 3D spectra

Why did wind tunnels not show this?


Relation to ‘laboratory’ 1D spectraRelation to ‘laboratory’ 1D spectra2222

3 )(4)( kuku kdkE kD yxkyxkE zzD d d ),,(2)(

2

1 u

kkkkkkkzk

z d )(4d ),(42

0

2

uu

kk

E

zk

D d 3

0zk

222zkkk

Dobler et al. (2003, P

RE

026304)


Third-order hyperviscosityThird-order hyperviscosity

Different resolution: bottleneck & inertial range

SS12)(

nn

Traceless rate of strain tensor

uuF 431631

visc 1n

3rd order dynamical hyperviscosity 3 22

32 S

Hyperviscous heat


Comparison: hyper vs normalComparison: hyper vs normal

onset of bottleneck at same position

height of bottleneck increased

2nd Result: inertial range unaffected by artificial diffusion

Hau

gen

& B

rand

enbu

rg (

PR

E, a

stro

-ph/

0402

301)


33rdrd Problem: compressibility? Problem: compressibility?

Direct simulation, =5 Direct and shock-capturing simulations, =1

Shocks sweep up all the field: dynamo harder?

-- or artifact of shock diffusion?

Bimodal behavior!


Potential flow subdominantPotential flow subdominant

Potential component more important,but remains subdominant

Shock-capturing viscosity:affects only small scales

ψ u


Flow outside shocks unchangedFlow outside shocks unchanged

Localized shocks: exceed color scale Outside shocks: smooth


Dynamos and Mach numberDynamos and Mach number

No signs of shocks in B-fieldor J-field (shown here)

advection dominates


33rdrd Result: dynamo unaffected Result: dynamo unaffectedby compressibility and shocksby compressibility and shocks

• Depends on Rm of vortical flow component

• Bimodal: Rm=35 (w/o shocks), 70 (w/ shocks)

Important overall conclusion:simulations hardly in asymptotic regime

• a need to reconsider earlier lo-res simulations: here discs


MRI: Local disc simulationsMRI: Local disc simulationsDynamo makes its own turbulence (no longer forced!)

Hyperviscosity 1283


Simulations with stratificationSimulations with stratification

cyclic B-fieldalpha-Omega dynamo?negative alpha

326431


High resolution direct simulationHigh resolution direct simulation

5123 resolution

singular!

2563 (direct, new) 323 (hyper, old)

26

Disc viscosity: mostly outside discDisc viscosity: mostly outside disc

Brandenburg et al. (1996)

const turb ss cHc HczHc ss )(turb z-dependence of

27

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


Magnetic “contamination” on larger scalesMagnetic “contamination” on larger scales

• Outflow with dynamo field (not imposed)

• Disc wind: Poynting flux

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


Unsteady outflowUnsteady outflow

transport from disc into the wind

BN/KL region in Orion:Greenhill et al (1998)vo

n R

ekow

ski e

t al.

(200

3, A

&A

398

, 825

)

Disc: mean field model

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)


Surprises from current researchSurprises from current research• B-field follows Kolmogorov scaling• Takes lots of resolution: bottleneck, diff-range• Dynamo basically ignores shocks

• Cosmic ray and thermal diffusion along B-lines• Self-consistent disc winds (proper radiation)• Partially ionized YSO discs• Dynamos at low : do they still work??

Future directionsFuture directions


Examples of such surprises: Examples of such surprises: small magnetic Prandtl numberssmall magnetic Prandtl numbers

definitiondefinitionRRmm==uurmsrms/(/(kkff))

Is there SS dynamo actionIs there SS dynamo actionbelow below PPmm=0.125?=0.125?

Haugen, Brandenburg, Dobler PRE (in press)

Comparion w/ hyper

Magneto-hydrodynamic turbulence: from the ISM to discs Axel Brandenburg (Nordita, Copenhagen)...

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