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Helical M agneto R otational I nstability and Issues in Astrophysical JetsPowerPoint Presentation

Helical M agneto R otational I nstability and Issues in Astrophysical Jets

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### Helical MagnetoRotational Instability and Issues in Astrophysical Jets

Jeremy Goodman1,3

Hantao Ji 2,3

Wei Liu 2,3

CMSO General Meeting

5-7 October 2005

1Princeton University Observatory

2Princeton Plasma Physics Lab

3CMSO

Research supported by DOE and by NSF grant AST-0205903

axial background field

free energy from differential rotation

basically ideal mode: VA~Vrot L-1

real growth rates, i.e. non-oscillatory

fast: Re(s) ~ Ω Vrot/r

axisymmetric

axial plustoroidal bkgd. field

potential field (J0=0)

free energy from differential rotation

persists in the resistive limit: L-1 >> VA,Vrot

complex growth rates, i.e. growth with oscillation

slow: Re(s) << Ω

Basic MRI

Helical MRI

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Marginal Stability Helical MRI tolerates more dissipation

Hollerbach & Rüdiger, PRL 124501 (2005)

Rüdiger et al. Astron. Nachr.326 (6) 409 (2005)

instability at slower rotation…

Basic MRI

Helical MRI

…and weaker field

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Our questions

- What is the physical nature of helical MRI ?
- why does it extend to arbitrarily large resistivity ?

- Is helical MRI really easier to realize experimentally?
- are the growth rates large enough to be measured?
- are the required toroidal fields achievable?
- can the mode grow at all with finite vertical boundaries?

- What are the astrophysical implications ?
- can this mode operate in weakly ionized disks where “standard” MRI may not?
- are jets a more natural context?

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

S, Rm 0 : Inertial Oscillations

+ Magnetic field decouples

+ Circulation v • dSisconserved,

absent viscosity

+ Straight vortex lines minimize energy

- background vorticity = 2

= “epicyclic frequency” (≠ k)

+ Dispersion relation of transverse waves:

2 = (cos)2

- depends on direction not wavelength

k

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Large resistivity (0 < S, Rm << 1)

inertial

oscillation

excitation if

kzBBz> 0

damping

resistive

diffusion

This is a quadratic form in kzBz & r-1Bcos

At least in WKB,

net excitation occurs

at Rm<<1 only if

…which excludes the

Keplerian case, .

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Experimental issues

- Growth rates are rather small
- < 1 sec-1 in typical geometry (r1= 5 cm, r2= 10 cm, gallium)
- may do better in a smaller system!

- may be swamped by Ekman circulation, etc.

- < 1 sec-1 in typical geometry (r1= 5 cm, r2= 10 cm, gallium)
- Large axial currents are needed
- e.g. B> 128 G @ 5 cm Iz > 3.2 kAmp

- Mode may not grow at all without periodic vertical boundaries (TBD) !
- Vphase of growing mode opposes background axial momentum flux Fz= -BBz/

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Astrophysical relevance

- Persistence to low Rm is interesting
- protostellar disks, white-dwarf disks in quiescence,...

- But helical MRI may not operate in disks
- seems to require < 2() 0.828, yet keplerian =1
- need B/Bz~ 2kzr ~ 10r/h >> 1 (h=disk thickness)
- a definite sign of vertical phase velocity seems needed; not clear what happens when mode meets surface of disk

- More natural geometry for this mode is in a jet
- effectively infinite along axis
- but jets are already prone to several vigorous instabilities
- pinch, kink, Kelvin-Helmholtz, ...

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Summary of helical MRI (to date)

- Sets in at much lower Rm & S than conventional MRI
- Appears to be a hydrodynamic mode (inertial oscillation) destabilized by resistive MHD
- free energy from differential rotation, not currents

- Growth requires an axial phase velocity opposing background BBz momentum flux
- may prevent growth for finite/nonperiodic axes

- Experimental verification may be at least as hard as for conventional MRI
- Relevance to keplerian accretion disks is doubtful

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Astrophysical jets: a bestiary

Protostellar jet

L~ 10 light-year

V~ 300 km s-1

ne~ 103 cm-3

nH~ 104 cm-3

T ~ 1 eV

B ~ 100 G

M87 jet

L ~ 104 lt-yr

V ~ c (max> 6)

optical synchrotron

AGN radio jets

V ~ c (jet~ few)

L~104-106 lt-yr

ne ~ 10-3 cm-3, np~ ?

e~ few 103

B ~ 100 G

synchrotron emission

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Astrophysical Jets: Issues

- Acceleration
- probably by rotating star/disk/black hole, magnetically coupled to gas/plasma/Poynting flux

- Collimation
- probably toroidal fields + exterior pressure

- Dissipation & field amplification
- Kelvin-Helmholtz against ambient medium
- force-free MHD modes (pinch, kink)
- internal shocks
- needed for particle acceleration

- reconnection (?)

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

Jets: A bibliography

- Begelman, Blandford, & Rees, Rev. Mod. Phys. 56(2), 255 (1984). “Theory of Extragalactic Radio Sources”
- de Gouveia dal Pino, E. M., Adv. Sp. Res. 35(5), 908 (2005). “Astrophysical jets & outflows”
- De Young, D. S., The Physics of Extragalactic Radio Sources, Univ. Chicago Press (2002).
- Spruit, H.C., “Jets from Compact Objects” in Proc. IAU Symp. #195 (San Francisco: Pub. Astron. Soc. Pacific), p. 113 (2000).

Goodman:Helical MRI and Jets

CMSO Gen. Mtg., 5-7 Oct. 2005

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