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Helical M agneto R otational I nstability and Issues in Astrophysical Jets. Jeremy Goodman 1,3 Hantao Ji 2,3 Wei Liu 2,3 CMSO General Meeting 5-7 October 2005 1 Princeton University Observatory 2 Princeton Plasma Physics Lab 3 CMSO.

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Helical m agneto r otational i nstability and issues in astrophysical jets

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


Helical m agneto r otational i nstability and issues in astrophysical jets

axisymmetric

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

inertial

oscillation

excitation if

kzBBz> 0

damping

resistive

diffusion

This is a quadratic form in kzBz & r-1Bcos

 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


Full local dispersion relation
Full local dispersion relation

Goodman:Helical MRI and Jets

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


Experimental issues
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.

  • 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= -BBz/

Goodman:Helical MRI and Jets

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


Astrophysical relevance
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
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 BBz 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
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
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
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