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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 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
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 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
Full local dispersion relation 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. • 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