1. Helical MagnetoRotational Instability 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 Research supported by DOE and by NSF grant AST-0205903

2. Goodman: Helical MRI and Jets CMSO Gen. Mtg., 5-7 Oct. 2005 axisymmetric axial background field free energy from differential rotation basically ideal mode: V A ~V rot L -1 real growth rates, i.e. non- oscillatory fast: Re(s) ~ V rot /r axisymmetric axial plus toroidal bkgd. field –potential field (J 0 =0) free energy from differential rotation persists in the resistive limit: L -1 >> V A,V rot complex growth rates, i.e. growth with oscillation slow: Re(s) << Basic MRIHelical MRI

3. 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) Basic MRI Helical MRI instability at slower rotation… …and weaker field

4. 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?

5. Goodman: Helical MRI and Jets CMSO Gen. Mtg., 5-7 Oct. 2005 S, Rm 0 : Inertial Oscillations k + Magnetic field decouples + Circulation v dS is conserved, 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

6. Goodman: Helical MRI and Jets CMSO Gen. Mtg., 5-7 Oct. 2005 Large resistivity (0 < S, Rm << 1) inertial oscillation resistive diffusion excitation if k z B B z > 0 damping At least in WKB, net excitation occurs at Rm<<1 only if This is a quadratic form in k z B z & r -1 B cos …which excludes the Keplerian case,.

7. Goodman: Helical MRI and Jets CMSO Gen. Mtg., 5-7 Oct. 2005 Full local dispersion relation

8. 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 (r 1 = 5 cm, r 2 = 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 I z > 3.2 kAmp Mode may not grow at all without periodic vertical boundaries (TBD) ! –V phase of growing mode opposes background axial momentum flux F z = - B B z /

9. 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 /B z ~ 2k z r ~ 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,...

10. 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 B B z 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

11. 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 n e ~ 10 3 cm -3 n H ~ 10 4 cm -3 T ~ 1 eV B ~ 100 G M87 jet L ~ 10 4 lt-yr V ~ c ( max > 6) optical synchrotron AGN radio jets V ~ c ( jet ~ few) L~10 4 -10 6 lt-yr n e ~ 10 -3 cm -3, n p ~ ? e ~ few 10 3 B ~ 100 G synchrotron emission

12. 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 (?)

13. 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).