1 / 13

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

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.

garvey
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

More Related