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Magnetically-Dominated Jet and Accretion Flows. David L. Meier Jet Propulsion Laboratory California Institute of Technology.

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Magnetically dominated jet and accretion flows

Magnetically-Dominated Jet and Accretion Flows

David L. Meier

Jet Propulsion Laboratory

California Institute of Technology

Relativistic Jet Workshop University of Michigan, Ann Arbor, MI December 17, 2005


  • Helical Kink Instabilities in Propagating Poynting-Flux-Dominated Jets

    • Simulations of non-relativistic jets

  • Magnetically-Dominated Accretion Flows Around Black Holes (MDAFs)

    • Microquasars: GRS 1915+105 in the low/hard & high/soft states

    • GRBs in hyper-critical accretion

  • Space Interferometer Mission (SIM) Observations to determine the site of non-thermal optical emission

    • The SIM project

    • Color-dependent delay observations (near-imaging in the optical at 50 rS resolution)

Propagation of (non-Relativistic) Poynting-Flux-Dominated Jets: Development of Helical Kinks(Nakamura & Meier 2004)

3d simulations of pfd jets nakamura et al 2001 nakamura meier 2004
3D Simulations of PFD Jets Jets: (Nakamura et al. 2001; Nakamura & Meier 2004)

  • Models of PFD jets have been built (e.g.: Li et al. 1992; Lovelace et al. 2001; Li et al. 2002; Vlahakis & Konigl 2002, 2003), but no full numerical simulations have produced highly relativistic jets yet

  • We have performed 3-Dnon-relativisticsimulations that show current-driven instabilities

  • Most well-knownC-D instabilityis the m = 0 sausage pinch (in a uniform pressure medium)

Helical kink develops in field

Magnetic field rotated at base

Results of 3d numerical simulations of poynting flux dominated jets
Results of 3D Numerical Simulations of Jets: Poynting-Flux-Dominated Jets

  • Jet is morestable if density gradient is very steep ( z -3) and jet is mildly PFD (60%)

  • Jet is moreunstable to m = 1 helical kink if density gradient is shallow ( z -2) and jet is highly Poynting-flux dominated (90%)

Results continued
Results (continued) Jets:

  • The helical kink (m=1) or screw mode is, by far, the dominant unstable current-driven mode in a decreasing density atmosphere

  • The fastest growing longitudinal wavelengths are around two (2) jet diameters

  • All jets that we simulated (60-90% Poynting dominated) eventually became kink unstable

  • A greater relative amount of Poynting flux (twist) causes the kink to appear earlier in the flow (Kruskal-Shafranov criterion)

  • A steeper density gradient makes the jet more stable (cf. Hardee, this conference)

  • This CD instability isdriven by a Lorentz force imbalancein the nearly force-free jet; it can be partiallystabilized by plasma rotation

  • The large scale kinks saturate and do not become turbulent

  • The kinks advect with the overall jet propagation speed and plasma flows along the helical kinks

Magnetically-Dominated Accretion Flows (MDAFs): A First Attempt to Produced a Consistent Theory of Black Hole Accretion and Jet Production 1. Observations & Phenomenology2. Physics & Models for MDAFs

Power spectrum changes with accretion state in microquasars like 1915 105









ADAF/corona turbulence should extend all the way to ~1 kHz (few rG). Instead, the ADAF is cut off at low freq. and has a QPO at ~3 Hz


vjet ~ vesc(100 rG)

~ 0.14 c

Power Spectrum Changes with Accretion State In Microquasars Like 1915+105

Gives important clues to the magnetic field structure and how a jet may form




Cool Disk

“Cool” Disk (< 3keV)

Morgan et al. (1997)

What is an mdaf

Tomimatsu & Takahashi (2001); Uzdensky (2004)

Magnetically-dominated accretion flow (MDAF)

Closely related to a “black hole magnetosphere”

Laminar, NON-turbulent accretion flow along strong magnetic field lines

TheMRI is turned off in the MDAF region

But MDAFs can be > 10 times larger than magnetospheres discussed generally heretofore

What is an MDAF?

  • Best thought of as an “accretion disk magnetosphere”, with

    • Field lines stretching inward toward the black hole, channeling the inner accretion flow

    • Field lines stretching outward, creating an MHD wind/jet

    • All rotating at the inner disk Keplerian rate K(rin) = K(rtr)

  • An MDAF can potentially form in the inner portion of a standard disk, ADAF, or any reasonable accretion flow

What are the properties of mdafs


Trans. Flow



What are the Properties of MDAFs?

  • MDAF accretion flow solutions show a nearly-radial in-spiral

  • May break up into several “spokes” or channels (rotating hot spots or “hot tubes or filaments”)

  • Signature of a non-axisymmetric MDAF would be a QPO at the transition radius orbital /Alfvén frequency

    A = VA /2rtr = (GM/rtr3)1/2/2 = 3 Hz m1-1 [rtr/100rG]-3/2

  • In addition to closed magnetic field lines, MDAFs will have open ones as well, emanating from the inner edge of the ADAF

  • A geometrically thick accretion flow (e.g., ADAF) that turns into an MDAF (large scale magnetic field) will naturally load plasma onto the open field lines

  • This is a natural configuration for driving a steady jet at the inner ADAF escape speed (Meier 2001)

    • VjetVesc(rtr) = (2GM/rtr)1/2 = 0.14 c [rtr/100rG]-1/2

  • The velocity of this jet also should increase as the MDAF radius decreases, and will be relativistic for small MDAFs

Uchida et al. (1999);

Nakamura (2001)

Mdafs and the fender belloni gallo model


No Jet?

Highly-Beamed or Poynting Jet?

MDAFs and the Fender, Belloni, & Gallo Model


MDAF inside re-filling disk


  • Disk transitions to ADAF at ~1000 rA by

  • Evaporation (Esin et al. 1997; Meyer et al. 2000)

  • ADIOS (Begelman & Celoltti 2004)

  • ADAF truncated to MDAF at ~100 rG

X-ray flux

QPO freq.

What would cause an adaf to be cut off at 100 r g
What would cause an ADAF to be cut off at ~100 r G?

  • The ADAF solution assumes a 2-Temperature flow

    • Hot ions (TiTvirial 1012 K) support the thick flow

    • Electrons remain around 1010 K, radiating copiously

  • But, if this doesn’t happen, and the ADAF remains a 1-T flow (Ti = Te= T 1010 K), it will collapse when

    • Tvirial > Te 1010 K

    • Or r < GM/ RTe 100 rG

  • Relation to MRI simulations: This collapse

    • Would not have been seen in most simulations, as they have no thermal cooling to pgas <<GM / r

McKinney & Gammie (2004)

This “ADAF collapse” scenario can produce a dramatic change in the turbulent flow at just the radius where we see a cutoff in the 1915+105 power spectrum

Preliminary mhd simulations of relativistically cooled adafs meier fragile 2006
Preliminary MHD Simulations of Relativistically-Cooled “ADAFs” (Meier & Fragile 2006)

  • Very preliminary, coarse-res 3-D MRI simulations

  • Added relativistic cooling of electrons (and ions) by synchrotron and inverse-Compton emission

  • Disk becomes thinner and magnetic field increases inside 100 rg when MRI and cooling are important, as predicted


Torus only

w/ mag field only

w/ cooling only

w/ cooling & field


Analytic solutions for magnetized accretion

H “ADAFs”  r

T r –1

  • New accretion solution #1:Magnetic-Advection or “transitional flow” (  1)

    • Still turbulent, but now inflow time < largest eddy turnover time

    • Tangled field is advected inward and s t r e t c h e d:

      • Br r –1 H –1  r –5/2 ; B vr–1 H –1  r –1/2

    • Pressure scales as pgas  r –3/2 and T  r 0 (“ADAF collapse”)

    • The viscosity parameter INCREASES INWARD: = BrB/4 pgas(r –3/2) 1

    •  becomes unity rapidly; this shuts off the MRI turbulence

H r 3/2

T r 0

  • New accretion solution #2:Magnetically-Dominated Accretion Flow(MDAF;   1)

    • Strong magnetic field turns off the MRI

    • NOT turbulent; laminar inflowalong strong field lines

    • Standard laminar MHD requires Br r –1/2; B r ;   1

    • Equivalent to accreting black hole magnetosphere

H r -1/2

T r 1/2

Analytic Solutions for Magnetized Accretion


  • ADAFs are NOT magnetically advective

    • Very turbulent: largest eddy turnover time < inflow time

    • Magnetic field components scale similarly Br B r –5/4

    • Pressure scales as pgas  r –5/2 and T  r –1 (“ion pressure supported”)

    • So, the viscosity parameter goes as = BrB/4pgas = constant  0 (0.01 – 1.0)

    • y = 4 es kTe/mec2  1 is a good simple energy equation for Te

A Complete Theoretical Model for Accretion and Jets in the Plateau State (actual analytic accretion flow models)

“Disk” Height

BZ Split Monopole with accretion


  • Rigidly-rotating (MDAF) region

  •  F = K(Rtrans)

    B  B (R / R)

“Disk” Temperature

A complete theoretical model for accretion and jets in the plateau state artist s conception
A Complete Theoretical Model for Accretion and Jets in the Plateau State (artist’s conception)

JET: vjet (2GM/rtr)1/2

100 rSch





The key assertions of the theoretical mdaf model

X Plateau State (artist’s conception)

The Key Assertions of the Theoretical MDAF Model

  • The two-temperature, ion-pressure-supported torus model of the hard state may not be correct

  • The inner accretion flow may be an inwardly-directed, magnetic-pressure-supportedmagnetosphere instead

  • The steady jet is produced by the open field lines of this magnetosphere

  • While the MDAF model differs from the ADAF model only in the inner ~100 M, it explains the following microquasar features:

    • The power fluctuation spectrum (BW-limited noise; LF QPOs)

    • The presence of a slow jet in the low/hard/plateau state

    • Increase in jet speed in the intermediate states with decreasing disk radius

    • Increase in QPO frequency with decreasing disk radius

Quasar astrophysics using the space interferometer mission sim
Quasar Astrophysics Using The Space Interferometer Mission (SIM)

Ann E. Wehrle, Key Project Principal Investigator

Michelson Science Center, Caltech

Dayton Jones (JPL), Stephen Unwin (JPL), David Meier (JPL), B. Glenn Piner (Whittier College)

Narrow-angle resolution: 1 as

Wide-angle/grid resolution: 4 as

Goals of our project:

- Search for binary black holes

- Determine site of quasar non-thermal optical emission

- Study motion of optical jet components on as level

Pseudo imaging of the quasar central engine with micro arcsecond resolution
Pseudo-Imaging of the Quasar Central Engine With Micro-arcsecond Resolution


Non-thermal component

(corona/MDAF or jet?)

SIM can determine the physical separation between red and blue light to ~ 1 as ( =50 rS @ 1Gpc for 109 M)

jet,opt /   20

Big blue bump

(accretion disk)

log Sn



0.4 - 1.0 µm

log n

Summary and conclusions
Summary and Conclusions Micro-arcsecond Resolution

  • Jets accelerated by strong magnetic fields

    • Can be helically-kink unstable in the Poynting-Flux-Dominated regime

    • But, they do not disrupt in these simulaitons

  • MDAFs

    • Provide a natural synthesis of BH accretion, magnetosphere, and MHD jet-production theories to produce the beginnings a complete picture of accretion and jet-production in black hole systems

    • For microquasars they naturally explain

      • BW-limited noise, QPOs, & jets in the plateau state

      • Increase in jet speed and QPO frequency with spectral softening (a la Fender et al. model)

    • May be important in GRB engines, but only where neutrino cooling dominates advection

  • SIM will be able to

    • Help determine the nature of the “non-thermal” power-law optical-IR emission