1. Aug. 13, 2004 Science Greg Madejski, GLAST lunch, 26 Aug
Review of the paper by Semenov, Dyadechkin, and Punsly on “Simulations of jets driven by black hole rotation”
Aug. 13, 2004 Science
Greg Madejski, GLAST lunch, 26 Aug

2. Unified picture of AGN

3. Brian Punsly gave a talk at a workshop on “Relativistic plasma in magnetic field” at SLAC/KIPAC last week, exactly on the subject of the article, so I will show his slides and simulations * Basic idea here is that large-scale magnetic field tied to the accretion disk and/or the black hole extracts the rotational energy which is resupplied by the infall of material in the disk, or slowing-down of the spin of the black hole * Punsly considers the extraction of rotational energy of the black hole where the magnetic field lines are “tied” to material that is already in the free-fall onto the black hole, but experiences frame-dragging (described by Kerr spacetime) * This is similar to the Blandford - Payne model where the magnetic field threads the accretion disk or Blandford - Znajek model where the field threads the black hole

4. If the field lines are anchored to the disk/hole, as the disk / hole rotates, the field lines are swept back from the axis * As the fluid (plasma) element begins to move outward, the B field forces it to rotate faster and faster -> the fluid elements move along the magnetic field as “beads on the wire” * Outward acceleration continues until the fluid attains roughly Alfven speed valf (defined when ½ r (valf)2 = B2/8p where B is magnetic field, and r is the plasma density) * Net result is for the matter to carry away angular momentum – very attractive feature, since getting rid of angular momentum is a problem in accretion disks (hard to transport outward through the disk…)

5. Importantly, the outflow can carry large amount of energy and angular momentum with relatively little matter content – the energy is transported by Poynting flux (if energy transport were to be via particles, the Compton cooling by circum-nuclear photons would be prohibitive)
This all implies that the flow is relativistic -> consistent with data on jets in active galaxies
This scenario is somewhat similar to the scenario for generation and acceleration of particles that are responsible for radiation in pulsars as given in the classic paper by Goldreich and Julian
The assumption here is that the “force-free” approximation holds – charges are assumed to be sufficiently free to act as sources of the field
In all cases, the equations are quite difficult to solve analytically, especially that we don’t know enough about the boundary conditions (poloidal/toroidal magnetic fields/currents are “self-interacting”)

6. In the Punsly approach, the goal is to form computer situations that would be appropriate for jets in AGN
The magnetized plasma is represented by magnetic flux tubes, which here are essentially “strings” (as the “wires with beads” above)
They assume “perfect MHD” - plasma can short out any magnetic field, no dissipation, etc.
They start with a “straight” B field tube, passing just outside of the event horizon of a black hole, and let it evolve
As the flux tube, presumably moving with the accretion flow, drifts inwards, and spirals faster and faster, as the plasma approaches co-rotation with the event horizon (required by frame-dragging)
The resulting structure appears to evolve into a relativistic jet
The new aspect here is that the twisting of the magnetic field lines, and the extraction of rotational energy of the black hole occurs via frame-dragging, present in the Kerr geometry, applicable to a rotating black hole
The resulting simulations indicate that (1) the jet collimation is due to the rotation of the black hole, and is aligned with the rotation axis, and (2) large amount of power can be extracted from the rotation

7. Broad-band spectrum of blazar PKS 1127-145

8. Initial State Rapidly rotating black hole a » M
Accretion of MHD flux tubes (vertical)
Existing magnetosphere built up by long term accretion of similar flux tubes

9. Method
Concentrate calculation on a representative flux tube, to increase numerical efficiency
MHD in curved space is mathematically equivalent to a set of nonlinear strings
Christensson, M.; Hindmarsh, M.. Phys Rev, D60, – (1999)
Strings are thin flux tubes

10. Accretion of Vertical Flux
Polarimetry shows large scale ordered flux in nearby galaxies
Jones, T. J. AJ 120, (2000)
Newtonian simulations show flux accumulation near the horizon
Igumenshchev, I.V.; Narayan, R.; Abramowicz, M.A. ApJ 592, (2003)

11. Accumulation of Flux Near the Horizon

12. Frame Dragging In flat space-time, Wp > -c/rsinq  Wmin < 0
In ergosphere, Wmin > 0,
Wmin ® WH as r ® r+

13. Energy Extraction From Black Hole
Rotational energy extractible
Negative energy states in ergosphere
w < 0 if bf < - c(r2 –2Mr + a2)1/2sinq/(W gff),
m = u0 bf (gff)½

14. Snapshots of the Simulation

15. Generation of Global Torsional Stress
The ergospheric plasma gets dragged forward, azimuthally, relative to the distance portions of the flux tube, by the gravitational field
Back reaction of the field re-establishes the Larmor helical trajectories by torquing the plasma back onto the field lines with J x B forces
Ampere’s law, J creates Bf < 0 upstream of the current flow, the field is rotating so there is a Poynting flux created
The J x B back reaction forces torque the plasma onto w < 0 trajectories – the influx spins-down the black hole
Physics of Black Hole Gravitohydromagnetics
Punsly, B. Black Hole Gravitohydromagnetics Springer-Verlag :New York (2001)

16. Global Jet Structure
A bona-fide jet (a collimated, relativistic outflow of mass) emerges from the ergosphere, bulk flow Lorentz factor of 2.5 , at r ~ 50 GM/c2
The quasar jet can be considered as bundle of thin flux tubes similar to those in our simulations

17. Jet Power S ~ (WHF)2 = (aF/2Mr+)2 ~ (aF/M)2
B ~ 103 G – 2 x 104 G that equate to F ~ 1033 G-cm G-cm2.
S  1045 – 5 x 1047 ergs/sec ~
SMAX ~ accretion flow luminosity

18. Surface Area of Ergosphere

19. Connection to Observations of Quasars
A collimated jet is produced (based on radio observations)
A power source (the black hole) that is decoupled from the accretion flow properties to first order
broadband, radio to UV, observations indicate that a quasar can emit most of its energy in a jet without disrupting the radiative signatures of the accretion flow
The suppression of the EUV in radio loud quasars (HST observations)
The velocity of the jet is relativistic (VLBI data)
The maximum kinetic luminosity of the quasar jets (broadband radio and X-ray observations of radio lobes)

20. Magnetically Arrested Accretion
Flux can be enhanced near the horizon by magnetic stresses partially balancing gravity
Narayan, R.; Igumenshchev, I. V.; Abramowicz, M. A. PASJ 55, (2003)

21. Magnetically Arrested Accretion

22. Magnetospheric Pressure Function
The total pressure (gas plus magnetic) of magnetosphere needs to be specified in initial state of string simulation, P
For strong magnetic fields: P » ½ FmnFmn

23. P for Magnetically Arrested Accretion
Near horizon in perfect MHD
Fiducial Simple Pressure Distribution
P~ (r-r+)-2