Global Simulations of Astrophysical Jets in Poynting Flux Dominated Regime Hui Li S. Colgate, J....

Global Simulations of Astrophysical Jets in Poynting Flux

Dominated Regime

Hui Li

S. Colgate, J. Finn, G. Lapenta, S. Li

Engine; Injection; Collimation; Propagation; Stability; Lobe Formation; Dissipation; Magnetization of IGM

Leahy et al.1996

I. Engine and Injection

Approach: Global Configuration Evolution without modeling the accretion disk physics. Replace accretion disk with a “magnetic engine” which pumps flux (mostly toroidal) and energy.

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Flux fn. (cylin.) Ψ = r2 exp(−r2 − k 2z2)

B =

Br = 2k 2z r exp(−r2 − k 2z2)

Bz = 2(1− r2) exp(−r2 − k 2z2)

Bφ =f (Ψ)

r = α r exp(−r2 − k 2z2)

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

q(r) = krBzBφ

= 2k(1− r2)

α

Mimicking BH-Accretion System? : Initial poloidal fields on “disk”, exponential drop-offf() : B profile, or disk rotation profile : toroidal/poloidal flux ratioJxB : radial pinching and vertical expansionJpxBp: rotation in direction, carrying angular momentum?

=5

=0.1

=3

Li et al.’05

Problems:No disk dynamicsFootpoints allowed to move, though could be in equilibriumNot precisely KeplerianMass loading?Dipole or Quadrupole

Injection

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∂B

∂t= B(r,z) γ(t)

1) An initial state modeled as a magnetic spring (=3).2) Toroidal field is added as a function of time over a small central region:

3) Adding twists, self-consistently collimate and expand.

Impulsive Injection: Evolution of a highly wound and compressed magnetic “spring” Continuous Injection: Evolution of “magnetic tower” with continuous injected toroidal and/or poloidal fields

II. Collimation; Propagation

Run A: impulsive injection, =50 vinj >> vA > cs

Run B: continuous injection, =3, =3 vA > cs, scanning through (vinj)

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Run A

|B| at cross-section

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Run A

Total |B|

Current density

Run A Run A-2Kinetic KineticMagneti

cMagnetic

III. Stability and Lobe Formation

Dynamic: moving, q-profile changing

3D Kink unstable in part of helix: twist accumulation due to inertial/pressure confinement

Pressure profile: hollow

Velocity profile ?

radius

height

Pressure EvolutionIn Implusive

Injection Case

Azimuthally averaged

Poloidal Flux (n=0)

radius

height

3D Flux Conversion

Continuous Injection

radius

height

Azimuthally Averaged

Poloidal Flux

Run B: Continuous Injection

Injected toroidal flux vs time

Poloidal flux at disk surface

Z (height)

T=0

T=4 T=8 T=12

T=16

B flux

A Moving “Slinky”

T=0 T=3

T=5 T=10

pressure

height

HelixStability

radius

Lobe Formation

Continuous Injection

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∂B

∂t= Bφ(r,z) γ (t)

1) An initial state modeled as a magnetic spring (=3).2) Toroidal field is added as a function of time over a small central region:

3) Adding twists, self-consistently collimate and expand.

Time

B flux

Kink unstable

High Injection Rate

Kink unstable

Conclusion: Lessons Learned

Field lines must “lean” on external pressure, concentrating twists to the central region --- collimation.

a) Static limit:

Expansion is fast, reducing the toroidal field per unit height. Velocity difference between the base and the head causes the head to undergo 3D kink, forming a fat head --- lobes (?).

b) Impulsive injection limit:

c) Continuous injection: Non-uniform twist distribution along height. Map out the dependence on injection rates.

In all cases, external pressure plays an important “confining” role, helping collimation and stability.