shule li, adam frank, eric blackman

Clumps With External Magnetic Fields, Their Interaction With Shocks, and the Effect of Magnetic Thermal Conduction

Shule Li, Adam Frank, Eric Blackman University of Rochester, Department of Physics and Astronomy. Rochester, New York 14627

A Panel of Simulation Images?

1. Previous works on MHD shocked clump simulations2. Description of the problem3. Goals and methods of the current study4. Table of Runs5. Simulations of MHD clumps with external magnetic field6. Simulations of MHD clumps with contained magnetic field7. Discussion and conclusion

Introduction

Outline

Problems involving magnetized clouds and clumps, especially their interaction with shocks are common in astrophysical environments and have been a topic of research in the past decade. The magnetic field structure, whether aligned with the shock or perpendicular to the shock, can have profound influence on the shocked behavior and evolution of the clump. Most previous numerical studies have focused on the scenario where the shocked clump is immersed in a uniform background. In this presentation we take one step further to assume a more realistic scenario wherethe clumps have the tangled magnetic field residing inside. These clumps can be formed when winds blowing through a magnetized clumpy background medium detach the medium along with the field lines. We will show that the contained magnetic field can have great influence on the post-shockclump evolution. Some of them may lead to observational evidence of the magnetic field structure inthe interstellar medium.

Sonic Mach number:

Density Contrast:

Alfvenic Mach number:

Magnetic Beta:

Clump crushing time:

clum p

am b

rc

r=

,

w ind

s am b

uM

c=

w indA

a

uM

v=

2,

2

2 s am b

a

c

vb

g=

1/ 2clum p

ccw ind

r

u

ct =

Meaningful Quantitieswind

ambientclump

Problem Description

Previous Results: Hydrodynamic Clumps

Density log plot at 2τcc (top) and 6τcc (bottom). Left: β = 4. Right: β = 256.

Field line plot at 2τcc (top) and 6τcc (bottom). Left: β = 4. Right: β = 256.

When the external field is parallel to the shock propagation direction:

No significant difference in terms of density evolution even for β = 1.

The criterion for the magnetic field removing K-H instabilities at the clump boundaries is: β < 1 along the boundary. The criterion for the magnetic field to stabilize R-T instabilities is roughly: β < χ/M.

But there is no place that themagnetic field becomes energetically dominant; that is, almost everywhere β >> 1.

Magnetic fields stretched over the top of the clump can have a significant stabilizing influence that improves the flow coherence.

Jones, T.W., Ryu, Dongsu, Tregillis, I.L. 1996 ApJ, 473, 365

Previous Results: Clumps with a Uniform External Magnetic Field

Density log plot at 2τcc (top) and 6τcc (bottom). Left: β = 4. Right: β = 256.

Field line plot at 2τcc (top) and 6τcc (bottom). Left: β = 4. Right: β = 256.

When the external field is perpendicular with the shock propagation direction:

The magnetic field is stretched and wrapped around the clump, which effectively confines the clump and prevents its fragmentation, even for moderately strong field β = 4. The clump embedded in the stretched field is compressed, but then, because of the strong confining effect of the field develops a streamlined profile and is not strongly eroded.

The magnetic pressure at the nose of the clump increases drastically, which acts as a shock absorber.

At later stage, the stretched field around the clump edge has β < 1 even for moderately strong initial field condition. This protects the clump from further disruption.

Jones, T.W., Ryu, Dongsu, Tregillis, I.L. 1996 ApJ, 473, 365

Previous Results: Clumps with a Uniform External Magnetic Field

With radiative cooling added to the simulation,people found that the shocked behavior of clumps can change drastically comparing to the addiabatic cases.

Bow shock and transmitted shock have differentcooling time. This fact divides the parameterspace into 4 different regimes.

Thin fragments which are dense and cold are developed after shock.

The boundary flows are streamlined when the bow shock cools efficiently.

Balk of cooled clump material tightly boundedby the bow shock is formed when transmitted shock cools efficiently.

The clump behavior depends heavily on actually cooling routine implemented in the simulation Code.

Fragile et al (2005 ApJ 619, 327)

Previous Results: Clumps with External Magnetic Field and Radiative Cooling

3D density contour at various clump crushing time for weak and strong aligned field.

3D density contour (left) and magnetic pressure (right) for weak aligned field, perpendicular field, and oblique shock cases, at 4τcc.

Min-Su Shin, James M. Stone, Gregory F. Snyder, 2008 ApJ, 680, 336

Previous Results: 3D Simulations on Shocked Clumps

Methodology

A Panel of Image of the Day?

AstroBEAR is a parallelized hydrodynamic/MHD simulation code suitable for a variety of astrophysical problems. Derived from the BearCLAW package written by Sorin Mitran, AstroBEAR is designed for 2D and 3D adaptive mesh refinement (AMR) simulations. The 2.0 version of the code shows good scaling in various tests up to 2000 processors. Users write their own project modules by specifying initial conditions and continual processes (such as an inflow condition). In addition, AstroBEAR comes with a number of multiphysical processes such as self gravity and thermal conduction, pre-built physical phenomena such as clumps and winds that can be loaded into a user module.

Methodology

MHD Equations

with

Radiative cooling is implemented via operator splitting, with several built-in cooling tables.In the presented simulations, we use Dalgano-Mcray cooling table.

Table of Runs

Field Strength(Magnetic β)

Field Structure Orientation(Relative to

Shock Direction)

Power Spectral index

BX1 0.5 External, Uniform

‖ -

BX2 8 External, Uniform

‖ -

BY1 0.5 External, Uniform

┴ -

BY2 8 External, Uniform

┴ -

BCTP 0.1 Contained, Toroidal Only

┴ -

BCTA 0.1 Contained, Toroidal Only

‖ -

BCPP 0.1 Contained, Poloidal Only

┴ -

BCPA 0.1 Contained, Poloidal Only

‖ -

BCRF1 0.1 Contained, Random

- 0

BCRF2 1 Contained, Random

- 0

BCRK1 0.1 Contained, Random

- -11/3

BCRK2 1 Contained, Random

- -11/3

Clump Density Contrastχ = 100

Ambient Densitynamb = 1 cc

Ambient TemperatureTamb = 10 K

Clump RadiusR = 150 AU

Shock Mach M = 10

Simulation Parameters

-1

4

MHD clumps with External Magnetic Field

http://www.pas.rochester.edu/~smurugan/


MHD clumps with Contained Magnetic Field

Case BCTP

http://www.pas.rochester.edu/~shuleli/HedlaMovie/torzvr.gif

http://www.pas.rochester.edu/~shuleli/HedlaMovie/torzvr.gif


Case BCTA

http://www.pas.rochester.edu/~shuleli/HedlaMovie/torxvr.gif

http://www.pas.rochester.edu/~shuleli/HedlaMovie/torxvr.gif


Case BCPP

http://www.pas.rochester.edu/~shuleli/HedlaMovie/polzvr.gif

http://www.pas.rochester.edu/~shuleli/HedlaMovie/polzvr.gif


Case BCPA

http://www.pas.rochester.edu/~shuleli/HedlaMovie/polxvr.gif

http://www.pas.rochester.edu/~shuleli/HedlaMovie/polxvr.gif


50% Cut Movies




Special Case: Toroidal Combined with Poloidal

http://www.pas.rochester.edu/~shuleli/HedlaMovie/tp1vr.gifhttp://www.pas.rochester.edu/~shuleli/HedlaMovie/tp2vr.gif

http://www.pas.rochester.edu/~shuleli/HedlaMovie/tp1vr.gif





Discussion and Conclusion 1: Ordered Field


Case BRF1, BRF2


Case BRK1,BRK2

http://www.pas.rochester.edu/~shuleli/HedlaMovie/kolsvr.gif




Magnetic Energy Line Plots: Ordered Field


Magnetic Energy Line Plots: Random Field


Kinetic and Thermal Energy Line Plots


Mixing Ratio Line Plots


Mixing Ratio Line Plots: Different Beta


Vorticity Line Plots


Power Spectrum Line Plots


Discussion and Quantitative Result


Conclusion 2: From Line Plots