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Shule Li, Adam Frank, Eric Blackman

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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?

Introduction

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 where

the 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-shock

clump evolution. Some of them may lead to observational evidence of the magnetic field structure in

the interstellar medium.

Outline

1. Previous works on MHD shocked clump simulations

2. Description of the problem

3. Goals and methods of the current study

4. Table of Runs

5. Simulations of MHD clumps with external magnetic field

6. Simulations of MHD clumps with contained magnetic field

7. Discussion and conclusion

Problem Description

Meaningful Quantities

wind

Density Contrast:

Sonic Mach number:

ambient

clump

Alfvenic Mach number:

Magnetic Beta:

Clump crushing time:

Previous Results: Hydrodynamic Clumps

Previous Results: Clumps with a Uniform External Magnetic Field

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

No significant difference in terms of density evolution even for Î² = 1.

The criterion for the magnetic field removing K-H instabilities at the clump boundaries is: Î² < 1 along the boundary. The criterion for the magnetic field to stabilize R-T instabilities is roughly: Î² < Ï‡/M.

But there is no place that the

magnetic field becomes energetically dominant; that is, almost everywhere Î² >> 1.

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

Density log plot at 2Ï„cc (top) and 6Ï„cc (bottom). Left: Î² = 4. Right: Î² = 256.

Field line plot at 2Ï„cc (top) and 6Ï„cc (bottom). Left: Î² = 4. Right: Î² = 256.

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

Previous Results: Clumps with a Uniform External Magnetic Field

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 Î² = 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 Î² < 1 even for moderately strong initial field condition. This protects the clump from further disruption.

Density log plot at 2Ï„cc (top) and 6Ï„cc (bottom). Left: Î² = 4. Right: Î² = 256.

Field line plot at 2Ï„cc (top) and 6Ï„cc (bottom). Left: Î² = 4. Right: Î² = 256.

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

Previous Results: Clumps with External Magnetic Field and Radiative Cooling

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 different

cooling time. This fact divides the parameter

space 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 bounded

by 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: 3D Simulations on Shocked Clumps

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

3D density contour (left) and magnetic pressure (right) for

weak aligned field, perpendicular field, and oblique shock

cases, at 4Ï„cc.

3D density contour at various clump crushing time for

weak and strong aligned field.

Methodology

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.

A Panel of Image of the Day?

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

Simulation Parameters

Ambient Density

namb = 1 cc

-1

Ambient Temperature

Tamb = 10 K

4

Clump Density Contrast

Ï‡ = 100

Clump Radius

R = 150 AU

Shock Mach

M = 10

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

MHD clumps with Contained Magnetic Field

Case BCTA

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

MHD clumps with Contained Magnetic Field

Case BCPP

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

MHD clumps with Contained Magnetic Field

Case BCPA

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

MHD clumps with Contained Magnetic Field

50% Cut Movies

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

MHD clumps with Contained Magnetic Field

Special Case: Toroidal Combined with Poloidal

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

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

MHD clumps with Contained Magnetic Field

Discussion and Conclusion 1: Ordered Field

MHD clumps with Contained Magnetic Field

Discussion and Conclusion 1: Ordered Field

MHD clumps with Contained Magnetic Field

Discussion and Conclusion 1: Ordered Field

MHD clumps with Contained Magnetic Field

Discussion and Conclusion 1: Ordered Field

MHD clumps with Contained Magnetic Field

Case BRF1, BRF2

MHD clumps with Contained Magnetic Field

Case BRK1,BRK2

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

MHD clumps with Contained Magnetic Field

Magnetic Energy Line Plots: Ordered Field

MHD clumps with Contained Magnetic Field

Magnetic Energy Line Plots: Random Field

MHD clumps with Contained Magnetic Field

Kinetic and Thermal Energy Line Plots

MHD clumps with Contained Magnetic Field

Mixing Ratio Line Plots

MHD clumps with Contained Magnetic Field

Mixing Ratio Line Plots: Different Beta

MHD clumps with Contained Magnetic Field

Vorticity Line Plots

MHD clumps with Contained Magnetic Field

Power Spectrum Line Plots

MHD clumps with Contained Magnetic Field

Discussion and Quantitative Result

MHD clumps with Contained Magnetic Field

Conclusion 2: From Line Plots