Latest Draping Talk

8/14/2019 Latest Draping Talk

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Jonathan Dursi, CITAChristoph Pfrommer, CITACITA|ICAT

Bubble-Wrap

For Bullets:The Draping ofMagnetic Fields

in GalaxyClusters


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on arXiv: arxiv.org/abs/0711.0213arxiv.org/abs/0706.3216

Paper with interactive 3D graphics:http://www.cita.utoronto.ca/~ljdursi/draping/
http://www.cita.utoronto.ca/~ljdursi/drapinghttp://www.cita.utoronto.ca/~ljdursi/draping


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Abel 1689Credit: NASA, N. Benitez (JHU), T.

Broadhurst (The Hebrew

University), H. Ford (JHU), M.Clampin(STScI), G. Hartig (STScI),

G. Illingworth (UCO/Lick

Observatory), the ACS Science

Team and ESA

Clusters: Thousands of galaxies within a radius of 1-10 Mpc


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Abel 2029

When X-ray satellites started to go up over the past couple of decades, we got a much diferentpicture of these galaxy clusters; the volume was filled with very hot (10-100 Million K; 1-10 keV),tenuous plasma that emitted in the X-rays -- and whats more, this wispy gas actually comprisesmore of the normal matter in these galaxy clusters than the galaxies themselves! This gas is awonderful laboratory for interesting fluid and plasma dynamics.


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Virgo:R. White (UA; optical), S. Snowden, R. Mushotzky (NASA/GSFC; X-ray)

ArchesNASA/CXC/Northwestern/F.Zadeh et al.

Hydra ANASA/CXC/SAO

http://chandra.harvard.edu/photo/1999/0087/

But the very fact that we can see this gas poses a puzzle. The gas is radiating in the Xrays at a ratethat should cause catastrophic cooling. As the central regions cool and fall inwards, outer regionsshould move inwards, become denser, and start cooling faster; this gas should have collapsedaway billions of years ago, vastly changing the makeup of the galaxies at the centre of the cluster.What is keeping it hot?
http://chandra.harvard.edu/photo/1999/0087/http://chandra.harvard.edu/photo/1999/0087/


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Bubbles inGalaxy Clusters

Radio Bubbles (radii 6-20 kpc),

seen as voids in X-rays

Thought to be inflated by high-energy jets from active centralgalaxies

Seen to have very sharpinterfaces

Conduction should dissipatethese in ~108 years

NASA/IoA/A.Fabian et al.

A related puzzle is the presence of bubbles in the cluster gas. These bubbles are thought to befilled with extremely hot plasma fed by jets -- jets launched by the supermassive black holes in thecentre of the central galaxy. So they represent a very plausible

(Image: The Perseus Cluster: thousands of galaxies, 100Mpc away. At core is the giant cannibal galaxy Perseus A (NGC 1275), accretingmatter as gas and galaxiest. Representing low, medium, and high energy x-rays as red, green, and blue colours respectively, this Chandra X-rayObservatory image shows remarkable details of x-ray emission from this monster galaxy and surrounding hot (30-70 million degrees C) clustergas. The bright central source is the supermassive black hole at the core of Perseus A itself. Dark circular voids just above and below the galaxycenter, each about half the size of our own Milky Way Galaxy, are believed to be magnetic bubbles of energetic particles blown by the accretingblack hole. Settling toward Perseus A, the cluster's x-ray hot gas piles up forming bright regions around the bubble rims.)


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Perseus:

A. Fabian (IoA Cambridge) et al., NASAhttp://apod.nasa.gov/apod/ap001031.html

This is the `skull picture, showing the same cluster at a somewhat more provocative angle andcolor, but it also shows that such bubbles persist for quite some distance through the interclustermedium
http://apod.nasa.gov/apod/ap001031.htmlhttp://apod.nasa.gov/apod/ap001031.html


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Cluster Bubbles

Bubbles existence at adistance from inflation pointis a puzzle

Purely hydrodynamic bubble

will rip itself to a smoke ringin one crossing time

Robinson, Dursi et al (2004)

Put bubble rise here


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Mergers of

Galaxy ClustersMinor mergers involve smallercluster falling into more massiveones

M. Bruggen, Bremen

Where an infalling smaller core or galaxy looses its identity by completely blending in with theenvironment has consequences for profiles of enrichment, populations...


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This is a poster of a huge cosmological simulation run by a team largely at the MPA in Germany ,the `Millenium Run. The history of these clusters is of a constant stream of mergers with infallingobjects, some quite small, some quite large. The final makeup of the cluster will depend on howthe mergers proceed.


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Applications toGalaxy Clusters:

MergersMinor mergers involve smallercluster falling into more massiveones

Stripping of small-mass ICMWhen/where does this occur?

Consequences forenrichment, ...

M. Bruggen, Bremen



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This is a still from the movie that was looping. It shows the basic idea of the draping of amagnetic field; the moving object sweeps up the field lines that it encounters, building up aconsiderable energy density; field lines can also slide around the object if they are far enough awayfrom the stagnation line. The build up of pressure at the head pushes more field lines aside, sothat there is a natural steady state that is reached. (Save more explanation for going over the movie

again.)


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Draping ofSolar wind field

around EarthHappens very quickly (figure toright -- 600 s)

Can induce magnetic field in

even a neutral atmosphereEarth Magnetic Field reversals

may not be catastrophic to lifeBirk et al (2004)

This isnt a new idea, and has been known (and observed) for many decades in solar-system circles.Comets and planets moving through solar field & wind undergo this phenomenon, and it has beenmeasured by satellites both directly and indirectly.This is a recent work showing what would happen to an unmagnetized Earth...


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Draping ofSaturns Field

over TitanObservable with CassiniEmission from draped field

Observed: `Magnetic Pile-UpBoundary, eg Bertucci et al2005, Neubauer et al 2006 S. A. Ledvina, UC Berkeley

Other bodies moving through other fields have similar dynamics; this is a figure showing a cartoonof Titan moving through the field around Saturn, and the resulting radiative processes that canindicate the strengthened, curved magnetic field. These processes are in principle observable withCassini


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Comets in Solar

WindDraping occurs and can distortvelocity, magnetic fields in windover significant distances

Wegman (2002)

Comets are another example of objects which may substantially distort an ambient magnetic fieldas well; recent work by Wegmen and others have shown that draping can measurably modify theinterplanetary magnetic field and velocity structure of the solar wind over significant distances.


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Applications to

Galaxy Clusters:Bubbles

Radio Bubbles (radii 6-20 kpc),seen as voids in X-rays, are seento have very sharp interfaces

Conduction should dissipatethese in ~108 years

Could bubble motions sweepup enough field to suppressconduction?

Xray/optical/radio; bubbles correspond to under-emission in radio.


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Applications toGalaxy Clusters:

MergersDoes magnetic field drapingsignificantly effect the dynamicsof infalling material?

Does it strongly effect stripping?

M. Bruggen, Bremen



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Previous Work:

Lyutikov 2004Analytics

Particularly along stagnation line

B

=1

1R30

r3

B

0; l

1

M2AR

Previous application to galaxy clusters -- fairly recent.


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Asai et al

(2004,5,6..)Numerics2d, 3d

`Kitchen sink - turbulentmagnetic field, conduction,...

Can draping effect conduction?Yes

Asai et al (2004...)

On the other extreme is work done in the `kitchen sink model, putting everything conceivable intoa simulation and looking to answer one question -- whether the magnetic field built up by drapingcan efect conduction. Can certainly answer that question under realistic conditions, but hard togain much insight into the process in this mode.


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Our Contributions

Linear theory analysis - can the thin layer doanything interesting?

3D, AMR numerical experiments of drapingof uniform magnetic fields - like what?

More careful analytic calculation in potential

flow approximation to compare tosimulations, understand dynamics - how?

Weve tried to really sink our teeth into this fairly simple problem so that we can really understand itand its properties, and then can slowly work our way up to including `kitchen sink physics. Weredoing that by using both simple numerical experiments and analytics to get as deep into theproblem as we can.


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Does it matter?

Can such a thin layer haveinteresting dynamic

effects?

Linear theory analysis

Three layers; velocity+/- U, magnetized layerof some thickness/

strength

R l i h T l K l i H l h lt


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0.02 0.05 0.1 0.2 0.5 1 2

l

1

1.5

2

3

5

7

10

kvA2

gstable

0.02 0.05 0.1 0.2 0.5 1 2

l

1

1.5

2

3

5

7

10

vA2U2

stable

Rayleigh-Taylor Kelvin-Helmholtz

If VA is a few times relevant velocity, can stabilize againstwavelengths an order of magnitude longer than thickness of layer

layer thickness layer thickness

stable

(AlfvnS

peed/GravSpeed)2

(AlfvnSpeed/ShearSpeed)2

stable


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VA = 0.2 U VA = 1.25 U

U

U

Run with v3.0 of the Athena code


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0.00 0.05 0.10 0.15

B

0.0

0.2

0.4

0.6

0.8

GrowthRate

Excellent agreement between theory and simulation!


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3D Simulations

using FLASHAMR very useful for focusingresolution in near draped layer

Large dynamic range between

size of traversed region andthickness of layer

Magnetic dynamics relativelystraightforward

These types of problems are sort of the poster children for adaptive mesh refinement, where highresolution can be applied only at the interesting layer, where the magnetic field is being built up,and in the turbulent wake of the moving projectile. AMR is especially important for 3Dsimulations, where the computational cost would be too high otherwise. We used the FLASH codefor these simulations...

Important to emphasize that 3d simulations are necessary


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FLASH MHD

Compressible

Ideal MHD: Locally neutral

Nonrelativistic

No (explicit)

magnetic diffusion,viscosity, thermal

diffusion

No displacement current


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FLASH MHD

`8 wave Godunov-type

scheme

2nd order accurate

Does not exactlymaintain

Uses diffusion to ensure

monopoles remain small

Mostly a problem forshocks

AMR, sharp interfaces

more important for this

problem than high order

accuracy

B = 0


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Sometimes,2D justisnt enough...


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-0.5 0.0 0.5

15

16

17

18

-0.5 0.0 0.5

15

16

17

18

-0.5 0.0 0.5

15

16

17

18

Magnetic Energy Density in 2D

Not only slingshots the bullet backwards, but squishes it, too...


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Foreshadowed

earlierAsai et al 2004, 2005 saw stronggrowth of magnetic field in 2d,but only commented on it

Simulation was not run longenough to see that there is nosteady state

2D

3DAsai et al (2005)


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3d simulations of a massive `bullet moving into a magnetized region of uniform field over thescales of interest. Bullet has a smooth density profile, and it moves into a region where a magneticfield is `turned on . Magnetic field initially


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vx vy vz


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!x

of kinematic solution

-2 0 2

26

28

30

32

34

36

38!

yof kinematic solution

-2 0 2

26

28

30

32

34

36

38!

zof kinematic solution

-2 0 2

26

28

30

32

34

36

38

!x

around draped projectile

-2 0 2

26

28

30

32

34

36

38!

yaround draped projectile

-2 0 2

26

28

30

32

34

36

38!

zaround draped projectile

-2 0 2

26

28

30

32

34

36

38

!x

/ u

-0.07 -0.03 0.00 0.03 0.07

!y

/ u

-0.4 -0.2 0.0 0.2 0.4

!z

/ u

-1.0 -0.7 -0.3 0.1 0.4

Potential

flowaroundsolid

sphere

3D AMR

results

y


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Analytic MHD

approachFlow ahead of projectile agreesquite well

Gives hope that potential flowcan tell us something about the

magnetic structureKinematic -- flow advects,stretches B, no back-reaction

v B

= 0

B = 0


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ro = 14.0088 r = 1.19687 pow = 3.00000

0 1 2 3 4B

13

14

15

16

17

y

Agreement with potential flow

zposi

tion

z

Magnetic field strength

y x

B

=

11

R30

r3

B

0

; l 1

M2A

R

Bx, By, Bz in `draping planeBx of kinematic MHD solution

38By of kinematic MHD solution

38Bz of kinematic MHD solution

38


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Potential

flow aroundsolid sphere

3d AMR

results

-2 0 2

26

28

30

32

34

36

-2 0 2

26

28

30

32

34

36

-2 0 2

26

28

30

32

34

36

Bx


-2 0 2

26

28

30

32

34

36

38B

y


-2 0 2

26

28

30

32

34

36

38B

z


-2 0 2

26

28

30

32

34

36

38

Bx /B0

-0.2 -0.1 0.0 0.1 0.2

By /B0

-0.2 0.7 1.6 2.5 3.4

Bz /B0

-2.1 -1.1 0.0 1.1 2.1

Bx, By, Bz in perpendicular planeBx of kinematic MHD solution

38By of kinematic MHD solution

38Bz of kinematic MHD solution

38


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Potential

flow aroundsolid sphere

3d AMR

results

-4 -2 0 2 4

26

28

30

32

34

36

-4 -2 0 2 4

26

28

30

32

34

36

-4 -2 0 2 4

26

28

30

32

34

36

Bx


-4 -2 0 2 4

26

28

30

32

34

36

38B

y


-4 -2 0 2 4

26

28

30

32

34

36

38B

z


-4 -2 0 2 4

26

28

30

32

34

36

38

Bx /B0

-0.3 -0.2 0.0 0.2 0.3

By /B0

-0.2 0.7 1.6 2.5 3.4

Bz /B0

-0.4 -0.1 0.2 0.5 0.8

PB

around draped core6

!"2 around draped core

6!"

2+ P

Baround draped core

6

MagneticPressure

RamPressure

TotalPressure


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-2 0 2

24

26

28

30

32

34

36

-2 0 2

24

26

28

30

32

34

36

-2 0 2

24

26

28

30

32

34

36

PB around draped core

-4 -2 0 2 4

24

26

28

30

32

34

36

!"2 around draped core

-4 -2 0 2 4

24

26

28

30

32

34

36

!"2

+ PB around draped core

-4 -2 0 2 4

24

26

28

30

32

34

36

0.00

0.03

0.05

0.08

0.10

!"

2+PB,planew

ithx=0

0.00

0.04

0.08

0.11

0.15

!"

2+PB,planewithy=0

DrapingPlane

PerpendicularPlane


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Magnetic FieldStrength in

Draped LayerField has to build not only toback react, but to redirect flow

To first order, depends only on

ram pressureMaximum magnetic fieldstrength ~ 2 x ram pressure

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Mean Ram Pressure

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Max.

MagneticPre

ssureonStagnationLine

Magnetic pressure = 2 x ram pressure

Data

Best fit ~ 2.2x ram pressure


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MagneticTension Force

of Cap Bent field lines - magnetic

tension

Field strength in cap greaterthan ram pressure seen byprojectile

Tension is dynamicallyimportant, even in 3D case

B2

4R

4u2

R

Tension force:


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DecelerationDue ToTension

Can be seen as projectilemoves into magnetized region

Hydrodynamic drag significantlyless

Scaling same as viscous drag

Magnitude can be measured

0 10 20 30 40 50 60 70

Time

0.22

0.23

0.24

0.25

ProjectileVelocity

Projectile in magnetized region


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DecelerationDue ToTension

Magnetic layer is strong enough(and curved enough) that itdominates deceleration

~ 4x stronger than viscous/turbulent drag for high Re

~ 3x stronger in thesesomewhat viscous (Re ~ 200)

simulations

0 0.0002 0.0004 0.0006 0.0008 0.001

3/8 x Ram Pressure / (core dens x R)

0

0.0005

0.001

0.0015

0.002

MeasuredDecelleration

1.87 x (3/8 (Ram Pressure)/(core dens x R))

Data


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Opening Angleof Drape

Comparison with 9 3Dsimulations

Correlation a little rattier thanother quantities --

Largest scales in simulations,some effects of BoundaryConditions

0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1

1.2

tan!

Opening angle ~ vA/U


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Many simulations, varying several parameters; here we vary only the velocity of the `bullet.



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Generation ofVorticity

Magnetic contact layer inducesvorticity in fluid elements whichcross it

Operates primarily in planealong field lines

Much less vorticity generationin other plane


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Long-termBehaviour

Evolution of core after it hasswept past roughly its ownmass

Mixed material `fills up drape

Highly constrained in otherplane!

Y li N M ti Fi ld X li N M ti Fi ld


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Long-termBehaviour




Y slice: No Magnetic Field

-3 -2 -1 0 1 2 3

16

17

18

19

20

X slice: No Magnetic Field

-3 -2 -1 0 1 2

16

17

18

19

20

Y slice: Beta=100

-2 -1 0 1 2

16

17

18

19

20

X slice: Beta=100

-2 -1 0 1 2

16

17

18

19

20

1 0 13 4 25 9 38 3 50 7 63 2 75 6

Conclusions


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Conclusions

Very quickly drape strong magnetized layer Even thin layer can have interesting effects

protecting object against indignities ofshearing into environment

Drape can slow down core by ~4x overhydro drag

Geometry gives probe of ambient field

Future work


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Future work

Direct visibility of draped layer?

Supersonic case

Underdense Bubble Turbulent field (what is smallest scale on

which a field gets draped?)

Other applications

Irresponsible Speculation:


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p pContaining Miras Tail?

NASA Galex

Y slice: No Magnetic Field X slice: No Magnetic Field


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Long-termBehaviour




-3 -2 -1 0 1 2 3

16

17

18

19

20

-3 -2 -1 0 1 2

16

17

18

19

20

Y slice: Beta=100

-2 -1 0 1 2

16

17

18

19

20

X slice: Beta=100

-2 -1 0 1 2

16

17

18

19

20

1 0 13 4 25 9 38 3 50 7 63 2 75 6


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on arXiv: arxiv.org/abs/0711.0213arxiv.org/abs/0706.3216

Paper with interactive 3D graphics:http://www.cita.utoronto.ca/~ljdursi/draping/

FLASH MHD Eqns
http://www.cita.utoronto.ca/~ljdursi/drapinghttp://www.cita.utoronto.ca/~ljdursi/draping


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FLASH MHD Eqns

Powell et al. 1999

Properly symmetrized; 8-waves


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Active Galaxiesto the rescue?

Central galaxies frequently veryactive.

Massive black holes in thecentre form engines for

extremely strong jets.Can this be heating the gas?

Documents

Latest Draping Talk