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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
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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
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 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
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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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
around draped projectile
-2 0 2
26
28
30
32
34
36
38B
y
around draped projectile
-2 0 2
26
28
30
32
34
36
38B
z
around draped projectile
-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
around draped projectile
-4 -2 0 2 4
26
28
30
32
34
36
38B
y
around draped projectile
-4 -2 0 2 4
26
28
30
32
34
36
38B
z
around draped projectile
-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.
Opening angle ~ vA/U
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Opening angle ~ vA/U
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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
Evolution of core after it hasswept past roughly its ownmass
Mixed material `fills up drape
Highly constrained in otherplane!
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
Evolution of core after it hasswept past roughly its ownmass
Mixed material `fills up drape
Highly constrained in otherplane!
-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?