1) The document discusses gas sloshing in galaxy clusters, which occurs when cool core gas is uplifted from the gravitational potential minimum and forms a contact discontinuity with hotter, less dense gas. 2) Simulations of galaxy cluster mergers show that interactions with subclusters can cause gas sloshing by accelerating the gas and dark matter components differently. 3) Observations reveal spiral-shaped cold fronts in galaxy clusters that are evidence of gas sloshing. Magnetic fields may stabilize these fronts by being draped across the interfaces.

1. The Physics of Gas
Sloshing in Galaxy Clusters
M. Markevitch (NASA/GSFC), D. Lee (Chicago),
M. Ruszkowski (Michigan), J. Stone (Princeton),
M. Kunz (Princeton), G. Brunetti (INAF),
S. Giacintucci (UMD)
John ZuHone (NASA/GSFC)

2. Galaxy Clusters
• Fascinating objects!
• Galaxies: star formation,
supernovae, active galactic
nuclei
• Intracluster medium:
diffuse (n ~ 10-4
-10-1
cm-3
),
hot (T ~ 107
-108
K),
magnetized (B ~ 0.1-10 μG),
plasma emits X-rays
• Dark matter: collisionless
particles that interact only by
gravity comprise vast majority
of the mass in clusters

3. What is Gas Sloshing?
• The signature: cold fronts in
relaxed cool-core clusters
• Spiral-shaped discontinuities
in surface brightness and
projected temperature
• Most easily explained by the
“sloshing” of the cool core
gas in the dark matter
potential well
• Cold gas has been uplifted
from the gravitational
potential minimum and
formed a contact discontinuity
in pressure equilibrium with
the hotter, less dense gas
Markevitch &Vikhlinin 2007

4. Observations of Gas
Sloshing
X-Ray Surface Brightness
XMM-Newton observations of A496 (Simona Ghizzardi)
Temperature (keV)
Dupke + 2007
Chandra

5. Observations of Gas Sloshing
XMM-Newton observations of A496 (Simona Ghizzardi)

6. Why Study Sloshing?
• The cold fronts potentially tell us very
interesting things about the detailed physics
of the ICM
• Puts constraints on transport processes in
the plasma
• Driving turbulence which reaccelerates
relativistic particles to produce radio
emission

7. What Causes Sloshing?
• Interactions with small
subclusters (Asascibar &
Markevitch 2006)
• A passing subcluster accelerates
both the gas and dark matter
components of the cluster core,
but the gas component is
decelerated by ram pressure,
resulting in a separation
between the two
• As the ram pressure weakens,
the cold core gas falls back into
the DM core, but overshoots it
and begins to “slosh”

8. • Using the FLASH and Athena codes
• Magnetohydrodynamics, Dark Matter, Gravity (self-
gravity or rigid potentials)
• Cooling,Thermal Conduction,Viscosity
• Physical setup (see Ascasibar & Markevitch 2006)
• Large, cool-core cluster merging with small subcluster
• Varying mass ratio R and impact parameter b of
subcluster (some with gas, some without)
• Finest Grid Resolutions Δx ~ 1-5 kpc
Simulations: A Sloshing
Laboratory

9. Interaction with
a gasless
subcluster
R = 5
b = 500 kpc
Temperature (keV) slice with DM contours
ZuHone, Markevitch,
and Johnson 2010

10. Interaction
with a gas-
filled
subcluster
R = 20
b = 1000 kpc
Temperature (keV) slice with DM contours
ZuHone, Markevitch,
and Johnson 2010

11. • Large velocity shears exist across the cold front; the
fronts should be susceptible to the effects of the
Kelvin-Helmholtz instability
• Thermal conduction, if present, should smooth out
the temperature gradient
• What could stabilize the front surfaces against these
effects?
• Viscosity?
• Magnetic fields?
Why Are the Fronts
Stable?

12. The Importance of
Magnetic Fields
• Clusters are weakly
magnetized (B
2
/8π ≪ pth)
• But this magnetization is still
physically important:
• Possible suppression of
instabilities and gas mixing
• Restriction of transport
processes to the field
lines
• Synchrotron emission
from relativistic particles

15. ν ν
≈

16. Bagchi et al 2005
10 F. Govoni et al.: A search for diffuse radio emission in relaxed, cool-core galaxy clusters
Fig. 6. Left: total intensity radio contours of Ophiuchus at 1.4 GHz with a FWHM of 91.4′′
× 40.4′′
, PA = −24.40
. The fi
level is drawn at 0.3 mJy/beam and the rest are spaced by a factor
√
2. The sensitivity (1σ) is 0.1 mJy/beam. The con
radio intensity are overlaid on the optical POSS2 image. Right: total intensity radio contours of Ophiuchus overlaid on t
X-ray image in the 0.5-4 keV band.
halos is interesting to investigate in the framework of the models
attempting to explain the formation of mini-halos.
In Fig. 8, we plot the radio power at 1.4 GHz of the mini-
halos versus those of the central cD galaxies. In addition to data
for A1835, A2029 and Ophiuchus we plot data for RXJ1347.5-
1145 (Gitti et al. 2007), A2390 (Bacchi et al. 2003), and Perseus
(Pedlar et al. 1990). All fluxes are calculated in a consistent way
from the fit procedure presented in Paper II.
The comparison between the radio power of mini halos and
that of the central cD galaxy, indicates that there is a weak ten-
dency for more powerful mini-halos to host stronger central ra-
dio sources. We recall that in a few clusters with cooling flows,
resolution of our new images ensures that the dete
emission is real and not due to a blend of discrete so
We analyzed the interplay between the mini-ha
cluster X-ray emission. We identified a similarity b
shape of the radio mini-halo emission and the cluster
phology of A2029, A1835, and Ophiuchus. We no
though all these clusters are considered to be relax
when analyzed in detail they are found to contain pec
features at the cluster center, which are indicative o
tween the mini-halo emission and some minor merg
Because of the large angular extension of Ophiuchu
sible to perform a point-to-point comparison of the r
Govoni et al 2009
3355
..::
#
,.11:
Govoni et al 2005

17. Sloshing with Magnetic
Fields
• B-fields may be
“draped” across the
fronts, which may
suppress instabilities,
diffusion, and
conductions (Vikhlinin
et al 2001, Lyutikov
2006, Asai et al. 2007,
Dursi 2007) Dursi Pfrommer 2007

18. Sloshing with Magnetic Fields
T (keV) B (G)

19. Sloshing with Magnetic Fields
T (keV)
No Fields With Fields

20. Viscosity and Cold Fronts
Viscous sloshing CFs in Virgo 7
Fig. 6.— Simulated X-ray images of the northern sloshing CF in the Virgo cluster at di↵erent viscosities. The top and bottom rows
are for low and high viscosity (10 3 and 0.1 of the Spitzer value), respectively. The left-hand-side column shows noiseless images, in
the right-hand-side column we added a random Poisson deviate to match the surface brightness and noise level of a simulated 300 ks
Chandra/ACIS-I observation. The structure of the CF di↵ers between low and high viscosity. The KHIs can be clearly seen in the former
case (see labels), in both the ideal and in the noisy image.
The left panels in Fig. 6 show the direct comparison of
surface brightness images at high and low viscosity along
the northern sloshing CF of the simulated Virgo cluster,
i.e. a smooth front in the high viscosity case and a ragged
front at low viscosity. This field of view corresponds to
two ACIS-I pointings of the Chandra X-ray observatory.
To evaluate the detectability of these structures in real
observations, we match the count density in the simu-
lated images to the surface brightness measured for the
Virgo cluster CF in the XMM-Newton exposure. Using
PIMMS, we scale it to a 300 ks Chandra/ACIS-I observa-
tion. With this exposure time, there will be ⇠100 source
counts per 0.5 kpc⇥0.5 kpc pixel (600
⇥600
) just behind
the CF. A random Poisson deviate is then added to each
0.5 kpc⇥0.5 kpc pixel to simulate the noise of a real ob-
servation. The resulting noisy images are shown in the
right column of Fig. 6. We neglect background in these
idealized simulations, because the count rate from the
5.2.2. Profiles
To further demonstrate the detectability of the KH
rolls in the simulated data, we extracted surface bright-
ness profiles across the CF in 1.5 wedges in both data
sets with the random Poisson deviate added. Two ex-
amples are shown in Fig. 7. We follow the classic ob-
servational data analysis strategy and fix the vertices of
the wedges at the cluster center. The wedge opening an-
gle of 1.5 corresponds to a linear distance of 2.5 kpc or
0.5 arcmin at the CF and is thus much narrower than
in our analysis of the XMM-Newton data. Despite the
added Poisson noise the predicted multiple edges in the
low viscosity case can be clearly detected and are marked
by vertical lines. The spacing between the surface bright-
ness edges (i.e. the spacing between the vertical lines -
3 to 4 kpc) is roughly the height of the KH rolls. The
height of these rolls is typically a third or half of the scale
Roediger et al
2012b
ZuHone et al 2010

21. Viscosity and Cold
Fronts
• What is the viscosity in the ICM?
• One obvious candidate is the viscosity resulting
from the ion collisions
• In the ICM, λmfp ≫ ρL, so, momentum transport is
modified strongly by the magnetic field:
!
!
• What is the effect of an anisotropic viscosity
compared to an isotropic viscosity?
Π = −3ν∥
ˆbˆb −
1
3
I ˆbˆb −
1
3
I : ∇v

22. Viscosity and Cold Fronts
ZuHone et al 2014, in prep.

23. Viscosity and Cold Fronts

24. Projected Mean
Velocity
ZuHone et al 2014, in prep.

25. ProjectedVelocity
Dispersion
ZuHone et al 2014, in prep.

26. Viscosity and Cold
Fronts
• It appears that at least qualitatively the
observed sharpness of cold fronts is
consistent with the inferred magnetic field
strength from observations and anisotropic
viscosity
• To a good approximation, this situation may
be described by an averaged isotropic
viscosity, roughly an order of magnitude less
than Spitzer

27. Thermal Conduction
!
• For similar reasons as viscosity, heat conduction is
very anisotropic, only transporting heat along the
field lines:
!
• If the cold front surfaces are “draped” by magnetic
fields, then in theory conduction should be
suppressed across the fronts, consistent with the
sharpness of the observed surfaces
Q = −κ∥
ˆbˆb · ∇T

28. Thermal Conduction
No Conduction Spitzer Conduction
500 kpc ZuHone et al 2013a

29. 3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
0 10 20 30 40 50 60
T(keV)
d (kpc)
a
S1
SC1
SC3
SC4
3.5
4
4.5
5
5.5
6
6.5
0 5 10 15 20 25 30 35 40 45 50
T(keV)
d (kpc)
b
S1
SC1
SC3
SC4
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
0 5 10 15 20 25 30 35 40 45 50
T(keV)
d (kpc)
c
S1
SC1
SC3
SC4
3.5
4
4.5
5
5.5
6
6.5
7
7.5
0 10 20 30 40 50
T(keV)
d (kpc)
d
S1
SC1
SC3
SC4
No Conduction
Spitzer
0.1 Spitzer

30. X-Ray Images
A2319
S1
SC1
SC3
ZuHone et al 2013a
No Conduction 0.1 Spitzer
Spitzer

31. Where Does the Heat
Come from?
The magnetic fields are not always perfectly draped
across the cold fronts ZuHone et al 2013a

32. Implications for
Conduction
• The inability of the magnetic field to
completely suppress conduction across cold
front surfaces is potentially strong evidence
for suppression of conduction along the field
lines
• Further simulations of clusters of different
temperatures and magnetic field structures
are necessary

33. Radio Mini-Halos
• Diffuse, regular radio
emission found in
relaxed clusters
• rh ~ 100-200 kpc
• α ~ 1.0-1.5
• Mazzotta Giacintucci
(2008) discovered a
correlation between
radio mini-halos and
cold fronts in two
galaxy clusters
RX J1720.1+2638
MS 1455.0+2232

34. Radio Mini-Halos
• Steep spectra
• Steep radial cutoff
• Not all cool-core
clusters possess them
Giacintucci et al 2014, in prep.

35. Reacceleration by
Turbulence
• Lower-energy electrons (γ ~ 102
)
can build up in the cluster over
time due to their longer cooling
times
• Then, these particles are
reaccelerated by MHD turbulence
generated by merging, via the
transit-time damping mechanism
(TTD, Brunetti Lazarian 2007),
where the electrons interact with
the fast magnetosonic modes
• In our case, moderate turbulence
(δv ~ 200 km/s) can be driven by
the sloshing motions
Projected Mass-Weighted vturb (km/s)
ZuHone et al 2013b

36. Accelerating Electrons
ρi-1,Ti-1,δvi-1,Bi-1
ρi,Ti,δvi,Bi
ρi+1,Ti+1,δvi+1,Bi+1
reacceleration
radiative
losses
Coulomb
losses
dPt =
4Dpp
p
−
dp
dt rad
−
dp
dt coll
dt
+ 2DppdWt
stochastic
momentum diffusion
Individual tracer particle
trajectories, with associated
relativistic Monte-Carlo
sample particles
stochastic
differential
equation for
evolving relativistic
particle energies
pj
pj+1
pj+2
pj-1

37. Relativistic
Electron
Acceleration
No emission from
these electrons
Emission from these
electrons
ZuHone et al 2013b

38. Radio-Emitting
Particles
(327 MHz)
ZuHone et al 2013b

39. Radio and Temperature
Profiles
NW
SE
0 50 100 150 200 250
r (kpc)
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
1
Sν(η/10−3
)(mJyarcsec−2
)
NW Radio
SE Radio
NW Temperature
SE Temperature
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
T(keV)
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
T(keV)
ZuHone et al 2013b

40. Radio Spectrum and Power
ZuHone et al 2013b

41. IC Emission
Psynch
PIC
=
uB
uCMB
ZuHone et al
2013b

42. Comparison With
Observations
x
RXJ1720.1+26
200 kpc
ZuHone et al 2013b

43. yt is a Python-based platform for analysis and
visualization of astrophysical* simulation†
data
*expanding into other fields
†
observational data too!
Turk et al. 2011, ApJS, 192, 9
Turk Smith 2011, arXiv:1112.4482

44. !
yt is designed to address physical,
not computational,
questions

45. “What is the average mass weighted temperature of the gas within a sphere of
radius 100 kpc, centered at the maximum gas density? Oh, and I want it in
keV.”
from yt.mods import *
from yt.utilities.physical_constants import kboltz
!
ds = load(IsolatedGalaxy/galaxy0030/galaxy0030)
!
sp = ds.h.sphere(max, (100,“kpc”))
!
T = dd.quantities[“WeightedAverageQuantity”](“temperature”,“cell_mass”)
!
print (kboltz*T).in_units(“keV”)

46. Fully-
Supported
Mostly-
Supported
In Progress
Enzo
FLASH
Nyx
Orion
Data In-Memory
Chombo
Athena
ART
Ramses
Gadget
Hydra
PKDGRAV
FITS Image Data

47. Formation of a Galaxy Cluster: Sam Skillman

48. Bolatto et al. 2013, Nature, 499, 450

49. Simulating Cluster
Observations
S-Z
(thermal+kinetic+relativistic corr.) X-ray

50. For more information:
http://yt-project.org

51. Summary
• The cores of “relaxed” galaxy clusters are not quite relaxed:
many of them exhibit cold fronts produced by gas sloshing
• The cold fronts’ relative absence of K-H instabilities may be
explained by the cluster magnetic field and Braginskii viscosity
• However, the magnetic field does NOT appear to be sufficient
to suppress conduction across the fronts, indicating thermal
conduction may be weak in the ICM
• Sloshing also drives turbulence, reaccelerating relativistic
electrons, producing radio minihalos consistent with observed
sources