Download - Gas Sloshing: Simulations and Observations
Gas Sloshing: Simulations and Observations
John ZuHone (NASA/GSFC, Maryland)
A2319
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
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”
4 ASCASIBAR AND MARKEVITCH
FIG. 3.— Evolution of the cold front induced by a purely dark matter satellite. Parameters of the encounter are R = 5 and b = 500 kpc; the pericenter distanceat the first core passage (which occurs at 1.37 Gyr) is ∼ 150 kpc. Color maps show the gas temperature (in keV) in a slice in the orbital plane. The temperaturescale shown in the top left panel (in keV) is the same for all panels. Arrows represent the gas velocity field w.r.t. the main dark matter density peak (for clarity,the velocity scale is linear at low values, then saturates). Contours are drawn at increments of a factor of 2 in the local dark matter density. The white cross showsthe center of mass for the main cluster DM particles (not for the whole system). The panel size is 1 Mpc.
and the total angular momentum is
J ≈R√2K
(1+R)2bM0
!
GM0
d(8)
Different mass ratios (R =2, 5, 20 and 100) and impact pa-rameters (b =0, 500 and 1000 kpc) have been investigated.The initial kinetic energy of the merger has been set to K =1/2.
3. MERGERWITH A GASLESS SUBCLUSTERWe first consider a simple case (which will also turn out
to be the most relevant), in which the infalling substructureis just a DM halo without any gas at all. This situation mayarise, for instance, if the satellite lost all its gas due to ram-pressure stripping during an earlier phase of the merger. As
we will see, such a merger does generate sloshing of the coolcentral gas and multiple cold fronts. Compared to a mergerin which both subclusters have gas (considered in the nextsection), the hydrodynamics in this case is relatively simpleand the underlying processes can be identified more easily.Figure 3 shows the evolution of an encounter with R = 5
and impact parameter b = 500 kpc. While mergers with suchmassive subclusters may be relatively rare, this choice allowsus to see the effects of the disturbance more clearly. For thesemerger parameters, the first core passage of the satellite takesplace at about t ≈ 1.37 Gyr from the start of the simulationrun, at a distance approximately 150 kpc from the minimumof the gravitational potential. Different values of R and b leadto different orbits, with different time and length scales. Theextent and intensity of the induced sloshing and subsequent
Large-Scale Sloshing
Large-Scale Sloshing
Rossetti et al 2013
Rossetti M. et al.: Abell 2142 at large scales: An extreme case for sloshing?
Figure 7: EPIC SB image (upper left), temperature map(upper right), pressure map(lower left) and entropy map (lower right). Mapswere obtained with a target S/N = 15. X-ray contours are overlaid on the thermodynamic maps, coordinates are right ascension anddeclination.
ity of the perturber. Therefore, the presence of a sharp front inthe large scale excess in A2142 may be another indication of amerging event that is not very minor. However, the more centralcold fronts in A2142, especially the NW one (Sec. 3.2.1), lookremarkably smooth and stable, while all cold fronts in simulatedviolent mergers appear disturbed by the onset of hydrodynam-ical instabilities. A2142 is an interesting case for simulationsto test the mechanisms which can suppress transport processesin the ICM and prevent the onset of Kelvin-Helmoltz instabili-ties, such as magnetic fields (ZuHone et al. 2013b) and viscosity(Roediger et al. 2013). These mechanisms should be e�cient atvery di↵erent scales (from the few kpc scale of the central fronts
to the Mpc scale of the SE one) and in di↵erent environments(both in the central dense regions of the cluster up to the rarefiedoutskirts). Moreover, they should be able to keep the fronts sta-ble also in the hypothesis that they are due to an intermediateand not minor merger.The metal abundance and temperature distributions in A2142(Sec. 3.5) also agree with predictions of simulations (Roedigeret al. 2011): the richer and cooler gas is associated to the regionsfeaturing a surface brightness excess. The gas in the large scaleexcess associated to the SE cold front is cooler but not signif-icantly metal-richer than other regions. If we assume the metalabundance to remain constant during the sloshing process, the
8
Flux
Rossetti M. et al.: Abell 2142 at large scales: An extreme case for sloshing?
Figure 7: EPIC SB image (upper left), temperature map(upper right), pressure map(lower left) and entropy map (lower right). Mapswere obtained with a target S/N = 15. X-ray contours are overlaid on the thermodynamic maps, coordinates are right ascension anddeclination.
ity of the perturber. Therefore, the presence of a sharp front inthe large scale excess in A2142 may be another indication of amerging event that is not very minor. However, the more centralcold fronts in A2142, especially the NW one (Sec. 3.2.1), lookremarkably smooth and stable, while all cold fronts in simulatedviolent mergers appear disturbed by the onset of hydrodynam-ical instabilities. A2142 is an interesting case for simulationsto test the mechanisms which can suppress transport processesin the ICM and prevent the onset of Kelvin-Helmoltz instabili-ties, such as magnetic fields (ZuHone et al. 2013b) and viscosity(Roediger et al. 2013). These mechanisms should be e�cient atvery di↵erent scales (from the few kpc scale of the central fronts
to the Mpc scale of the SE one) and in di↵erent environments(both in the central dense regions of the cluster up to the rarefiedoutskirts). Moreover, they should be able to keep the fronts sta-ble also in the hypothesis that they are due to an intermediateand not minor merger.The metal abundance and temperature distributions in A2142(Sec. 3.5) also agree with predictions of simulations (Roedigeret al. 2011): the richer and cooler gas is associated to the regionsfeaturing a surface brightness excess. The gas in the large scaleexcess associated to the SE cold front is cooler but not signif-icantly metal-richer than other regions. If we assume the metalabundance to remain constant during the sloshing process, the
8
Temperature
Rossetti M. et al.: Abell 2142 at large scales: An extreme case for sloshing?
Figure 6: Residual image from the azimuthal average in concentric annuli (left) and in elliptical annuli (right). X-ray contours areoverlaid, coordinates on the images are right ascension and declination.
left panel). This alternation of excesses and crossing of profilesin opposite directions is a generic feature of the sloshing sce-nario (Roediger et al. 2012) and was noticed also in Perseus bySimionescu et al. (2012).The SE cold front of A2142 is a record breaking feature: at 1Mpc from the center, it is the outermost cold front, detected asboth a surface brightness and temperature discontinuity and notobviously associated to a moving subcluster, ever observed in agalaxy cluster (see also Sec. 4.5). Moreover, it is detectable as asurface brightness discontinuity over a broad angular range (70degrees), which corresponds to a linear scale of 1.2 Mpc at adistance from the center of 1 Mpc.
4.2. Comparison with simulations
The residual surface brightness images of A2142 shown in Fig. 6can be compared with the predictions of numerical simulationsto test the possibility that the fronts in A2142 are caused bysloshing. For instance, Roediger et al. (2011, 2012) show pre-dicted residual images from ad-hoc simulations of the Virgocluster and A496 to reproduce the observed features and to in-fer the characteristics of the minor mergers that induced thesloshing. To perform a similar analysis on A2142, new tailoredsimulations are needed. A full hydro-dynamical N-body treat-ment will be required, because the rigid potential approxima-tion (Roediger & Zuhone 2012) may not be completely validin the outskirts (at 1 Mpc from the center, where we observethe SE cold front) . If the ellipticity of A2142 reflects the el-lipticity of the potential well, the position and shapes of coldfronts may be di↵erent from spherical simulations. Therefore,we limit the comparison with simulations at a qualitative level,and we refer for a more complete discussion to a forthcoming
paper (Roediger et al. in prep.).In Fig. 8, we show a simulated residual image for A496 withthe orbit of the perturber in the plane of the sky that we rotatedto match the geometry of A2142. The morphological similar-ity between the observed and simulated maps is striking: theyboth show concentric excesses corresponding to the central coldfronts and a third excess at larger scale. In this geometry, the per-turber should be moving in the west-east direction and shouldbe now located in the east, but we do not have indication of asubcluster consistent with this orbit. Another possible match be-tween observations and simulations could be obtained by rotat-ing the residual map in Fig. 8 180�, so that the simulated NWcold front would match the observed SE one, and the more cen-tral discontinuities would be the central cold fronts. However,we would expect a larger scale excess in the NW direction withthis geometry, which is not seen in the residual maps obtainedwith either XMM-Newton (Fig. 6) or ROSAT.The main di↵erence between observed and simulated maps is
the larger scale of the sloshing phenomenon in A2142: coldfronts are located at about twice the distance from the centerpredicted by simulations. Cold fronts can be reproduced in sim-ulations of massive clusters at those large scales if the sloshingphenomenon persists for about 2 Gyr or if they move outwardswith a higher velocity, following a merger that is not very mi-nor in terms of impact parameter, mass, and infall velocity ofthe subcluster). Another key di↵erence is the presence of a sharpfront delimiting the SE excess in A2142, while large scale fea-tures in simulations never show sharp discontinuities (Roedigeret al. 2011, 2012). As already mentioned, full hydrodynamicalN–body simulations are needed to characterize sloshing featuresat Mpc scales. However, we noticed that the surface brightnesscontrast in simulated central cold fronts depends on the veloc-
7
Residuals
~1 Mpc
Abell 2142
Large-Scale Sloshing
Walker, Fabian, & Sanders 2014
2 S. A. Walker et al.
Figure 1. Top Left:Exposure corrected, background subtracted, point source subtracted and adaptively smoothed mosaic X-ray image in the 0.7-7.0 keV bandfrom XMM-Newton. Top Right: Chandra image of the same region in the 0.7-7.0keV band, showing two central cold fronts which cannot be fully resolvedin the XMM image. Bottom Left:Residuals of the 0.7-7.0keV XMM-Newton image after dividing by the azimuthal average, showing the prominent swirlingexcess to the south. The original image was binned into a Voronoi tesselation with each region containing at least 100 counts. After division by the azimuthalaverage the image was then smoothed with a Gaussian kernel Bottom Right: Temperature map for the same region as the other panels, showing that the southernexcess swirl in the surface brightness residuals corresponds to colder gas. The Chandra data have been used for the central 300kpc of the temperature map,and the XMM-Newton data for the regions outside 300kpc. All of the panels have had their coordinates matched.
c⃝ 0000 RAS, MNRAS 000, 000–000
2 S. A. Walker et al.
Figure 1. Top Left:Exposure corrected, background subtracted, point source subtracted and adaptively smoothed mosaic X-ray image in the 0.7-7.0 keV bandfrom XMM-Newton. Top Right: Chandra image of the same region in the 0.7-7.0keV band, showing two central cold fronts which cannot be fully resolvedin the XMM image. Bottom Left:Residuals of the 0.7-7.0keV XMM-Newton image after dividing by the azimuthal average, showing the prominent swirlingexcess to the south. The original image was binned into a Voronoi tesselation with each region containing at least 100 counts. After division by the azimuthalaverage the image was then smoothed with a Gaussian kernel Bottom Right: Temperature map for the same region as the other panels, showing that the southernexcess swirl in the surface brightness residuals corresponds to colder gas. The Chandra data have been used for the central 300kpc of the temperature map,and the XMM-Newton data for the regions outside 300kpc. All of the panels have had their coordinates matched.
c⃝ 0000 RAS, MNRAS 000, 000–000
~800 kpc
RXJ2014.8-2430
• Information on this from simulations is currently limited due to: • Most investigations of sloshing focused on the core region • Algorithmic limitations (Roediger & ZuHone 2012) • Small parameter space of simulations
~500 kpc
M ~ 1015 M⊙, R = 1:5, b = 0.5 Mpc,
gasless subcluster, ~8 Gyr since core passage
M ~ 6 ×1014 M⊙, R = 1:3, b = 1.5 Mpc,
gas-filled subcluster, ~8.5 Gyr since core passage
~1.5 Mpc
Sloshing and ICM Physics Beyond Hydrodynamics
200 kpc
A 2 1 4 2 A2142 wavelets
200 kpc
Roediger et al 2012
Irregular cold fronts in NGC 7618/UGC 12491 3
Fig. 2.— Chandra/ACIS-S image of NGC 7618 in the0.5-2.0 keV band, background-subtracted, exposure corrected,Gaussian-smoothed to 6 arcsec. The logarithmic color scale is cho-sen to highlight the substructure of the cold front. Prominentfeatures are labelled. The dashed arc marks the cold front.
Fig. 3.— Same as Fig. 2 but for UGC 12491, Gaussian-smoothedto 4 arcsec.
south-west which, however, terminates in two wings, oneto the south-south-east, one to the north-north-west. Itstail appears to be split at about 30 kpc north-east fromthe nucleus and possibly again at 50 kpc to the north.Alternatively, these splits in the tail could be regardedas wings or distortions along the outside edge of the tail.In both groups, these CF substructures have linear scalesof about 15 kpc.To demonstrate significance of the nose feature at
NGC 7618, we compared the brightness of this featurewith the adjacent background level. We performed thisanalysis on the raw image in the 0.7 to 1.4 keV band,where the ratio of source to background counts has beenoptimized only by the choice of energy band. We placedthe elliptical region 1 shown in Fig. 4 over the nose. El-lipses 2 and 3 are at the same distance from the galaxycenter, and ellipses 4 to 7 are placed north of the CF. Allellipses have the same size. We ensured that all ellipsesare not contaminated by the brighter emission inside the
Fig. 4.— Raw Chandra/ACIS-S image of NGC 7618 in the 0.7-1.4 keV band, Gaussian-smoothed to 6 arcsec. The ellipse 1 coversthe ”nose” feature, ellipses 2 and 3 are at the same distance fromthe galaxy center, and ellipses 4 to 7 are placed such that theycover patches of high background. All ellipses have the same size,the number of counts in them is listed in Table 1.
CF. The number of counts in each ellipse is listed in Ta-ble 1. Ellipse 2 is the brightest of the background ellipsesand contains 42 counts. Assuming Poisson noise impliesa standard deviation of � = 6.5. The 60 counts in ellipse1 on the nose feature are 2.7 � above the backgroundlevel as defined by ellipse 2. The average backgroundlevel of regions 2 to 7 is 35 counts, corresponding to� = 5.9. Therefore the counts in the nose regions are4 � above this level. The length scale of the confidentlydetected structures is about 15 kpc. With the currentdata, smaller structures cannot be detected at compara-ble significance, because, assuming a comparable surfacebrightness also in smaller structures, the significance,i.e. the excess of source counts above the backgrounddivided by the standard deviation of the background, isproportional to the considered length scale. To betterdefine the CF shape, deeper observations are required.We suggest that the distortions in these CFs are the
result of KHIs, which are expected to arise due to shearflows along the CFs and are routinely seen in non-viscoushydrodynamical simulations (e.g. Fig. A1 in Roedigeret al. 2011, also Roediger et al. 2012; ZuHone et al.2010). As outlined in Sect. 1 above, both distorted CFsand smooth, arc-like ones have been observed, and thepresence or absence of KHI-like distortions constrainsthe e↵ective viscosity of the ICM and tangential mag-netic fields along the fronts, which can both suppress thegrowth of the KHI. After a short remark on the e↵ect ofgravity we discuss these two ICM properties below.Gravity suppresses the KHI (Chandrasekhar 1961) at
wavelengths above length scales of
�max
⇡ 18 kpc
✓D
1.5
◆�1
✓U
200 km s�1
◆2
⇥ (1)
✓g
3⇥ 10�8 cm s�2
◆�1
with D = ⇢1
/⇢2
, (2)
Irregular cold fronts in NGC 7618/UGC 12491 3
Fig. 2.— Chandra/ACIS-S image of NGC 7618 in the0.5-2.0 keV band, background-subtracted, exposure corrected,Gaussian-smoothed to 6 arcsec. The logarithmic color scale is cho-sen to highlight the substructure of the cold front. Prominentfeatures are labelled. The dashed arc marks the cold front.
Fig. 3.— Same as Fig. 2 but for UGC 12491, Gaussian-smoothedto 4 arcsec.
south-west which, however, terminates in two wings, oneto the south-south-east, one to the north-north-west. Itstail appears to be split at about 30 kpc north-east fromthe nucleus and possibly again at 50 kpc to the north.Alternatively, these splits in the tail could be regardedas wings or distortions along the outside edge of the tail.In both groups, these CF substructures have linear scalesof about 15 kpc.To demonstrate significance of the nose feature at
NGC 7618, we compared the brightness of this featurewith the adjacent background level. We performed thisanalysis on the raw image in the 0.7 to 1.4 keV band,where the ratio of source to background counts has beenoptimized only by the choice of energy band. We placedthe elliptical region 1 shown in Fig. 4 over the nose. El-lipses 2 and 3 are at the same distance from the galaxycenter, and ellipses 4 to 7 are placed north of the CF. Allellipses have the same size. We ensured that all ellipsesare not contaminated by the brighter emission inside the
Fig. 4.— Raw Chandra/ACIS-S image of NGC 7618 in the 0.7-1.4 keV band, Gaussian-smoothed to 6 arcsec. The ellipse 1 coversthe ”nose” feature, ellipses 2 and 3 are at the same distance fromthe galaxy center, and ellipses 4 to 7 are placed such that theycover patches of high background. All ellipses have the same size,the number of counts in them is listed in Table 1.
CF. The number of counts in each ellipse is listed in Ta-ble 1. Ellipse 2 is the brightest of the background ellipsesand contains 42 counts. Assuming Poisson noise impliesa standard deviation of � = 6.5. The 60 counts in ellipse1 on the nose feature are 2.7 � above the backgroundlevel as defined by ellipse 2. The average backgroundlevel of regions 2 to 7 is 35 counts, corresponding to� = 5.9. Therefore the counts in the nose regions are4 � above this level. The length scale of the confidentlydetected structures is about 15 kpc. With the currentdata, smaller structures cannot be detected at compara-ble significance, because, assuming a comparable surfacebrightness also in smaller structures, the significance,i.e. the excess of source counts above the backgrounddivided by the standard deviation of the background, isproportional to the considered length scale. To betterdefine the CF shape, deeper observations are required.We suggest that the distortions in these CFs are the
result of KHIs, which are expected to arise due to shearflows along the CFs and are routinely seen in non-viscoushydrodynamical simulations (e.g. Fig. A1 in Roedigeret al. 2011, also Roediger et al. 2012; ZuHone et al.2010). As outlined in Sect. 1 above, both distorted CFsand smooth, arc-like ones have been observed, and thepresence or absence of KHI-like distortions constrainsthe e↵ective viscosity of the ICM and tangential mag-netic fields along the fronts, which can both suppress thegrowth of the KHI. After a short remark on the e↵ect ofgravity we discuss these two ICM properties below.Gravity suppresses the KHI (Chandrasekhar 1961) at
wavelengths above length scales of
�max
⇡ 18 kpc
✓D
1.5
◆�1
✓U
200 km s�1
◆2
⇥ (1)
✓g
3⇥ 10�8 cm s�2
◆�1
with D = ⇢1
/⇢2
, (2)
• 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?
Cold Front Preservation
Magnetic Field Draping
Dursi & Pfrommer 2007 Asai et al 2007 ZuHone et al 2011
(see also: Vikhlinin et al 2001, Lyutikov 2006, Keshet et al 2010, Reiss & Keshet 2012)
Sloshing with Magnetic Fields
T (keV) B (G)
Sloshing with Magnetic FieldsT (keV)
No Fields With Fields
Sloshing with Magnetic FieldsMetallicity (Z⊙)
No Fields With Fields
Entropy and Metallicity
ICM Microphysics
In the ICM, λmfp ≫ ρL, so momentum and heat transport are modified strongly by the magnetic field:
Π = −3ν∥
!
b̂b̂−1
3I
"!
b̂b̂−1
3I
"
: ∇v
Q = −κ∥b̂b̂ ·∇T
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 rowsare for low and high viscosity (10�3 and 0.1 of the Spitzer value), respectively. The left-hand-side column shows noiseless images, inthe right-hand-side column we added a random Poisson deviate to match the surface brightness and noise level of a simulated 300 ksChandra/ACIS-I observation. The structure of the CF di↵ers between low and high viscosity. The KHIs can be clearly seen in the formercase (see labels), in both the ideal and in the noisy image.
The left panels in Fig. 6 show the direct comparison ofsurface brightness images at high and low viscosity alongthe northern sloshing CF of the simulated Virgo cluster,i.e. a smooth front in the high viscosity case and a raggedfront at low viscosity. This field of view corresponds totwo 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 theVirgo cluster CF in the XMM-Newton exposure. UsingPIMMS, we scale it to a 300 ks Chandra/ACIS-I observa-tion. With this exposure time, there will be ⇠100 sourcecounts per 0.5 kpc⇥0.5 kpc pixel (600⇥600) just behindthe CF. A random Poisson deviate is then added to each0.5 kpc⇥0.5 kpc pixel to simulate the noise of a real ob-servation. The resulting noisy images are shown in theright column of Fig. 6. We neglect background in theseidealized simulations, because the count rate from thebackground is <10% of the rate from the gas inside thecold front and thus insignificant.The KH rolls in the low viscosity case are clearly visi-
ble in the data with the random deviate added, and theyare again absent in the high viscosity case. The KH rollsspan spatial scales of several kpc. The variations in sur-face brightness due to the KH rolls in the low viscositysimulation are as large as ⇠20%. There are ⇠4000 countsin a 5 kpc ⇥ 2 kpc region behind the cold front in thesimulated Chandra image. Thus we could in principledetect variations in surface brightness of ⇠5% at 3� con-fidence with a real observation. The KH rolls on scales ofa few kpc, if present, would be easily detectable at morethan 10� confidence in such a deep Chandra observation.Additionally, we could observe KH rolls on smaller scalesat lower significance. Twenty percent variations of sur-face brightness could be detected at 4� confidence in 1kpc⇥1 kpc scale regions.
5.2.2. Profiles
To further demonstrate the detectability of the KHrolls in the simulated data, we extracted surface bright-ness profiles across the CF in 1.5� wedges in both datasets 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 ofthe wedges at the cluster center. The wedge opening an-gle of 1.5� corresponds to a linear distance of 2.5 kpc or0.5 arcmin at the CF and is thus much narrower thanin our analysis of the XMM-Newton data. Despite theadded Poisson noise the predicted multiple edges in thelow viscosity case can be clearly detected and are markedby 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. Theheight of these rolls is typically a third or half of the scalelength of the KH rolls. Thus the edges spaced roughly4 kpc apart in the low viscosity profile signify KHI scalelengths of ⇠10 kpc. The presence of these edges in areal observation would immediately give the typical scalelength of KH rolls, and these rolls should be present if⌫
ICM
⌧ ⌫
Spitzer
. In contrast, the surface brightness pro-file of the high viscosity simulation can be well describedwith a single power law with no evidence of an edge orchange in slope inside the contact discontinuity of theCF.
5.2.3. Statistical characterization
At low viscosity, there is a wealth of structure insidethe CF. We created the power spectral density (PSD)function of the emission behind the CF in both cases tosearch for a signature in the Fourier domain of the spa-tial scales where the KH rolls are present. The PSD isindeed larger in the low viscosity simulation on scaleswhere the KH rolls are present, but we could not di-
Roediger et al 2013
4Roed
igeret
al.2012
plan
eat
thefinal
timestep
forf
µ
=0,10
�3
,0.01
and0.1
fromtop
tobottom
.Ataviscosity
f
µ
10
�3,
allCFs
areclearly
distorted
andmad
eragged
bytheKHI.W
ithincreasin
gviscosity,
thefronts
becom
eless
ragged,an
dstru
ctures
atprogressively
largerscales
aresuppressed
.Interestin
gly,even
thesm
allphysical
viscosityof
10�3
Spitzer
erasessom
eof
thesm
allestpertu
rbation
spresent
intheinviscid
simulation
.Finally,
thefronts
arealm
ostcom
pletely
smooth
inthehigh
viscositycase
(f
µ
=0.1)
exceptfor
twolarge
KHrolls
separated
by⇠
40kp
calon
gtheSW
,where
theshear
flow
isstron
gest(⇠
500km
s �1).
Distortion
sat
smaller
length
scalesthou
ghare
absent
athigh
viscosityat
this
locationas
well,
whereas
smaller
distortion
sare
present
atthislocation
atlow
erviscosity.
Oursim
ulation
sdem
onstrate
that
theviscosity
ismore
e�cient
insuppressin
gtheKHIthan
expected
fromthe
linear
analysis.
There
areseveral
reasonsfor
this
dif-
ference:
thegrow
thtim
eis
derived
fromthelin
earsta-
bility
analysis.
Thee↵
ectof
theviscosity
isto
reduce
shear
velocities,which
applies
totheflow
parallel
tothe
interfaceas
well
asthevelocity
pertu
rbation
intheper-
pendicu
lardirection
.Thu
s,while
thelin
earan
alysispre-
dicts
only
aslow
edgrow
thof
theKHI,butstill
agrow
th,
atlon
gertim
escalesviscosity
shou
ldshu
to↵
thegrow
thcom
pletely
andthu
sbemore
e�cient
than
expected
.We
dem
onstrate
this
behavior
analytically
andnu
merically
inasep
aratepublication
(Roed
igeret
al.,in
prep
ara-tion
).Furth
ermore,
theslosh
ingCFsare
curved
inter-faces
embedded
inabackgrou
ndgravitation
alpotential
andastratifi
edatm
osphere,
whereas
thean
alyticesti-
mate
assumes
aplan
arinterface,
nostratifi
cationan
dno
gravity.Thegravity
atthenorth
ernCFsuppresses
KHIs
atwavelen
gthsab
ove⇠
50kp
can
dwill
thusslow
dow
nthegrow
thof
instab
ilitiesat
somew
hat
smaller
wave-
length
s,i.e.
thewavelen
gthsseen
inthesim
ulation
s.Fi-
nally,
theslosh
ingCFsare
special
contactdiscontinu
itiesthat
arecontinu
ously
reformed
bytheslosh
ingprocess,
which
interactswith
theKHIan
dmay
mod
ifyits
growth
atlon
gtim
escales.For
example,
theou
tward
smotion
oftheCFstretch
estherelevant
wavelen
gths,which
reduces
thegrow
thrate
andam
plitu
de(C
hurazov
&Inogam
ov2004).
4.OBSERVABLE
FEATURES
4.1.X-ra
yim
ages
We
calculate
synthetic
X-ray
images
byprojectin
gn
2ICM
⇤(T
ICM
)alon
gthelin
e-of-sight(L
OS),
where
⇤(T)
isthecoolin
gfunction
accordingto
Sutherlan
d&
Dop
ita(1993)
andweassu
meametallicity
of0.3
solar.Figu
re3
disp
laysthepred
ictedX-ray
images
fortheviscosity
sup-
pression
factorsf
µ
=10
�3
andf
µ
=0.1.
Wewill
referto
these
twoviscosities
aslow
andhigh
viscosity,resp
ec-tively.Astheinner
CFsare
likelyto
bedistorted
bytheAGN
activityin
theVirgo
cluster
center(Form
anet
al.2007),
wefocu
son
thestru
cture
oftheou
ternorth
ernfront.
Theshear
flow
alongthis
frontis
weakest
intheNW
,lead
ingto
asm
ooth,sharp
frontin
theNW
indep
endent
ofviscosity.
Alon
gthenorth
(N)an
dtheeast
ofthefront
theshear
flow
isstron
ger(⇠
300km
s �1)
andform
sdis-
tinct
structu
resdep
endingon
theviscosity
(Fig.
3).At
high
viscosity,thefront
formsasm
ootharc
here
aswell,
inviscid10�3 Spitzer viscosity(”low viscosity case” in text)
10�2 Spitzer viscosity0.1 Spitzer viscosity(”high viscosity case” in text)
Fig.2.—
Tem
pera
ture
slicesin
the
orb
ital
pla
ne
at
the
final
timestep
,fo
rSpitzer-ty
pe,
i.e.tem
pera
ture
dep
enden
t,visco
sitiesw
ithsu
ppressio
nfa
ctors
f
µ
=0,1
0�3,0
.01
and
0.1
from
top
tobottom
.In
creasin
gth
evisco
sityera
sespro
gressiv
elyla
rger
sub-
structu
realo
ng
the
fronts.
We
hav
eorien
tedth
eim
ages
such
that
they
com
pare
toth
esitu
atio
nobserv
edin
Virgo
,i.e.
north
isup
and
west
isrig
ht
(seeR
oed
iger
etal.
2011
for
deta
ils).
butit
isragged
atlow
viscosity.Individ
ual
KH
rollsat
⇠15
kpcsize
canbeidentifi
edas
triangu
lar-shap
edirregu
larities.They
givethefront
asaw
toothlike
ap-
pearan
ce.A
furth
ercharacteristic
pattern
ismultip
lead
jacentbrightn
essedges
with
aspacin
gof
abou
t5kp
cparallel
tothemain
front.Wehave
labelled
these
fea-tures
inthezoom
-inin
thetop
pan
elin
Fig.
3.
4Roed
igeret
al.2012
plan
eat
thefinal
timestep
forf
µ
=0,10
�3
,0.01
and0.1
fromtop
tobottom
.Ataviscosity
f
µ
10
�3,
allCFs
areclearly
distorted
andmad
eragged
bytheKHI.W
ithincreasin
gviscosity,
thefronts
becom
eless
ragged,an
dstru
ctures
atprogressively
largerscales
aresuppressed
.Interestin
gly,even
thesm
allphysical
viscosityof
10�3
Spitzer
erasessom
eof
thesm
allestpertu
rbation
spresent
intheinviscid
simulation
.Finally,
thefronts
arealm
ostcom
pletely
smooth
inthehigh
viscositycase
(f
µ
=0.1)
exceptfor
twolarge
KHrolls
separated
by⇠
40kp
calon
gtheSW
,where
theshear
flow
isstron
gest(⇠
500km
s �1).
Distortion
sat
smaller
length
scalesthou
ghare
absent
athigh
viscosityat
this
locationas
well,
whereas
smaller
distortion
sare
present
atthislocation
atlow
erviscosity.
Oursim
ulation
sdem
onstrate
that
theviscosity
ismore
e�cient
insuppressin
gtheKHIthan
expected
fromthe
linear
analysis.
There
areseveral
reasonsfor
this
dif-
ference:
thegrow
thtim
eis
derived
fromthelin
earsta-
bility
analysis.
Thee↵
ectof
theviscosity
isto
reduce
shear
velocities,which
applies
totheflow
parallel
tothe
interfaceas
well
asthevelocity
pertu
rbation
intheper-
pendicu
lardirection
.Thu
s,while
thelin
earan
alysispre-
dicts
only
aslow
edgrow
thof
theKHI,butstill
agrow
th,
atlon
gertim
escalesviscosity
shou
ldshu
to↵
thegrow
thcom
pletely
andthu
sbemore
e�cient
than
expected
.We
dem
onstrate
this
behavior
analytically
andnu
merically
inasep
aratepublication
(Roed
igeret
al.,in
prep
ara-tion
).Furth
ermore,
theslosh
ingCFsare
curved
inter-faces
embedded
inabackgrou
ndgravitation
alpotential
andastratifi
edatm
osphere,
whereas
thean
alyticesti-
mate
assumes
aplan
arinterface,
nostratifi
cationan
dno
gravity.Thegravity
atthenorth
ernCFsuppresses
KHIs
atwavelen
gthsab
ove⇠
50kp
can
dwill
thusslow
dow
nthegrow
thof
instab
ilitiesat
somew
hat
smaller
wave-
length
s,i.e.
thewavelen
gthsseen
inthesim
ulation
s.Fi-
nally,
theslosh
ingCFsare
special
contactdiscontinu
itiesthat
arecontinu
ously
reformed
bytheslosh
ingprocess,
which
interactswith
theKHIan
dmay
mod
ifyits
growth
atlon
gtim
escales.For
example,
theou
tward
smotion
oftheCFstretch
estherelevant
wavelen
gths,which
reduces
thegrow
thrate
andam
plitu
de(C
hurazov
&Inogam
ov2004).
4.OBSERVABLE
FEATURES
4.1.X-ra
yim
ages
We
calculate
synthetic
X-ray
images
byprojectin
gn
2ICM
⇤(T
ICM
)alon
gthelin
e-of-sight(L
OS),
where
⇤(T)
isthecoolin
gfunction
accordingto
Sutherlan
d&
Dop
ita(1993)
andweassu
meametallicity
of0.3
solar.Figu
re3
disp
laysthepred
ictedX-ray
images
fortheviscosity
sup-
pression
factorsf
µ
=10
�3
andf
µ
=0.1.
Wewill
referto
these
twoviscosities
aslow
andhigh
viscosity,resp
ec-tively.Astheinner
CFsare
likelyto
bedistorted
bytheAGN
activityin
theVirgo
cluster
center(Form
anet
al.2007),
wefocu
son
thestru
cture
oftheou
ternorth
ernfront.
Theshear
flow
alongthis
frontis
weakest
intheNW
,lead
ingto
asm
ooth,sharp
frontin
theNW
indep
endent
ofviscosity.
Alon
gthenorth
(N)an
dtheeast
ofthefront
theshear
flow
isstron
ger(⇠
300km
s �1)
andform
sdis-
tinct
structu
resdep
endingon
theviscosity
(Fig.
3).At
high
viscosity,thefront
formsasm
ootharc
here
aswell,
inviscid10�3 Spitzer viscosity(”low viscosity case” in text)
10�2 Spitzer viscosity0.1 Spitzer viscosity(”high viscosity case” in text)
Fig.2.—
Tem
pera
ture
slicesin
the
orb
ital
pla
ne
at
the
final
timestep
,fo
rSpitzer-ty
pe,
i.e.tem
pera
ture
dep
enden
t,visco
sitiesw
ithsu
ppressio
nfa
ctors
f
µ
=0,1
0�3,0
.01
and
0.1
from
top
tobottom
.In
creasin
gth
evisco
sityera
sespro
gressiv
elyla
rger
sub-
structu
realo
ng
the
fronts.
We
hav
eorien
tedth
eim
ages
such
that
they
com
pare
toth
esitu
atio
nobserv
edin
Virgo
,i.e.
north
isup
and
west
isrig
ht
(seeR
oed
iger
etal.
2011
for
deta
ils).
butit
isragged
atlow
viscosity.Individ
ual
KH
rollsat
⇠15
kpcsize
canbeidentifi
edas
triangu
lar-shap
edirregu
larities.They
givethefront
asaw
toothlike
ap-
pearan
ce.A
furth
ercharacteristic
pattern
ismultip
lead
jacentbrightn
essedges
with
aspacin
gof
abou
t5kp
cparallel
tothemain
front.Wehave
labelled
these
fea-tures
inthezoom
-inin
thetop
pan
elin
Fig.
3.
Viscosity and Cold Fronts
ZuHone et al 2014a, arXiv:1406.4031
Viscosity and Cold Fronts
ZuHone et al 2014a, arXiv:1406.4031
Viscosity and Cold Fronts
ZuHone et al 2014a, arXiv:1406.4031
similar
Viscosity and Cold Fronts
ZuHone et al 2014a, arXiv:1406.4031
dissimilar
– 27 –
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
S1SC1SC3SC4
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
S1SC1SC3SC4
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
S1SC1SC3SC4
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
S1SC1SC3SC4
Fig. 5.— Temperature profiles of cold fronts in simulations without conduction and with varying
prescriptions for conduction, along the profiles marked with the corresponding letters in Figure 3.
Conduction reduces the magnitude and increases the width of the jumps to varying degrees.
No Conduction
Spitzer
0.1 Spitzer
Sloshing and Thermal Conduction (ZuHone et al 2013a)
A2319
S1
SC1
SC3No Conduction 0.1 Spitzer
Spitzer
Sloshing and Thermal Conduction (ZuHone et al 2013a)
Sloshing and Radio Mini-Halos
Radio Mini-Halos• Steep spectra • Steep radial cutoff • Not all cool-core
clusters possess them
Giacintucci et al 2014
Models• CRe which produce ~GHz emission have tcool ≪ tdiff, so we
need a replenishing source
• Reacceleration models:
• Turbulence reaccelerates existing population of CRe with γ ~ few hundred up to γ ~ 104
• Hadronic/secondary models:
• pCR + pth ⇒ π0 + π+ + π- + anything π± ⇒ μ± + νμ μ± ⇒ e± + νμ + νe
π0 ⇒ 2γ
No emission from these electrons
Emission from these electrons
ZuHone et al 2013b
Projected Mass-Weighted vturb (km/s)
Reacceleration Models
Radio-Emitting Particles
(327 MHz)
ZuHone et al 2013b
Reacceleration Models
NW
SE
0 50 100 150 200 250r (kpc)
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
1
Sν(η/10−
3)(m
Jyarcsec
−2)
NW RadioSE RadioNW TemperatureSE 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
Reacceleration Models
Spectral SteepeningMapping particle acceleration in RX J1720.1+2638 11
0.5
1.5
2.5
spectral index
beam
C
50 kpc
65
4
3
2
1
a b
FIG. 8.— (a) Grayscale image of the spectral index distribution between 617 MHz and 1480 MHz in the minihalo and head-tail radio galaxy. The image hasbeen computed from images with similar noise (30 µJy beam−1) and same u− v range and restoring beam of 8′′ × 6′′. Overlaid are the 617 MHz contours fromFig. 2a. (b) Spectral index between 617 MHz and 1480 MHz as a function of the distance from the cluster center (white cross) along the minihalo tail (black,filled points). The profile has been derived using the independent circular regions shown in the inset, with r = 8′′ (regions 1 to 4) and r = 10′′ (regions 5 and 6).For a comparison, we also report the spectral index of the central part of the minihalo (C) computed in a r = 18′′ region (white circle in the inset) and excludingthe point source at the BCG. Errors are 1σ. The ellipse in the lower left corner of the inset shows the beam size.
ficient along the field lines for GeV particles, D∥ ≃ 1/4L2/τ ,where τ is the diffusion time and L is the diffusion scale.Again, for a conservative estimate, we assume an optimisticpicture in which a magnetic field with intensity B ∼ 2.5µG(that maximizes the electron lifetime) is mostly aligned alongthe tail of the minihalo, as seen in MHD simulations of thesloshing cool cores ZuHone et al. (2011). We also assumethat there are no significant perturbations or waves on smallscales that would reduce the diffusion along the field linesdue to scatter of the particle pitch angle. The spatial diffusioncoefficient required to explain the observed spectral steepen-ing is shown in Fig. 9(b). The required values are very large— orders of magnitude higher than current estimates for ourGalaxy (Berezinskii et al. 1990).Following Brunetti & Jones (2014), we also note that, even
in the absence of micro-scale perturbations that could stronglyreduce diffusion along the field lines, the field should be ad-vected and perturbed by large-scale gas motions, includingturbulence. The required minimum values of D∥ derived inFig. 9(b) place a lower limit on the effective mean-free pathof particles and — because particles travel strictly along thefield lines — on the minimum coherence (or tangling) scalesof the magnetic fields. Using D∥ ∼ 1/3clmfp from Fig. 9(b),where c is the speed of light, we find lmfp > 5 kpc, which isin tension with the minimum scales of magnetic field fluc-tuations observed in similar environments (Kuchar & Enßlin2011). Thus, diffusion of relativistic electrons originating inthe central region outwards along the field lines is not a feasi-ble explanation for the observed spectral behavior of the mini-halo tail.
6.2. Minihalo confinementIn Fig. 10(a), we show a Chandra X-ray image of
RX J1720.1, obtained from the combination of three obser-
vations (ObsIDs 1453, 3224 and 4631, for a total clean expo-sure of 42.5 ks; see Mazzotta & Giacintucci 2008 for details),showing the complex core of this otherwise relaxed cluster(Fig. 1). Two cold fronts, located on the opposite sides fromthe cluster center, appear to form a spiral structure that isseen in numerous simulations of sloshing of the central low-entropy gas in cluster cores (e.g., Ascasibar & Markevitch2006, Zuhone et al. 2011). In panel (b), we overlay the 617MHz radio brightness contours of the minihalo on the sameX-ray image. As previously noticed by Mazzotta & Giac-intucci (2008), the radio emission appears entirely containedwithin these cold fronts. The new, higher-sensitivity radio im-age shows that the minihalo tail is more extended than it wasin the earlier data, and traces the SE cold front remarkablywell.In panel (c), we present an overlay of the radio contours on
the Chandra projected temperature map, obtained using theobservations ObsID 3224 and 4631 (for a total clean expo-sure of 34.5 ks) following the algorithm described in Bour-din & Mazzotta (2008). Temperature values are derived fromspectra from overlapping square bins of varying scales, allow-ing us to map the temperature variations using a B2-splinewavelet transform. This algorithm has been adapted to theChandra ACIS-I instrument responses, using the backgroundmodel of Bartalucci et al. (2014). The wavelet transform hasbeen thresholded at 1σ and detects significant features on an-gular scales 0.5′′−8′′. The radio emission correlates well withthe cool gas spiral structure seen in the core of RX J1720.1.Panel (d) shows a snapshot from Z13 simulations of a radiominihalo in a relaxed cluster of similar mass, formed by tur-bulent reacceleration of electrons in a sloshing cool core. Thesimilarity of simulations with the minihalo in RX J1720.1 isstriking.The radial profiles of the radio and X-ray brightness in the
Giacintucci et al 2014
ZuHone et al 2014b, arXiv:1403.6743
Hadronic ModelsSpectral steepening from rapid changes in B (Keshet 2010)
ZuHone et al 2014b, arXiv:1403.6743
Hadronic Models
Summary
• Lots of activity, in both observations and simulations
• Some big open questions:
• How do you form large-scale fronts? With bigger kicks? Something particular about the thermodynamic profiles?
• Does the presence of sharp fronts really constrain thermal conduction to be very small?
• What is the ICM viscosity? How do we distinguish the effect of viscosity from that of the magnetic field by itself? Can we?
• What is the origin of radio mini-halos? How do we explain spectral steepening like in RXJ1720?