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


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


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


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


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

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.Ataviscosity

f

µ

10

�3,

allCFs

areclearly

distorted

andmad

eragged

bytheKHI.W

ithincreasin

gviscosity,

thefronts

becom

eless

ragged,an

dstru

ctures

atprogressively

largerscales

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.Interestin

gly,even

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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

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gest(⇠

500km

s �1).

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sat

smaller

length

scalesthou

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athigh

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this

locationas

well,

whereas

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atlow

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Oursim

ulation

sdem

onstrate

that

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ference:

thegrow

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derived

fromthelin

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analysis.

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applies

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well

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s,while

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onstrate

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analytically

andnu

merically

inasep

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(Roed

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).Furth

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ndgravitation

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thean

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nally,

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ously

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mod

ifyits

growth

atlon

gtim

escales.For

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plitu

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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.


ZuHone et al 2014a, arXiv:1406.4031



similar



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


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


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?

gas sloshing: simulations and observations

Science