the physics of gas sloshing in galaxy clusters

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)

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

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

Observations of Gas Sloshing

X-Ray Surface Brightness

XMM-Newton observations of A496 (Simona Ghizzardi)

Temperature (keV)

Dupke + 2007

Chandra

Observations of Gas Sloshing

XMM-Newton observations of A496 (Simona Ghizzardi)

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

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”

• 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

Interaction with a gasless

subcluster

R = 5

b = 500 kpc

Temperature (keV) slice with DM contours

ZuHone, Markevitch, and Johnson 2010

Interaction with a gas-

filled subcluster

R = 20

b = 1000 kpc

Temperature (keV) slice with DM contours

ZuHone, Markevitch, and Johnson 2010

• 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?

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

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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 first contourlevel 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 contours of the

radio intensity are overlaid on the optical POSS2 image. Right: total intensity radio contours of Ophiuchus overlaid on the ChandraX-ray image in the 0.5-4 keV band.

halos is interesting to investigate in the framework of the modelsattempting 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 datafor 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 wayfrom the fit procedure presented in Paper II.

The comparison between the radio power of mini halos andthat 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,the cD galaxy can be a low power radio source or even radioquiet. This is indicative of a recurrent radio activity with a dutycycle of AGN activity that is lower than the cooling time andlower than the radio mini-halo time life. Therefore, we do not ex-pect a strong connection between cD and mini-halo radio power,and the position of Ophiuchus in the diagram implies that thiscluster is undergoing a low radio activity phase of the centralcD. We propose that this is important and that further studiesand more robust statistical analyses are necessary to prove thatmini-halo emission is directly triggered by the central cD galaxy.

6. Conclusions

Mini-halos in clusters are still poorly understood sources. Theyare a rare phenomenon, which have been found so far in only afew clusters. A larger number of mini-halo discoveries and moreinformation about their physical properties is necessary to dis-criminate between the different mechanisms suggested for trans-ferring energy to the relativistic electrons that power the radioemission.

To search for new mini-halos, we have analyzed deep ra-dio observations of A1068, A1413, A1650, A1835, A2029, andOphiuchus, carried out with the Very Large Array at 1.4 GHz.

We have found that at the center of the clusters A1835,A2029, and Ophiuchus, the dominant radio galaxy is surroundedby a diffuse low surface brightnessmini-halo. The relatively high

resolution of our new images ensures that the detected diffuseemission is real and not due to a blend of discrete sources.

We analyzed the interplay between the mini-halos and thecluster X-ray emission. We identified a similarity between theshape of the radio mini-halo emission and the cluster X-ray mor-phology of A2029, A1835, and Ophiuchus. We note that, al-though all these clusters are considered to be relaxed systems,when analyzed in detail they are found to contain peculiar X-rayfeatures at the cluster center, which are indicative of a link be-tween the mini-halo emission and some minor merger activity.Because of the large angular extension of Ophiuchus, it is pos-sible to perform a point-to-point comparison of the radio and X-ray brightness distributions. The close similarity between radioand X-ray structures in this cluster is demonstrated by the cor-relation between these two parameters. We fitted the data with apower law relation of the type I1.4GHz ∝ I1.51±0.04X .

A hint of diffuse emission at the center of A1068 and A1413is present with low significance (2−3σ), and before classificationas mini-halos, further investigation is needed. In addition, in thefield of view of one of our observations, we report the serendipi-tous detection of a giant radio galaxy, located at RA=10h39m30sDEC=39◦47′19′′, of a total extension ∼1.6 Mpc in size.

Finally, the comparison between the radio power of mini ha-los and that of the central cD galaxy, reveals that there is a weaktendency for the more powerful mini-halos to host stronger cen-tral radio sources.

Discriminating between the different scenarios proposed formini-halo formation is difficult using present radio data. We notethat the radio-X ray connection in the Ophiuchus cluster maysupport secondary models. On the other hand, the analyses ofthe clusters studied here appear to indicate that mini-halos arenot a common phenomenon in relaxed system, a result that is incloser agreement with primary models.

Acknowledgements. FG and MM thank the hospitality of the Harvard-Smithsonian Center for Astrophysics where most of this work was done. Supportwas provided by Chandra grants GO5-6123X and GO6-7126X, NASA con-tract NAS8-39073, and the Smithsonian Institution. This research was partiallysupported by ASI-INAF I/088/06/0 - High Energy Astrophysics and PRIN-INAF2005. We are grateful to the referee Pasquale Mazzotta for very usefulcomments that improved this paper. We would like to thank Rossella Cassano

Govoni et al 2009

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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

Sloshing with Magnetic Fields

T (keV) B (G)

Sloshing with Magnetic FieldsT (keV)

No Fields With Fields

Viscosity and Cold FrontsViscous 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

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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 2012b

ZuHone et al 2010

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?

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Projected Mean Velocity


Projected Velocity Dispersion



• 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

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∥b̂b̂ ·∇T

Thermal ConductionNo Conduction Spitzer Conduction

500 kpc ZuHone et al 2013a

– 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 (

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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 (

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d (kpc)

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4.5

5

5.5

6

6.5

7

7.5

8

8.5

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0 5 10 15 20 25 30 35 40 45 50

T (

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5.5

6

6.5

7

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T (

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d (kpc)

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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

X-Ray Images

A2319

S1

SC1

SC3

ZuHone et al 2013a

No Conduction 0.1 Spitzer

Spitzer

Where Does the Heat Come from?

The magnetic fields are not always perfectly draped across the cold fronts ZuHone et al 2013a

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

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

Radio Mini-Halos• Steep spectra • Steep radial cutoff • Not all cool-core

clusters possess them

Giacintucci et al 2014, in prep.

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

Accelerating Electrons

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Radio and Temperature Profiles

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Radio Spectrum and Power

ZuHone et al 2013b

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Comparison With Observations

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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

!yt is designed to address physical,

not computational, questions

“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”)

Fully-Supported

Mostly-Supported

In Progress

Enzo FLASH Nyx

Orion Data In-Memory

Chombo Athena

ART Ramses

Gadget Hydra

PKDGRAV FITS Image Data

Formation of a Galaxy Cluster: Sam Skillman

Bolatto et al. 2013, Nature, 499, 450

Simulating Cluster Observations

S-Z (thermal+kinetic+relativistic corr.) X-ray

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

http://yt-project.org

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

the physics of gas sloshing in galaxy clusters

Science