An azimuthally resolved study of the cold front in Abell 3667

8.7 MB·

by  Y. Ichinohe

MNRAS000,1–13(2016) Preprint6February2017 CompiledusingMNRASLATEXstylefilev3.0
An azimuthally resolved study of the cold front in
Abell 3667
Y. Ichinohe,1(cid:63) A. Simionescu,2 N. Werner3,4 and T. Takahashi2
1Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan
2Institute of Space and Astronautical Science (ISAS), JAXA, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan
3MTA-E¨otv¨os University Lendu¨let Hot Universe Research Group, P´azma´ny P´eter s´eta´ny 1/A, Budapest, 1117, Hungary
4Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotla´ˇrska´ 2, Brno, 611 37, Czech Republic
7
1
0
2
ABSTRACT
n
Themicrophysicalproperties,suchaseffectiveviscosityandconductivity,oftheweakly
a
J magnetizedintergalacticplasmaarenotyetwellknown.Weinvestigatetheconstraints
that can be placed by an azimuthally resolved study of the cold front in Abell 3667
1
using ∼500 ksec archival Chandra data. We find that the radius of the interface fluc-
3
tuates with position angle and the morphology of the interface is strikingly similar to

] recent numerical simulations of inviscid gas-stripping. We find multiple edges in the
E
surface brightness profiles across the cold front as well as azimuthal variations, which
H are consistent with the presence of Kelvin-Helmholtz Instabilities (KHI) developing
. along the cold front. They indicate that the characteristic length scale of KHI rolls is
h
around 20–80 kpc. This is the first observational indication of developing KHIs along
p
a merger cold front in a galaxy cluster. Based on the KHI scenario, we estimated the
-
o upper limit of the ICM effective viscosity. The estimated value of µ(cid:46)200 g/cm/s is at
r most 5% oftheisotropic Spitzer-like viscosity. The observed apparentmixing towards
t
s the outer edges away from the tip of the front provides an additional evidence for
a suppressed viscosity.
[

Key words: galaxies: clusters: individual: Abell 3667 – galaxies: clusters: intraclus-
1
ter medium – X-rays: galaxies: clusters
v
6
2
0
1
1 INTRODUCTION calandX-rayobservationsofthesystemrevealedelongated
0
double-peakedX-raymorphologyinthenorthwest-southeast
. Among gravitationally collapsed structures, clusters of
2 direction, in which the locations of the two brightest galax-
0 galaxies are the largest and most recently formed (and still iescoincidewiththetwoX-raypeaks(Sodreetal.1992).A
7 forming). They evolve to the typical mass of 1014-15M(cid:12) via moreindepthopticalstudybyOwersetal.(2009a)showed
1 accretion of smaller structures and successive mergers of
thatthemembergalaxydistributionissignificantlybimodal,
: smaller clusters or groups (Sarazin 2002). Most of the in-
v andtheoffsetofthepeculiarvelocitiesofthetwogalaxydis-
tergalactic medium (IGM) currently observable resides in
i tributions is ∼500 km/s.
X galaxyclusterswhereitisreferredtoasintraclustermedium
r (ICM). In the radio band, its most prominent feature is the
a Although most of the baryons reside in the IGM/ICM, northwestern extended radio emission (Rottgering et al.
many questions remain about the physics of this diffuse 1997). This feature is classified as a radio relic, and is the
plasma. The most fundamental and important open issues brightest known source in this class. The radio spectral in-
regard the basic microphysical properties of the IGM, such dex shows steepening from the outer edge toward the clus-
asitseffectiveviscosity,thermalconductivity,geometryand tercentre,indicatingtheagingofthenon-thermalelectrons
strength of the magnetic fields, turbulence, mixing time- (Hindsonetal.2014).Attheoppositesideoftheradiorelic
scale, and heating-cooling balance. withrespecttotheclustercentre,lessprominentradiorelics
Abell 3667 is a nearby (z = 0.055, Sodre et al. 1992) are also observed (Rottgering et al. 1997). Roettiger et al.
non-cool-core cluster of galaxies known for the various in- (1999) studied the system numerically and indicated that
dications of its recent merger in a wide range of electro- these relics are one of the consequences of merger activity.
magnetic wavelengths: radio, optical and X-ray. Early opti- Inadditiontotherelics,ithasbeensuggestedrecentlythat
Abell3667alsohostsanothertypeofdiffuseradioemission,
which connects these relics (radio bridge), and which may
(cid:63) E-mail:[email protected] be associated with the ICM turbulence due to this merger
(cid:13)c 2016TheAuthors
2 Y. Ichinohe et al.
(Carretti et al. 2013; Riseley et al. 2015). The overall radio
Table 1. Summary of the observations used in this paper. The
structure is aligned well with the major axis of the X-ray netexposuretimeisafterthedatascreening.
emission and the axis of the galaxy bimodality.
Thenorthwesternradiorelicisextensivelystudiedalso ObsID Date Netexposuretime(ksec)
in the X-ray band. Finoguenov et al. (2010) and Sarazin
513 2000-11-03 43
et al. (2013) investigated the thermodynamic structure
889 2001-09-22 50
around the relic using XMM-Newton, and observed a sharp
5751 2006-06-21 126
dropofthetemperatureandthesurfacebrightness,indicat-
5752 2006-06-21 59
ing that the origin of the relic is a merger shock with the
5753 2006-06-21 74
Mach number of M ∼ 2. Subsequent Suzaku observations 6292 2006-06-21 45
also confirmed the result (Akamatsu et al. 2012; Akamatsu 6295 2006-06-21 47
& Kawahara 2013), further indicating that the plasma may 6296 2006-06-21 49
beoutofthermalequilibriuminthisregion.Itsnon-thermal
nature has also been extensively explored, but the problem
of whether the X-ray emission associated with the relic is 68% confidence level for one parameter. Throughout this
thermalornon-thermalisstilltoberesolved(Fusco-Femiano paper, we assume the standard ΛCDM cosmological model
et al. 2001; Rephaeli & Gruber 2004; Nakazawa et al. 2009; withtheparametersof(Ωm,ΩΛ,H0)=(0.3,0.7,70km/s/Mpc).
Finoguenov et al. 2010; Akamatsu et al. 2012).
Initially, the X-ray brightness edge opposite to the
northwestern relic was thought to be also a shock front 2 OBSERVATIONS, DATA REDUCTION, AND
(Markevitch et al. 1999). The Chandra observation of the DATA ANALYSIS
brightness drop surprisingly revealed that this is not the
case,butinstead,theedgeisa“coldfront”whichistheinter- Abell3667wasobservedninetimesintotalusingtheChan-
facebetweenacool,densegasvolumeandthehot,tenuous dra ACIS-I detectors. We selected eight ObsIDs (513, 889,
ambientmedium(Vikhlininetal.2001b).Abell3667isone 5751, 5752, 5753, 6292 and 6295) which have the satellite
ofthefirstclustersinwhichacoldfrontwasobservedwhile, exposuretimeofabove10ksec.Wereprocessedthearchival
todate,itisknownthatcoldfrontsareobservationallymore standardlevel1eventlistsproducedbytheChandrapipeline
common than shock fronts (Markevitch & Vikhlinin 2007; in the standard manner1 using the CIAO software package
Owers et al. 2009b). (version 4.7) and the CALDB (version 4.6.5) to apply the
The thinness of the cold front, which cannot be re- appropriate gain maps and the latest calibration products.
solved even with the Chandra angular resolution, has of- The net exposure times of each observation after screening
feredusawealthofindicationsregardingICMmicrophysics. aresummarizedinTable1.Theresultingtotalnetexposure
Vikhlinin et al. (2001b) first suggested that transport pro- time is ∼500 ksec.
cesses are heavily suppressed across the interface, and also We removed bad pixels and also applied the standard
pointedouttheabsenceofhydrodynamicinstabilitiesatthe data grade selections. We examined the light curve of each
front. Vikhlinin et al. (2001a) estimated the magnetic field observation in the 0.3-10 keV energy band with the stan-
strength required to keep the front hydrodynamically sta- dardtimebinningmethodrecommendedintheCIAOofficial
ble. Vikhlinin & Markevitch (2002) considered the role of analysisguides,toexcludeperiodsofanomalouslyhighback-
gravityforthestability,whileChurazov&Inogamov(2004) ground.Blank-skybackgroundfilesprovidedbytheChandra
suggestedtheintrinsicwidthoftheinterfacecanalsostabi- teamwereprocessedinasimilarmannerandwerescaledby
lizethefront.Mazzottaetal.(2002)pointedoutasignature the ratio of the photon counts in the data to those in the
of a possible very-large-scale developing instability. backgroundinthehighenergyband(9.5-12keV)wherethe
effective area of the telescope is effectively zero.
Thecoldfrontisalsostudiednumericallybye.g.,Heinz
et al. (2003), and the predictions are confirmed by deeper
data:thethermodynamicmapsbasedontheXMM-Newton
2.1 Imaging analysis
and Chandra observations revealed that cold, low-entropy
and high-metallicity gas is uplifted toward the tip of the We created the exposure and vignetting corrected, back-
front (Briel et al. 2004; Lovisari et al. 2009; Datta et al. ground subtracted Chandra images (flat-fielded image) fol-
2014),whiletheshapeofthefrontitselfwasobservedtobe lowing the procedure presented by Ichinohe et al. (2015).
mushroom-like (Owers et al. 2009b). The resulting image is shown in Figure 1.
Becauseofitsprominenceandproximity,thiscoldfront
is a rather well studied one, as mentioned above. However,
the studies done so far have not focused on the azimuthal 2.2 Surface brightness profiles
information of the front. Since hydrodynamic instabilities
Inordertoinvestigateazimuthalvariationsofthecoldfront,
occur on the interface, the azimuthal variation should con-
we extracted surface brightness profiles for the directions
tainalotofinformationaboutthemicrophysicalproperties
indicatedbythewhitepartial-annulus-shapedregionsshown
oftheICM,inasimilarwayastheradialdependencedoes.
inFigure1.Wedeterminedthecentreofthesepartialannuli
Abell3667isrelativelynearby,andthefrontisverypromi-
so that their radial directions are roughly perpendicular to
nent, with a large opening angle, which make it the ideal
target for such a study regarding the azimuthal variation.
This is the topic of the present manuscript. 1 CIAO 4.7 Homepage, Data Preparation;
Unless otherwise noted, the error bars correspond to http://cxc.harvard.edu/ciao/threads/data.html
MNRAS000,1–13(2016)
The cold front in Abell 3667 3
nuit2 fitting library integrated in the ROOT data analysis
frameworktominimizeχ2.TheresultsarediscussedinSec-
tion 3.2.
150º-165º 2.3 Deprojected thermodynamic profiles
Thanks to the high-quality deep observation of ∼500 ksec,
165º-180º we are able to investigate the deprojected thermodynamic
properties with an azimuthal resolution of 15◦ for a single
cold front. Figure 1 shows in green the 10 directions from
180º-195º each of which we extracted a deprojected thermodynamic
profile. For the spectral fitting, we used XSPEC (version
12.8.2)(Arnaud1996)tominimizeχ2.TheX-rayemissionis
195º-210º
modeledasasingle-temperaturethermalplasmausingapec
model(Smithetal.2001).Weusedthemodelprojcttoin-
210º-225º corporate the effect of the projection of outer gas volumes,
under the assumption of spherical symmetry. We fixed the
225º-240º
metallicity to the values obtained from the projected ther-
240º-255º 285º-300º modynamicprofiles.Weusedthechemicalabundancetable
255º-270º 270º-285º
2 arcmin determined by Lodders (2003). In the spectral fitting, the
128 kpc
typical reduced χ2 is 1.02, with the typical number of de-
grees of freedom (NDF) of 1500.
Figure 1. σ=0.98 arcsec Gaussian smoothed, exposure and vi-
gnetting corrected, background subtracted Chandra image (0.6-
7.5keV)ofAbell3667.Theoverlaidwhitesectorsdenotethedi-
3 RESULTS
rectionsalongwhichthesurfacebrightnessprofilesareextracted
(seealsoFigures2andB1).Thegreensectorsdenotetheregions 3.1 Global morphological features
fromwhichthedeprojectedthermodynamicprofilesareextracted
(see also Figures 4, C1 and C2). The black arrows indicate the In the flat-fielded image (Figure 1), the cold front, the
brightnessdipandexcess(seeSection3.1). abruptsurfacebrightnessdropthatazimuthallyextendsfor
∼500 kpc, is clearly visible on the southeastern part of the
cluster.
the cold front. The narrower sectors have an opening angle
The interface appears abrupt in terms of the drop of
of5◦ andthewidersectorsare15◦ wide,correspondingtoa
thesurfacebrightness.Ontheotherhand,itvisuallyseems
lengthofarcof22kpcand67kpcattheradiusofthefront.
to have an azimuthal variation in terms of the radii or the
To model the shape of the surface brightness profiles
curvature radius, which has not been explicitly pointed out
quantitatively, we assumed that the underlying radial den-
previously.Thesurface-brightnesscontrastacrosstheinter-
sity profile n(r) is expressed as a broken power law with a
faceisstrongtowardssoutheast,butgraduallyweakenedto
jump of normalization at the break;
the north and south along the front, forming a mushroom-
n(r)= nj12(cid:16)n0r(cid:16)(cid:17)r−1r2α(cid:17)2−α1(r (r<≤r)r12) , (1) like sAhabprei.ghtness dip exists to the north of the cluster’s
0 r12 12 brightness peak, and a brightness excess, which seems to
where r and j are the radius of the break and the am- extend anti-clockwise from the brightness peak, exists fur-
12 12
plitude of the jump there, n is the overall normalization, ther out (see the black arrows in Figure 1). This feature
0
andα andα arethepower-lawslopesofthedensityprofile wasfirstmentionedinMazzottaetal.(2002)whosuggested
1 2
inside and outside the front. that this shape is due to the development of hydrodynamic
Ignoring line emission, the emissivity of the ICM is de- instability.
scribed using the emissivity of thermal bremsstrahlung ra- Wealsoconfirmedthatthetwo-dimensionalthermody-
diation (cid:15) =ξ(T,Z)n2, where n is the density and ξ(T,Z) is a namicstructure,using500ksecChandradatawithcontour-
coefficientwhichweaklydependsontemperatureandmetal- binningalgorithm(Sanders2006),whosebinsarethemody-
licity.Assumingsphericalsymmetryandapproximatingξto namicallyindependenttoeachother,isconsistentwithpre-
be constant, the surface brightness profile S(x) can be ob- vious observations (Mazzotta et al. 2002; Briel et al. 2004;
tained by integrating the density profile along the line-of- Lovisarietal.2009;Dattaetal.2014;Hofmannetal.2016,
sight direction y; see Appendix A).
(cid:90) ∞ (cid:90) ∞ x(1+s2)n(x(1+s2))
S(x)=2A n2(r)dy=4A √ ds, (2)
0 0 s2+2 3.2 Azimuthally resolved surface brightness
properties
where xisthecoordinatealongwhichthesurfacebrightness
profile is extracted, A is a constant which includes both the Figure 2 shows the azimuthal variations of the best-fitting
effect of ξ and the effect of ∝r−2 decrement of the intensity parametersofourassumeddensitymodel(Equation1).The
(cid:112)
andsisatransformedvariableusingr= x2+y2=x(1+s2). black/red and the gray/magenta points represent the best-
We fitted this model to the extracted profiles using the Mi- fittingparametersforthesurfacebrightnessprofileextracted
MNRAS000,1–13(2016)
4 Y. Ichinohe et al.
3.0
2.5
p
m
2.0
u
j
1.5
1.0
6.5
azimuth [deg]
6.0
5.5
]
n
mi 5.0
rc 4.5
a
k [ 4.0
a
e 3.5
r
b
3.0
2.5
22..00
azimuth [deg]
1.5
1.0
e 0.5
p
o
sl 0.0
0.5
inner
1.0
outer
1.5
0.014 azimuth [deg]
0.012
n
o
ti 0.010
a
z
ali 0.008
m
r
o
N 0.006
0.004
0.002
150 200 250 300
azimuth [deg]
Figure 2.Theazimuthalvariationsofthebest-fittingparametersoftheprojectedbrokenpowerlawmodels.Top row:thejump j12 in
densityatthebreak,Second row:theradiusofthebreakr12,Third row:theslopeinside(inner)/outside(outer)theinterface(α1,α2).
Bottomrow:thenormalizationinside(inner)/outside(outer)theinterface(j12n0,n0).Inthebottomtwopanels,thered/magentapoints
representthevaluesinsidethebreak,wheretheblack/graypointsrepresentthevaluesoutsidethebreak.Thedifferencebetweenblack
andgrayorbetweenredandmagentaistheopeningangleofthesectors(15◦ and5◦).
MNRAS000,1–13(2016)
The cold front in Abell 3667 5
for the wider (15◦) sectors and the narrower (5◦) sectors 3.3 Azimuthally resolved deprojected
(for the actual surface brightness profiles, in which we can thermodynamic properties
also recognize the azimuthal variations clearly, refer to Fig-
Figure 4 shows the azimuthal variations of the thermo-
ure B1).
dynamic quantities (the deprojected density, temperature,
All of the parameters show significant azimuthal varia-
pressure and entropy, and the projected Fe abundance) just
tions.Theazimuthalprofileofthejump j isclearlypeaked
12 under and above the interface, together with the ratio of
at around 210◦-240◦, and has a relatively symmetric shape.
the inner quantity to the outer quantity. For the complete
Theoveralltrendisthesameintheprofileoffinerazimuthal
deprojected thermodynamic profiles (from −150 arcsec to
resolution(5◦,grey),butthereseemtobeasystematicbump
300 arcsec), refer to Figures C1 and C2.
and a systematic dip of the jump amplitude around 220◦-
Generally,atthehigh-contrastpartsofthefront(195◦-
225◦ and 235◦-250◦, respectively. The overall trend of the
270◦), clearly both the density and the temperature show
jump, which peaks in the middle of the cold front, is qual-
a jump by a factor of ∼2-3. Since the jumps of the density
itatively consistent with the recent results by Walker et al.
and the temperature are in the opposite sense, the entropy
(2016),whoappliedtheGaussiangradientmagnitudefilter-
alsoexhibitsalargejumpandthepressureshowsanalmost
ing method to the same cold front.
continuous profile. Underneath the front, the entropy and
Although the profile of the break r is more or less
12 the temperature profiles seem to show downtrends toward
constant at azimuths of 170◦-300◦, it shows an indication
the interface, while the density profiles show uptrends. On
of a downward-convex shape, which may or may not be at-
theotherhand,atthelow-contrastpartofthefront(<195◦
tributed to the misalignment between the sectors and the
and 270◦ <) the temperatures show milder jumps, resulting
cold front. On top of the convex shape, it shows azimuthal
in relatively bigger/smaller jumps in the pressure/entropy
variations of relatively large length scale, about 15◦-25◦.
profiles.TheseratiosareconsistentwiththeresultsbyOw-
Theprofileoftheouterpower-lawslopeα showsmod-
1 ers et al. (2009b) who examined the front focusing only on
eratechanges,whereasthatoftheinnerpower-lawslopeα
2 the highest-contrast part (about 210◦-240◦). The projected
shows an asymmetric, two-peaked shape. The inner power-
Fe abundance ratio indicates a slight decrease in the lower-
lawslopesbecomepositivearoundthehighestcontrastpart
contrast parts, but due to the large errorbars, it is difficult
ofthefront,implyingthedensityincreasestowardthefront.
to derive any significant statements.
Althoughtheprofileoftheouternormalizationn shows
0
moderate changes, that of the inner normalization j n
12 0
shows the two-peaked shape similar to that of the inner
slope. The difference between the inner normalization and
the outer normalization are large at the central azimuths, 4 DISCUSSION
reflecting the higher contrast of the image there.
4.1 Origin of the cold front
Whenavolumeofgas,stratifiedinitsgravitationalpotential
well, is subjected to ambient flow, a very sharp cold front
willquicklyform(Markevitch&Vikhlinin2007).Ithasbeen
3.2.1 Multiple edges in the surface brightness profiles
shown in a number of numerical simulations that, in such a
Although fitting the surface brightness profiles with a pro- situation,theshapeofthefrontwillbemushroom-likewhen
jected broken power law model (Equation 1) yields reason- itisseenfromadirectionperpendiculartotheflowdirection
able fits, we see some systematic residuals in the sectors of (Heinz et al. 2003; Roediger et al. 2015a,b).
210◦-225◦ and 225◦-240◦ (see the top panels of Figure 3). In addition to the mushroom-shape in the image, the
Indeed, each fit improves by > 3σ level when the surface front also shows a characteristic thermodynamic struc-
brightnessprofilesarefittedwithaprojecteddouble-broken ture. That is, the dense core gas with low-entropy and
power law model using the radial density profile of high-metallicity is gradually uplifted during the motion,
and finally reaches the leading edge of the front. This
n(r)= njj21032(cid:16)njr202r33(cid:16)n(cid:17)r0−2r3α(cid:16)(cid:17)3rr−1223α(cid:17)2(−rα232(r(cid:16)<1r21rr2<)(cid:17)−rα1≤r(2r3)≤r12) , (3) leleonawtdrostIhpnteyoo/futrteorhmncetap.setehr,aetarumsroseedaeynnndainmhiFigcihgesustrtre-umc1t,euttrahelelicwsihthyaeprgeeasothfisethjuleoswftreobsnett--
isclearlymushroom-shaped,andtheedgesofthefrontseem
where r /r are the radii of the inner/outer breaks, j /j to be dissolved into the ambient medium. The deprojected
12 23 12 23
are the jumps at the inner/outer breaks, n is the normal- thermodynamic profiles (see Figure 4, and also Figures C1
0
ization and α /α /α are the innermost/middle/outermost andC2)aswellastheprojectedonesintheliterature(Maz-
1 2 3
power-lawslopes(∆χ2 =29.7and16.6for∆NDF=3respec- zottaetal.2002;Brieletal.2004;Lovisarietal.2009;Datta
tively for the sectors 210◦-225◦ and 225◦-240◦, compared to etal.2014;Hofmannetal.2016,seealsoFigureA1)clearly
the single-broken power law model). displaythethermodynamicstructuretypicalofupliftedcore
The bottom panels of Figure 3 show the fitting results gas.Inaddition,thepressuremapwhichishighlyelongated
using the projected double-broken power law model. The in the northwest-southeast direction, and also a number of
residuals are mitigated (see the arrows in Figure 3). The observationalindications,e.g.thegalaxydistributionwhich
densityjumpsaresignificant; j =1.68+0.31and j =1.65−0.23 iswellalignedalongthemajoraxis(Proustetal.1988;Ow-
12 −0.23 23 −0.22
forthe210◦-225◦ sectorand j =1.21±0.07and j =2.59± ers et al. 2009a) and the radio relics located to northwest
12 23
0.10 for the 225◦-240◦ sector. andsoutheast(Rottgeringetal.1997),suggestthatthecold
MNRAS000,1–13(2016)
6 Y. Ichinohe et al.
0.3×10−3 210°-225° 0.3×10−3 225°-240°
0.25 0.25
ghtness2]arcmin 0.2 χ2/NDF = 266.02/184 ghtness2]arcmin 0.2 χ2/NDF = 209.651/178
e bri2/cm0.15 e bri2/cm0.15
Surfac s/sec/ 0.1 Surfac s/sec/ 0.1
[ct [ct
0.05 0.05
-30 0.030×10−31 2 3 4 5 6 7 8 9 -30 0.030×10−31 2 3 4 5 6 7 8 9
1 0.02 1 0.02
al/ 0.01 al/ 0.01
u 0 u 0
esid−−00..0021 esid−−00..0021
R−0.03 R−0.03
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
r [arcmin] r [arcmin]
0.3×10−3 210°-225° 0.3×10−3 225°-240°
0.25 0.25
ghtness2]arcmin 0.2 χ2/NDF = 236.302/181 ghtness2]arcmin 0.2 χ2/NDF = 193.1/175
e bri2/cm0.15 e bri2/cm0.15
Surfac s/sec/ 0.1 Surfac s/sec/ 0.1
[ct [ct
0.05 0.05
-30 0.030×10−31 2 3 4 5 6 7 8 9 -30 0.030×10−31 2 3 4 5 6 7 8 9
1 0.02 1 0.02
al/ 0.01 al/ 0.01
u 0 u 0
esid−−00..0021 esid−−00..0021
R−0.03 R−0.03
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
r [arcmin] r [arcmin]
Figure 3.Thetoptwopanelsrepresentthefittingresultsfortheprojectedbrokenpowerlawmodel(left:210◦-225◦,right:225◦-240◦).
In the bottom two panels, the best-fitting projected double-broken power law models are overlaid instead of the best-fitting projected
single-brokenpowerlaw(left:210◦-225◦,right:225◦-240◦).Theblackarrowsrepresentthepositionsoftheedges.
front is forming because of a merger very close to the sky nounced and the sub-opening-angle scale variations are no
plane. longer clearly visible.
We also point out the striking similarity of the X-ray Givenalltheargumentsabove,wesuggestthatthefront
imagetothenumericalsimulationbyRoedigeretal.(2015b) is formed via a merger event taking place nearly in the sky
who modeled the inviscid stripping of an initially extended plane.Notethatgassloshingparalleltothelineofsightdi-
atmospheresubjectedtotheambientflowofitshostcluster rection is another possible interpretation (Kitayama et al.
duringtheinitialrelaxationphase(Figure5).Thecoldfront 2014). Testing these different scenarios would require mea-
in Abell 3667 (Figure 5 bottom) is especially similar to the surementsoftheline-of-sightvelocityinsideandoutsidethe
inviscid simulation result at 780 Myr before the pericentre interfacebyDopplershiftmeasurements,whichcanonlybe
passage (Figure 5 top) in two perspectives; (1) the opening performed with high resolution X-ray spectroscopy.
of the front or the angle where the stripping starts, and
moreimportantly,(2)thevariationsofthefrontradiiwhose
4.2 Gas dynamics
length scale is smaller than the opening angle of the entire
cold front (sub-opening-angle scale variation). From the thermodynamic information, we can estimate the
ItisalsoshowninthenumericalsimulationsbyRoedi- velocity of the cool gas relative to the ambient medium as
ger et al. (2015b) that the impact of the inclination an- hasbeendoneintheliterature(Vikhlininetal.2001b;Lan-
gle of the line-of-sight direction with respect to the direc- dau & Lifshitz 1959): by approximating the cool gas as a
tion perpendicular to the merger plane is relatively strong blunt body subjected to an ambient flow, and neglecting
above ∼30◦, for which case the interface becomes less pro- the change in the gravitational potential along the stream-
line, the ratio of the pressure of the flow at the stagnation
point p to the pressure of the flow in the free streaming
0
3 Roediger E., et al.,“Stripped Elliptical Galaxies as Probes of region p is a function of the cloud velocity v;
1
ISnmCtairlMs,isp8ipo0Pni6nh.:gy10soi4cf,st:1h5IepI.pV.Si(tr2igr0or1eE5d,lJliubpnutetic1aM0l)iMx.e(cid:13)8cd9?A”,AVTSish.ceRoueAspsratorndodupchIenydsviiwcsaciltidhJopGuearrs-- pp10 = (cid:16)(cid:16)1γ+2+1(cid:17)γ(γ−2+11M)/(γ1−21(cid:17))γ/M(γ−112)(cid:18)γ(−M12γM−≤1121(cid:19))−1/(γ−1) (M1>1) , (4)
MNRAS000,1–13(2016)
The cold front in Abell 3667 7
5.01e 3
4.5 inner 3.0 inner/outer
4.0
Density3[cm]− 2233....0505 outer ratio 22..05
1.5
1.0 1.5
1.1
e 12 azimuth [deg] 1.0 azimuth [deg]
mperatur[keV] 1068 ratio 00000.....56789
Te 4 0.4
0.3
0.022
0.020 azimuth [deg] 2.5 azimuth [deg]
Pressure3keV cm]−000000......000000011111802468 ratio 112...050
[
00..0000461e3 0.5
1.2 azimuth [deg] 0.7 azimuth [deg]
] 1.0 0.6
Entropy2keV cm 000...468 ratio 000...345
[ 0.2 0.2
e 01..00 azimuth [deg] 0.18 azimuth [deg]
c 7
ojectedbundanSolar] 000...468 ratio 3456
Pre a[ 0.2 2
F 1
0.0 0
160 180 200 220 240 260 280 300 160 180 200 220 240 260 280 300
azimuth [deg] azimuth [deg]
Figure4.Theazimuthalvariationsofthethermodynamicquantitiesjustinside(inner;black)andoutside(outer;red)thefront.Theleft
panelsshowtheazimuthalvariationsofthedeprojecteddensity,thedeprojectedtemperature,thedeprojectedpressure,thedeprojected
entropy and the projected Fe abundance from top to bottom. The right panels show the ratio of the inner value to the outer value for
thecorrespondingquantities.
where γ=5/3 is the adiabatic index of the monoatomic gas 4.3 Kelvin-Helmholtz instability
and M =v/c is the Mach number of the free stream, with
1 s 4.3.1 Sub-opening-angle scale variations
c being the free-stream sound speed.
s
What makes the cold front in Abell 3667 a particularly in-
terestingtargetareitsvariationsonazimuthalscalessmaller
Assuming that the azimuthal range of 210◦-240◦ rep- thantheopeningangleoftheentirefront(sub-opening-angle
resents the tip of the front and using p ∼ 0.0134 ± scale variation). This variation may have been missed in
0
0.0004 keV cm−3 (average of the bins just below the front) othercoldfrontsbecausethestudiesdonesofarhavefocused
and p ∼ 0.0092+0.0005 keV cm−3 (average of the outermost mainly on the width of the front and the surface brightness
1 −0.0004
bins)fromthedeprojectedthermodynamicprofiles(seealso profiles have been extracted from much wider sectors (e.g.
FiguresC1andC2),theMachnumberofthefreestreamis Owersetal.2009b;Ghizzardietal.2010;Dattaetal.2014).
calculated at M1 =0.70±0.06. This value is consistent with As we pointed out in the previous Section, the radii of
the previous estimation by Datta et al. (2014) but smaller thefrontshowazimuthalvariations,andthevariationissim-
than the previous estimation of 1.0±0.2 by Vikhlinin et al. ilar to the inviscid simulation results (Figure 5 top panel).
(2001b); this discrepancy may be due to the indirect mea- Actually, high-viscosity (Re=46 at pericentre, 0.1 Spitzer
surementofne byVikhlininetal.(2001b),whoinferredthe viscosity) simulation results are qualitatively inconsistent
density assuming that the surface brightness profile follows with our observations because they predict much smoother
a β model. interfaces (Figure 5 middle panel). This suggests that the
Reynolds number of the ICM is much higher in Abell 3667.
Roediger et al. (2015b) suggest that, in the inviscid
The sound speed c in the free stream is calculated stripping, the momentum transfer between two gas phases
(cid:112) s1
using c = γkT /µm , where kT is the temperature of the occurs via Kelvin-Helmholtz instabilities (KHIs), while in
s1 1 p 1
free stream, and µ = 0.6 is the mean particle weight with theviscouscase,itdoesviaviscosity.Thesimulationresults
respect to the proton mass m . Using kT = 6.9+0.4 keV and (Figure 5 top panel) clearly show KHIs occurring close to
p 1 −0.3
M = v/c , the velocity of the cool gas is estimated at v = thetipofthefrontanddevelopingtowardtheedge,strongly
1 s1
950±80 km s−1. suggestingthatourazimuthalvariationsoftheinterfaceare
MNRAS000,1–13(2016)
8 Y. Ichinohe et al.
the signatures of the onset of developing KHIs. We investi-
gate the scenario more in detail later in Sections 4.3.4 and
inviscid 4.3.5.
4.3.2 Multiple edges
Recently it has been suggested by Roediger et al. (2013b)
that, when there are developing KHIs at a cold front, the
surface brightness profile across the front exhibits multiple
edges,similarlytoourcase.Thedifferencesinradiibetween
thebreaksare∆r ≡r −r =0.26+0.02arcminand∆r =
break 23 12 −0.04 break
0.46+0.03 arcmin respectively for the sectors 210◦-225◦ and
−0.05
225◦-240◦,whichcorrespondtotheactuallengthsof∆r =
break
17+1 kpc and ∆r =30+2 kpc.
−3 break −3
Roedigeretal.(2013b,a)furthersuggestedthatthesep-
aration between the edges corresponds to about a fourth to
a half of the scale length of the KH rolls. From ∆r val-
break
ues, the scale length of the KH rolls is thus estimated at
around 30-120 kpc, which is consistent with the observed
viscous sub-opening-angle scale variation of the interface (see also
Section 4.3.4).
Figure 6 shows the projected thermodynamic profiles
for the corresponding sectors. In the profiles extracted for
the sector 210◦-225◦ (Figure 6 left), we see a jump of the
temperature and entropy at the inner edge while they are
continuousattheouteredge,whichmeansthatthethermo-
dynamic properties between the edges are similar to those
oftheouterambientgas.Giventhatthebreakradiiaredif-
ferentbetweenthesectors210◦-215◦ and215◦-225◦ asshown
inFigure2,itislikelythatthemultipleedgesinthisdirec-
tionarecausedbythefluctuationofthebreakradiiandthe
thermodynamicpropertiesbetweentheedgesaredominated
by the outer ambient gas.
Incontrast,intheprofilesextractedforthesector225◦-
240◦ (Figure6right),weseeajumpofthetemperatureand
entropy at the outer edge while they are continuous at the
inner edge. Moreover, the pressure profile seems to exhibit
adeficitbetweentheedges.AsshowninFigure2,thebreak
radii measured in the 15◦ resolution are consistent with the
break radii measured in the 5◦ resolution. This means that
both the multiple edges and the thermodynamic structure
inthisdirectionarenotattributabletothesimpleazimuthal
resolutioneffectunlikethecaseofthe210◦-225◦ sector(pre-
viousparagraph),stronglyindicatingtheexistenceofapro-
jected KHI layer.
UndertheKHIscenario,thepressuredeficitcanbeex-
plained:asKHIeddiescollapseintosmallereddiesandulti-
matelyintoturbulence,theturbulentpressuremaysupport
the total pressure, lowering the apparent gas pressure. The
deficitofthepseudopressureof∆p˜ ∼0.1×10−3 istranslated
to the physical pressure deficit of ∆p∼4.4×10−3 keVcm−3×
Figure 5. Top: X-ray image (0.7-1.1 keV) of simulated gas- (l/50 kpc)−1/2, where l is the line-of-sight depth of the struc-
stripped galaxy for the inviscid atmosphere. Middle: The same ture. Assuming the pressure deficit is caused by the KHI
imageasthetoppanelbutfortheviscous(Re=46atpericentre, turbulence, we estimate the typical turbulent strength at
0.1Spitzerviscosity)atmosphere.Bottom:Figure1,40◦clockwise v ∼ 350 km/s, using ∆p = ρv2, where ρ is the mass den-
rotated. The size of each simulation box is ∼100 kpc, while that sity and v is the turbulent velocity dispersion. This value is
of the X-ray image is ∼1.1 Mpc. The top and the middle panels smaller than the typical shear strength at the interface and
are reproduced from Figure 6 (third column, fourth row panel)
is compatible with the above mentioned scenario.
andFigure8(thirdcolumn,fourthrowpanel)inRoedigeretal.
Allthesemeasurementsareconsistentwiththescenario
(2015b),respectively3.
thatKHIsaredevelopingontheinterface.Recentlytheexis-
tenceofKHIshasbeensuggestedonthesloshingcoldfronts
intheCentaurusandtheOphiuchusclusters(Sandersetal.
MNRAS000,1–13(2016)
The cold front in Abell 3667 9
2.01e 4 2.01e 4
y 1.8 y 1.8
sit 1.6 sit 1.6
n n
e 1.4 e 1.4
d d
o 1.2 o 1.2
d d
u 1.0 u 1.0
e e
s 0.8 s 0.8
P P
0.6 0.6
V] 9 r [arcmin] V] 9 r [arcmin]
e e
k 8 k 8
e [ 7 e [ 7
atur 6 atur 6
er 5 er 5
p p
m 4 m 4
Te 1.301e 3 Te 1.301e 3
e r [arcmin] e r [arcmin]
ur 0.9 ur 0.9
s s
s s
pre 0.8 pre 0.8
o 0.7 o 0.7
d d
u u
se 0.6 se 0.6
P P
05..501e3 05..501e3
y 4.5 r [arcmin] y 4.5 r [arcmin]
op 4.0 op 4.0
ntr 3.5 ntr 3.5
o e 3.0 o e 3.0
d 2.5 d 2.5
u u
e 2.0 e 2.0
s s
P 1.5 P 1.5
1.0 1.0
3.0 3.5 4.0 4.5 5.0 5.5 6.0 3.0 3.5 4.0 4.5 5.0 5.5 6.0
r [arcmin] r [arcmin]
Figure 6. Projected thermodynamic profiles in the two directions where we see multiple edges in the corresponding surface brightness
√
profiles (Left: 210◦-225◦ and Right: 225◦-240◦). The panels are the pseudo density (calculated using n˜ = N/A where N is the apec
normalization and A is the area of the spectral extraction region in pixel2), the temperature (kT), the pseudo pressure (n˜kT) and the
pseudoentropy(kTn˜−2/3)fromtoptobottom.Theverticalgraybandsdenotetheedgesinthesurfacebrightnessprofiles.
2016;Werneretal.2016b),andalsoonthemergercoldfront Figure 2). Here we investigate the properties of the fluctu-
in the NGC 1404 galaxy (Su et al. 2016). That said, to our ation by examining the azimuthal profile with finer angular
knowledge,this is the firstobservational indication of KHIs resolutions.
near the tip of a merger cold front in a galaxy cluster.
Figure 7 left shows the azimuthal profile of the break
radii (165◦-270◦) extracted in 5◦, 2.5◦, and 1.25◦ resolutions
(see also the second panel of Figure 2 for the 5◦ and 15◦
4.3.3 Gas mixing at the mushroom edge
profiles). We find that the overall shapes of the profiles are
As shown in Figure 4, the temperature and the entropy similar to each other. However, in the finer resolution pro-
jumps are relatively moderate at the edge of the front (i.e. files, we find substructures which are missed even in the 5◦
165◦-195◦,270◦-300◦)comparedwiththetipofthefront(i.e. profile.
195◦-270◦). Given that these edge azimuths correspond to
theedgeofthemushroom-shapeintheimage,thisdifference Thebreakradiiprofilesmaybeaffectedbye.g.themis-
isprobablyduetothemixingofthegasinducedbythefully alignment between the normal of the interface and the di-
developed, turbulent KHIs. In the case of KHI-induced gas rection of the sectors from which the profiles are extracted.
mixing, the Fe abundance is also expected to show a mod- In order to mitigate such effects and focus on the fluctua-
erate change at the edge compared to the tip. However, we tionsofthebreakradiithemselves,wecomputedtherelative
don’tseeanysignificantdifferencealongtheinterfaceinthe fluctuation profiles by dividing each profile by the spline-
projected Fe abundance profile shown in the bottom panel interpolated profile using an opening angle of 15◦. Figure 7
in Figure 4. Note that in the projected Fe abundance map rightshowstheazimuthalprofilesoftherelativefluctuation
shown in Figure A1 (which has higher statistics per each of the break radii for the corresponding left panels.
bin), we see that the contrast of the Fe abundances across
In the 2.5◦ resolution profile, we see sequential bump-
the interface seems to be stronger near the tip of the front
like structures, which are missed in the 5◦ profile (see the
than at the edge of the front.
curves in Figure 7). In the 1.25◦ profile, we also see the
similar sequential bump-like structures, although they are
less prominent due to the larger errorbars. The fact that
4.3.4 Detailed view of the fluctuation of break radii
the bumps are less prominent in this resolution indicates
The length scales of the fluctuation of the break radii ap- that the data quality is insufficient for (cid:46) 1.25◦ resolutions.
pear to be limited in the range of 10◦-25◦ when we look at Thecharacteristicsizeofthesequentialbumpsis20-80kpc,
theazimuthalprofileinthe5◦ resolution(seegraypointsin which is similar to the value inferred from the differences
MNRAS000,1–13(2016)
10 Y. Ichinohe et al.
Figure7.Left:thebreakradiishownindifferentazimuthalresolution.5◦,2.5◦and1.25◦fromtoptobottom.Right:relativefluctuation
created by dividing each corresponding left panel by the spline-interpolated break radii profile in 15◦ resolution. The black curves
denotethe“sequentialbumps”(seethetextbelow).The x-axesonthetoparethephysicallengthalongthecoldfrontwiththeorigins
correspondingto225◦.
of the radii of the breaks in the surface brightness profiles This relation means that for a fixed viscosity, the dif-
(30-120 kpc; see Section 4.3.2). ference of the shear strengths results in the difference of
the length scales of the KHI modes which can develop. In
other words, when a value of the effective viscosity µ is
4.3.5 Upper limit of the ICM effective viscosity given, the perturbation of length-scale λ is suppressed if
λ<λ =µRe /ρV.
AssumingthatKHIsareactuallydevelopingontheinterface crit crit
Whenasphereissubjectedtoincompressibleidealflow,
and that the scales of the fluctuations (sequential bumps)
the speed of the fluid on the sphere v(θ) is expressed using
representthelengthscalesoftheKHIeddies,wecanextract
v(θ)=3Vsinθ/2,whereV isthespeedoftheflowandθisthe
implications for the effective viscosity of the ICM.
anglebetweentheflowandthedirectionoftheradiusvector
In general, finite shear flow induces exponentially de-
of a given position on the sphere. Therefore, assuming that
veloping KHIs. If the gas were inviscid and incompress-
theinterfaceisspherical,wecancalculatetheflowspeedat
ible, KHIs would develop on all length scales. However, the
each azimuth.
growthoftheperturbationissuppressedwhentheReynolds
Figure8showstheλ valuesateachazimuthforvari-
number Re of the ICM in the hot layer (outside the inter- crit
ous viscosity values. In plotting them, we assumed that the
face) is below the critical value
axisofsymmetrywithrespecttotheambientflowisat225◦.
Re= ρλV <Re ∼64√∆, (5) For the density values, we used the deprojected ones (see
µ crit Section3.3).Theblackcrossesroughlyrepresentthesequen-
tialbumpsthatwepointedoutintheprevioussection.Note
where ρ is the density, λ is the length scale, V is the shear
that we neglected the effect of advection of the instabilities
strength, µ is the viscosity, ρ and ρ are the densities of
1 2
along the interface for simplicity.
the two gas phases on the two sides of the interface, and
∆ = (ρ +ρ )2/ρ ρ (Roediger et al. 2013a; Chandrasekhar The instabilities whose length scales are <λcrit must be
1 2 1 2
suppressed. However, in Figure 7 we identified several in-
1961).NotethatRoedigeretal.(2013a)estimatedthevalue
stability candidates which we indicate as black crosses in
of 64 with a simple analytic argument. Th√ey offere√d some
moreconservativeestimationsofRe =10 ∆or16 ∆,but Figure8.Therefore,theviscosityabove∼200g/cm/sisun-
crit
likelybecausewewouldnotfindthesequentialbumpswith
giventhatwedonotseedevelopingKHIsinFigure5middle
(Re=46),wethinkthesecriticalReynoldsnumbersaretoo such high viscosity values. Consequently, assuming the ze-
roth order analytical derivation of Equation 5, the upper
conservative4.
limit of the ICM viscosity is ∼200 g/cm/s.
Theestimatedupperlimitdependsonthenumerousas-
4 The Reynolds number of 46 is the pericentre value and not
exactlythevalueonthespotat−780Myr.However,thedensity,
size,andvelocityonthespotat−780Myrarerespectively∼1/3 wethinkitissafetouse46astheReynoldsnumberonthespot
times,(cid:38)6times,and(cid:38)1/2timesthevaluesatthepericentre,and intheaboveargument.
MNRAS000,1–13(2016)