Chandra Observations of the Spectacular A3411-12 Merger Event
Felipe Andrade-Santos, Reinout J. van Weeren, Gabriella Di Gennaro, David Wittman, Dongsu Ryu, Dharam Vir Lal, Vinicius M. Placco, Kevin Fogarty, M. James Jee, Andra Stroe, David Sobral, William R. Forman, Christine Jones, Ralph P. Kraft, Stephen S. Murray, Marcus Brüggen, Hyesung Kang, Rafael Santucci, Nathan Golovich, William Dawson
DDraft version October 17, 2019
Typeset using L A TEX twocolumn style in AASTeX62
CHANDRA
OBSERVATIONS OF THE SPECTACULAR A3411–12 MERGER EVENT
Felipe Andrade-Santos,
1, 2
Reinout J. van Weeren, Gabriella Di Gennaro, David Wittman, Dongsu Ryu, Dharam Vir Lal, Vinicius M. Placco,
7, 8
Kevin Fogarty,
9, 10
M. James Jee,
11, 4
Andra Stroe, ∗ David Sobral,
12, 3
William R. Forman, Christine Jones, Ralph P. Kraft, Stephen S. Murray, Marcus Br¨uggen, Hyesung Kang, Rafael Santucci,
16, 17
Nathan Golovich, and William Dawson Clay Center Observatory, Dexter Southfield, 20 Newton Street, Brookline, MA 02445, USA Center for Astrophysics | Harvard & Smithsonian , 60 Garden Street, Cambridge, MA 02138, USA Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands Department of Physics, University of California, Davis, CA 95616, USA Department of Physics, School of Natural Sciences, UNIST, Ulsan 44919, Republic of Korea National Centre for Radio Astrophysics - Tata Institute of Fundamental Research, Post Box 3, Ganeshkhind P.O., Pune 41007, India Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Joint Institute for Nuclear Astrophysics, Center for the Evolution of the Elements, East Lansing, MI 48824, USA Division of Physics, Math, and Astronomy, California Institute of Technology, Pasadena, CA, USA Space Telescope Science Institute, Baltimore, MD, USA Yonsei University, Department of Astronomy, Seoul, Republic of Korea Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK Department of Physics and Astronomy, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218, USA Hamburger Sternwarte, University of Hamburg, Gojenbergsweg 112, D-21029 Hamburg, Germany Department of Earth Sciences, Pusan National University, Busan 46241, Republic of Korea Instituto de Estudos S´ocio-Ambientais, Planet´ario, Universidade Federal de Goi´as, Goiˆania, GO 74055-140, Brazil Instituto de F´ısica, Universidade Federal de Goi´as, Campus Samambaia, Goiˆania, GO 74001-970, Brazil Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA
ABSTRACTWe present deep
Chandra observations of A3411–12, a remarkable merging cluster that hosts themost compelling evidence for electron re-acceleration at cluster shocks to date. Using the Y X − M scaling relation, we find r ∼ . M = (7 . ± . × M (cid:12) , kT = 6 . ± . M g , = (9 . ± . × M (cid:12) . The gas mass fraction within r is f g = 0 . ± .
01. Wecompute the shock strength using density jumps to conclude that the Mach number of the mergingsubcluster is small ( M ≤ . +0 . − . ). We also present pseudo-density, projected temperature, pseudo-pressure, and pseudo-entropy maps. Based on the pseudo-entropy map we conclude that the clusteris undergoing a mild merger, consistent with the small Mach number. On the other hand, radio relicsextend over Mpc scale in the A3411–12 system, which strongly suggests that a population of energeticelectrons already existed over extended regions of the cluster. Keywords: galaxy clusters: general — cosmology: large-structure formation INTRODUCTIONGalaxy cluster mergers are the most energetic eventsin the present day Universe and involve kinetic energieson the order of ∼ − erg. Direct evidence for clustermergers has been found from the morphology of the X-ray emission (e.g., Jones & Forman 1984, 1999; Mohr [email protected] ∗ Clay Fellow et al. 1995; Buote & Tsai 1996; Jeltema et al. 2005;Lagan´a et al. 2010; Andrade-Santos et al. 2012, 2013)and the presence of shocks (e.g., Markevitch et al. 2002)in the intracluster medium (ICM), as well as from theasymmetric spatial and velocity distributions of clustergalaxy populations (Dressler & Shectman 1988).The identification and study of merging clusters is ofconsiderable astrophysical interest for several reasons.First, such major mergers are rare events, and have aprofound, long lasting influence on the thermodynamicevolution of the ICM. Major mergers are believed to be a r X i v : . [ a s t r o - ph . H E ] O c t Andrade-Santos et al. responsible for the general division of clusters into cool-core and non-cool-core clusters (Henning et al. 2009).Mergers can also affect a wide range of other clusterrelated phenomena, including AGN activity in clustergalaxies (Ma et al. 2010; Sobral et al. 2015) and starformation (Lagan´a et al. 2008; Sobral et al. 2015; Stroeet al. 2015, 2017). Second, cluster mergers are an ideallaboratory to study the properties of dark matter. X-rayand optical (lensing) studies have put strong constraintson the self-interaction of dark matter and have shownthat it must be nearly collisionless (Clowe et al. 2004,2006; Bradaˇc et al. 2006, 2008; Randall et al. 2008; Daw-son et al. 2012).Simulations of large-scale structure formation showthat galaxy clusters grow through gas accretion fromlarge-scale filaments and mergers of smaller clusters andgroups. These mergers are characterized by the enor-mous amounts of energy involved ( ∼ erg), long life-times (Gyr), and large physical scales (Mpc). Most ofthe gravitational energy released during a merger eventis converted to thermal energy via shocks and turbu-lence (see Markevitch & Vikhlinin 2007, for a review).In addition, a small fraction ( < M )cluster merger shocks can accelerate enough particles toexplain the observed radio synchrotron brightness. Ac-cording to standard diffusive shock acceleration theory(DSA; Drury 1983), the acceleration efficiency is verylow for M (cid:46) A3411–12
A3411–12 (also known as PLCKESZ G241.97+14.85– see Figure 1) is a relatively nearby ( z = 0 . ∼ . Chandra
X-ray image shows that the clus-ter has a cometary shape with a well-defined subclus-ter core visible in the northwestern part of the system(A3411). Fainter X-ray emission is found surroundingthe subcluster core and this emission seems to be partof a second, larger subcluster (A3412). There is no clearsurface brightness peak corresponding to the primarycluster core (A3412 – see Figure 2), which suggests theprimary cluster has been disrupted by the collision withthe subcluster (A3411 – see Figure 2), as has been thecase for A2146 (Russell et al. 2011; Menanteau et al.2012). Giovannini et al. (2013) have also found that theradio halo at the center of A3411-12 has a low power(log P = 23 .
16 W Hz − ). The global ICM temperatureof A3411–12 is ∼ . × erg s − within r = 1.34 Mpc (vanWeeren et al. 2013).More recently, van Weeren et al. (2017) found, in themerging galaxy cluster A3411–12, the most compellingevidence for re-acceleration at cluster shocks to date.The authors identified a tailed radio galaxy connectedto the relic. In addition, spectral flattening is observedat the location where the fossil plasma meets the relicand, at the same location, an X-ray surface brightnessedge is observed.van Weeren et al. (2017) also presented a clusteringanalysis applied to the three-dimensional galaxy dis-tribution (right ascension, declination, and redshift) oftheir spectroscopic sample of cluster members (obtainedwith Keck). They considered mixtures of 1 to 7 multi-variate Gaussian components. They found that, of themodels considered, the two-component Gaussian modelis the most favored one, indicating a bi-modal distri-bution. They also investigated the redshift and ve-locity dispersion of each subcluster. They found sim-ilar velocity dispersions for the northern (A3411) andsouthern (A3412) subclusters, 1110 +100 − km s − and1190 +100 − km s − , respectively. These velocity disper-sions translated into mass estimates of 1 . +0 . − . × M (cid:12) and 1 . +0 . − . × M (cid:12) for the A3411 and A3412 subclus-ters, respectively. With the mass estimates and redshiftdistributions, they concluded that core passage for theA3411-A3412 merger event occurred about ∼ Chandra collected were emitted andthat the plane of the merger event is seen relatively close
HANDRA
OBSERVATIONS OF A3411–12 Figure 1.
Composite image of the A3411–A3412 field: optical (Subaru – RGB), 0.5-2.0 keV X-ray (
Chandra – in blue), 325and 610 MHz radio (GMRT – in red), and the galaxy density distribution (purple). A3411–12 presents a clear cool core in thenorth and a large (Mpc scale) radio relic in the south. In the north there is an overdensity of galaxies at the cluster redshift,located in the cool core (X-ray: bright blue, galaxy density: purple) region, whereas another peak in the galaxy distribution(purple) is seen in the relic region (red) in the south. (9 ◦ –41 ◦ ) to the plane of the sky crossing the cluster cen-ter, implying that the shock is seen close to edge-on. Itis worthy mentioning that in the current work we finda much smaller total mass for the system of M =(7 . ± . × M (cid:12) , in very good agreement with the Planck estimated mass of M = (6 . ± . × M (cid:12) (Planck Collaboration et al. 2016). In this paper we characterize this cluster based onChandra X-ray observations, present temperature, den-sity, pressure, and entropy maps, as well as densityjumps related to cold and shock fronts. We show that ifindeed the density jumps trace shocks, they are mild, in-dicating that a population of energetic electrons alreadyexisted over extended regions of the cluster based on the Andrade-Santos et al.
A3412A34112 Mpc = 11.6’
Figure 2.
Chandra image of the A3411–12 field overlaid by galaxy iso-density contours in blue. extension of the radio relics in the A3411–12 system.The cosmology assumed for our analysis has Ω M = 0 . Λ = 0 . H = 70 km s − Mpc − , implying a linearscale of 2 .
88 kpc arcsec − at the A3411–12 luminositydistance of 812 Mpc ( z = 0 . X-RAY OBSERVATIONS AND DATAREDUCTIONWe observed A3411 with the
Chandra
X-ray Observa-tory (ACIS-I detectors, VF mode, ObsIds 13378, 15316– PI Murray, and 17193, 17496, 17583, 17585, 17584 – PIvan Weeren). The data were reduced using the software
CHAV which follows the processing described in Vikhlininet al. (2005), applying the calibration files
CALDB 4.6.7 .The data processing includes corrections for the timedependence of the charge transfer inefficiency and gain,and a check for periods of high background (none werefound – the total exposure time is 211 ks). Also, read-out artifacts were subtracted and standard blank skybackground files were used for background subtraction.Figure 2 shows the combined image of all observationsin the 0.5–2.0 keV energy band.Since the focus of this paper is solely on X-ray dataand their results, we refer the reader to van Weeren et al. (2017) for the details on the optical and radio reductionsperformed to create the image displayed on Figure 1. OVERALL CHARACTERISTICS OF THECLUSTER3.1.
Emission measure profile
In this section we outline the procedures used to com-pute the emission measure profile. We refer the readerto Vikhlinin et al. (2006) for a detailed description ofthe method.First we detected compact sources using wavdect inthe 0.7–2.0 keV or 2.0–7.0 keV bands and then maskedthese from the spectral and spatial analyses (we alsomasked the bullet (cool-core in A3411) – see top leftpanel of Figure 3). We then measured the surface bright-ness profiles in the 0.7–2.0 keV energy band, which max-imizes the signal to noise ratio in
Chandra data. Thereadout artifacts and blank-field background (see sec-tion 2.3.3 of Vikhlinin et al. 2006) were subtracted fromthe X-ray images, and the result was exposure-correctedusing exposure maps (computed assuming an absorbedoptically-thin thermal plasma with kT = 5 . Z (cid:12) , plus the Galactic column density thatinclude corrections for bad pixels and CCD gaps, butdo not take into account spatial variations of the ef-fective area. Finally, we subtracted any small uniformcomponent corresponding to soft X-ray foreground ad-justments that may be required.Following these steps, we extracted the surface bright-ness profiles in narrow concentric annuli ( r out /r in =1 .
05) centered on the X-ray centroid (determined ex-cluding the masked regions) and computed the
Chan-dra area-averaged effective area for each annulus (seeVikhlinin et al. 2005, for details on calculating the effec-tive area). Using the observed projected temperature,effective area, and metallicity as a function of radius,we converted the
Chandra count rate in the 0.7–2.0 keVband into the emission integral, EI = (cid:82) n e n p dV , withineach cylindrical shell. The X-ray morphology of A3411–12 exhibits an irregular shape (see Figure 2), however,this is mostly due to the bullet in the northern partof the cluster. When we mask the bullet, the clusterexhibits a more elongated and symmetrical shape. Tocompute the emission measure and temperature profileswe assumed spherical symmetry. In this case, the spher-ical assumption is expected to have only small effects onthe total mass of the cluster when using Y X as a proxy, NH was fixed to the Galactic value, taking into account notonly the 21 cm map of the Galactic atomic hydrogen but also themolecular contribution (NH total = NHI + NH = (4 .
67 + 1 . × = 5 . × HANDRA
OBSERVATIONS OF A3411–12 Table 1.
Parameters for the emission measure profile (Equation 1) n r c r s α β γ (cid:15) n r c2 β (10 − cm − ) (kpc) (kpc) (10 − cm − ) (kpc)1 . ± .
19 260 ± ± . ± .
10 0 . ± .
20 0 . ± .
11 0 . ± .
10 1 . ± .
07 736 ±
52 0 . ± . Note —Columns list best fit values for the parameters given by Equation 1.
Table 2.
Parameters for the Temperature Profile (Equations 2 and 3) T T min r t r cool a † cool a † b c (keV) (keV) (kpc) (kpc)13 . ± . . ± . ±
173 400 ±
104 1.9 0 5 . ± . . ± . Note —Columns list best fit values for the parameters given by Equations 2 and 3. † fixed value. as presented by Kravtsov et al. (2006). They showedthat Y X is a robust mass indicator with remarkably lowscatter of only ≈ M for fixed Y X , regard-less of whether the cluster is relaxed or not. We then fitthe emission measure profile assuming the gas densityprofile follows Vikhlinin et al. (2006): n e n p = n ( r/r c ) − α (1 + r /r ) β − α/ r γ /r γ s ) (cid:15)/γ + n (1 + r /r ) β . (1)This relation is based on a classic β -model, modifiedto account for the power-law type cusp and the steeperemission measure slope at large radii. In addition, a sec-ond β -model is included, giving extra freedom to charac-terize the cluster core. For further details on this equa-tion we refer to Vikhlinin et al. (2006). The relation be-tween the electron number density and gas mass densityis given by ρ g = µ e n e m a , where m a is the atomic massunit and µ e is the mean molecular weight per electron.For a typical metallicity of 0.3 Z (cid:12) , the reference valuesfrom Anders & Grevesse (1989) yield µ e = 1 . n e /n p = 1 . n p is the proton number density.The best fit parameters of Equation 1 are listed in Ta-ble 1. Figure 3 presents the best fit emission measureprofile, as well as the density and gas mass profiles de-rived from the best fit emission measure. The gas massprofile is then used to compute the total mass using the Y x relation (Section 4).3.2. Gas Temperature Radial Profiles
Most clusters present a temperature profile that has abroad peak within 0.1–0.2 r . Vikhlinin et al. (2006)present a 3D temperature profile that describes thesegeneral features. At large radii, the temperature profilecan be reasonably well represented as a broken powerlaw with a transition region: T ( r ) = ( r/r t ) − a (1 + ( r/r t ) b ) c/b . (2)At small radii, the temperature profile can be de-scribed as T cool ( r ) = ( x + T min /T ) / ( x + 1) , (3)where x = ( r/r cool ) a cool . The final analytical expressionfor the 3D temperature profile is, T ( r ) = T × T cool ( r ) × T ( r ) . (4)This temperature model has significant functionalfreedom (8 parameters) and can adequately describe al-most any smooth temperature distribution. Thus, weuse this model, from Vikhlinin et al. (2006), to describethe temperature distribution of the hot gas in A3411–12.To construct the temperature profile, we extractedspectra from 7 annuli in the radial range from ∼
100 to ∼ APEC model. For the fitting wefixed NH to the Galactic value of 5 . × (see Sec-tion 3.1). We then followed the procedures described r and r are used to define a radius at the over-densityof 200 and 500 times the critical density of the Universe at thecluster redshift, respectively. Andrade-Santos et al.
Figure 3.
X-ray image (upper left), projected emissivity (upper right), gas density (lower left), and enclosed gas mass (lowerright) profiles for A3411–12. Top left panel shows the 0.5-2.0 keV, background-subtracted, exposure map corrected ACIS-Iimage. The total filtered
Chandra exposure is 211 ks. Blue ellipses correspond to the masked X-ray point sources (we alsomasked the bullet (cool-core in A3411)) and the black cross corresponds to the cluster center (determined by computing theX-ray centroid in a circle of ∼ n e = 1 . × n p , where n e and n p are the electron and proton number densities, respectively. Bottom left panel shows theelectron number density profile. The solid line shows the electron number density profile obtained from the emissivity profilegiven by Equation (1). Bottom right panel shows the gas mass profile, with the dashed vertical line indicating r . The dashedlines in the electron number density and gas mass profiles show the 68% confidence range. above to obtain the 2D and 3D temperature profiles.The measured 2D (black data points), fitted 2D (bluesolid line), and 3D (red solid line) temperature profilesare presented in Figure 4. The 2D temperature pro- file was computed by projecting the 3D temperature,weighted by gas density squared using the spectroscopic-like temperature (Mazzotta et al. 2004, provides a for-mula for the temperature which matches the spectro- HANDRA
OBSERVATIONS OF A3411–12 Figure 4.
Azimuthally averaged, radial temperature pro-file. Observed projected temperatures are shown by pointswith error bars. The 3D model and its projected effectivetemperatures (the latter to be compared with the data) areshown by the red and blue curves, respectively. Dashed linesshow the 1 σ uncertainty ranges. scopically measured temperature within a few percent): T = T spec ≡ (cid:82) ρ T / dz (cid:82) ρ T − / dz (5)To estimate the uncertainties in the best values forthe parameters of this analytical model, we performedMonte-Carlo simulations. This model for T ( r ) (Equa-tion 4) allows very steep temperature gradients. In someMonte-Carlo realizations, such profiles are mathemati-cally consistent with the observed projected tempera-tures. However, large values of temperature gradientsoften lead to unphysical mass estimates, such as pro-files with negative dark matter density at some radii.We solved this issue by accepting only Monte-Carlo re-alizations in which the best-fit temperature profile leadsto ρ tot > ρ gas in the radial range r ≤ . r , where ρ tot = ρ gas + ρ dark matter . Also, in the same radial range,we verified that the temperature profiles are all convec-tively stable, i.e. d ln T /d ln ρ g < / CLUSTER MASS ESTIMATESUsing the gas mass and temperature, we estimatedthe total cluster mass from the Y X – M scaling relationof Vikhlinin et al. (2009), M , Y X = E − / ( z ) A YM (cid:18) Y X × M (cid:12) keV (cid:19) B YM , (6)where Y X = M gas , × kT X , M gas , is computed us-ing the best fit parameters of Equation (1), and T X is the measured temperature in the (0.15–1) × r range. A YM = (5 . ± . × h / M (cid:12) and B YM =0 . ± .
03 (Vikhlinin et al. 2009). Here, M Y X , is thetotal mass within r , and E ( z ) = [Ω M (1 + z ) + (1 − Ω M − Ω Λ )(1 + z ) + Ω Λ ] / is the function describing theevolution of the Hubble parameter with redshift.Using Equation (6), r is computed by solving M , Y X ≡ ρ c (4 π/ r , (7)where ρ c is the critical density of the Universe at thecluster redshift. In practice, Equation (6) is evaluatedat a given radius, whose result is compared to the eval-uation of Equation (7) at the same radius. This processis repeated in an iterative procedure, until the fractionalmass difference is less than 1%. We estimated 1 σ un-certainties in the Y X derived masses using Monte Carlosimulations. We also added to the Monte Carlo pro-cedure a 1 σ systematic uncertainty of 9% in the massdetermination, as discussed by Vikhlinin et al. (2009). RESULTS5.1.
Masses
Following the approach outlined in Section 4, weobtain M , Y X = (7 . ± . × M (cid:12) , in verygood agreement with the Planck estimated mass of M , Y SZ = (6 . ± . × M (cid:12) (Planck Collabo-ration et al. 2016) despite the merger morphology. Thisis due to the fact that both Y X and Y SZ are insensitive tothe cluster dynamical state (Kravtsov et al. 2006; Say-ers et al. 2013). This mass leads to r ∼ . kT = 6 . ± . × r ,and a gas mass of M g , = (9 . ± . × M (cid:12) . Thegas mass fraction within r is f g = 0 . ± . Images
Figure 2 shows the merged, flat-fielded (vignettingand exposure corrected), and background subtracted0 . − Chandra
ACIS-I image of A3411–12. The image reveals the presence of large scale diffuseemission, which originates from optically-thin thermalplasma with kT ∼ Andrade-Santos et al.
DensityPressure EntropyTemperature
Figure 5.
Top left: pseudo-density. Top right: projected temperature. Bottom left: pseudo-pressure ( P = kT × n e ). Bottomright: pseudo-entropy ( K = kT /n / ). Color bar indicates the temperature. All maps are in logarithmic scale and darker colorsrepresent higher values. The white ellipses represent the excluded point source regions. These figures are described in detail inthe text. The distribution of the hot X-ray emitting gas revealsa complex morphology, indicating an active merger his-tory (van Weeren et al. 2013; Giovannini et al. 2013;van Weeren et al. 2017). In particular, the gas distribu-tion is not symmetric, but is elongated in the southeast-northwest direction. In addition, the image shows thepresence of sharp surface brightness edges in the centralregions of the cluster (see Figure 8).The above features are characteristic signatures of amerger, which has likely perturbed the hot gas distri-bution. To explore the nature of these features, andhence, constrain the merger history of the cluster, we derive surface brightness, density, and temperature pro-files, which are discussed in the following sections.5.3.
Temperature, Pressure and Entropy Maps
In this section we present pseudo-density, projectedtemperature, pseudo-pressure, and pseudo-entropymaps for A3411–12, extracted from the
Chandra ob-servations. For typical cluster temperatures (k T = 3 –10 keV) and metal abundances ( Z = 0.1 – 0.5 Z (cid:12) ), thebroadband response of Chandra to optically thin ther-mal emission from hot gas can be reasonably assumedto be constant with gas temperature. As an example,for a fixed emission measure, the 0.5–2.5 keV count rateof the
Chandra
ACIS-I declines by only ∼
17% when kT HANDRA
OBSERVATIONS OF A3411–12 Figure 6.
Geometry of flow past a denser and colderregion. Here the Bullet cluster is used as a textbook exampleof cold front and bow shock formations. Zones 0, 1, and 2are those near the stagnation point, in the undisturbed freestream, and past the bow shock, respectively. While coldfronts may be the result of many different physical events inthe cluster, the density discontinuities in them form for thesame basic reason: whenever a gas density peak encountersa flow of ambient gas, a contact discontinuity quickly forms. increases from 4 to 12 keV. Therefore, we can ignore the
Chandra response and assume that the count rate perunit volume of the gas is directly proportional to thesquare of the gas density. Thus, from the surface bright-ness we can map the projected density of the cluster,and combining that with a temperature map we can alsocompute the pseudo pressure and entropy maps usingthe following relations: n e ∝ S / , (8) P = n e kT ∝ S / T, (9) K = n − / kT ∝ S − / T, (10)where S and T are the surface brightness and tempera-ture maps.We extracted spectra in regions that were created us-ing contbin , an algorithm for binning X-ray data usingcontours on an adaptively smoothed map. The gener-ated bins closely follow the surface brightness, and areideal where the surface brightness distribution is notsmooth, or the spectral properties are expected to followthe surface brightness (Sanders 2006). The regions wereselected to have a minimum S/N of 50 in the 0.5–7.0keV band. Background (sky + detector + readout) andexposure maps were used. The temperature map wascreated by fitting, in the 0.5–7.0 keV band, an absorbedplasma model (XSPEC – wabs*apec ) to the spectrumdata in each region. NH was fixed to Galactic value of5 . × (see Section 3.1). In Figure 5 we present the projected density, tem-perature, pressure, and entropy maps for A3411. Thedensity and pressure maps present very smooth spatialvariations, however the temperature map presents largevariations within relatively small distances. The homo-geneity of the pressure map across the north surfacebrightness discontinuity shows that the pressure variessmoothly indicating a cold front, in contrast with shockfronts which present pressure jumps. The entropy mapis significantly more homogeneous than the temperaturemap, especially in the inner regions, suggesting an isen-tropic process. An isentropic process is the equivalent tothe thermodynamic process which is reversible and adia-batic, meaning that no heat is dissipated. This suggeststhat the merger pushed the low entropy gas back fromthe core causing it to spread in the downstream, how-ever, in a mild way, so heat dissipation did not happen.On the other hand, the inhomogeneity of the tempera-ture map in the same region suggests that the gas hasbeen mixed. 5.4. Shock and Cold Fronts
For a detailed description of the physics of shock andcold fronts in galaxy clusters, please refer to Markevitch& Vikhlinin (2007); Vikhlinin et al. (2001). Here wediscuss briefly the theory behind such phenomena, whichwill be relevant in the following analysis.Let us consider a dense and cold gas cloud movingacross a hotter gas. In Figure 6, we show an example ofthis setup. Far upstream from the dense cloud, the gaswill be moving (relative to the dense gas cloud) freely.This region is referred to as the free stream and willbe labeled with the index 1 (See Figure 6). The hotgas decelerates as it approaches the dense gas cloud, ap-proaching zero velocity at the edge of the dense cloud.This region is referred to as the stagnation point andwill be labeled with the index 0. The density disconti-nuities in cold fronts form whenever a gas density peakencounters a flow of ambient gas, causing a contact dis-continuity to quickly form. Furthermore, if the velocityof the dense gas cloud exceeds the sound speed of thehot gas, a bow shock forms at some distance upstreamfrom the dense cloud. The region just inside the bowshock will be indexed as 2 (see Fig. 6 for a visual de-scription of the regions discussed above). The ratio ofpressures in the free stream (1) and at the stagnationpoint (0) is a function of the cloud speed v (Section 114of Landau & Lifshitz 1959): p p = (cid:0) γ − M (cid:1) γγ − , M ≤ (cid:0) γ +12 (cid:1) γ +1 γ − M (cid:16) γ − γ − M (cid:17) − γ − , M > Andrade-Santos et al. S X [ p h o t o n s c m s a r c m i n ] Bullet
Total bkg (sky + inst) [0.5-2.0 keV]Source [0.5-2.0 keV]
Distance [arcmin] S X [ p h o t o n s c m s a r c m i n ] North
Total bkg (sky + inst) [0.5-2.0 keV]Source [0.5-2.0 keV]
Distance [arcmin]
Figure 7.
Surface brightness profiles across the northern sector. Left: we present the surface brightness across A3411–12bullet (cold front). Right: we present the surface brightness further north where a hint of a bow shock is detected. The totalbackground level (i.e. instrumental and astrophysical) is shown by the blue line, with the ± σ uncertainties (blue dashed lines).On the bottom of each panel, the residuals (i.e. S X , obs − S X , mod ∆ S X , obs ) are displayed. Table 3.
Density jumps and Mach numbersSector r shock (arcmin) C M
Bullet 1 . +0 . − . . +0 . − . cold-frontNorthern 3 . +0 . − . . +0 . − . . +0 . − . Southern 4 . +0 . − . . +0 . − . cold-frontSoutheast inner 3 . +0 . − . . +0 . − . . +0 . − . Southeast outer 6 . +0 . − . . +0 . − . . +0 . − . Note —Columns list best fit values for the parameters givenby Equations 14 and 15. where M = v/c is the Mach number in the free streamand γ is the adiabatic index of the gas. The pressure ra-tio dependence on the square of the Mach number leadsto a large increment in the pressure ratio for relativelysmall changes in the velocity of the cloud, therefore thecloud velocity can be measured rather accurately evenif the pressure uncertainties are relatively high.As mentioned earlier, if the speed of a blunt body ex-ceeds the speed of sound, a bow shock forms at some dis-tance upstream. The shape of this structure is consistentwith an ellipse centered on the center of curvature of thecold front. If the surface brightness discontinuity is in-terpreted as a shock front, it is straightforward to derivethe expected temperature jump, the shock propagationvelocity and the velocity of the gas behind the shock, us-ing the Rankine-Hugoniot shock equations (Section 85 Table 4.
TemperatureSector r in (arcmin) r out (arcmin) k T (keV)N Cold-front 0 1.20 5 . +0 . − . N Downstream 1.20 3.48 7 . +0 . − . N Upstream 3.48 8 5 . +0 . − . S Cold-front 0 4.65 6 . +0 . − . S Downstream 4.65 11 6 . +1 . − . SE I Downstream 0 3.04 6 . +0 . − . SE I Upstream 3.04 11 4 . +0 . − . SE O Downstream 0 6.34 5 . +0 . − . SE O Upstream 6.34 11 2 . +1 . − . Note —Columns list the sector used to extract the temperature(N – north, S – south, SE I – southeast inner, SE O – southeastouter), the inner and outer radii, and temperature. of Landau & Lifshitz 1959): ρ ρ = (1 + γ ) M γ − M , (12) T T = 2 γM − γ + 1 γ + 1 ρ ρ . (13)where ρ /ρ and T /T are the ratios of densities andtemperatures in the downstream (2) and free stream (1)regions, respectively.5.4.1. Modeling the density jumps
HANDRA
OBSERVATIONS OF A3411–12 Figure 8.
Blue: sectors used for surface brightness extraction. Black: radio contours indicating the location of radio relics.Black contours display the radio emission of A3411–12 at the 3 σ rms level, with σ rms = 0 . µ Jy beam − . Following Owers et al. (2009), we can fit the surfacebrightness profile across a shock assuming spherical sym-metry for the gas density profile, which is given by twopower laws (broken power law): n ( r ) = Cn , (cid:16) rr shock (cid:17) − α , r ≤ r shock n , (cid:16) rr shock (cid:17) − α , r > r shock (14)where C is the density compression ( ρ /ρ ), and r shock is the radius at the shock (where the surface brightnessdiscontinuity is located). C is directly related to theMach number via the Rankine-Hugoniot equations pre-sented in Equation (12). For mono-atomic gas, γ = 5 / C = 4 M M . (15) The gas density at the shock upstream region is typi-cally very low, which makes measuring the temperaturejump quite difficult, A3411–12 being no exception de-spite our very good Chandra data.5.4.2.
Northern Cold and Shock Fronts
Cold fronts are found in many galaxy clusters (BulletCluster, A2029, A2204, RXJ1720, Ophiuchus, A2142,A3667, A1644, A520, and many more Markevitch &Vikhlinin 2007). While cold fronts may be the resultof many different physical events in the cluster, the den-sity discontinuities in them form for the same basic rea-son: whenever a gas density peak encounters a flow ofambient gas, a contact discontinuity quickly forms.Here, we measure the surface brightness profile in awedge towards the north of A3411, centered on thebright northern cool core. The left panel of Figure 7shows the cold front signature, as modeled by a broken2
Andrade-Santos et al. S X [ p h o t o n s c m s a r c m i n ] South-East inner
Total bkg (sky + inst) [0.5-2.0 keV]Source [0.5-2.0 keV]
Distance [arcmin] S X [ p h o t o n s c m s a r c m i n ] South-East outer
Total bkg (sky + inst) [0.5-2.0 keV]Source [0.5-2.0 keV]
Distance [arcmin]
Figure 9.
Surface brightness profiles across the southeast sector. Left: we present the surface brightness across A3411–12southeast. Right: we present the surface brightness further south where a hint of an edge is detected. The total backgroundlevel (i.e. instrumental and astrophysical) is shown by the blue line, with the ± σ uncertainties (blue dashed lines). On thebottom of each panel, the residuals (i.e. S X , obs − S X , mod ∆ S X , obs ) are displayed. S X [ p h o t o n s c m s a r c m i n ] South
Total bkg (sky + inst) [0.5-2.0 keV]Source [0.5-2.0 keV]
Distance [arcmin]
Figure 10.
Surface brightness profiles across the south sec-tor. The total background level (i.e. instrumental and astro-physical) is shown by the blue line, with the ± σ uncertain-ties (blue dashed lines). On the bottom of each panel, theresiduals (i.e. S X , obs − S X , mod ∆ S X , obs ) are displayed. power law (Equation 14). The density jump factor is C = 1 .
99. The right panel of Figure 7 shows what maybe the bow shock, at 2 (cid:48) .3 upstream from the cold front,modeled as another broken power law. The density jumpis C = 1 . +0 . − . , which implies M = 1 . +0 . − . (with a 90% confidence upper limit of M < .
6) if we interpretthis density discontinuity as a shock front. We used aBayesian information criterion (BIC) to compare a sin-gle power law model to a broken power law model. Forthe single power law model, we obtain BIC = 75.9 ( χ = 67.75). For the broken power law model, we obtainBIC = 75.2 ( χ = 54.74). Despite the slightly lower BICin favor of the density jump, no clear conclusion can bedrawn from the current data. The density jumps andMach numbers for all sectors are presented in Table 3.Table 4 shows the temperature at the regions pre-sented in Figure 8, which are determined by the sur-face brightness jumps. Towards the north, the cool corebecomes very clear in the surface brightness profile, aswell as the temperature jump from inside to outside ofthe stagnation point. Further north, the temperaturejump and density discontinuities are only suggestive ofa shock front. Indeed, computing the Mach number us-ing temperature (Equation 13) associated with all threesuggestive shock fronts (in the Northern, Southeast In-ner, and Outer sectors) leads to unconstrained results.5.4.3. Southeast Radio Relic, Cold Front, and PossibleShock Front
Measuring the surface brightness towards the south-east of A3411–12, we also see the suggestion of an up-stream bow shock (right panel of Figure 9).The surface brightness discontinuity presented in thesoutheast inner region (see left panel of Figure 9) hasbeen associated with a shock-front, responsible for elec-
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OBSERVATIONS OF A3411–12 C = 1 . +0 . − . and M = 1 . +0 . − . (with a90% confidence upper limit of M < . Southern Cold Front
Measuring the surface brightness towards the brightX-ray clump in the south of A3411–12, we also see an-other cold front signature, as the X-ray surface bright-ness profile is very well modeled by a broken power law(Figure 10). Measuring an upstream bow shock, how-ever, is not possible due to the very low statistic at sucha large distance from the cluster X-ray bright regions.For this sector we measure C = 1 . +0 . − . . MERGING SCENARIOOptical, X-ray, and radio data indicate that A3411–12is undergoing a major merger. van Weeren et al. (2017)showed that the optical data indicates a clear bimodalgalaxy distribution, with velocity dispersion indicatinga merger with a 1:1 mass ratio, and a radial velocitydifference between the two peaks compatible with zero,suggesting a merger on the plane of the sky. The X-ray data show a bullet-like cool core in the north withextended diffuse X-ray emission in the south, also highlysuggestive of a merger happening mostly in the directionsouth-north on the plane of the sky. Cold fronts in thesouth and north regions also support this, as well aswhat seems be a bow shock upstream from the northcold front density discontinuity. Assuming this densitydiscontinuity to be a shock, we measure a Mach numberof M = 1 . +0 . − . . The radio data show a large, Mpcscale relic in the south, a typical signature found in theoutskirts of many merging clusters.Thanks to the very good Chandra
X-ray data, we areable identify and constrain what seems to be a shock inthe south (Southeast Outer sector – it is important tonote that we cannot constrain the temperature, there-fore the nature of the density jump), with a Mach num-ber of M = 1 . +0 . − . . In van Weeren et al. (2017), thebest fit for the density jump at the location of the ra-dio relic gives M = 1 .
2, with a 90% confidence upperlimit of
M < .
4, also suggesting a low Mach number.Here we measure at the location of the radio relic pre-sented in van Weeren et al. (2017) (Southeast Inner sec-tor) M = 1 . +0 . − . .6.1. Merger Analogs
To model the dynamics of the merger we used themethod of Wittman (2019), who uses the projected sep-aration, relative line-of-sight velocity, and masses to se-lect analog systems from a cosmological N-body simu- lation. We followed that work in using the Big Multi-dark Planck (BigMDPL) Simulation (Klypin et al. 2016)hosted on the cosmosim.org website, but we updatedthe cluster parameters as follows. First, the X-ray mor-phology strongly suggests that the subclusters are stilloutgoing, so we eliminate analog systems that are in thereturning phase. Second, our M estimate implies atotal virial mass ≈ . × M = 10 × M (cid:12) . This islower than the 16 × M (cid:12) total mass used by Wittman(2019), who noted that the only available mass estimateavailable then was a dynamical mass likely to be biasedhigh. Because the velocity dispersions of the two sub-clusters are almost equal and our X-ray data do notconstrain the mass ratio, we search for analog systemswith subcluster virial masses of (5 ± . × M (cid:12) .The resulting constraints are: the subcluster separa-tion vector is >
74 ( >
60) degrees from the line of sightat 68% (95%) confidence; the time since pericenter pas-sage is 460-790 (340-820) Myr at the same confidencelevels; the maximum relative speed reached near peri-center passage, v max , is 2000–2500 (1900–2800) km s − ;and the relative speed at the time of observation is 540–1100 (320–1400) km s − . Note that the maximum rel-ative speed of the analog halos is likely to be underes-timated due to confusion in assigning particles to over-lapping halos (Wittman 2019).These estimates are consistent with the shock posi-tion as follows. Hydrodynamical simulations of a merg-ing cluster (Springel & Farrar 2007) indicate that shocksare launched from near the center of mass (CM) aroundthe time of pericenter passage. The maximum speed v max sets the speed of the shock front; over time thesubclusters slow substantially (and eventually fall back)while the shock slows little. Hence the analogs predictthat shock fronts have been traveling at (cid:38) − in CM coordinates for 650 Myr, for a distance of (cid:38) (cid:38)
800 kpc. In fact we find ∼ as well as the analog speed beingbiased low by several hundred km s − .If the shock propagates at ≈ − in CM co-ordinates as suggested by the 1.1 Mpc separation, thisimplies ≈ − relative to the unshocked gas,or M ≈ . The smaller Mach number we find couldbe due to line-of-sight projections of different parts ofthe 3-D shock front. It could also be due to slowing of For k T ∼ ∼ − . Andrade-Santos et al. the shock over time: although Springel & Farrar (2007)found that the slowing was only about 10%, their sim-ulations extended only 300 Myr past pericenter, whilewe are observing A3411 much later, ≈
650 Myr afterpericenter passage. Addressing these issues will requiredetailed hydrodynamical simulations, beyond the scopeof this paper. FORMATION OF RADIO RELICSFrom our analysis of the density jumps across surfacebrightness discontinuities we conclude that if they areindeed shocks, they are very mild. However, radio relicsextend over Mpcs in the A3411–12 system (see radioemission (red) in Figure 1). The fact that we observevery extended radio relics in a cluster with such low-Mach number shocks is indicative that a population ofenergetic electrons already existed over extended regionsof the cluster.The southeast inner edge has been discussed in vanWeeren et al. (2017) where it is argued that this edge isa shock front where particles from a nearby tailed radiogalaxy are being re-accelerated. While there is evidencefor a mild density jump at this location, the
Chandra data are not deep enough to confirm the presence of atemperature jump. This means that in principle thisedge could also trace a cold front. Given that this edgetraces a relic, a shock interpretation is more likely, asthis has been confirmed for numerous other relics (e.g.,van Weeren et al. 2019). However, a cold front (con-tact discontinuity) might also be able to explain someof the observed radio features. Magnetic field lines arethought to be stretched along the cold front interface(Lyutikov 2006; Dursi, & Pfrommer 2008). An align-ment of magnetic field might explain the increase of theobserved polarization fraction of the radio relic at thislocation. If the ICM magnetic field is also locally en-hanced at the cold front, this will result in a flatteningof the radio spectral index, providing that the underly-ing spectrum contains a spectral cutoff (i.e., is curved).A higher magnetic field strength will then “illuminate” adifferent part of the underlying electron spectrum, caus-ing the observed spectral index to flatten (Katz-Stoneet al. 1993). A curved spectrum with a spectral breakis naturally expected due to electron energy losses inthe tail of the AGN. Although a shock scenario remainsmore likely, future temperature measurements will beimportant to confirm or rule out a cold-front scenariofor the origin of the relic. CONCLUSIONSIn this paper we presented deep
Chandra observa-tions of the merging cluster A3411–12. This remark-able cluster hosts the most compelling evidence forelectron re-acceleration at cluster shocks to date. Wepresent gas temperature, X-ray luminosity, gas and to-tal masses, and gas fraction profiles. We computedthe shock strength using density jumps to concludethat the Mach number is small ( M ≤ . +0 . − . ). Wealso presented pseudo-density, projected temperature,pseudo-pressure, and pseudo-entropy maps. Based onthe pseudo-entropy map we conclude that the clusteris undergoing a mild merger, consistent with the smallMach number. On the other hand, radio relics spanover Mpcs in the A3411–12 system, which indicates thata population of energetic electrons already existed overextended regions of the cluster. In the southeast of thesystem there is evidence for a mild density jump, how-ever our Chandra data are not deep enough to confirmthe presence of a temperature jump. Therefore, we can-not determine if this edge traces a cold front or a shock.Future higher precision temperature measurements aretherefore important to test the shock re-acceleration sce-nario for radio relic formation.We thank Joseph DePasquale for creating the spectac-ular image displayed in Figure 1. F.A.-S. acknowledgessupport from
Chandra grant G05-16133X. R.J.vW.acknowledges support from the VIDI research pro-gramme with project number 639.042.729, which isfinanced by the Netherlands Organisation for Scien-tific Research (NWO). G.D.G acknowledges supportfrom the ERC Advanced Investigator programme New-Clusters 321271. W.R.F., and C.J. are supported bythe Smithsonian Institution. C.J. acknowledges sup-port from
Chandra grant G016619003. M.J.J. acknowl-edges support for the current research from the Na-tional Research Foundation of Korea under the pro-grams 2017R1A2B2004644 and 2017R1A4A1015178.D.R. and H.K. acknowledge support for the currentresearch from the National Research Foundation ofKorea under the programs 2016R1A5A1013277 and2017R1A2A1A05071429. V.M.P. acknowledges partialsupport for this work from grant PHY 1430152; PhysicsFrontier Center/ JINA Center for the Evolution of theElements (JINA-CEE), awarded by the US NationalScience Foundation (NSF). A.S. acknowledges supportfrom the Clay Fellowship. Part of this was work per-formed under the auspices of the U.S. DOE by LLNLunder Contract DE-AC52-07NA27344.
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OBSERVATIONS OF A3411–12
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OBSERVATIONS OF A3411–12 A. DENSITY JUMPS AND MACH NUMBER DISTRIBUTIONSHere we present the density jumps and Mach number distributions from Figures 7, 9 and 10. They show thedistribution of solutions for the fitted parameters from the X-ray surface brightness profiles across the wedges presentedin those figures. N = 1.99 +0.090.05 = 0.10 BULLET 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.101234 N = 1.70 +0.090.09 = 0.09 SOUTH
Figure A.1.
Distribution of density jumps for the cold fronts in the northern and southern sectors. Left: distribution of densityjumps from the MCMC simulations from the cold-front in the northern sector (the bullet). Right: Same as the left panel, exceptfor the southern cold-front. Andrade-Santos et al. N = 1.22 +0.200.14 = 0.17 NORTH 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00.51.01.52.02.53.03.54.0 N = 1.15 +0.140.09 = 0.12 NORTH1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40.00.51.01.52.02.5 N = 1.19 +0.210.13 = 0.21 SOUTHEAST INNER 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00.51.01.52.02.53.03.54.0 N = 1.13 +0.140.08 = 0.15 SOUTHEAST INNER1.0 1.2 1.4 1.6 1.8 2.0 2.20.00.51.01.52.0 N = 1.31 +0.220.17 = 0.20 SOUTHEAST OUTER 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00.51.01.52.02.53.0 N = 1.21 +0.150.12 = 0.14 SOUTHEAST OUTER
Figure A.2.
Distribution of density jumps (left panels) and Mach numbers (right panels) for the discontinuities in the northerand southern sectors. Top panels: distributions of density jumps and Mach numbers from the MCMC simulations from thediscontinuity in the northern sector. Center panels: same as top panels, except for the southeast inner sector. Bottom panels:same as top panels, except for the southeast outer sector.
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OBSERVATIONS OF A3411–12 B. MCMC CORNER PLOTSHere we present the MCMC “corner plots” (Foreman-Mackey 2016, 2017) from Figures 7, 9 and 10. They showthe distribution of solutions for the fitted parameters from the X-ray surface brightness profiles across the wedgespresented in those Figures. For all corner plots, contour levels are drawn at [0 . , . , . , . σ levels. Figure B.1.
The MCMC “corner plot” for the distribution of solutions of the fitted parameters from the X-ray surfacebrightness profiles across the bullet discontinuity (see left panel in Figure 7). Andrade-Santos et al.
Figure B.2.
The MCMC “corner plot” for the distribution of solutions of the fitted parameters from the X-ray surfacebrightness profiles across the northern discontinuity (see right panel of Figure 7).
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OBSERVATIONS OF A3411–12 Figure B.3.
The MCMC “corner plot” for the distribution of solutions of the fitted parameters from the X-ray surfacebrightness profiles across the discontinuity in the southeast outer wedge (see left panel in Figure 9). Andrade-Santos et al. . . . . . . . . . n . . . . . r b r e a k . . . . . . . . . . . . . . . . . n . . . . . r break . . . . Figure B.4.
The MCMC “corner plot” for the distribution of solutions of the fitted parameters from the X-ray surfacebrightness profiles across the discontinuity in the southeast inner wedge (see top right panel in Figure 9).
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