To the Edge of the Perseus Cluster

Azimuthally Resolved X-Ray Spectroscopy to the Edge of the Perseus Cluster

Abstract

We present the results from extensive, new observations of the Perseus Cluster of galaxies, obtained as a Suzaku Key Project. The 85 pointings analyzed span eight azimuthal directions out to , to and beyond the virial radius , offering the most detailed X-ray observation of the intracluster medium (ICM) at large radii in any cluster to date. The azimuthally averaged density profile for is relatively flat, with a best-fit power-law index significantly smaller than expected from numerical simulations. The entropy profile in the outskirts lies systematically below the power-law behavior expected from large-scale structure formation models which include only the heating associated with gravitational collapse. The pressure profile beyond shows an excess with respect to the best-fit model describing the SZ measurements for a sample of clusters observed with Planck. The inconsistency between the expected and measured density, entropy, and pressure profiles can be explained primarily by an overestimation of the density due to inhomogeneous gas distribution in the outskirts; there is no evidence for a bias in the temperature measurements within the virial radius. We find significant differences in thermodynamic properties of the ICM at large radii along the different arms. Along the cluster minor axis, we find a flattening of the entropy profiles outside , while along the major axis, the entropy rises all the way to the outskirts. Correspondingly, the inferred gas clumping factor is typically larger along the minor than along the major axis.

keywords:
X-rays: galaxies: clusters: X-rays, galaxies: clusters: individual: Perseus
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iint \savesymboliiint \savesymboliiiint \savesymbolidotsint \restoresymbolTXFiint \restoresymbolTXFiiint \restoresymbolTXFiiiint \restoresymbolTXFidotsint

1 Introduction

Approximately 90 per cent of the baryonic mass in massive clusters of galaxies lies in the intracluster medium (ICM), a hot diffuse plasma that fills the clusters’ gravitational potentials. The physical properties of the ICM, including the temperature, density, and chemical composition, can be inferred from X-ray spectra. Until recently, however, the thermodynamic properties of the majority of the ICM ( per cent by volume, spanning radii beyond 60% of the virial radius1) could not be measured directly because of its low surface brightness and the high particle backgrounds of orbiting X-ray satellites.

Due to its relatively low particle background compared to flagship X-ray satellites like the Chandra X-ray observatory and XMM-Newton, Suzaku has become the instrument of choice for studying cluster outskirts in X-rays. The growing list of clusters studied out to their virial radii includes PKS0745-191 (George et al. 2009; Walker et al. 2012a), A2204 (Reiprich et al. 2009), A1795 (Bautz et al. 2009), A1413 (Hoshino et al. 2010), A1689 (Kawaharada et al. 2010), A2142 (Akamatsu et al. 2011), Hydra A (Sato et al. 2012), the Coma Cluster (Simionescu et al. 2013), A2029 (Walker et al. 2012c), the Centaurus Cluster (Walker et al. 2013), and the Perseus Cluster (Simionescu et al. 2011). The fossil group RX J1159+5531 has been studied by Humphrey et al. (2012). The Virgo Cluster has been robustly studied to by XMM-Newton (Urban et al. 2011). For a comprehensive review, see Reiprich et al. (2013).

A common finding of these studies is a deviation of the observed entropy profiles in the cluster outskirts from naive expectations. In a cluster formed by gravitational collapse, and in which no additional heating or cooling occurs, the entropy is expected to follow a power-law with (Voit et al. 2005). However, the observed entropy profiles in clusters tend to flatten at large radii, differing from the expected value by a factor of in the outskirts (Hoshino et al. 2010; Simionescu et al. 2011; Urban et al. 2011). This phenomenon can in principle be attributed to several possibilities, including increased gas clumping at large radii (Simionescu et al. 2011; Urban et al. 2011), a hypothesis supported to some extent by simulations, e.g. Nagai & Lau (2011). Hoshino et al. (2010) and Akamatsu et al. (2011) proposed that differences in the electron and ion temperatures in the cluster outskirts, resulting from the relatively long equilibration time at low densities (Ettori & Fabian 1998), can result in the temperatures being underestimated. At some level, both effects will be at play (Akamatsu et al. 2011).

Lapi et al. (2010) and Cavaliere et al. (2011) proposed the weakening of accretion shocks as the clusters get older to be the reason for the entropy profile flattening. As the accretion shock propagates outward, the gas falls through a progressively smaller potential drop, thus reducing the entropy gain at the shock.

Radially and azimuthally resolved spectroscopy of galaxy cluster outskirts is challenging, and most measurements to date have been limited in spatial resolution to one data point between . Nonetheless, some Suzaku studies have been able to azimuthally resolve the spectroscopic properties of several nearby massive clusters. George et al. (2009) and Walker et al. (2012a) analyzed four directions in PKS0745-191 (), finding no statistically significant azimuthal variation. Bautz et al. (2009) observed Abell 1795 () along two directions, finding significant differences in the surface brightness in the outskirts. Kawaharada et al. (2010) defined four directions (offsets) in their observation of Abell 1689 (). They measured an isotropic distribution of the physical properties, with the exception of the northeast direction in the range, where the temperature and the entropy are significantly higher than in the other three directions. Eckert et al. (2012) studied a sample of 31 clusters observed with ROSAT to infer that, beyond , galaxy clusters deviate significantly from spherical symmetry.

The nearby Perseus Cluster (A 426, , Struble & Rood 1999) is the brightest X-ray cluster in the sky. Because of this, it was one of the first and remains one of the best studied objects in X-rays (e.g. Gursky et al. 1971; Forman et al. 1972; Allen et al. 1992; Ettori et al. 1998; Fabian et al. 2003; Simionescu et al. 2011; Fabian et al. 2011). The cluster’s X-ray emission is peaked on the optically brightest cluster galaxy (BCG) NGC 1275 (RA 3h19m48.1s, DEC ). Simionescu et al. (2011) used of Suzaku data to study the ICM of the Perseus Cluster out to the virial radius (, as inferred from these data) along two directions towards the northwest and the east. With these data, they were able to resolve the radial interval between and , for the first time, into independent radial bins. They found these two arms of Perseus to be broadly consistent in the outskirts, but inside the temperature profile along the eastern arm is systematically lower due to the presence of a cold front. Modeling the total mass, they reported, based on the current Suzaku calibration, that the inferred gas mass fraction exceeds the cosmic mean in the outskirts. Assuming this excess to be due to the presence of gas density clumps, and correcting for this, they obtained density, pressure, and entropy profiles consistent with the theoretical predictions for gravitational collapse. Recently, Simionescu et al. (2012) used a combination of ROSAT, XMM-Newton and Suzaku observations to find an evidence for large-scale sloshing motions of the ICM in the Perseus Cluster, the first time such motions have been observed on large scales.

In this work we expand the effort of Simionescu et al. (2011) adding six new arms of Suzaku data to the study of the Perseus Cluster, for a total of eight azimuthal directions covering the cluster out to beyond the virial radius. The total Suzaku exposure time is . Results on the distribution of metals in the cluster derived from these data are discussed by Werner et al. (submitted). The results on all other thermodynamic quantities are reported here. In Sect. 2 we describe the reduction of the data and the extraction of science products. Sect. 3 describes the main results of the analysis. In Sect. 4, we discuss the implications of our findings. Sect. 5 summarizes our results and conclusions. A discussion of the impact of systematic errors, including the influence of background fluctuations and stray light on the results, can be found in the appendix.

Throughout the paper we adopt CDM cosmology with , and . At the redshift of the Perseus Cluster one arcminute corresponds to a physical scale of . Our reference value for the virial radius is (Simionescu et al. 2011). All errors quoted are 68 per cent confidence unless otherwise stated.

2 Observations and Data Analysis

2.1 Reduction and Analysis of Suzaku Data

A total of 85 Suzaku pointings targeting the Perseus Cluster were obtained as a Suzaku Key Project during AO 4–6. These pointings cover eight azimuthal arms from the center out to a radius of , with a nominal exposure time of per arm. The data from the X-ray Imaging Spectrometers (XIS) 0, 1 and 3 were analyzed and are reported here.

The central pointing (obtained separately from the Key Project) and the eastern (E) and the northwestern (NW) arms, which each consist of 7 pointings, were observed in July and August 2009 (AO 4). These have been previously discussed by Simionescu et al. (2011). We have reprocessed the data for these arms using new calibration products and an updated analysis of point sources and image artefacts, aiming for consistency in the analysis across all 8 arms. The western (W) and southern (S) arms consist of 11 pointings each, observed in August 2010 (AO 5). A change of observational strategy is responsible for the increased number of pointings. This was done in order to expose the same area of the sky at large radii with two different parts of the detectors, and thus be able to better address systematic issues such as possible stray light contamination. The four remaining arms – north (N), northeast (NE), southeast (SE) and southwest (SW), consisting of 12 pointings each – were observed in August and September 2011 (AO 6). The observations were carried out in “diamond configuration” with one of the detector corners pointing towards the bright cluster center in order to minimize the stray light contamination.

We label the pointings with integers starting at the offset pointing closest to the central one for each arm. In the case of overlapping pointings we use half-integer indexing (so that, for example, pointings W5 and NE5 have the same distance from the cluster center and pointing N3.5 lies between and partly overlaps with N3 and N4). Fig. 1 shows the layout of the pointings on the sky.

Figure 1: Digitized Sky Survey (DSS) image of the Perseus Cluster region. Overplotted are the positions of the Suzaku pointings from AO 4 (red), AO 5 (magenta for integer and cyan for half-integer pointings, respectively) and AO 6 (black and blue). For clarity we individualy label only the AO 4 offset pointings. Observations with corresponding indices from different AOs lie at the same distances from the cluster centre. In green we show the position of the Chandra pointings at large radius reported here (Sect. 2.2). The new XMM-Newton pointing at large radius (Sect. B.5) is marked with a blue circle. The dashed circle shows the cluster’s virial radius at . The brightest feature at the western edge of the DSS image is the star Algol ( Per).

Data Cleaning

Initial cleaned event lists were obtained using the standard screening criteria proposed by the XIS team2. We also checked for likely solar wind charge-exchange (SWCX) emission contamination using the WIND SWE (Solar Wind Experiment) data, following the analysis of Fujimoto et al. (2007) and, in the case of affected pointings (N7, W7 and W7.5), have used only data above , where no SWCX lines are expected. We filtered out times of low geomagnetic cut-off rigidity (COR). Ray-tracing simulations of spatially uniform extended emission were used to perform vignetting corrections (Ishisaki et al. 2007). For the XIS 1 data obtained after the reported charge injection level increase on June 1st 2011, we have excluded two adjacent columns on either side of the charge-injected columns (the standard is to exclude one column on either side).

Imaging Analysis

We extracted and co-added images from all three XIS detectors in the energy band. Regions of around the detector edges were removed, as were all pixels with an effective area less than 50 per cent of the on-axis value. Instrumental background images in the same energy range were extracted from night Earth observations. These were subtracted from the cluster images before the vignetting correction was applied. The resulting background- and vignetting-corrected mosaic image is shown in Fig. 2.

Figure 2: Exposure- and vignetting-corrected mosaic of the Perseus observations in the range with the detector edge regions removed as described in the text. The white dashed circle centered on the BCG NGC 1275 marks the nominal virial radius at . We highlight the locations of candidate point sources with white circles. The image has been smoothed with a Gaussian with width of , the color bar shows the surface brightness in units of  counts/s/arcmin.

We have identified (and excluded from the subsequent analysis) a list of candidate point sources using the CIAO tool wavdetect. For this search we used a single wavelet radius of 1 arcmin (7.2 pixels), which is approximately matched to the Suzaku half-power radius (). In addition to the 140 candidate point sources identified in this way, we removed a  circle in an area of enhanced surface brightness in the N arm (associated with a background cluster; Brunzendorf & Meusinger 1999) and a  circle around the galaxy IC 310.

The flux of the dimmest identified candidate point source is . Assuming this flux to be the detector sensitivity across the entire exposure in all the pointings, the number of detected candidate point sources is consistent with the expected value obtained from the curve of the Chandra Deep Field South.

Spectral Analysis

For each arm, we extracted a set of spectra from 17 annular regions centered on NGC 1275. These spectra exclude regions associated with the detector edges and candidate point sources. The spectra were rebinned to have at least one count per channel. Night Earth observations were used to obtain the instrumental backgrounds. Appropriate response matrices were constructed for each region. Ancillary response files were calculated with ray-tracing simulations using xissimarfgen, employing the detector contamination files from July 2012.

Spectral modelling was carried out using XSPEC (version 12.7, Arnaud 1996), and the extended C-statistic estimator. We used the energy range for XIS0 and XIS3 and for XIS1. The Galactic absorption was set individually for each pointing to the average column of the Leiden/Argentine/Bonn Survey calculated at the position of the given pointing (Kalberla et al. 2005). We modeled the cluster emission in each spectral region as single temperature plasma in collisional ionization equilibrium using the apec plasma code (Smith et al. 2001). We adopt the solar abundance table from Feldman (1992).

Modeling the X-ray Foreground and Background

Assuming, based on the results described below, an absence of significant cluster emission beyond a radius of (or ), we have used the pointings indexed 6 and above (21 pointings in total) to determine the X-ray foreground/background (CXFB). The N arm was not used for this purpose due to the presence of a background group. In addition to Suzaku data, we also used spectra from the ROSAT All Sky Survey extracted from circular regions with a radius of 1 degree in the outer part of each arm to help constrain the low-energy spectral components.

Our background spectral model includes four components – a power-law to model the unresolved point sources (e.g. De Luca & Molendi 2004) and three thermal components modeling the local hot bubble (LHB, Sidher et al. 1996), the Galactic halo (GH, Kuntz & Snowden 2000), and a potential 0.6 keV foreground component, respectively. The power-law and the LHB components (which we term isotropic background components), as well as the temperatures of the GH and the 0.6 keV component, were assumed to be constant across the mosaic. The normalizations of the GH and 0.6 keV components were allowed to vary from arm to arm. Due to the presence of the background group, model components for the N arm were obtained by averaging the results for the neighboring NE and NW arms, weighted by their statistical errors. Due to their origin within the Galaxy, all thermal background components had their redshifts set to zero and their metallicity set to Solar values. All CXFB components are absorbed by the Galactic column density, except for the LHB due to the proximity of its origin to the Solar system. The fitted CXFB model components are listed in Tab. 1.

Isotropic background components
power-law index
power-law flux
flux
Anisotropic background components
flux flux
E
NE
N
NW
W
SW
S
SE
Table 1: Summary of the CXFB spectral model components. The temperatures are given in keV and fluxes in ergs/s/cm/arcmin in the range.

2.2 Reduction and Analysis of Chandra Data

Chandra ACIS-I observations targeting the northwestern arm of the Perseus Cluster at a radius () were taken on 2011 November 5-11. The observations were performed in the VFAINT mode, which improves the rejection of cosmic ray events. The total exposure time of the four overlapping pointings after cleaning is 144 ks. The standard level-1 event lists were reprocessed using the CIAO (version 4.4) software package. The images were produced following the procedures described in Ehlert et al. (2013). The analysis of the point source population detected by Chandra is described in detail in Sect. B.4.

3 Results

3.1 Suzaku Surface Brightness Profiles

Figure 3: The surface brightness profiles along the different arms corrected for CXFB in the energy range (top) and the residuals after dividing by the azimuthally averaged profile (bottom). The most prominent feature is the cold front along the E (black) arm inside that reaches into NE (red) and SE (brown) arms. Outside () the W and SW arms are the brightest, revealing the presence of the large-scale spiral discussed in Simionescu et al. (2012). Positions of and are indicated with dotted lines.

Fig. 3 shows the surface brightness profiles in the band along the eight Perseus arms after removing candidate point sources. In constructing the profiles, the CXFB surface brightness was determined separately for each arm from the weighted average brightness measured beyond 2 Mpc. We subtracted this, assuming it to be constant across the arm, and added its error in quadrature to the statistical error in each bin. Tab. 2 lists the measured CXFB surface brightness for each arm.

In order to better show the surface brightness features in the individual arms, we plot the ratio of the surface brightness in a given arm to the average surface brightness at a given radius in the bottom panel of Fig. 3.

arm
E
NE
N
NW
W
SW
S
SE
Table 2: Left column: CXFB surface brightness for each of the arms including the statistical error obtained by weighed fitting of the image surface brightness outside 2 Mpc by a constant. Right column: Power law index describing the surface brightness profiles in the range.

The cold front along the E arm between radii of (), first discussed by Simionescu et al. (2011), is clearly evident in the profile. The effects of this cold front extend to the neighboring arms, NE and SE, also enhancing their surface brightness at those radii. From () the SW and W arms display a brightness excess, showing evidence for the large-scale sloshing/swirling motion of the ICM discussed by Simionescu et al. (2012).

The results of fitting the surface brightness data in the () range with a power-law model, excluding those regions influenced by the presence of the eastern cold front, are shown in Tab. 2. The X-ray surface brightness profiles to the N, NW, E and W are significantly flatter than those toward the south.

3.2 Projected Spectral Results

Figure 4: Projected temperature profiles along the individual arms. Dotted lines mark the positions of and the virial radius at (Simionescu et al. 2011) corresponding to the outer bound of the last-but-one annulus. The last data point lies completely outside the virial radius. Top: arms that appear the most relaxed, center: arms influenced by the presence of the eastern cold front (indicated by the black arrow), bottom: arms exhibiting increased surface brightness and decreased temperature at large radii due to gas sloshing (Simionescu et al. 2013).

Temperature profiles measured from the projected spectra are shown in Fig. 4. For clarity, all of the profiles are shown divided into three groups, according to the morphological similarities among the arms.

No major substructure, i.e. cold front or evidence for large scale sloshing (Simionescu et al. 2012), is observed along the N, NW and S arms, and we will refer to these as the relaxed directions. Residual contamination from the extended emission of a background group gives rise to a region of enhanced surface brightness beyond towards N, which influences the spectral results. Towards the NW the temperature quickly drops, reaching values where emission lines appear - this allows us to tightly constrain the temperature in the last data point.

The SE, E and NE arms are all influenced by the presence of the cold front at (0.7 Mpc), as discussed for the E arm by Simionescu et al. (2011), evidenced by a dip in the respective temperature profiles at the same radii where their surface brightness is boosted.

The W and SW arms show an increase of the surface brightness beyond the radius of the eastern cold front. Simionescu et al. (2012) associated this brightness excess with large scale sloshing/swirling; therefore, we group these two arms and refer to them as the “sloshing” arms.

In order to reduce the impact of statistical uncertainties, we have also examined the results of simultaneously fitting spectra from multiple arms. These are shown in Fig. 5, in red the results using the three relaxed (N+NW+S) and in blue using all eight arms. In both cases, we exclude N spectra from the outermost annulus due to the contamination of the ICM emission by a background group.

Figure 5: Average profiles of projected temperature for the simultaneous fitting of all (blue) and relaxed (red) arms. In both cases, data for the N arm beyond were excluded due to contaminating emission from a background galaxy group.

There are differences among the individual arms (and subsets of arms, as shown by Fig. 5). Most notably, along the cluster’s minor (north–south) axis, which roughly corresponds to the relaxed arms, the temperature tends to drop towards the outskirts faster than along the major (east–west) axis.

In the appendix, we present a thorough analysis of the systematic uncertainties related to background fluctuations, point source exclusion, stray light, etc. We find our results to be generally robust to all the systematic tests that have been conducted.

Results from the observed metallicity distribution are reported elsewhere (Werner et al. 2013, submitted).

3.3 Deprojected Spectral Results

Method for Obtaining the Profiles

Assuming spherical symmetry in the individual arms, we have carried out a deprojection analysis using the XSPEC model projct. For this analysis, we fixed the ICM metallicity to everywhere (this is in agreement with the measured projected profile; Werner et al. 2013). We determined uncertainties in the derived properties using Markov chain Monte Carlo simulation steps. Fig. 6 shows the resulting profiles of deprojected temperature (), electron density (), pressure (), and entropy ().

Figure 6: Deprojected profiles. The arms are divided into the same groups as in Fig. 4. Neighboring annuli in a given arm may be tied together to reduce ‘ringing’ artifacts in the deprojection. Top left panel: the deprojected temperature profiles. The best fit of the temperature model of Vikhlinin et al. (2006) to the average temperature profile is shown in grey. Top right panel: electron density profiles. The -model fit to the azimuthaly averaged density profile is shown in grey. Bottom left panel: pressure profiles. In grey we overplot the Planck Collaboration et al. (2013) model. Bottom right panel: entropy profiles. In grey we plot the baseline power-law relation of Voit et al. (2005) with the normalization fixed to the expected value calculated following Pratt et al. (2010, see main text).

Taking the weighed average of the deprojected results from all arms and for the subset of three relaxed arms (N, NW, S) we create the azimuthally-averaged profiles of temperature, density, pressure, and entropy shown in Fig. 7.

Figure 7: Azimuthally averaged profiles of the ICM properties for all arms (red) and the subset of relaxed arms (blue). Black arrow indicates the position of the cold front to the east of the cluster center. Top left: Temperature profile with its best fit model from Vikhlinin et al. (2006) shown as a dashed line. Top right: Density profile with its best fit -model (dashed line). Bottom left: Pressure profile with overplotted best-fit theoretical models by Arnaud et al. (2010) (dashed line) and Planck Collaboration et al. (2013) (solid line). The only free parameter in the fits was . Bottom right: Entropy profile. Dashed line shows the power-law with normalization fixed to the value calculated according to Pratt et al. (2010). In solid black line we plot the best fit entropy profile by Walker et al. (2012b).

Reference Model for the Temperature

Vikhlinin et al. (2006, see also ) introduce an analytical three-dimensional temperature model that extends to large radii in clusters

(1)

The model has eight free parameters that allow it to closely describe many features of a smooth temperature distribution. The best-fit parameters for the average profile of all arms and for the average of the subset of relaxed arms (N, NW, S) are shown in Tab. 3. We overplot the former profile in the top left panel of Fig. 7.

all arms relaxed arms
4.06 5.30
0.72 0.88
294 261
6.72 6.98
1.6 1.1
0.33 0.18
16.24 271
2.36 1.29
Table 3: Best fit parameters of the analytical three-dimensional temperature model from Eqn. 1 for the average profile of two sets of arms.

Reference Models for the Density

We have fitted the density profiles along individual arms, as well as the azimuthally averaged profile and the average profile of the relaxed arms, with an isothermal -model (Cavaliere & Fusco-Femiano 1978),

(2)

We restrict our fits to radii in order to avoid the cool core. The results are shown in Tab. 4. The parameter of the average profile () is in approximate agreement with the canonical value for large clusters . We obtain a slightly lower value when fitting the average of the relaxed arms (). The best fit azimuthally averaged -model profile is shown in the top right panel of Fig. 7.

arm -model index
E
NE
N
NW
W
SW
S
SE
average
relaxed
Table 4: Results of the analytical modeling of density. The last two rows show the parameters of the azimuthally averaged profile and the average profile of the relaxed arms. The last column contains the indices of the power law fits to the individual arms beyond () to avoid the influence of the cold front towards the E.

Fitting the profiles for the 8 arms independently, we notice significant differences between the best fit parameters. Fixing the core radius to the average profile value of , we measure a spread of values across the eight arms of .

Power-law modeling of density profiles of galaxy clusters, , has proved popular due to its simplicity and also due to the fact that the -model at radii behaves like a power-law. We fit a power-law model separately to the density profile of each arm for (), thus avoiding the influence of the cold front towards the east. The fitted power-law indices are shown in the last column of Tab. 4 and show similar trends to the surface brightness slopes in Tab. 2, with the steepest gradients on the southern side of the cluster. We report a relatively flat azimuthally averaged density profile, falling off with radius with an index of outside (or ), in agreement with the average slope previously reported by Simionescu et al. (2011) for the average between only the E and NW arms. Fitting a power-law model to the average density profile for results in a flattening, with .

Reference Models for the Pressure

Nagai et al. (2007) propose a generalized pressure profile of the form

(3)

where , , is the concentration parameter defined at , and the indices , and are the profile slopes in the intermediate, outer and central regions, respectively. is the ratio of the Hubble constant at redshift with its present value and is the total cluster mass enclosed within .

Using a set of 33 local () XMM-Newton clusters with data extending to , Arnaud et al. (2010) find the best fitting parameters to be . Recently, Planck Collaboration et al. (2013) studied the pressure profiles of 62 Planck clusters between , finding the best fit set of parameters .

Shown in the bottom left panel of Fig. 7, we have fitted the average Perseus pressure profile with the generalized pressure model for , leaving as the only free parameter (while expressing as a function of self-consistently) and fixing the other parameters to the two sets of values mentioned above. The resulting values for are in agreement with each other: and . Overall, the model is a reasonable fit. However, in the cluster outskirts () the Suzaku data lie above the model, before dropping below in the last annulus (not shown in Fig. 7).

We fit the Planck Collaboration et al. (2013) pressure profile in the same way to the individual arms and find to be larger along the cluster major (east–west) as compared to the minor (north–south) axis.

We note that Simionescu et al. (2011) measured  arcmin for the NW arm, which is approximately 10% lower than the best fit average value for using Eqn. 3. This difference could be attributed to asymmetries intrinsic to the cluster itself (minor axis vs. major axis). This uncertainty in measuring implies that the value of may also be up to 10% larger than the value adopted throughout this paper, which is based on the mass model of Simionescu et al. (2011).

Reference Models for the Entropy

In a cluster formed by gravitational collapse, and in which no additional heating or cooling occurs, the entropy is expected to follow a power-law of the form

(4)

where (Voit et al. 2005; Pratt et al. 2010). We assumed and used our best-fit value in calculating .

As shown in Fig. 6, in each of the relaxed directions, we observe a flattening of the entropy profile with respect to this expected power-law beyond .

For the E, SE and NE arms, the characteristic dip in the entropy profiles between radii of 20 and 35 arcmin is jointly caused by increased density and low temperature associated with the eastern cold front. The entropy beyond the cold front () in these arms increases steadily with radius (with the exception of the SE direction, where we observe a drop in entropy beyond ).

The SW and W arms are affected by sloshing at large radii, which results in an excess density and surface brightness. This leads the entropy to flatten in these arms (forming a dip in the SW case) at the radii corresponding to the large-scale sloshing; the entropy increases again further out, rising steeper than in both arms.

The bottom right panel of Fig. 7 shows the average entropy profile for the Perseus Cluster. We find an excess of entropy in the cluster center () with respect to the power-law model in Eqn 4. This is consistent with the presence of excess ICM heating in the cluster center as favoured by cosmological studies (e.g. Voit 2005; Cavagnolo et al. 2009; Mantz et al. 2010). The average profile diverges downwards from a power-law shape at . The ratio of the expected and measured value of the entropy is at the virial radius.

For comparison, we fitted the normalization of a power-law profile, with its index fixed to 1.1, to the weighed average of the three relaxed arms between , avoiding both the cool cluster core and the cluster outskirts, as well as the cold front and the large-scale sloshing, present in the other arms. The best-fit normalization was higher than the value calculated using Eqn. 4. Taking the average profile of all the eight arms in the range, we also fitted it with a power-law with both the normalization and the power-law index as free parameters, obtaining an index of , significantly flatter than the theoretical value of .

Using a set of the clusters observed with modest spatial resolution out to the virial radius and beyond, Walker et al. (2012b) find, that the entropy profile in the range can be fitted with an analytical function

(5)

with .

We fit the profile from Eqn. 5 to the entropy averaged over all 8 arms, and to the subsample of three relaxed arms, with the resulting parameters shown in Tab. 5.

A B
Walker et al. (2012b)
Perseus average
relaxed arms
Table 5: Best fit parameters of the Walker et al. (2012b) entropy profile to the averaged entropy distribution for all 8 directions and for the 3 relaxed arms.

3.4 Analysis of the Surface Brightness Fluctuations

Figure 8: Background subtracted and flat-fielded Chandra image of the Perseus Cluster outskirts towards the NW. We mark the identified point sources by white circles.

In order to search for possible bright gas clumps in the cluster outskirts, we have analyzed the surface brightness (SB) fluctuations in the Chandra observation targeting the region of the NW arm at , as well as in the whole Suzaku mosaic of the Perseus Cluster. We have measured the power spectrum of fluctuations using the modified variance method (Arévalo et al. 2012), which accounts for gaps in the data due to excluded point sources.

Fig. 8 shows the region of the NW arm at observed with Chandra, and the identified point sources. No obvious extended sources were seen in the image. We determined that the population of the point sources detected in this region is consistent with that expected from field surveys such as the Chandra Deep Field South (see Sect. B.4). The global structure due to the smooth ICM emission was removed by dividing the image by the best-fit model centered on the core of the Perseus Cluster.

The power spectrum of the surface brightness fluctuations reveals a slight increase in the 2D power above the Poisson noise level, which could be either due to the clumpiness of the gas on scales or due to unresolved point sources. We estimate the contribution of the faint, unresolved point sources from the distribution of resolved point sources (see also Churazov et al. 2012), which is reasonably well approximated by the power-law . The contribution of the faint point sources to the power spectrum is , while the contribution of the resolved sources is , where and are the smallest and highest detected point source fluxes, respectively. In our case, counts and counts. Therefore, we expect the contribution of the unresolved point source population to our measured power spectrum to be at the level of  per cent relative to the contribution of the resolved bright sources. The power spectrum due to the unresolved point sources can thus be calculated as , where and are the power spectra with and without the resolved sources, respectively. After the subtraction of the Poisson noise and of the expected power spectrum of the unresolved point sources, the measured 2D power spectrum of the surface brightness fluctuations is consistent with zero. We therefore conclude, that the slight increase of power above the Poisson noise in the Chandra data can be plausibly associated with unresolved point sources. We note, that even if clumping is present in the gas at these radii (), the signal may be difficult to detect because of smearing due to the long line of sight that we probe in the cluster outskirts. The clumps could also simply be small and faint and therefore unresolved by Chandra.

The study of SB fluctuations with the Suzaku satellite is more complicated. Our analysis of the PSF of the Suzaku mirrors shows that the power spectrum of SB fluctuations on spatial scales smaller than is suppressed by a factor of 4 due to the convolution with the PSF. To understand the impact of faint point sources, which remain unresolved in our Suzaku data, we have compared the SB fluctuations of the Chandra observation after excluding only the point sources detected by Suzaku with the level of fluctuations after excluding all the Chandra point sources. We have found that, at a distance of from the cluster core, corresponding to the location of the deep Chandra pointing, the SB fluctuations on scales smaller than are dominated by the population of point sources unresolved by Suzaku. We therefore conclude that Suzaku observations of the Perseus Cluster cannot be used to study SB fluctuations on scales smaller than , which is comparable to the field of view of a single Suzaku pointing. Structure on larger scales is seen in the form of the large-scale sloshing described in Simionescu et al. (2012) and throughout this paper.

4 Discussion

The density, entropy, and pressure profiles in the outskirts of the Perseus Cluster show interesting azimuthal variations, as well as intriguing departures from the expected behaviors in the azimuthally averaged profile shapes.

We report a relatively flat azimuthally averaged density profile, falling off with radius with an index of outside (or ). There is currently a large scatter in the values of the density slopes near reported in the literature, with values ranging from for A2142 (Akamatsu et al. 2011) to for the Virgo Cluster (Urban et al. 2011), or for A1689 (Kawaharada et al. 2010). Measurements which indicate shallow density slopes are challenging to explain theoretically. Simulations predict relatively steep density profiles in the cluster outskirts with , steepening to at around (Roncarelli et al. 2006).

Compared to the expected power-law entropy profile given by Eqn. 4, we measure an excess in the central (); beyond (), the profile lies systematically below the expectation. Using a combination of SZ and X-ray data for 6 cool core clusters, Eckert et al. (2013) have recently argued that the entropy profiles outside were in agreement with Eqn. 4, which is clearly in tension with our current measurements. Eckert et al. (2013) point out that the entropy excess in cluster cores may have caused the normalization of the model to be overestimated in previous publications, where this normalization was allowed as a free parameter in the fit, rather than being fixed based on Eqn. 4. While this is indeed possible, we show that, even when fixing both the normalization and index of the power-law model for the expected entropy behavior, we still find an entropy deficit at large radii in the azimuthally averaged profile. This is consistent with the conclusion of Walker et al. (2013), who combined the entropy profiles obtained from X-ray spectroscopy for 13 clusters.

In addition, the azimuthally averaged pressure profile shows an excess between with respect to the best-fit model describing the SZ measurements for a sample of clusters observed with Planck (Planck Collaboration et al. 2013).

In the case of X-ray observations, the quantities that are measured directly are the gas density and temperature. In order to determine which of these quantities contribute primarily to the deviations of the pressure and entropy from the expected trends at large radii, we may use the self-similar profiles for pressure and entropy (Eqn. 3 and Eqn. 4, respectively) to solve for the expected density and temperature profiles:

(6)
(7)
Figure 9: Ratios between measured ICM temperature (left) and density (right), and their expectations obtained from Eqns. 6 and 7, respectively.

Along each arm, we have determined the ratios between the measured temperatures and densities, and the expected values predicted from the equations given above. These ratios are shown in Fig. 9. This allows us to look in more depth at the influence of morphological features in the individual arms on the average density, entropy and pressure profiles.

The eastern cold front is clearly visible as a dip in the entropy profiles along each of the affected arms (NE, E, SE), which coincides both with a temperature decrement and with a density increase with respect to the expected profiles at . Signatures of the large scale sloshing are present in the SW and W arms, where we see excess density in the range, causing an apparent flattening of the entropy profiles along these directions.

The density in the cluster outskirts is higher than the expected value for all of the arms. At the virial radius (), the biggest excess is seen along the relaxed arms (N, NW, S). This coincides with the cluster’s minor (north-south) axis, where the entropy was observed to flatten most significantly with respect to the expected power-law model. In the case of temperature, the measured and expected values in the outskirts are consistent within the 2  confidence level, with the only exception of the outermost points of the N and NW arms. We conclude therefore that the inconsistency between the expected and measured entropy and pressure profiles can be explained primarily by an overestimation of the density due to gas clumping in the outskirts.

In Fig. 10, we compare the ratios of the measured over expected gas densities for the eight different arms of the Perseus Cluster by overplotting the individual panels of the right-hand side of Fig. 9, as well as the azimuthal average. If the density in the cluster outskirts is indeed overestimated primarily due to gas clumping, then the square of this plotted ratio is essentially equivalent to the gas clumping factor defined as .

The azimuthally averaged gas clumping exhibits a peak at , which is caused by the presence of the eastern cold front. Beyond , the level of gas clumping in the averaged profile increases steadily with radius.

The values reported here are lower than the gas clumping factors initially presented in Simionescu et al. (2011), who find a of 2.5–4 in the range from for the NW arm. This is partly due to the different baseline model for the entropy (here, the normalization was fixed to the predictions from numerical simulations, while Simionescu et al. 2011 used the best-fit normalization for the observed profile) and partly due to the possible mass modeling bias associated with the instrument calibration, and which affected the clumping estimation based on the gas mass fraction excess with respect to the cosmic mean.

Simulations by Nagai & Lau (2011) show that gas clumping is more pronounced in dynamically active systems. From this, one might naively expect this effect to be most significant along the cluster’s major axis, where the gas accretion predominantly takes place. We observe the opposite trend: the highest clumping factor inside is seen along the cluster’s minor axis. This could be explained if the clumps were more easily destroyed in more dynamically active regions, which may be beyond the gas physics and spatial resolution of current state-of-the-art simulations. Although our Chandra analysis found no direct detection of gas clumps at along the NW arm, we cannot rule out the presence of clumping because, even if this effect is important, the signal may be difficult to detect due to smearing caused by the long line of sight that we probe in the cluster outskirts. It is also possible that the individual clumps are small and faint, and therefore unresolved by Chandra - analogous to a fine mist, where the individual drops are unresolved to our eyes.

Alternative explanations for the flattening of the entropy profiles near the virial radius, such as weakening of accretion shocks proposed by Lapi et al. (2010) and Cavaliere et al. (2011) or electron ion non-equilibrium (Hoshino et al. 2010; Akamatsu et al. 2011), would cause the observed temperatures to be lower than the expected profile given by Eqn. 6, but would not produce an excess in the observed density and pressure. These effects may be partly responsible for the temperature biases seen in the outermost annuli towards the N and NW, but appear not to be important elsewhere within the Perseus Cluster.

Figure 10: Profiles of the ratios of the measured over expected gas densities for the eight different arms of the Perseus Cluster (points) and the azimuthally averaged profile (lines).

The discontinuities in the inferred deprojected temperature and density of the ICM along the NW arm, implying a sharp downturn in entropy and pressure beyond , suggest – at face value – the presence of a shock front. The apparent density and temperature jumps at along the NW arm, however, imply inconsistent Mach numbers. After correcting for the underlying density profile using our best-fit -model, we find a density jump of at this discontinuity, implying a Mach number of . After correcting for the underlying temperature profile, using the Planck Collaboration et al. (2013) pressure profile combined with the best-fit -model, we find a temperature jump of at the , implying a Mach number .

These values are within the range determined by Akamatsu & Kawahara (2013), from a systematic X-ray analysis of six giant radio relics near the outskirts of four clusters of galaxies observed with Suzaku. Akamatsu & Kawahara (2013) report significant temperature jumps across the relics for CIZA 2242.8-5301, Abell 3376, Abell 3667NW, and Abell 3667SE, with the Mach numbers estimated from the X-ray temperature or pressure profiles being in the range from 1.5–3. In their sample, the shocks are also more clearly seen in the temperature than in the surface brightness or density profiles.

However, the discontinuities in the temperature and density profiles near the virial radius are difficult to interpret in light of the results shown in Fig. 9. If the observed discontinuity were a shock, the post-shock temperature immediately inside the virial radius would be higher than expected based on the self similar profiles, which is not seen. Instead, the temperature discontinuity is created by the fact that the temperature immediately outside appears to be biased low, under the assumption that the self-similar profiles for the entropy and pressure hold beyond . We therefore cannot draw any robust conclusions regarding the presence of a shock at the virial radius along this direction, although the thermodynamic properties of the gas beyond along the NW arm certainly suggest the onset of intriguing physical processes which go beyond self-similarity.

5 Conclusions

We have presented the results of the analysis of Suzaku Key Project observations of the Perseus Cluster from its center out to along eight azimuthal directions. We detected the ICM emission out to the virial radius () in all directions. In five arms, we were able to study the ICM beyond the virial radius. Our main conclusions are:

  • The azimuthally averaged density profile for is relatively flat, with a best-fit power-law index significantly smaller than expected from numerical simulations. The entropy profile in the outskirts lies systematically below the power-law behavior expected from large-scale structure formation models which include only the heating associated with gravitational collapse. The pressure profile beyond shows an excess with respect to the best-fit model describing the SZ measurements for a sample of clusters observed with Planck (Planck Collaboration et al. 2013).

  • The inconsistency between the expected and measured density, entropy, and pressure profiles can be explained primarily by an overestimation of the density due to gas clumping in the outskirts. There is no evidence for a bias in the temperature measurements, with the exception of the outermost two data points towards the N and NW.

  • We found significant differences in thermodynamic properties of the ICM at large radii along the different arms. Along the cluster minor (north–south) axis, we find a flattening of the entropy profiles outside , while along the major (east–west) axis, the entropy rises all the way to the outskirts. Correspondingly, the inferred gas clumping factor is typically larger along the minor than along the major axis.

  • We find no bright gas clumps or surface brightness fluctuations associated with gas clumping in a deep Chandra observation of the Perseus Cluster outskirts () along the NW direction. The clumping signal may, however, be difficult to detect due to smearing caused by the long line of sight that we probe in the cluster outskirts.

Acknowledgments

We acknowledge the support by Suzaku grants NNX09AV64G and NNX10AR48G, Chandra grant GO2-13144X, NASA ADAP grant NNX12AE05G and XMM-Newton grant NNX12AB64G. This work was supported in part by the U.S. Department of Energy under contract number DE-AC02-76SF00515. AM acknowledges the support by the NSF grant AST-0838187.

Appendix A Projected Results

In Table 6 and 7, we show the projected values for the ICM temperature and XSPEC normalization, respectively. Throughout the sections of this Appendix, the XSPEC normalization is defined as  cm arcmin.

Annulus Temperature (keV)
Radius Width N NW W SW S SE E NE
6.7 3
9.7 3
12.7 3
15.7 3
18.7 3
21.7 3
24.7 3
27.7 3
30.7 3
33.7 3.3
37 5
42 5
47 6
53 7
60 10
70 12
82 13
Table 6: Projected temperatures along the individual arms. The properties of the annuli are given in arcminutes, the radius is the distance from the cluster center to the inner edge of the given annulus.
Radius Width N NW W SW S SE E NE
6.7 3
9.7 3
12.7 3
15.7 3
18.7 3
21.7 3
24.7 3
27.7 3
30.7 3
33.7 3.3
37 5
42 5
47 6
53 7
60 10
70 12
82 13
Table 7: Projected XSPEC spectrum normalizations, in units of times the standard definition from Appendix A.

Appendix B Background-Related Systematic Uncertainties

b.1 CXFB Variations

To test the influence of possible CXFB variations over the area of our mosaic, we have examined spectra extracted from  wide annular regions at . In total, we examined 23 regions (three from each of seven3 arms plus one from the W and one from the S arms that extend further out). Starting from our default background model, we simultaneously refitted the normalizations of all CXFB components in each region, with the exception of the LHB (whose variation does not have a significant influence on the results). From the measured values, we estimate the dispersion of the individual CXFB components across the mosaic. For the power-law component, we used the complete set of 23 normalizations. In the case of the anisotropic CXFB components, we took the standard deviation of the normalization of regions selected from the given and the two adjacent arms (in the vicinity of the N arm, we used only two arms, since no data from this arm has been used in the CXFB analysis). Tab. 8 shows the average values and their variations for the anisotropic components and the power-law component.

The standard deviations were used as the bracketing values to upscale and downscale, one at a time, the normalizations of the individual CXFB components, in each arm refitting in each case the ICM model.

arm component
GH 0.6 keV
E
NE
N
NW
W
SW
S
SE
power-law
all
Table 8: XSPEC normalizations and their standard deviations for the CXFB model components along the individual arms. The values are normalized to times the standard definition from Appendix A.

The uncertainties in the ICM temperature and normalization profiles obtained in this way are plotted over the original results in Fig. 11. The systematic errors, with the exception of a few data points beyond the virial radius, lie within the statistical error bars of the individual values, and the trends remain robust.

Figure 11: Projected temperature and normalization profiles and the systematic errors determined from up- and downscaling the CXFB model parameters by the values shown in Table 8. The individual lines - full (power-law), dotted (GH), and dashed (hot component) - show the bracketing values for the measurements resulting from potential background variations.
Figure 12: Statistical errors of the projected temperature profiles (points) and the systematic errors estimated using bootstrap analysis (lines).
Figure 13: Same as Fig. 12 but for normalizations.

To further investigate the influence of the CXFB variations on our results, we followed a bootstrap approach, as described in Simionescu et al. (2013). In order to obtain a set of spectra with approximately the same number of counts, as well as to extract a statistically meaningful number of spectra from each arm, we divided each of the background pointings into quadrants and divided the event files from each detector into parts with exposure times of approximately 5 ks. In total, we extracted 272 spectra per detector from all the arms in this way, with at least 24 spectra per detector per arm.

From each arm we randomly selected out of the spectra that had been extracted from that arm, allowing for repetition, and simultaneously used the sets from all the (seven) arms to re-determine the best-fit CXFB model in the same way as the original model, described in the main text. We use this new CXFB model to re-fit the ICM emission.

We repeated this procedure 1000 times, each time with a different randomly selected set of background spectra, and determined the distributions of the best-fit temperatures and normalizations and their 68% confidence intervals. These are shown in Fig. 12 (temperature) and Fig. 13 (normalization), respectively. We find that the uncertainties due to background fluctuations are smaller than the 1- statistical error bars for all of our measurements.

b.2 Uncertainty of the Non-X-ray Background

Figure 14: Systematic errors on the projected temperature (left panel) and XSPEC normalization (right panel) profiles determined by conservatively up- and downscaling the NXB by 3% for all detectors simultaneously. Points show the statistical errors of the best-fit values, lines show the bracketing values for the measurements resulting from potential NXB variations.

The Suzaku non-X-ray background (NXB) is known to be remarkably stable, with an uncertainty smaller than (Ishisaki et al. 2007). In order to examine the sensitivity of our results to potential uncertainties in the NXB, we simultaneously up- or downscaled the NXB by 3% for all detectors and refitted the spectra using our default model. The bracketing values for the projected temperatures and XSPEC normalizations are shown in Fig. 14. In all cases the systematic uncertainties are smaller than the statistical errors. We note that this is a pessimistic estimate of the background fluctuations, as the NXB level is unlikely to be either increased or decreased by the same (maximal) amount in all detectors simultaneously.

b.3 Point Source Identification in Suzaku

Correctly identifying and excluding point sources when studying the ICM, especially with the modest spatial resolution of Suzaku, provides another source of uncertainty. To test the influence of the point source identification method, we re-analysed the data for the SW arm excluding two sets of point sources obtained with different (extreme) techniques. In the “minimal” selection we chose, by visual inspection, only the most obvious sources, identifying only three sources within and one at . In the “maximal” selection, we obtained a set of 22 point sources in the region and 12 sources with by running the CIAO tool wavdetect on the Perseus mosaic with a more aggressive significance threshold of . The three visually identified sources were part of the maximal set. To account for the different sensitivity to point source detection, we refitted the original CXFB model using the data extracted from with the power-law normalization as the only free parameter for both point source sets, and used these updated CXFB models in the analysis.

Fig. 15 shows the projected temperature and normalization profiles for the original, minimal and maximal sets of point sources. We see a good agreement between the measured ICM properties independent of the excluded point sources, with the exception of the normalization beyond , where the measured value is about of the original when excluding the maximal set of point sources. We carried out an analogous test in all the arms where we performed deprojection beyond the virial radius (NW, W, SE, E). Some influence of the point source exclusion on the spectral fitting results is found in the E and W arms, where the normalizations in the outermost annulus (outside ) decrease by and , respectively, when the maximal point source set is used, compared to the original set. The main conclusions of our analysis, however, remain robust.

Figure 15: Projected temperature (top) and XSPEC normalization (bottom) profiles for three different sets of point sources excluded in the SW arm.

b.4 Point Sources in the Chandra Data

The point source analysis in the deep Chandra observation centered around 0.7 along the NW arm has been performed using the procedure discussed in Ehlert et al. (2013). In short, this procedure begins with an aggressive search for candidate sources using the CIAO routine WAVDETECT (Freeman et al. 2002), and refines the source catalog using the ACIS-EXTRACT point-source analysis package4 (Broos et al. 2010, 2012). We use ACIS-EXTRACT to simulate the Chandra point spread function5 (PSF) at the positions of each candidate point source in each of the four observations of this field. ACIS-EXTRACT also computes the background counts within background regions surrounding the sources, accounting for contributions from neighboring sources.

In order to refine the catalog and remove spurious sources, we then utilize the no-source binomial probability to determine the likelihood that source counts are due to fluctuations in the background (see Appendix A of Weisskopf et al. 2007). For this study, we present the results for all sources that satisfy  in the full band (), although the results are consistent with those measured in the soft () and hard () bands. The final set of identified point sources is shown in Fig. 8.

We used the same procedure discussed in Ehlert et al. (2013) to determine, for each position in the field of view, the minimum point source flux to which our detections are sensitive (i.e. the sensitivity map). The full band point source flux limit for the combined 150 ks of Chandra observations is .

The cumulative number density of point sources above a given flux () is calculated as

(8)

where is the total survey area sensitive to the source flux . The dominant uncertainty is the Poisson noise in the total number of sources. The expected Poisson fluctuations for a sample of size are estimated using the 1- asymmetric confidence limits of Gehrels (1986).

The cumulative number counts for sources in this region of the Perseus Cluster are shown in Fig. 16, together with the CDFS results in the same energy band (Ehlert et al. 2013; Lehmer et al. 2012) and the results from the COSMOS survey (Ehlert et al. 2013). All fluxes have been corrected for Galactic absorption.

Based on the curve of the Perseus field, there is no significant evidence for additional point sources above the levels expected from deep and medium-deep X-ray surveys in the field, down to a full band flux limit of .

We therefore do not detect X-ray bright, unresolved clumps, suggesting that if gas clumping is important here, the individual clumps must be spatially extended with respect to the Chandra PS