Starting from the definition of the normalization of the APEC model (Mewe et al. 1985; Smith et al. 2001; Mewe et al. 1986; Smith & Brickhouse 2000)
(calculated individually, but generally 1.2),
where the terms are defined as in Eq. (9). For a double model the expression for n(r) is:
The unabsorbed surface brightness at a projected distance, x from the center over an energy range between E1 and E2 is
where r2 = x2 + l2 and is the emissivity function for a plasma of temperature T and metalicity Zat energy E. This can be rewritten in terms of n01 and n02 as:
Solving the integral gives the standard expression for the double model in terms of surface brightness:
where LIi and are as defined in Eq. (12). Using this relation along with the fact that , we find:
Inserting these values into Eq. (A.2) to find an expression for n(r) in terms of n0, we get
Inserting this expression of n(r) into Eq. (A.1) and solving for n0, we recover Eq. (12).
From the definition of surface brightness (Eq. (A.3)), a
cluster at redshift z, of a region with an angular radius x, has
an integrated surface brightness (or Flux
energies E1 and E2:
where is the electron density, is the proton density, is the emissivity function as defined in Eq. (A.3). To remove the redshift dependence of the projected region size, we convert the projected region of angular radius x to a cylindrical region of physical radius R, such that . Equation (B.1) becomes:
where is angular diameter distance, is the luminosity distance and I(R) is defined as in Eq. (20). Therefore the total counts collected by a telescope for an observation of length , in an energy band from E1 to E2, of a cylindrical region of physical radius R is:
where and are the absorption from Galactic hydrogen and the effective area of the telescope at energy E, respectively. We can calculate for an absorbed thermal model using XSPEC with an appropriate ARF and RMF. Specifically, since normalization , XSPEC can be used to find the constant of proportionality . From the definition of (see Eq. (A.1)):
Using an on-axis Chandra ARF and RMF, we determined (122.3 photons cm5 s-1) for an energy band from 0.5-7.0 keV, with Z = 0.25 solar, cm-2and our median observation time (44 ks), redshift (0.047) and virial temperature (4.3 keV). Inserting our determined value of into Eq. (B.5) and solving for I, such that C = 10 000 counts, yields h71-2 cm-3. Therefore using the criterion that our median observation would have determined by circle with 10 000 counts, equivalent regions from other observations would have:
Kempner et al. 2002). In determining the temperature profile and global cluster temperature the latter was excluded. This SCC cluster hosts a well-studied radio relic, which is close to but not connected to the central radio galaxy (e.g. Slee et al. 2001). The central region of this cluster requires a double thermal model out to 11 (12 h71-1 kpc). Feretti et al. 1999). Fujita et al. (2004,2002) revealed an X-ray tongue extending northwest. This SCC cluster hosts a radio relic, that is close to but not connected to the central radio galaxy (e.g. Slee et al. 2001). The central region of this cluster requires a double thermal model out to 15 (16 h71-1 kpc). Hudson et al. 2006). As noted in Hudson et al. (2006), the hydrogen column density is higher than measured in the radio ( cm-2 Kalberla et al. 2005) and therefore we left it free for all spectral fits. We find a hydrogen column density of cm-2 for our fit to the overall cluster. Sakelliou & Ponman 2004). The temperature profile of this cluster peaks at the X-ray center. Giovannini et al. 1999). We included an early observation (before 2001), since the later observation was offset, with the cluster center in the corner of a CCD. The BCG closest to the X-ray peak is 34 h71-1 kpc away, making it one of fourteen clusters with the BCG >12 h71-1 kpc from the X-ray peak. Takizawa et al. (2003) first presented the Chandra data of A3112, interpreting the radio active central cD galaxy as interacting with the ICM. Bonamente et al. (2007) claim a soft excess and hard excess in this cluster that may be related with the central radio active BCG. We do not see a similar effect, however we do not separately fit the 1 -2 5 annulus that Bonamente et al. (2007) fit. We do confirm that the 1 -2 5 annulus is isothermal in our kT-profile so that their result is not due to a temperature fluctuations in the cluster. This SCC cluster is one of sixteen clusters for which no data exist for the BCG central velocity dispersion. 10, this model raises to yr-1making it larger than yr-1. We emphasize that this result overestimates and in any case , making it an odd SCC cluster. In all other cases the Fornax cluster remains an outlier. In the case of the CCT the value falls to 0.4 h71-1/2 Gyr moving the Fornax cluster to the left in Fig. 6. (1) , not surprisingly, remains almost the same, photons cm-2 s-1 arcsec-2. The shift to the left in this case makes the Fornax cluster even more of an outlier. (2) , likewise, remains almost identical, . Unlike, , the shift to the left in this case makes the Fornax cluster more similar to other SCC clusters. (3) is, of course, unaffected by the density model, however moving the Fornax cluster to the left makes it more consistent with the other SCC clusters. (4) The cooling radius remains almost identical, increasing to 0.03 r500. Additionally moving the Fornax cluster to the left makes it even more of an outlier. (5) /M500 increases slightly to h71-1 yr-1. Moving the Fornax cluster to the left makes the trend of decreasing /M500 with CCT worse, but it is more consistent with other groups with short CCT. (6) /M500, is raised slightly, . Similar to /M500, moving the Fornax cluster to the left makes the trend with CCT worse, but makes it more consistent with the other groups. We emphasize that the Fornax cluster is still an outlier in all six cases, and that these values are the other extrema, with the true value somewhere between these and where they are plotted in Fig. 6. The physical interpretation is that it is possible that Fornax is in the process of forming a cool core (i.e. it has a nascent core in the terms of Burns et al. (2008)) and therefore is dynamically different from the other SCC clusters that have well-established cores. The central region of this cluster requires a double thermal model out to 170 (15.9 h71-1 kpc).
This cluster, along with A0478 and NGC 1550, has a significantly higher hydrogen column density than measured at radio wavelengths ( cm-2 Kalberla et al. 2005). We fit all spectra with the column density free. For the fit to the overall spectrum we find cm-2. This cluster has two major galaxies near the X-ray peak, which resides between the two of them (10 h71-1 kpc from the closest). Of the 16 clusters in which no information about the BCG central velocity dispersion is available, this cluster has the shortest CCT. The central region of this cluster requires a double thermal model out to 38 (26 h71-1 kpc).okas et al. (2006) report A3158 as a relaxed cluster based on the velocity dispersion of the galaxies. The X-ray emission appears to be elliptical and there are two cDs near the cluster center, one of which lies at the X-ray peak. This cluster definitely does not have a bright core, with a central density of only cm-3. The temperature profile peaks in the center at 5.7 keV. Kalberla et al. 2005). We fit all spectra with the column density free. Our fit to the overall cluster yields a column density of ( cm-2), consistent with the value found by Sanderson et al. (2005). This cluster has the highest spectral mass deposition rate of any HIFLUGCS cluster, making it an ideal candidate for a grating observation. Unfortunately the RGS data from a long XMM-Newton exposure was virtually unusable (de Plaa et al. 2004). This SCC cluster is also one of sixteen clusters in which no data for the BCG central velocity dispersion are available. Kalberla et al. 2005). We fit all spectra with the column density free. Our fit to the overall cluster yields a column density of cm-2. The column density appears to peak towards the center of the cluster, having a value of cm-2 in the innermost annulus. Belsole et al. (2005). This is one of sixteen clusters for which no data about the BCG central velocity dispersion are available. Henriksen & Tittley (2002); Finoguenov et al. (2006) presented detailed analyses of this merging system. Dupke et al. (2007a) studied the longest of the three Chandra observations of this cluster in depth. They argue that there is a cold front at the center of this cluster, which is caused by an off-center passage of a smaller dark matter halo. Bagchi et al. (2006) report the existence of double relics, one to the east of the cluster center and one to the west. Nevalainen et al. (2004) found a diffuse, hard excess with the BeppoSAX PDS at 2.7 significance. The BCG of this cluster is 1 Mpc from the X-ray peak, the most distant of any cluster in the sample and one of eight clusters with a separation of >50 h71-1 kpc. There is a radio galaxy with bent jets very close to the X-ray peak (Mittal et al. 2009). Optically it is clearly much fainter than the BCG and is most likely an AGN that may have been activated by the merger. The jets are bent in the opposite direction to the elongation of the cluster, possibly bent from ICM ram pressure. Tittley & Henriksen (2001) discovered a filament between A3391 and the nearby cluster A3395. Donnelly et al. (2001) claim A3395s and A3395e are near first core passage. Kempner & David (2004) originally presented an analysis of the Chandra data. Dupke et al. (2007b) presented a detailed analysis of the XMM-Newton and Chandra data suggesting that it is a line-of-sight merger. The X-ray image seems somewhat perturbed with elliptical isophotes with alternating NW-SE shifted centers, reminiscent of sloshing, already noted by Kempner & David (2004). The BCG is 24 h71-1 kpc from the X-ray peak, making it one of fourteen clusters with the separation >12 h71-1 kpc. There is, however, a slightly fainter galaxy closer (<12 h71-1 kpc) to the X-ray peak that is radio active, whereas the BCG is not. The peculiar velocity of the BCG is one of five clusters that is more than 50% of the velocity dispersion. This WCC cluster is one of the three WCC/NCC clusters with CCT 1 h71-1/2 Gyr (i.e. not on the border between SCC and WCC) and a systematic temperature decrease at the cluster center. Kassim et al. 2001). Henry et al. (2004) presented a detailed analysis of this merging system using the XMM-Newton observation. Only the pre-2001 Chandra observation is used, since it was the only one that contained the cluster core. More recent observation have been made but do not cover the cluster center and therefore are not useful for core studies. The BCG for this cluster is 714 h71-1 kpc away from the X-ray peak, making it one of eight clusters where this separation is >50 h71-1 kpc. Nulsen et al. 2005). Sato et al. (2007) recently presented a Suzaku observation of this cluster. This cluster has two bright galaxies near the core, one of which is cospatial with X-ray peak. Both galaxies have a clearly visible diffuse X-ray component (Yamasaki et al. 2002). Cortese et al. 2006; Sun et al. 2005) and optical evidence suggests that this is a merging system (Cortese et al. 2004). The X-ray image appears rather disturbed with several off-centered bright sources. Sun & Vikhlinin (2005) studied the survival of galaxy coronae in this system. This cluster hosts a radio relic (Gavazzi & Trinchieri 1983). The BCG of this cluster is 666 h71-1 kpc from the X-ray peak making it one of eight clusters where this separation is >50 h71-1 kpc. It is also one of five clusters where the BCG peculiar velocity is >50% of the cluster velocity dispersion. Sanders & Fabian 2002). The central region of this cluster requires a double thermal model out to 72 (16.5 h71-1 kpc). Reiprich et al. (2004) analyzed the XMM EPIC observation of this cluster. They found the flux of the northern (smaller) subclump is below the HIFLUGCS flux limit whereas the flux of the southern (larger) subclump is above the flux limit. Therefore for purposes of this analysis the smaller subclump was excluded from spatial and spectral analysis. Additionally Reiprich et al. (2004) found evidence that the smaller sub-clump was being stripped as it passes through the ICM. This is one of sixteen clusters in which the central velocity dispersion of the BCG is unavailable. The central region of this cluster requires a double thermal model out to 32 (30 h71-1 kpc). Donahue et al. 2005). Mittal et al. (2009) find an upper-limit to the bolometric radio luminosity of h71-2 erg s-1. The original short Chandra observation showed a flat temperature profile (Donahue et al. 2005). However, the longer, mosaiced observations show a slight temperature decrease in the central region. Due to the elevated entropy in the core, Donahue et al. (2005) concluded a major AGN outburst had disrupted the cooling flow. This cluster is one of four clusters on the border between SCC and WCC. Its CCT (1.2 h71-1/2 Gyr) is slightly longer than the 1 Gyr cutoff. Moreover this cluster shows a central temperature decrease typical of SCC clusters. This is one of sixteen clusters in which the central velocity dispersion of the BCG is unavailable. Donahue et al. (2005) claim this is a radio quiet CC cluster, however Mittal et al. (2009) detect central radio emission with a bolometric luminosity of 1040 h71-2 erg s-1. Gonzalez et al. (2000) fit the optical light out to 670 h100-1 kpc, over one quarter of . The X-ray structure looks quite round and shows no evidence of external interaction. However, the X-ray peak does not dominate as much as in SCC clusters and there is no evidence of a central temperature drop. This WCC is one of sixteen clusters in which the central velocity dispersion of the BCG is unavailable. Willson 1970). Rossetti et al. (2007) presented the XMM and Chandra analysis of this cluster, concluding that it had a cool core that had survived a merger. We find evidence of a slight temperature drop in the core of this WCC cluster. Giacintucci et al. (2005) report the detection of a radio halo (also see Venturi et al. 2000) and argue for a merger scenario between A3562 and SC 1329-313. Finoguenov et al. (2004) presented a detailed analysis of the XMM observation of this cluster. The BCG of this cluster is 31 h71-1 kpc from the X-ray peak, making it one of fourteen clusters where this separation is >12 h71-1 kpc. However, the BCG is located in a chip gap, so the separation may simply be an instrumental effect (i.e. the peak on the BCG may not be detected due to the chip gap). The XMM observation also shows an offset between the X-ray peak and BCG but on a scale of only 23 h71-1 kpc (Zhang, private communication). Crawford et al. 2005). Early core studies with Chandra were done by Fabian et al. (2001) and Markevitch et al. (2001). Fabian et al. (2001) found a CCT of 0.4 h71-1/2 Gyr, approximately the same age as they estimate for the filament. The difference between their measurement for CCT and our measurement is probably due to the different values of used to determine CCT. In order to keep consistency between clusters we determined the CCT at 0.004 r500, however at the redshift of A1795 we are able to determine the CCT at an even smaller radius which gives a CCT 0.5 h71-1/2 Gyr, consistent with Fabian et al. (2001). Moreover, their technique for determining CCT is slightly different from ours. Markevitch et al. (2001) found a cold front in the core of A1795, which they attribute to sloshing gas. Oegerle et al. (2001) studied FUSE observations and found an upper limit for (20 kpc yr-1, consistent with our measurement of 15 yr-1. Johnstone et al. (2005) analyzed the Chandra data from A3581. They find a point source coincident with the powerful radio source PKS 1404-267 at the cluster center. They find a central temperature drop to 0.4 at the cluster center, similar to our measurement of 0.5 .
Cohen et al. 2007). Böhringer et al. (2005) reported the results to the Chandra observation of this cluster. This cluster was originally not included in HIFLUGCS because its X-ray flux is only slightly (<20%) above the flux limit. RX J1504 appears only marginally extended in the ROSAT All-Sky Survey. Additionally the galaxy at the center of the X-ray emission is classified as AGN (Machalski & Condon 1999) and its optical spectrum shows emission lines. It was assumed that even if there is only a small AGN contribution from the central AGN to the total X-ray flux (20%), the cluster would fall below the flux limit. However, the Chandra image reveals that there is actually no significant point source emission at the center of this cluster (Böhringer et al. 2005), which argues against any significant contamination by AGN emission. Therefore, this cluster is included into HIFLUGCS. The BCG features a compact and flat-spectrum radio source (Mittal et al. 2009). This SCC cluster is one of sixteen clusters in which the BCG's central velocity dispersion is not available. Clarke et al. (2004) studied the core of this cluster in detail with Chandra. Blanton et al. (2001) found prominent X-ray cavities in the original Chandra observation. They determined these cavities to be cospatial with radio lobes from the central radio source. Mazzotta et al. 2004). MKW3S is one of sixteen clusters in which data about the BCG's central velocity dispersion are not available. This cluster is a member of the Hercules Supercluster. Chatzikos et al. (2006) suggest that the cluster is involved in an unequal mass merger and that one cool core has survived the merger. Feretti & Giovannini (1994) identified a WAT 19 (1.6 h71-1 Mpc) south south-west of the cluster center. The jets of the WAT are bent away from the center of the cluster. In the NRAO VLA Sky Survey at 1.4 GHz (NVSS Condon et al. 1998), there appears to be a diffuse radio source 91 (124 h71-1 kpc) to the southwest of the cluster center. It is unclear whether this source is associated with the central radio source. Markevitch et al. 2000). The separation between the BCG and the X-ray peak is 23 h71-1 kpc for this cluster, making it one of fourteen with this value >12 h71-1 kpc. This is one of sixteen clusters in which no data is available for the BCG's central velocity dispersion. It is possible this cluster hosts a radio halo, but the evidence remains dubious (Giovannini & Feretti 2000). Henriksen & White 1996), Sanderson et al. (2006a) found it to be an NCC cluster and likely merger system. Feretti et al. 2001). The separation between the BCG and X-ray peak is 158 h71-1 kpc for this cluster, making it one of eight clusters where this value is >50 h71-1. Our measurement of (16 keV) is higher than the value of 12 keV found by Markevitch & Vikhlinin (2001) with data from the original, shorter Chandra observation. However, a recent measurement by Vikhlinin et al. (2009), using the same Chandra as we, finds keV, more consistent with our result. The difference between our result and Vikhlinin et al. (2009) is barely inconsistent within 1 and is probably due to differences in the techniques used to determine in this extremely hot cluster. This is the second most distant and hottest cluster in the HIFLUGCS sample. This is one of sixteen clusters for which data on the BCG's central velocity dispersion are not available, however, since the BCG is not cospatial with the X-ray peak so this information is not important for our analysis. Reiprich et al. (2009) determined the temperature of this cluster out to r200 using Suzaku. They find that the temperature declines all the way from 0.3 r200 to r200, consistent with predictions of simulations. This is one of sixteen clusters where data on the BCG's central velocity dispersion is not available. Donahue et al. (2005) claim it to be a radio quiet CC cluster, but Mittal et al. (2009) detect central radio emission with a bolometric luminosity of h71-2 erg s-1. Although this is not particularly luminous, it is consistent with radio activity in other CC clusters (Mittal et al. 2009). Due to elevated entropy in the core, Donahue et al. (2005) concluded a major AGN outburst had disrupted the cooling flow. Like many WCC clusters, this cluster shows a flat temperature profile. However, we point out that the same was true of A1650 until a deeper observation revealed a slight temperature drop in the core. This is one of sixteen clusters in which the central velocity dispersion of the BCG is unavailable.
This well-known merging cluster is the only one of two NCC clusters
that shows a systematic temperature decrease in the center. The
temperature decrease is the largest of any NCC or WCC cluster.
Surprisingly, the separation between the BCG and X-ray peak is
h71-1 kpc for this cluster, making it one of eight
clusters where this value is >50
h71-1 kpc. Since this
separation is quite large, the cool gas is not associated with the
BCG. It is most likely this gas is the remnant of a CC (perhaps from
a merging group) that has been stripped from its central galaxy. This
cluster hosts both a radio halo and relic
(e.g. Clarke & Ensslin 2006; Bridle & Fomalont 1976)
Following a method to determine the residual CXB (similar to what is
described in Sect 2.3), we measured the surface brightness
profile out to 750
h71-1 kpc (0.5
fit this surface brightness profile to a double-
model and the
temperature profile to a broken powerlaw. The slope of the inner kTprofile was fixed at zero and the outer kT profile fit well to a
powerlaw of slope -0.36 with a break radius of 4
h71-1 kpc). Using the fit to the temperature profile and
double -model, we find a virial mass and radius of
Mpc respectively, consistent with
the results of Zappacosta et al. (2006).
Table 2: Observational parameters.
Table 3: Derived parameters.