Joint 30 GHz SZA + 90 GHz SZA + CARMA fits
7.2 Validity of the Arnaud pressure profile
Arnaud et al. (2010) fit characteristic cool-core (CC), morphologically disturbed (NCC) as well as a uniform (UNIV) cluster pressure profiles, Table (7.1), to their 33 XMM-Newton observed galaxy cluster sample at z<0.2 via the parametric form
P(r) =P500 P0
(rrs)c"1 + (rrs)a#(b−c)a
- M500 3×1014h−170M#
.αp+α!p
. (7.1)
The characterisitic pressure at r500, denoted by P500, is defined as
P500 = 3à 8πàe
fBM5002/3
/500G−1/4H(z)2 2
04/3
(7.2) with αp andα!p taking into account the mass biases of the profiles 1. The scale radius,rs is defined as rs= rc500500.
1 This is caused by the hydrostatic equilibrium assumption in the M500-YXrelation and the corresponding normalization correction throughαpand its associated radial dependence throughα!p
7.2. Validity of the Arnaud pressure profile 125 It has only been recently, that such profiles have also been fitted to SZ observations from different instruments spanning a wider redshift range than the Arnaud sample. The red- shift distribution for cool-core (CC) and non-cool core (NCC) clusters is shown in Fig. 7.2 for the reported Planck release 1, Bolocam, Arnaud, SPT and APEX-SZ samples.
All of these experiments use partially different classifications for cooling core galaxy clusters. Arnaud et al. (2010) define cooling cores by their central density and morpho- logically disturbed systems by their centre shift parameter. The condition for cooling core classification is h(z)−2ne,0>4×10−2cm−3. The Planck sample uses the same classification criteria. The BOXSZ sample defines cooling core clusters via the X-ray luminosity ratio within R <0.05 R500 and R500 (Sayers et al. 2013). Morphologically disturbed systems are defined by the centroid shift parameter under the condition thatw500≥0.01, following the classification by Arnaud et al. (2010) (see section 3.5). The APEX-SZ sample takes the morphological classifications from literature relying, amongst others, on cooling time estimates, central surface brightness peak strength and the degree of projected ellipticity (Bender et al. submitted).
The SPT sample of 83 high redshift, 0.3>z<1.2, clusters explores several classifica- tion parameters (McDonald et al. 2013). The galaxy cluster sample selection in Fig. 7.2 was made via the central entropy grading selection; K0 <30 keV cm2 indicating cooling cores and K0 >30 keV cm2 describing morphologically disturbed clusters.
Table 7.1: Arnaud model best-fit parameter values
Morphology P0 c500 a b c
Cool Core 3.249 1.128 1.2223 5.49 0.7736 Universal 8.403 h−3/270 1.177 1.051 5.4905 0.3081 Non-Cool core 3.202 1.083 1.4063 5.49 0.3798
The galaxy cluster number statistics at high redshift is still quite low and some of the samples are biased towards lower redshifts from the CC side. This is not surprising since the fraction of classical core galaxy clusters is thought to decrease with increasing redshift (Vikhlinin et al. 2007) - cool core clusters being thought to evolve from cooling core clus- ters that have less pronounced X-ray central peaks (McDonald et al. 2013).
The Planck, Arnaud and Bolocam experiments fit GNFW profiles to their samples, varying not only the normalization and scale parameters, as is currently done with APEX- SZ data, but also the slope parameters of the profiles. The fixed parameters are determined according to the characteristic scales probed by the different instruments.
Arnaud et al. (2010) leave all the parameters as free variables except for the outer slope parameter, b, which is fixed at 5.4905. BOXSZ fix the concentration parameter and vary the normalization and all three slope parameters. The Planck sample keeps the central slope parameter, c, fixed to 0.31 while varying all other parameters. In all samples, P500 was derived from the M−YX relation.
The corresponding best-fit 3D de-projected pressure profiles are shown in Fig. 7.1 for the universal, cool-core and non-cool core cases. The BOXSZ best-fits are consistent with
the Arnaud profiles within the error bars (Sayers et al. 2013). The Planck profiles agree with the Arnaud profiles within the range 0.1−1.0R500 (Planck Intermediate Results V 2013).
Due to the lack of information of the Arnaud, Planck, APEX-SZ and Bolocam samples at high-redshift, the evolution of the inner pressure profile could not be probed. Recently, SPT has mapped 83 high redshift, 0.3<z<1.2, galaxy clusters, McDonald et al. (2013), the sample being shown in the magenta histogram in Fig. 7.2. These SPT clusters were followed up with Chandra. The Chandra exposure time does not allow for a detailed spectroscopic analysis to be made but under the assumptions of hydrostatic equilibrium, spherical symmetry and using constraints from the Duffy mass-concentration relation, Duffy et al (2008), and the M500−P500 relation by Nagai et al. (2007), McDonald et al.
(2013) derive a 3-bin temperature profile for each cluster.
Subject to these assumptions, a central temperature value was extrapolated towards small radii, r <0.012R500 (McDonald et al. 2013), and in combination with the central density parameter, which was obtained from X-ray surface brightness observations, the central cooling times and entropies were derived for their galaxy cluster sample. The main findings by McDonald et al. (2013) concentrate on the property of cool-core clus- ters at high redshift. Although the central brightness cuspiness decreases as a function of redshift, the cooling properties of the clusters do not, suggesting that galaxy clusters have been cooling over a long time with a feedback mechanism that prevents cooling below entropy levels of 10 keV cm2. Whereas the central density profiles show a mild evolution as a function of redshift for morphologically disturbed clusters, the average central den- sity profile of clusters with central entropy levels <30 keV cm2 increases significantly as a function of decreasing redshift.
McDonald’s temperature fitting technique does not allow for annular spectroscopic fitting in the central cluster regions due to low X-ray photon number counts but an iter- ative joint dark matter profile/temperature/surface brightness fit under the assumptions of hydrostatic equilibrium and sphericity suggests that cooling flow clusters were cooler at higher redshift, though the significance of this result is affected by the high uncertainties in the derived central temperature values.
If the feedback properties should indeed change as a function of redshift, this would have consequences for the mass/observable scaling relations since these non-gravitiational effects could introduce potential biases into mass-proxy analyses (McDonald et al. 2013).
In addition, the lack of strong cool-core systems at high redshift (z<0.75) suggests that high redshift studies will need to resort to methods complementary to the surface bright- ness peak parameter characteristics in order to select morphologically relaxed systems for scaling relations that reduce the intrinsic scatter caused by morphological bias effects.
At low redshifts, the pressure profile from morphologically disturbed clusters and re- laxed clusters can be discriminated in the central regions. So far, the highest redshift clusters for which Arnaud profiles have been fitted via SZ observations come from the APEX-SZ and Bolocam samples. The APEX-SZ sample adopts a GNFW fit with fixed slope parameters set to (a=0.9, b=5.0, c=0.4), whereas the BOXSZ sample leaves all slope parameters and the normalization parameter as free parametrs only fixing the concentra- tion. One can therefore deduce from Fig. 7.2 that the highest redshift morphologically disturbed cluster which was included in an Arnaud/Gnfw model fit with free slope param-
7.2. Validity of the Arnaud pressure profile 127 eters is at z= 0.833.
The evolution of the cluster pressure profile as a function of redshift is therefore still an open issue, although the central gas density evolution shown by McDonald et al. (2013) in conjunction with their tentative decreasing mean central temperature discovery for cool- core clusters, suggests that the cool-core pressure profile could become more shallow in the central cluster regions as a function of redshift.
The study of galaxy cluster pressure profiles as a function of redshift would thus shed light on the following issues:
• The dependence of the evolution of pressure profiles on different morphological states.
• In combination with X-ray surface brightness information and global temperature measurements under the assumption of spherical symmetry, pressure profiles can be used to derive the temperature profiles for a sample of clusters, enabling the study of their morphology dependence.
• The items above will enhance our understanding of feedback processes in galaxy clusters, which, in turn, will help to quantify the influence of non-gravitational effects on cluster scaling relations.
Figure 7.1: A Comparison of the best-fit 3D universal (black), cool-core (blue), non- cool core (red) profiles for the Arnaud (solid), Bolocam (dashed) and Planck (dot-dashed) sample. The confidence intervals are omitted for the purpose of clarity. The BOSX sample is reported to be consistent with the Arnaud profile (Sayers et al. 2013) and the Planck sample agrees with it within the range 0.1−1.0 R500 (Planck Intermediate Results V 2013).
Figure 7.2: Sample redshift distribution for relaxed (top) and morphologically disturbed (bottom) clusters: Arnaud (red), Planck (green), SPT (magenta), Bolocam (blue), APEX- SZ (orange). The Chandra observed X-ray follow-up SPT sample by McDonald et al.
(2013) has greatly extended the redshift range over which cool-core and non-cool core clusters are studied via X-ray observations. The analysis of the samples in terms of profile fittings differ in the number of fixed parameters.