Conclusiones

From the image of the X-ray surface brightness in Figure 2.1, it is evident that the peak of the X-ray emission is unambiguously associated with the cool and dense region around wBCG.

Also, the pressure profile derived from the X-ray data (see Figure2.6) clearly shows that the gas pressure is increasing towards the X-ray peak. The question arises whether one should expect a very prominent peak in the SZ signal at exactly the same location, which will then dominate the overall SZ signal. To answer this question I plot in Figure 2.6 the interpolated X-ray pressure profile 𝑃(𝑟) multiplied by 𝑟 (dashed line). This quantity, 𝑃(𝑟) × 𝑟, characterises the contribution of a region with size ∼ 𝑟 to the projected pressure map, i.e., the amplitude of a peak in the SZ

0.01 0.10 1.00

Pressure[keVcm−3 ]

SZ SZ 68% CL

X-ray X-ray × r

0 5 10 15 20 25

Temperature[keV]

100 1000

Radius [kpc]

10⁻³ 10⁻² 10⁻¹

Density[cm−3 ]

0.10 Radius [arcmin] 1.00

Figure 2.6: Azimuthally-averaged radial profiles of the deprojected thermodynamic properties of RX J1347.5–1145 based on Chandra X-ray data. The red, dashed line in the top panel represents the product of the radial distance and the pressure profile obtained by interpolating the deprojected pressure radial distribution. For a comparison, I also report the pressure model (blue line in the top panel) derived through the joint image-visibility analysis of the SZ observations discussed in Section2.2.1.

images. It is found to be a growing function of the radius up to 𝑟 ∼ 100 kpc, implying that the central region is playing a sub-dominant role when compared to scales of the order of few hundreds of kiloparsecs in the projected pressure map. Considering that the typical inner slope for the pressure profile in cool-core clusters 𝛾 is less than 1, it is not surprising that no strong cusp is expected at the position of the cool core.

2.2 Reconstruction of the pressure profile 35

1.5 3.0 4.5 20 0 20

xPS[arcsec] 40 20 0 20

yPS[arcsec]

5 10 15 20

iPSi[mJy] 1.5 1.0 0.5 0.0

↵PS

1.5 1.0 0.5 0.0

a

40 0 40

x_gNFW[arcsec] 80 40 0 40

y_gNFW[arcsec] 0.25 0.50 0.75 1.00 P_ei[keV cm ³]

8 16 24

rs[arcmin] 0.25 0.50 0.75 1.00

"

50 0 50

0[deg]

Figure 2.7: Same of Figure2.3but for the ellipsoidal model of Section2.2.3.

The rather modest contribution of the core gas to the overall SZ effect signal makes the definition of a cluster centre from the sole inspection of RX J1347.5–1145 SZ images ambiguous.

As seen when imaging the point source-subtracted visibilities in Figure2.5, the distribution of the SZ signal is indeed fairly smooth across the cool-core region around wBCG. In fact, recent works generally agree that the SZ signal peaks at a location offset south-east of the X-ray surface brightness peak (e.g.,Kitayama et al. 2016). I therefore relax all priors on the centroid position and the assumption of spherical symmetry and try to build a model for the pressure distribution based solely on the SZ data. I use the modelling set-up adopted in Section2.2.1, but I substitute the spherical gNFW distribution, with centre fixed to the X-ray peak, with a free-centroid elliptical gNFW pressure profile, allowing for eccentricity and arbitrary orientation on the plane of the sky. The coordinates of SZ centroid are bounded to the combined ALMA+ACA mosaicked field of view by the introduction of uniform priors. Along with the pressure normalisation 𝑃_ei and the profile characteristic radius 𝑟_s, I further allow the inner slope of the gNFW profile 𝛾 to vary.

Again, the other two indices are fixed to the cool-core values ofArnaud et al. (2010). For this analysis, I now assume an electron temperature of 12.5 keV, estimated by averaging the X-ray temperature profile of Figure2.6 within 1 arcmin from the position of the X-ray peak. Finally, I fit for the cylindrically integrated Compton 𝑦 by assigning a Gaussian prior based on the value

Parameter Units Mean 16^thperc. 84^th perc.

𝑥_gnfw arcsec 5.62 5.39 5.87

𝑦_gnfw arcsec −7.06 −7.34 −6.77

𝑃₀ 10⁻¹keVcm⁻³ 1.57 1.38 1.74

𝑟_s arcmin 2.39 2.31 2.52

𝜀 – 0.648 0.628 0.667

𝜃 degree −36.2 −38.4 −34.1

𝛾 – 0.563 0.534 0.598

𝑥_ps 10⁻² arcsec 47.40 47.02 47.78

𝑦_ps 10⁻² arcsec 50.55 50.32 50.77

𝑖_psi mJy 4.146 4.137 4.155

𝛼_ps – −0.431 −0.465 −0.399

Table 2.5: Same of Table2.4, but for the case of the ellipsoidal gNFW pressure profile.

derived from the Planck MILCA Compton 𝑦 map. All the other free parameters of the gNFW model are assigned wide uninformative uniform priors. The specific details of the above priors on the model parameters are listed in Table2.3. Again, the prior-only sampling shows no biases in the reconstruction of the model parameters due to the assumption on the corresponding prior distributions (Figure2.7).

As with the previous case of the spherical profile, Figure2.8shows the posterior probability density function of the sampled parameters, while a summary of the best-fitting model parameters is reported in Table2.5. The cluster pressure distribution appears to be described by a slightly eccentric profile. The inner slope of the gNFW model is found to be steeper than that reported by Arnaud et al. (2010) for both the universal and morphologically disturbed profiles, but still lower than for the cool-core sample of clusters. I tested this result by varying the intermediate and outer slopes, but found no significant changes in the estimated value of the inner parameter.

The map of the model-subtracted interferometric data, together with the image of the inferred best-fitting SZ distribution, is presented in the bottom panels of Figure2.5. No residual structures highlighting possible overpressure in the intracluster medium within RX J1347.5–1145 are de-tected at a significant level with respect to the image noise. In particular, the residual amplitude of the SZ effect to the south-east is dramatically reduced when shifting the centroid away from the X-ray peak and allowing for ellipticity. This suggests that the SZ excess may be at least partially ascribed to purely geometric effects, which is a consequence of the intrinsic eccentricity of RX J1347.5–1145 in the inner ∼ 200 kpc region. It is worth noting that the centroid of the el-lipsoidal pressure model is consistent with the position of the SZ peak reported byKitayama et al.

(2016). Since the presence of a strong local overpressure may easily result in a non-negligible offset between these positions, such fair agreement further suggests that the pressure structure may be more regular than could be derived from X-ray analyses.

2.2 Reconstruction of the pressure profile 37

xPS[arcsec] 0.496 0.504 0.512

yPS[arcsec] 4.1254.1504.175

Figure 2.8: Same of Figure2.4but for the case of the ellipsoidal gNFW pressure profile. Due to the larger number of parameters, I had to increase the burn-in and sampling phases to 4000 and 8000 steps, respectively.