I here provide the 𝑢𝑣 radial plots of the data and respective gNFW models for all the VACA LoCA clusters (Figure 4.11). As discussed in Section 4.3, all the model profiles show a fairly good agreement with data over the range of probed angular scales, while being affected by a large scatter at short baselines due to the lack of large-scale information. MOO J0345−2913 and MOO J0917−0700 clearly manifest positive modes at small 𝑢𝑣-scales, while the data points for MOO J2146−0320 are positively offset with respect to the models. These may arise due to off-centre SZ components unaccounted for by the model, or due to extended (positive) emission.

However, in the case of MOO J0345−2913, the discrepancy is on the level of 1𝜎. On the other hand, the SZ signal from both MOO J0917−0700 and MOO J2146−0320 show a complex structure (see Section4.3.2), and deviations from a gNFW model are not unexpected.

To get a more immediate sense of the reconstructed models, I show in Figure 4.12the dirty images of VACA LoCA observations. As there are no sensible differences between the model and residual dirty images generated with different gNFW models, I here consider only the case of a universal pressure profile (Arnaud et al. 2010). I again emphasise that all the images reported here are only for illustrative purposes, and were not used in this analysis.

ClusterID𝑧phot𝜆𝑀500𝜎eff𝑀500𝜎eff𝑀500𝜎eff𝑀500𝜎eff𝑀500𝜎eff––(10 14𝑀)–(10 14𝑀)–(10 14𝑀)–(10 14𝑀)–(10 14𝑀)–universalcool-coredisturbedPlanckMcDonaldetal.2014 SignificantdetectionMOOJ0129−16401.05+0.04−0.0549±72.57+0.30−0.307.772.09+0.24−0.298.073.47+0.32−0.407.632.75+0.32−0.387.853.72+1.28−1.117.12MOOJ0345−29131.08+0.03−0.0453±71.78+0.20−0.295.321.51+0.21−0.245.712.09+0.24−0.385.351.66+0.31−0.315.582.14+0.94−0.745.24MOOJ0917−07001.10+0.05−0.0558±71.66+0.31−0.384.261.48+0.22−0.324.491.93+0.49−0.673.681.55+0.38−0.454.201.77+0.85−0.933.412.13+0.40−0.491.83+0.26−0.382.67+0.56−0.842.13+0.49−0.602.67+1.39−1.47MOOJ1139−17061.31+0.03−0.0553±72.24+0.36−0.523.811.74+0.24−0.363.823.16+0.66−0.873.402.24+0.62−0.573.786.76+3.89−3.424.35MOOJ1342−19131.08+0.04−0.0541±61.95+0.31−0.314.531.58+0.22−0.225.422.29+0.37−0.375.091.91+0.35−0.395.272.40+0.94−0.834.25MOOJ1414+02271.02+0.07−0.0641±72.75+0.32−0.326.992.24+0.31−0.266.803.55+0.74−0.416.982.88+0.66−0.537.044.37+1.91−1.816.94MOOJ2146−03201.16+0.05−0.0550±71.86+0.34−0.525.351.58+0.27−0.345.552.58+0.56−0.665.731.95+0.47−0.615.625.13+4.57−3.295.942.04+0.42−0.561.67+0.31−0.403.49+0.78−1.142.29+0.69−0.794.44+2.52−3.39

WeakdetectionMOOJ1223+24201.09+0.04−0.0451±71.17+0.27−0.382.400.94+0.21−0.352.541.33+0.34−0.612.540.90+0.32−0.442.531.52+0.86−0.922.23MOOJ2147+13141.01+0.06−0.0738±61.82+0.34−0.421.261.56+0.26−0.381.341.62+0.43−0.521.592.06+0.51−0.501.232.27+1.10−1.261.35 NondetectionMOOJ0903+13101.26+0.05−0.0829±50.30+0.18–0.29+0.17−0.200.830.27+0.16−0.160.880.27+0.18−0.180.610.32+0.22–

Table4.4:EstimatedmassesoftheVACALoCAsampleclusters.SeeSection4.3formoredetailsabouttheeffectivesignificanceestimate𝜎eff.ThetwomassvaluesprovidedforMOOJ0917−0700andMOOJ2146−0320correspondtothemassesofeachoftheindividualSZcomponentsdetected.

4.5 Supplementary material 85

MOO J0129 1641 MOO J0345 2913

3 2 1 0 1

MOO J0903+1310 MOO J0917 0700

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MOO J1139 1706 MOO J1223+2420

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MOO J1342 1913 MOO J1414+0227

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Arnaud et al. 2010, universal Arnaud et al. 2010, cool core Arnaud et al. 2010, disturbed

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Arnaud et al. 2010, universal Arnaud et al. 2010, cool core Arnaud et al. 2010, disturbed

Planck 2013

Arnaud et al. 2010, universal Arnaud et al. 2010, cool core Arnaud et al. 2010, disturbed

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Arnaud et al. 2010, universal Arnaud et al. 2010, cool core Arnaud et al. 2010, disturbed

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MOO J0129 1641 MOO J0345 2913

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MOO J0903+1310 MOO J0917 0700

3 2 1 0 1

MOO J1139 1706 MOO J1223+2420

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MOO J1342 1913 MOO J1414+0227

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Figure 4.11: Comparison of the 𝑢𝑣 profiles of all the gNFW flavours adopted in the analysis of the VACA LoCA data. The data are binned so that each bin contains the same number of visibilities (here set to 2500 for plotting purposes). Before averaging, I shifted the phase centre to the position of cluster centroid to minimise the ringing effect due to non-zero phases. I do not plot any model profile for MOO J0903+1310 as the SZ signal is not detected.

1^h29^m15^s 12^s 09^s

Figure 4.12: Dirty images of the raw (left), model (center), and residual (right) data of VACA LoCA observations. All the images are generated by applying a multi-frequency naturally-weighted, imaging scheme, and extend out to where the ACA primary beam reaches 20% of its peak amplitude. To better highlight the SZ features in each field, I apply a 10 k𝜆 taper but do not correct for the primary beam attenuation. Further, as for Figure 4.3, I removed the most significant point-like sources from the raw interferometric data.

4.5 Supplementary material 87

14^h14^m42^s 39^s 36^s 33^s

Chapter 5 Conclusions

At present, ALMA+ACA is the only millimetre/submillimetre facility that can provide measure-ments of the SZ effect at an angular resolution better than ∼ 8 arcsec. This thesis is devoted to understanding in detail ALMA+ACA potentialities for the study of the physics of galaxy clusters over an unprecedented range of spatial scales. In particular, central to this doctoral work has been the exploration of the novel opportunities offered by the measurements of the SZ signal as a win-dow both independent and complementary to X-ray observations on the complex phenomenology exhibited by the intracluster medium. A summary of the main results presented in the previous chapters is reported below.

• The joint analysis of single-dish and interferometric observations of the SZ effect can provide a straightforward answer to the issues related to interferometric filtering as well as limited resolution of single-dish facilities. The techniques have been applied to a combination of measurements of the SZ effect from RX J1347.5–1145. Previous X-ray-motivated SZ studies of RX J1347.5–1145 have highlighted the presence of an excess SZ signal south-east of the X-ray peak. The joint SZ image-visibility pressure model, when centred at the X-ray peak, confirms this. However, the presence of two almost equally bright giant elliptical galaxies separated by ∼ 100 kpc makes the choice of the cluster centre ambiguous, and allows for considerable freedom in modelling the structure of the galaxy cluster. For instance, the SZ signal can be well-described by a single smooth ellipsoidal generalised NFW profile, where the best-fitting centroid is located between the two brightest cluster galaxies. This leads to a considerably weaker excess SZ signal from the south-eastern substructure. Further, the most prominent features seen in the X-ray can be explained as predominantly isobaric structures, alleviating the need for highly supersonic velocities, although overpressurised regions associated with the moving subhaloes are still observed.

• The combination of deep, high-resolution interferometric SZ effect observations with priors from an independent X-ray analysis allowed for getting constraints on the mechanism governing electron heating across the shock front in the Bullet Cluster. In the case of instantaneous electron-ion temperature equilibration, the shock Mach number is found to be M = 2.08^+0.12_−0.12, in ≈ 2.4𝜎 tension with the independent constraint from Chandra, MX = 2.74 ± 0.25. The assumption of purely adiabatic electron temperature change

across the shock leads to M = 2.53^+0.33_−0.25, in better agreement with the X-ray estimate MX =2.57 ± 0.23 derived for the same heating scenario. The analysis is however limited by systematics related to the overall cluster geometry and the complexity of the post-shock gas distribution.

• The analysis of the VACA LoCA sample provided significant detections of the SZ effect from seven out of the ten VACA LoCA clusters, two weak detections and only one non-detection.

Remarkably, this result is largely independent of the specific model assumed for describing the cluster pressure profiles. However, the limited angular dynamic range of the ACA alone, short observational integration times, and possible contamination from unresolved sources limit the detailed characterisation of the cluster properties and the inference of the cluster masses within scales appropriate for the robust calibration of mass-richness scaling relations.

On the one hand, all results listed above highlight how ALMA+ACA can play a central role in yielding tremendous progress in our understanding of the physical processes ongoing within galaxy clusters. From a purely observational point of view, the possibility of discriminating between contaminant sources and the SZ effect at high angular resolution is key for getting a clean view of the small-scale features in the pressure distribution of the intracluster medium. In turn, the characterisation of the physical and thermodynamic properties of intracluster pressure substructures through SZ measurements and the combination with X-ray-derived information represent an unparalleled observational tool for getting deep insights in the extreme physics of the intracluster plasma. Further, the extraordinary angular resolution and sensitivity of ALMA+ACA allows for overcoming the limitations of current wide-field SZ surveys in detecting faint and high-redshift clusters due to their significant beam smearing effect. Thus, although the mapping speed is clearly not competitive when compared to the one of other ground-based survey facilities, the combination of ALMA and ACA further provides the means for observing the evolution of clusters and proto-clusters in the distant Universe.

On the other hand, the limitations introduced by the radio-interferometric observations are evident. First, the lack of short-spacing information makes ALMA+ACA-only studies of the SZ effect impractical in the case of nearby systems. In order to get sensible constraints on the pressure distribution of the intracluster medium, any analyses have to rely on external large-scale data, either SZ or X-ray. Second, in the case of more distant systems, the limited dynamic range of probed scales allows one to access the SZ signal only in the direction of the very central region of galaxy clusters, potentially biasing the inference of their global properties.

Both improved spatial and spectral resolution, larger instantaneous field of view, and the ability to recover zero-spacing information will vastly improve future SZ studies. In the next few years, ALMA Bands 1 (35-51 GHz;Di Francesco et al. 2013, Huang et al. 2016) and 2 (67-116 GHz;

Yagoubov et al. 2020) will further increase the maximum recoverable scale and thus the sensitivity of ALMA and the ACA to diffuse, low surface brightness signals on arcminute scales. At the same time, new thermal and kinematic SZ imaging possibilities with bolometric/photometric arrays such as TolTEC on the 50m Large Millimeter Telescope (Bryan et al. 2018), MUSTANG-2 on the 100m GBT (Dicker et al. 2014), and NIKA2 on the IRAM 30-meter telescope (Adam

5.1 Future prospects 91

et al. 2018a) will deliver such data through targeted cluster observations. However, in order to provide sufficient overlap with the interferometric data in Fourier space, while also probing higher frequencies and spatial scales >10⁰, a new wide-field (> 1^◦) single-dish facility, such as the Atacama Large Aperture Submm/mm Telescope (AtLAST; see, e.g., Klaassen et al. 2019, Mroczkowski et al. 2019a) or the Large Submillimeter Telescope (LST; Kawabe et al. 2016), is required.

5.1 Future prospects

All the works based on ALMA+ACA observations of the SZ effect that are currently published (Kitayama et al. 2016, Basu et al. 2016, Ueda et al. 2018, Kitayama et al. 2020, Gobat et al.

2019,Lacy et al. 2019,Brownson et al. 2019), as well as the ones presented in this thesis, mainly represent exploratory studies of ALMA+ACA capabilities in measuring the SZ effect from a variety of astrophysical environments. High-resolution imaging and detection of the SZ effect is however slowly becoming a tool routinely employed for probing the warm and hot Universe. Here, I provide an overview of future works and potential applications of ALMA+ACA measurements of the SZ effect.