Mapping the hot gas temperature in galaxy clusters using X-ray and Sunyaev-Zel'dovich imaging

We propose a method to map the temperature distribution of the hot gas in galaxy clusters that uses resolved images of the thermal Sunyaev-Zel’dovich (tSZ) effect in combination with X-ray data. Application to images from the New IRAM KIDs Array (NIKA) and XMM-Newton allows us to measure and determine the spatial distribution of the gas temperature in the merging cluster MACS J0717.5+3745, at $z=0.55$. Despite the complexity of the target object, we find a good morphological agreement between the temperature maps derived from X-ray spectroscopy only – using XMM-Newton ($T_{\mathrm{X}\mathrm{M}\mathrm{M}}$) and Chandra ($T_{\rm CXO}$)--andthenewgas-mass-weightedtSZ+X-rayimagingmethod($T_{\rm SZ}$). We correlate the temperatures from tSZ+X-ray imaging and those from X-ray spectroscopy alone and find that $T_{\mathrm{S}\mathrm{Z}}$ is higher than $T_{\rm XMM}$andlowerthan$T_{\rm CXO}$by$\sim 10%$ in both cases. Our results are limited by uncertainties in the geometry of the cluster gas, contamination from kinetic SZ ($\sim 10\mathrm{\%}$), and the absolute calibration of the tSZ map ($7\mathrm{\%}$). Investigation using a larger sample of clusters would help minimise these effects.