Mass Estimation of Galaxy Clusters with Deep Learning II: CMB Cluster Lensing

We present a new application of deep learning to reconstruct the cosmic microwave background (CMB) temperature maps from the images of microwave sky, and to use these reconstructed maps to estimate the masses of galaxy clusters. We use a feed-forward deep learning network, mResUNet, for both steps of the analysis. The first deep learning model, mResUNet-I, is trained to reconstruct foreground and noise suppressed CMB maps from a set of simulated images of the microwave sky that include signals from the cosmic microwave background, astrophysical foregrounds like dusty and radio galaxies, instrumental noise as well as the cluster's own thermal Sunyaev Zel'dovich signal. The second deep learning model, mResUNet-II, is trained to estimate cluster masses from the gravitational lensing signature in the reconstructed foreground and noise suppressed CMB maps. For SPTpol-like noise levels, the trained mResUNet-II model recovers the mass of a single galaxy cluster with a 1-$\sigma$ uncertainty $\Delta M_{\rm 200c}^{\rm est}/M_{\rm 200c}^{\rm est} =$ 1.37 and 0.51 for input cluster mass $M_{\rm 200c}^{\rm true}=10^{14}~\rm M_{\odot}$ and $8\times 10^{14}~\rm M_{\odot}$, respectively. For input cluster mass $M_{\rm 200c}^{\rm true}=3\times 10^{14}~\rm M_{\odot}$, these uncertainties are a factor of $1.4$ larger than would be achieved by a maximum likelihood estimator (MLE) on foreground-free maps with the input noise levels, but better by a factor of $1.5$ than the MLE with foregrounds.