Galaxy cluster optical mass proxies from probabilistic memberships

Robust galaxy cluster mass estimates are fundamental for constraining cosmological parameters from counts. For this reason, it is essential to search for tracers that, independent of the cluster's dynamical state, have a small intrinsic scatter and can be easily inferred from observations. This work uses a simulated data set to focus on photometric properties and explores different optical mass proxies including richness, optical luminosity, and total stellar mass. We have developed a probabilistic membership assignment that makes minimal assumptions about the galaxy cluster properties, limited to a characteristic radius, velocity dispersion, and spatial distribution. Applying the estimator to over 919 galaxy clusters with $z_{phot}<$0.45 within a mass range of $10^{12.8}$ to $10^{15}$ M$_\odot$, we obtain robust richness estimates that deviate from the median true value (from simulations) by -0.01$ \pm $0.12. The scatter in the mass-observable relations is $\sigma_{log_{10}(M|\mathcal{R})}=$0.181 $\pm$ 0.009 dex for richness, $\sigma_{log_{10}(M|L_\lambda)}=$0.151 $\pm$ 0.007 dex for optical luminosity, and $\sigma_{log_{10}(M|M_\lambda^*)}=$0.097 $\pm$ 0.005 dex for stellar mass. We also discuss membership assignment, completeness and purity, and the consequences of small centre and redshift offsets. We conclude that the application of our method for photometric surveys delivers competitive cluster mass proxies.