Self-calibration of cluster dark energy studies: Observable-mass distribution

Abstract

The exponential sensitivity of cluster number counts to the properties of the dark energy implies a comparable sensitivity to not only the mean but also the actual distribution of an observable-mass proxy given the true cluster mass. For example a 25% scatter in mass can provide a $\ensuremath{\sim}50%$ change in the number counts at $z\ensuremath{\sim}2$ for the upcoming SPT survey. Uncertainty in the scatter of this amount would degrade dark energy constraints to uninteresting levels. Given the shape of the actual mass function, the properties of the distribution may be internally monitored by the shape of the observable mass function. As a proof of principle, for a simple mass-independent Gaussian distribution the scatter may be self-calibrated to allow a measurement of the dark energy equation of state of $\ensuremath{\sigma}(w)\ensuremath{\sim}0.1$. External constraints on the mass variance of the distribution that are more accurate than $\ensuremath{\Delta}{\ensuremath{\sigma}}_{\mathrm{ln}M}^{2}<0.01$ at $z\ensuremath{\sim}1$ can further improve constraints by up to a factor of 2. More generally, cluster counts and their sample variance measured as a function of the observable provide internal consistency checks on the assumed form of the observable-mass distribution that will protect against misinterpretation of the dark energy constraints.