An Optical Observational Cluster Mass Function at $z\sim1$ with the ORELSE Survey

We present a new mass function of galaxy clusters and groups using optical/near-infrared wavelength spectroscopic and photometric data from the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) survey. At $z\sim1$, cluster mass function studies are rare regardless of wavelength and have never been attempted from an optical/near-infrared perspective. This work serves as a proof of concept that $z\sim1$ cluster mass functions are achievable without supplemental X-ray or Sunyaev-Zel'dovich (SZ) data. Measurements of the cluster mass function provide important contraints on cosmological parameters and are complementary to other probes. With ORELSE, a new cluster finding technique based on Voronoi tessellation Monte-Carlo (VMC) mapping, and rigorous purity and completeness testing, we have obtained $\sim$240 galaxy overdensity candidates in the redshift range $0.55<z<1.37$ at a mass range of $13.6<\log(M/M_{\odot})<14.8$. This mass range is comparable to existing optical cluster mass function studies for the local universe. Our candidate numbers vary based on the choice of multiple input parameters related to detection and characterization in our cluster finding algorithm, which we incorporated into the mass function analysis through a Monte-Carlo scheme. We find cosmological constraints on the matter density of $\Omega_{m} = 0.250^{+0.104}_{-0.099}$ and on the amplitude of fluctuations of $\sigma_{8} = 1.150^{+0.260}_{-0.163}$. While our $\Omega_{m}$ value is close to concordance, our $\sigma_{8}$ value is $\sim2\sigma$ higher because of the inflated observed number densities compared to theoretical mass function models owing to how our survey targeted overdense regions. With Euclid and several other large, unbiased optical surveys on the horizon, VMC mapping will enable optical/NIR cluster cosmology at redshifts much higher than what has been possible before.