The Massive and Distant Clusters of WISE Survey 2: Splashback Radii to z=1.65 from Galaxy Density Profiles

The Massive and Distant Clusters of WISE Survey 2 (MaDCoWS2) is a WISE-selected catalog of galaxy clusters at $0.16000$ deg$^2$. In this paper, we derive splashback radii for this cluster ensemble from galaxy density profiles and constrain the mass threshold of the survey as a function of redshift. We use MaDCoWS2 cluster candidates at $0.4\leq z \leq 1.65$ divided into subsamples with different signal-to-noise (S/N$_{\rm P}$) and redshifts, cross-correlated with galaxies from the CatWISE2020 catalog, to obtain average surface density profiles. We perform a Markov Chain Monte Carlo analysis to derive parameter estimates for theoretical models consisting of orbiting and infalling terms. A distinct splashback feature is detected in all subsamples. The measured splashback radii span from $0.89^{+0.02}_{-0.02}h^{-1}$ comoving Mpc/cMpc ($0.61^{+0.02}_{-0.02}h^{-1}$ proper Mpc/pMpc) at $\overline{z}=0.45$ to $1.27^{+0.05}_{-0.05}h^{-1}$ cMpc ($0.53^{+0.04}_{-0.04}h^{-1}$ pMpc) at $\overline{z}=1.54$. We also find that splashback radii increase with $S/N_{\rm P}$ at fixed redshift. The resultant splashback radii constrain the redshift dependence of the mass of MaDCoWS2 clusters at fixed $S/N_{\rm P}$. We calculate $M_{\rm 200m}$ from the radii using a relation based on a cosmological simulation. MaDCoWS2 $M_{\rm 200m}$ values derived from the simulation-based relation are lower than the expected values based on weak-lensing observations. More robust mass constraints will come from calibrating splashback radii derived from galaxy density profiles with weak lensing shear profiles from facilities such as $\textit{Euclid}$, Rubin, and $\textit{Roman}$.