Forecasting the $Y_{500}-M_{500}$ scaling relation from the NIKA2 SZ Large Program

One of the key elements needed to perform the cosmological exploitation of a cluster survey is the relation between the survey observable and the cluster masses. Among these observables, the integrated Compton parameter $Y$ is a measurable quantity in Sunyaev-Zeldovich (SZ) surveys, which tightly correlates with cluster mass. The calibration of the relation between the Compton parameter $Y_{500}$ and the mass $M_{500}$ enclosed within radius $R_{500}$ is one of the scientific goals of the NIKA2 SZ Large Program (LPSZ). We present an ongoing study to forecast the constraining power of this program, using mock simulated datasets that mimic the large program sample, selection function, and typical uncertainties on $Y_{500}$ and $M_{500}$. We use a Bayesian hierarchical modeling that enables taking into account a large panel of systematic effects. Our results show that the LPSZ can yield unbiased estimates of the scaling relation parameters for realistic input parameter values. The relative uncertainties on these parameters is $\sim 10\%$ for the intercept and slope of the scaling relation, and $\sim 34\%$ for its intrinsic scatter, foreshadowing precise estimates to be delivered by the LPSZ.