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.
