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One of the key elements needed to perform the cosmological exploitation of acluster survey is the relation between the survey observable and the clustermasses. Among these observables, the integrated Compton parameter $Y$ is ameasurable quantity in Sunyaev-Zeldovich (SZ) surveys, which tightly correlateswith cluster mass. The calibration of the relation between the Comptonparameter $Y_{500}$ and the mass $M_{500}$ enclosed within radius $R_{500}$ isone of the scientific goals of the NIKA2 SZ Large Program (LPSZ). We present anongoing study to forecast the constraining power of this program, using mocksimulated datasets that mimic the large program sample, selection function, andtypical uncertainties on $Y_{500}$ and $M_{500}$. We use a Bayesianhierarchical modeling that enables taking into account a large panel ofsystematic effects. Our results show that the LPSZ can yield unbiased estimatesof the scaling relation parameters for realistic input parameter values. Therelative uncertainties on these parameters is $\sim 10\%$ for the intercept andslope of the scaling relation, and $\sim 34\%$ for its intrinsic scatter,foreshadowing precise estimates to be delivered by the LPSZ.

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