The impact of halo properties, energy feedback, and projection effects on the mass-SZ flux relation

We present a detailed analysis of the intrinsic scatter in the integrated Sunyaev-Zel′dovich (SZ) effect-cluster mass (Y-M) relation, using semianalytic and simulated cluster samples. Specifically, we investigate the impact on the Y-M relation of energy feedback, variations in the host halo concentration and substructure populations, and projection effects due to unresolved clusters along the line of sight (the SZ background). Furthermore, we investigate at what radius (or overdensity) one should measure the integrated Sunyaev-Zel′dovich effect (SZE) and define cluster mass so as to achieve the tightest possible scaling. We find that the measure of Y with the least scatter is always obtained within a smaller radius than that at which the mass is defined; e.g., for M₂₀₀ (M₅₀₀), the scatter is least for Y₅₀₀ (Y₁₁₀₀)The inclusion of energy feedback in the gas model significantly increases the intrinsic scatter in the Y-M relation due to larger variations in the gas mass fraction than in models without feedback. We also find that variations in halo concentration for clusters of a given mass explain why the integrated SZE provides a better mass proxy than the central decrement. Substructure is found to account for approximately 20% of the observed scatter in the Y-M relation. Above M₂₀₀ = 2 × 10 ¹⁴ h^-1 M_⊙, the SZ background does not significantly affect cluster mass measurements; below this mass, variations in the background signal reduce the optimal angular radius within which one should measure Y to achieve the tightest scaling with M₂₀₀.