  Cosmological constraints derived from galaxy clusters rely on accurate
predictions of cluster observable properties, in which feedback from active
galactic nuclei (AGN) is a critical component. In order to model the physical
effects due to supermassive black holes (SMBH) on cosmological scales, subgrid
modeling is required, and a variety of implementations have been developed in
the literature. However, theoretical uncertainties due to model and parameter
variations are not yet well understood, limiting the predictive power of
simulations including AGN feedback. By performing a detailed parameter
sensitivity study in a single cluster using several commonly-adopted AGN
accretion and feedback models with FLASH, we quantify the model uncertainties
in predictions of cluster integrated properties. We find that quantities that
are more sensitive to gas density have larger uncertainties (~20% for Mgas and
a factor of ~2 for Lx at R500), whereas Tx, Ysz, and Yx are more robust
(~10-20% at R500). To make predictions beyond this level of accuracy would
require more constraints on the most relevant parameters: the accretion model,
mechanical heating efficiency, and size of feedback region. By studying the
impact of AGN feedback on the scaling relations, we find that an
anti-correlation exists between Mgas and Tx, which is another reason why Ysz
and Yx are excellent mass proxies. This anti-correlation also implies that AGN
feedback is likely to be an important source of intrinsic scatter in the
Mgas-Tx and Lx-Tx relations.
