We examine the scaling relations between the mass of a supermassive black hole (SMBH) and its host galaxy properties at $1.2<z<1.7$ using both observational data and simulations. Recent measurements of 32 X-ray-selected broad-line Active Galactic Nucleus (AGNs) are compared with two independent state-of-the-art efforts, including the hydrodynamic simulation MassiveBlackII (MBII) and a semi-analytic model (SAM). After applying an observational selection function to the simulations, we find that both MBII and SAM agree well with the data, in terms of the central distribution. However, the dispersion in the mass ratio between black hole mass and stellar mass is significantly more consistent with the MBII prediction ($sim0.3~$dex), than with the SAM ($sim0.7~$dex), even when accounting for observational uncertainties. Hence, our observations can distinguish between the different recipes adopted in the models. The mass relations in the MBII are highly dependent on AGN feedback while the relations in the SAM are more sensitive to galaxy merger events triggering nuclear activity. Moreover, the intrinsic scatter in the mass ratio of our high-$z$ sample is comparable to that observed in the local sample, all but ruling out the proposed scenario the correlations are purely stochastic in nature arising from some sort of cosmic central limit theorem. Our results support the hypothesis of AGN feedback being responsible for a causal link between the SMBH and its host galaxy, resulting in a tight correlation between their respective masses.
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