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A Bayesian Monte-Carlo Analysis of the M-sigma Relation

We present an analysis of selection biases in the M-sigma relation using Monte- Carlo simulations including the sphere of influence resolution selection bias and a selection bias in the velocity dispersion distribution. We find that the sphere of influence selection bias has a significant effect on the measured slope of the M-sigma relation, modeled as β_intrinsic = -4.69 + 2.22β_measured, where the measured slope is shallower than the model slope in the parameter range of β> 4, with larger corrections for steeper model slopes. Therefore, when the sphere of influence is used as a criterion to exclude unreliable measurements, it also in- troduces a selection bias that needs to be modeled to restore the intrinsic slope of the relation. We find that the selection effect due to the velocity dispersion distribution of the sample, which might not follow the overall distribution of the population, is not important for slopes of β~ 4-6 of a logarithmically linear M-sigma relation, which could impact some studies that measure low (e.g., β< 4) slopes. Combining the selection biases in velocity dispersions and the sphere of influence cut, we find the uncertainty of the slope is larger than the value without modeling these effects, and estimate an intrinsic slope of β= 5.28^{+0.84}_{-0.55}.