We present an analysis of selection biases in the M _ { bh } - \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 _ { bh } - \sigma relation , modeled as beta _ { intrinsic } = -4.69 + 2.22 \beta _ { measured } , where the measured slope is shallower than the model slope in the parameter range of \beta > 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 introduces 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 \beta \sim 4 –6 of a logarithmically linear M _ { bh } - \sigma relation , which could impact some studies that measure low ( e.g. , \beta < 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 \beta = 5.28 _ { -0.55 } ^ { +0.84 } .