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Supermassive black hole -- host galaxy relations are key to the computationof the expected gravitational wave background (GWB) in the pulsar timing array(PTA) frequency band. It has been recently pointed out that standard relationsadopted in GWB computations are in fact biased-high. We show that when thisselection bias is taken into account, the expected GWB in the PTA band is afactor of about three smaller than previously estimated. Compared to otherscaling relations recently published in the literature, the median amplitude ofthe signal at $f=1$yr$^{-1}$ drops from $1.3\times10^{-15}$ to$4\times10^{-16}$. Although this solves any potential tension betweentheoretical predictions and recent PTA limits without invoking other dynamicaleffects (such as stalling, eccentricity or strong coupling with the galacticenvironment), it also makes the GWB detection more challenging.

Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays