compared with their unobscured counterparts, and increases sub-linearly with AGN luminosity. We embody these findings with a star formation rate (SFR) $\propto \sqrt{L_{\rm{X}}} (1+z)^{1.6}$, but assume different normalizations for the type I and II AGN. This luminosity and redshift dependence is similar to that measured for quasars by Serjeant & Hatziminaoglou (2009) and the luminosity dependence matches that of local Seyfert 1s (Thompson et al. 2009).

For type I AGN, we normalise the relation using the measurements of type I SDSS AGN at z=0.15 by Kim et al. (2006), which have a median SFR of 0.5. The median log L(\[OIII\]$\lambda5007$) of this sample, as inferred from Fig. 4(b) of Kim et al., is 41.4 () which equates to log L$_{\rm{X}}=42.6$ using the log L$_{\rm{X}}$–log L(\[OIII\]$\lambda5007$) relation of eqn. (1) of Silverman et al. (2009). Thus for type I AGN:

$${\rm SFR} = 0.63 \sqrt{L_{\rm{X}} /10^{43}} (1+z)^{1.6} \Msunpyr.$$

For the type II AGN (Compton-thin and Compton-thick), we base our results on the $z=0.1$ SDSS type II AGN sample of Kauffmann et al. (2003), focussing on the sub-sample of strong-lined sources with log L(\[OIII\])$>$ 40.5 indicated by the red dots in Fig. 10 of Silverman et al. (2009). Referring once more to 