Determining star formation rates in active galactic nuclei hosts via stellar population synthesis

The effect of active galactic nuclei (AGNs) feedback on the host galaxy, and its role in quenching or enhancing star formation, is still uncertain due to the fact that usual star formation rate (SFR) indicators - emission-line luminosities based on the assumption of photoionization by young stars - cannot be used for active galaxies as the ionizing source is the AGN. We thus investigate the use of SFR derived from the stellar population and its relation with that derived from the gas for a sample of 170 AGN hosts and a matched control sample of 291 galaxies. We compare the values of SFR densities obtained via the H α emission line ( $\rm \Sigma SFR_{Gas}$ ) for regions ionized by hot stars according to diagnostic diagrams with those obtained from stellar population synthesis ( $\rm \Sigma SFR_\star$ ) over the last 1 to 100 Myr. We find that the $\rm \Sigma SFR_\star$ over the last 20 Myr closely reproduces the $\rm \Sigma SFR_{Gas}$ , although a better match is obtained via the transformation: $\mbox{log($ \rm \Sigma SFR_\star $)} = (0.872\pm 0.004)\mbox{log($\rm \Sigma SFR_{Gas}$)} -(0.075\pm 0.006)$ (or $\mbox{log($\rm \Sigma SFR_{Gas}$)} = (1.147\pm 0.005)\mbox{log($ \rm \Sigma SFR_\star $)} +(0.086\pm 0.080)$ ), which is valid for both AGN hosts and non-active galaxies. We also compare the reddening obtained via the gas H α/H β ratio with that derived via the full spectral fitting in the stellar population synthesis. We find that the ratio between the gas and stellar extinction is in the range 2.64 ≤A_Vg/A_V⋆ ≤ 2.85, in approximate agreement with previous results from the literature, obtained for smaller samples. We interpret the difference as being due to the fact that the reddening of the stars is dominated by that affecting the less obscured underlying older population, while the reddening of the gas is larger as it is associated with a younger stellar population buried deeper in the dust.