Quasar host galaxies in the FORS deep field

Context. The evolution of quasar host galaxies is still hardly studied at high redshifts ($z>2$), although this is a very interesting redshift range as both the quasar activity and the star formation rate density have their peak at $z\approx$ $2{-}3$. This makes it especially interesting to study properties of quasar host galaxies, such as the star formation rate or the black hole mass at this redshift. A proper classification of quasar host galaxies at high redshift would help to answer the question which role quasars play in galaxy evolution. Aims. In this paper we study different properties of quasars and their host galaxies at high redshifts up to $z\approx3.4$. We compare our results to those of other authors and discuss the correlation between galaxy evolution and quasar activity. Methods. We analysed broad-band images in eight filters (from U to K) of eight quasars in the FORS Deep Field with redshifts between $z=0.87$ and $z=3.37$. A fully 2-dimensional decomposition was carried out to detect and resolve the host galaxies. Using the magnitudes in different filters, we investigated the presumed galaxy type, galaxy age, star formation rate and the mass of the central black hole of the host galaxies. In addition, the masses of the central black hole for the whole sample were derived using the corresponding quasar spectra. Results. We were able to resolve the host galaxies of two out of eight quasars between $z=0.87$ and $z=2.75$. Additionally, two host galaxies were possibly resolved. Conclusions. The resolved low-redshift quasar ($z=0.865$) was identified as a late type galaxy with a moderate star formation rate of $1.8~M_{\odot}/{\rm yr}$ hosting a supermassive black hole with a mass of $\la$$10^{8}~M_{\odot}$. The resolved high redshift host galaxy ($z=2.7515$) shows moderate star formation of $4.4{-}6.9~M_{\odot}/{\rm yr}$, for the black hole mass we found a lower limit of >$10^{7}~M_{\odot}$. All quasars host supermassive black hole with masses in the range ~$10^{7}{-}10^{9}~M_{\odot}$. Our findings are well consistent with those of other authors