We present some results from our HST archival image study of 71 QSO host galaxies .
The objects are selected to have z \leq 0.46 and total absolute magnitude M _ { V } \leq - 23 in our adopted cosmology ( H _ { 0 } = 50 km s ^ { -1 } Mpc ^ { -1 } , q _ { 0 } = 0.5 , \Lambda = 0 ) .
The aim of this initial study is to investigate the composition of the sample with respect to host morphology and radio loudness , as well as derive the QSO host galaxy luminosity function .
We have analyzed available WFPC2 images in R or I band ( U in one case ) , using a uniform set of procedures .
The host galaxies span a narrow range of luminosities and are exceptionally bright , much more so than normal galaxies , usually L > L ^ { * } _ { V } .
The QSOs are almost equally divided among three subclasses : radio-loud QSOs with elliptical hosts , radio-quiet QSOs with elliptical hosts , and radio-quiet QSOs with spiral hosts .
Radio-loud QSOs with spiral hosts are extremely rare .
Using a weighting procedure , we derive the combined luminosity function of QSO host galaxies .
We find that the luminosity function of QSO hosts differs in shape from that of normal galaxies but that they coincide at the highest luminosities .
The ratio of the number of quasar hosts to the number of normal galaxies at a luminosity L _ { V } is \mathcal { R } = ( L _ { V } / { 11.48 L ^ { * } _ { V } } ) ^ { 2.46 } , where L ^ { * } _ { V } corresponds to M ^ { * } _ { V } = -22.35 , and a QSO is defined to be an object with total nuclear plus host light M _ { V } \leq - 23 .
This ratio can be interpreted as the probability that a galaxy with luminosity L _ { V } will host a QSO at redshift z \approx 0.26 .