4 Analysis

In each of the images, we first masked out the companion objects and the ghosts due to the telescope. We then obtained the surface brightness profiles of the galaxies using the IRAF task ellipse. The resulting profiles were fitted over the radius range from 3 times the FWHM of the PSF up to the point where the galaxy surface brightness level falls below $2\times \sigma$ of the background level. We have systematically fitted an exponential disk and a de Vaucouleurs r^1/4 law. The results are shown in Fig. 4, where the residuals from the subtraction of the fitted profiles to the real profiles are also plotted. Out of the 10 objects for which we can extract some morphological information, two of the host-galaxies are most probably barred spirals, the rest being ellipticals or very early type spirals (see Table 2). We note that in general the number of points we can use to fit either profile is not large enough to unambiguously distinguish between the two fitted profiles. At small radii, the excess of light between the observed profile and the model disk can be due to the presence of a bulge. The morphology indicated in column #10 of Table 2 is determined considering both the 2D luminosity spatial distribution and the 1D profile. It is apparent that to discriminate between both morphologies, the S/N ratio must be high at large radii.

The magnitudes of the hosts have been derived by integrating the r^1/4 profiles for all the objects. Indeed, it can be seen in Fig. 4 that there is an excess of light at small radii compared to the disk profile for all objects. This suggests that in our sample, the disk galaxies also have a strong bulge and/or a strong bar. This is confirmed by the 2D luminosity distribution. Results are given in Table 2. We have also subtracted a scaled version of the most suitable PSF for each nucleus (imposing a non-negative profile in the center, see Márquez et al. 1999) The resulting host magnitudes, computed by integrating the PSF-subtracted images, are in good agreement with those obtained from the profile fitting (see Table 2).

In order to test our fitting procedure, we have generated images of model elliptical and disk galaxies with scale-lengths and effective surface brightness within the range derived from the data. The same orientation and axis ratio is given to all of them. A point source is added in the center of the galaxy to mimic the quasar. An appropriate amount of noise is added, and then the images are convolved with a typical observed PSF. The mock data images are analyzed in the same way as real data.

Figure 6: Test of the fitting procedure on disk-galaxies. We plot here the difference between the input and output magnitudes versus the input magnitude in the case the host-galaxy has the same magnitude as the quasar. A dot surrounded by a circle means that the fit by an r1/4 law is at least as good as the fit by an exponential disk

Figure 7: Test of the fitting procedure on elliptical galaxies. We plot here the difference between the input and output magnitudes versus the input magnitude. Triangles correspond to the systems where the QSO contributes to the total luminosity as the host-galaxy does, squares represent those cases in which the host luminosity is half that of the QSO

We first note that an elliptical galaxy is always recognized as an elliptical galaxy by the fitting procedure, whereas a disk-galaxy is better fitted by a r^1/4 law when the unresolved point-source contributes more than half the total light. This is illustrated in Fig. 5. This means that, at least with data of similar quality to those presented here, the fraction of elliptical galaxies in the sample may be overpredicted. Going deeper, at least 0.5 to 1 mag, should help solve this problem as it is apparent that the distinction between spiral and elliptical profiles is easier when the galaxy is detected at larger distances from the central point-source.

It is interesting to note that the output magnitudes are brighter than the input in both cases, elliptical or disk galaxies (see Figs. 6 and 7). The reason for this is probably the difficulty in determining the extension of the PSF wings which, if not subtracted properly, will artificially increase the flux of the host-galaxy. In the case of spirals, the difference is as large as 0.6 mag when the contribution of the point-source is the same as the contribution of the host-galaxy (see Fig. 6). For the ellipticals, the difference is less but still important when the QSO dominates the total flux.

Note that the ratio between the QSO and the host-galaxy luminosities is expected to increase with redshift. The above bias tends to imply that host-galaxy luminosities could be overestimated.