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Astron. Astrophys. 358, 88-94 (2000)

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3. Analysis

3.1. Deconvolution

3.1.1. The deconvolution method

The images were deconvolved using the MCS algorithm. This method is based on the principle that the resolution of a deconvolved image must be compatible with its sampling, which is limited by the Nyquist frequency. The deconvolved image is decomposed into a sum of deconvolved point-sources plus a background smoothed on the length scale of the final resolution. The intensities and positions of the point-sources as well as an image of the more extended objects are given as output of the deconvolution procedure. Image decomposition allows objects blended with or even superposed on point-sources to be studied in some detail.

In order to check if the deconvolved model is compatible with the data, a residual map is computed. The residual map contains in each pixel the [FORMULA] of the fit of the model image (re-convolved with the PSF) to the original data of that pixel. The [FORMULA] image is used to determine the appropriate weight attributed to the smoothing of the image of extended sources in order to avoid under- or over-fitting of the data (see MCS for further details). A deconvolution compatible with the data should show a flat residual map with a mean value of 1 all over the image.

The MCS algorithm makes it possible to simultaneously deconvolve several frames. The advantage of this process is to derive the optimally constrained deconvolved frame which is simultaneously compatible with several different images of a given object. This results in a more accurate decomposition of the data than the deconvolution of one single combined frame. Moreover, applying the algorithm to many dithered frames leads to a deconvolved image with an improved sampling.

3.1.2. Application to the data

Simultaneous deconvolution of the U-band data from 1996 had already strongly indicated extended broad band emission in the direction of Q0151+048A (see Fig. 1). However, although the shape of the extended emission was similar to the one found in narrow-band (Fynbo et al. 1999), it was unclear to which extent systematic errors in the determination of the PSF influenced the detection and hence the signal-to-noise ratio of the object was too uncertain to constrain its morphology and luminosity.

[FIGURE] Fig. 1. Contours of the deconvolved U-band from 1996. The resolution is 0:0035 and the axis are in units of arcsec. The contour levels are -9, -6, -3, 3 [FORMULA] 1[FORMULA] of the sky noise and thereafter spaced logarithmically in factors of 1.5, with the dotted contours being negative. The field is 12[FORMULA]12 arcsec2, North is up and East to the left.

There are two bright stars in the field of Q0151+048, referred to as psfA and psfB (see Fynbo et al. 1999). However, our new deep I-band data revealed that psfB has a faint red companion star at a projected distance of 0:007. In the I-band it is 4.3 magnitude fainter than psfB, in the B-band it is 6.3 magnitudes fainter than psfB, and in the U-band it remains undetected. In the following we only use psfA for the determination of the PSF.

We adopted for the deconvolved image a pixel size of 0:000541 (half of the original one), and a final resolution of 3 pixels FWHM, or 0:0016 (the Nyquist limit is 2 pixels FWHM).

3.1.3. Results

Fig. 2 shows the deconvolved images in all three bands I, B and U. The images show the five sources already known to be in the field, namely the three point-sources qA, qB and the star s, and the two faint galaxies gA and gB south west of qA (see Fynbo et al. 1999 for details). However, there is also significant extended emission under the point-source emission from qA in all three bands. This emission have nearly identical morphology in the I and B bands with contours centred on the position of qA and with a slight elongation with position angle [FORMULA] east of north. The shape and intensity of the extended U-band emission under qA (Fig. 2 right panel) is consistent with the shape and intensity derived from the 1996 U-band data (Fig. 1). Since the two sets of U-band data have been obtained with two different instruments, the consistency between the two measurements makes strong systematic errors unlikely. The morphology of the U-band emission is significantly more extended than the B and I morphology, about 4.5[FORMULA]2.2 arcsec2, and has a position angle of about 100o east of north. This is very similar to that of the Ly[FORMULA] source S4, which extends over 6[FORMULA]3 arcsec2 with position angle 98o east of north.

[FIGURE] Fig. 2. Contour plots of 12[FORMULA]12 arcsec2 surrounding the two QSOs from the deconvolved I-band frame (left) , B-band frame (middle) and U-band frame (right) . The three point-sources s, qB and qA are seen on the diagonal from the upper left corner (s) to the centre (qA). The resolution is 0:0016. North is up and east to the left. Seen is the extended emission under qA and the two galaxies gA and gB south of qA.

The extended emission towards qA is [FORMULA]4 magnitudes fainter than that of the point-source emission. This high contrast makes it difficult to determine the exact ratio between the luminosity of the extended source ([FORMULA]) and that of qA ([FORMULA]). Several deconvolution solutions with different luminosity [FORMULA] ratios are compatible with the residual map constructed as described above. Thus, there is some degeneracy between the plausible solutions found by the algorithm.

In order to demarcate the range of plausible solutions, a grid of 15 deconvolved images in each band was calculated, representing 5 different luminosity ratios [FORMULA] and with 3 different values of the Lagrangian smoothing parameter applied during the deconvolution (see MCS for a description of the Lagrangian smoothing parameter). The solutions with the highest [FORMULA] ratios were unphysical since they have a ring-shaped morphology, i.e. a hole at the position of the QSO. The lowest values of [FORMULA] were rejected by inspection of the residual map mentioned above. The resulting range of magnitudes for the extended emission is given in Table 3. The solutions shown in Fig. 2 are those with the highest acceptable values of [FORMULA]. Our conclusions concerning the morphology of the extended emission in the three bands are, however, unchanged for all solutions within the acceptable range.


Table 3. Photometry of qA, qB and the extended sources under qA and qB. The magnitudes given for ExtA under Deconvolution is measured in a circular aperture with diameter 3.5 arcsec. The magnitudes for S4 and HGa under PSF-subtraction are determined by model fits as described in the text. The upper limits to the magnitudes of HGb are 2[FORMULA]. The magnitudes of gA and gB are measured in a circular aperture with diameter 1.35 arcsec.)

In the B-band there is also significant extended emission under the PSF of the fainter neighbour quasar qB.

3.2. Object based image decomposition

In conclusion of the previous section: i) There is clear evidence for extended broad band (U, B and I) emission in the vicinity of the quasars Q0151+048A,B; ii) the morphology of the extended object(s) is identical in B and I but significantly different in U; iii) the U-band morphology is more extended and similar to the morphology of the Ly[FORMULA] emission from the DLA absorbing galaxy (S4).

Those conclusions would suggest that the extended emission in this field is made up of three individual components: The DLA absorbing galaxy, the host galaxy of qA and the host galaxy of qB. The different morphology in the four different bands would then indicate that the objects have different spectral energy distributions (SEDs).

In order to investigate this further we decomposed the superimposed images into individual objects with different SEDs. For this image decomposition we applied the same procedure we used for the narrow band image analysis (Fynbo et al. 1999), but here we add more components. We consider point-sources, de Vaucouleurs profiles and exponential profiles. The best decomposition is determined as the minimum [FORMULA] fit following an iterative procedure as described below.

3.2.1. B-band data

The B-band image is more than a magnitude deeper than the I and U-band images in terms of the background rms surface brightness. Our first step was therefore to produce optimized models of the galaxies from the B-band data. For the decomposition we considered the following 8 components: Three point-sources (qA, qB, s), four galaxies to be fitted (gA, gB and the host galaxies of qA and qB, in what follows named HGa and HGb), and one galaxy of "frozen" morphology (the DLA absorbing galaxy S4). For S4 we adopted the model determined from the narrow-band data (Fynbo et al. 1999). Note that most of the objects do not overlap significantly, thus allowing us to fit them independently.

The bright star psfA was used with DAOPHOT II (Stetson 1997) to define the PSF. We then employed the iterative [FORMULA] minimization procedure detailed in Fynbo et al. 1999, to decompose the image of qA into a point-source and a de Vaucouleurs galaxy model (convolved with the PSF). For the calculation of the [FORMULA] we excluded a circular region of radius 0.65 arcsec centred on qA due to the large PSF-subtraction residuals. After ten iterations a stable solution was found. The same procedure repeated with an exponential-disc profile instead of the de Vaucouleurs profile resulted in a much poorer fit. A significant positive residual, centred about 1 arcsec east of qA, was left after this procedure. The most plausible interpretation of the residual is that it originates from the DLA absorbing galaxy S4. As S4 is known to extend across the position of the bright quasar, measuring its flux from a direct aperture measurement is impossible because of the large PSF subtraction residuals. Instead we made a grid of models to determine the flux of S4 via minimum [FORMULA] fitting. For a given assumed B magnitude of S4 we first subtracted the correctly scaled exponential-disc model as determined from the original Ly[FORMULA] image (Fynbo et al. 1999). For that given B magnitude of S4 we then repeated the iterative fitting of a de Vaucouleurs profile to the remaining flux. The final model was chosen to be the model with the smallest [FORMULA] measured in an area excluding pixels less than 0.65 arcsec from qA. The improvement in the fit due to the inclusion of the S4 model was significant ([FORMULA] = -21). We also fitted the profiles of the two galaxies gA and gB. For gA the best fit was obtained with an exponential-disc profile, whereas the best fit for gB was obtained with a de Vaucouleurs profile.

Fig. 3b shows a 14x14 arcsec2 field of the area after subtraction of the qA and qB PSFs as determined from the minimum [FORMULA] fit. The residuals, after the additional subtraction of the final models for HGa, gA and gB can be seen directly below (Fig. 3e). The magnitude of HGb was measured on this final subtracted image.

3.2.2. U and I band data

The well constrained galaxy models determined from the high signal-to-noise B image were subsequently used to decompose the U and I-band data. Since the combined seeing of the U-band data was poorer than that of the B image, we first smoothed the galaxy models to the seeing of the U-band data. For a large grid of U-band magnitudes of S4 and HGa we then subtracted scaled versions of the smoothed S4 and HGa galaxy models, fitted and subtracted the quasar point source component using DAOPHOT II, and finally calculated the [FORMULA] in an area excluding pixels less than 0.8 arcsec from qA. The final model was selected to be that which had the smallest [FORMULA]. The U magnitudes of the galaxies gA and gB were determined in the same way. For the decomposition of the combined I-band data, which have a better seeing than the B-band data, we first smoothed the I-band image to the seeing of the B image and then proceeded as for the U-band data.

Results of this procedure can be seen in Fig. 3a,d and Fig. 3c,f for the I and U-bands respectively. As for the B-band data the upper frames show the fields after subtraction of final fits of qA and qB only, while in the lower frames the fitted models of galaxies HGa, gA and gB have also been subtracted. The magnitudes (and estimated associated errors) of objects resulting from the fitting procedure are listed in Table 3.

[FIGURE] Fig. 3a-f. Contour plots of 14x14 arcsec2 surrounding the two QSOs from the final combined and PSF subtracted frames in a  I-band, b  B-band and c  U-band. North is up and east to the left. Seen is residual extended emission under qA. Also seen are the two galaxies gA and gB south of qA. The contour levels are -9, -6, -3, 3 [FORMULA] 1[FORMULA] of the sky noise and thereafter spaced logarithmically in factors of 1.5, with the dotted contours being negative. d -f  show the same region after subtraction of the galaxy fits of HGa, gA and gB as described in the text. The most plausible explanation for the residual east of the position of qA is the absorber galaxy S4.

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000