4.4.2 Comparison of Surface Brightness Profiles

For all the 97 possible pairs of galaxies observed more than once in the same filter, we calculated the difference of the surface brightness profiles, $\Delta\mu(r) = \mu_{\rm obs.\,a}(r)-\mu_{\rm obs.\,b}(r)$, and examined the plots of $\Delta\mu(r)$ vs. $\log r$. Nine of these plots are shown in Fig.  to exemplify characteristic features seen in these comparisons.

The most prominent feature in the 97 $\Delta\mu(r)$ plots is the seeing effect. A typical example is panel (a), where the first observations has worse seeing than the second (cf. Table ). The same effect is also seen in panel (d) and (g); and also in panel (f) and (i) with the opposite sign, since $\Delta {\rm seeing}$ is negative here. The shown comparisons of R256 (panel d), R269 (panel e), and R273 (panel c) are all from the same pair of images, and yet the seeing effect is very different for the three galaxies. This is because their profiles are quite different. R256 has a `normal' profile, R269 has a flat or even decreasing profile towards the center due to dust, and R273 has a very steep profile towards the center (it has a central cusp). Panel (b) shows R234, which due to the problems with the spectral calibration lamp (cf. Sect. , p. ) was observed twice just after each other. The seeing is almost the same for the two images, and sure enough, the two profiles match very well even at very small radii.

A few of the plots show systematic differences at large radii. The worst example is R336, panel (f) and (i). A possible explanation could be a wrong sky determination. For R336 our sky determinations need to be off by 2.5 ADU (2.2%) and 8 ADU (2.7%) for Johnson B and Gunn r, respectively. (The number quoted for the given filter is the amount that needs to be added to the sky level used for the first observation, or equivalently the amount that needs to be subtracted from the sky level used for the second observation.) A manual sky determination (the median value in empty regions of the image) indicates that the used sky levels are off by 0.3 ADU and 3 ADU, respectively. Thus a wrong sky determination can only explain a minor part of the observed discrepancy. It seems likely that the discrepancy could originate from the iterative fit. R336 was fitted iteratively with R337 (see the images on p.  and ). An additional complication is that R336 is located close to the edge of both images it is in, with a distance to the edges of $\log(r/{\rm arcsec})$ = 1.7-1.8, and with different sides being outside the image in the two observations. R256 and R269 also show systematic differences at large radii, but these are not significant within the estimated errors. These two galaxies were also fitted iteratively.

Anyway, in all cases the quantities we are mostly interested in, such as ${r_{\rm e}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$, are only moderately affected, cf. Table . The derivation of these parameters takes the seeing into account, as described in Sect.  (p. ). Further, due to the correlation between the errors in ${r_{\rm e}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ (cf. Sect. , p. ), the combination of the two that enters the fundamental plane, approximately ${\log{r_{\rm e}}}- 0.328 {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$, does not vary by more than typically 0.01.

 

 

Table: Internal Comparison of Surface Brightness Profiles - Info

Panel	ID	Filt.	Night a	Night b	$\Delta {\rm seeing}$	$\Delta m(10'')$	$\Delta \log {r_{\rm e}}$	$\Delta {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$	$\Delta {\rm \lq\lq FP''}$
(a)	R234	GR	1	3 (#2)	0.74''	-0.003	0.00	0.02	-0.007
(b)	R234	GR	3 (#1)	3 (#2)	-0.03''	0.004	-0.01	-0.03	-0.000
(c)	R273	GR	1	3	0.84''	-0.001	0.01	0.07	-0.013
(d)	R256	GR	1	3	0.84''	0.005	-0.02	-0.07	0.003
(e)	R269	GR	1	3	0.84''	0.005	0.04	0.12	0.001
(f)	R336	GR	4 (#1)	4 (#2)	-0.11''	-0.019	0.03	0.10	-0.003
(g)	R256	JB	1	3	0.90''	-0.001	-0.03	-0.13	0.013
(h)	R269	JB	1	3	0.90''	0.002	0.07	0.19	0.008
(i)	R336	JB	4 (#1)	4 (#2)	-0.06''	-0.004	0.04	0.16	-0.012

 

Notes: See caption to Fig. . The two observations, `obs. a' and `obs. b', are identified by the night number. For galaxies observed twice on the same night, the two observations are denoted `(#1)' and `(#2)', still in chronological order. $\Delta {\rm seeing}$ should be compared with the shape of the $\Delta\mu(r)$ vs. $\log r$ plots in Fig. . The derivation of ${\log{r_{\rm e}}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ takes the seeing into account, as described in Sect.  (p. ). The other differences listed quantify the effect of the differences in $\mu(r)$. ``FP'' is the combination of ${\log{r_{\rm e}}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ that enters the fundamental plane, and is defined by ``FP'' = ${\log{r_{\rm e}}}- 0.328 {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$.