4.2.1 Determination of the Sky Background Level

One method to determine the sky background level is to identify so-called empty regions of the image and measure the level in these. However, that is quite subjective, and sometimes there is even significant signal from the galaxies everywhere in the image. Instead, we used a less subjective method to determine the sky background level. The method does not use the image in question directly, but is based on the intensity profile $I_0^{({\rm e})}(r)$ determined from the ellipse fit. To the outer parts of this profile a suitable function is fitted, and the asymptotic value for $r \rightarrow \infty$ is taken to be the sky background level.

Specifically, for normal E and S0 galaxies (here meaning non-cD galaxies) we fitted the following two functions

$$I(r) = \mbox{sky} + \frac{I_0}{r^\alpha}, \; \alpha=2,3 \quad \mbox{(for non-cD galaxies)}$$ (4.4)

to the outermost points in the intensity profile, and the sky background level `sky' was taken to be the mean of the two determinations (i.e. $\alpha=2$ and $\alpha=3$). The `outermost points' are defined as the points where the intensity from the galaxy is less than 0.2 times the sky background level. The uncertainty on the sky background level is taken to be half the difference between the two determinations, unless this is less than a specified minimum value, in which case that is used instead. This is done in order to take systematic effects into account, like how well one can do flat fielding. The minimum relative uncertainty was set to 1% for Gunn r, and 0.5% for Johnson B and U. In all cases but for the cD galaxy R269, the uncertainty was calculated from the minimum value.

cD galaxies have per definition a more shallow profile than normal E and S0 galaxies, and are therefore better fitted by the two functions

$$I(r) = \mbox{sky} + \frac{I_0}{r^\alpha}, \; \alpha=1,2 \quad \mbox{(for cD galaxies)} \enspace .$$ (4.5)

We used these for the galaxy R269, only.

For both set of functions, to obtain a good fit we sometimes excluded a few of the outer points from the fit.