Astron. Astrophys. 359, 447-456 (2000)

3. Measurement of nuclear off-center positions

The procedure we adopted for the determination of the offset distance of a nucleus to the center of the galaxy is straightforward. Our basic tool was the image processing package MIDAS provided by ESO. Within the context SURFPHOT we used the algorithm FIT/ELL3 to fit a series of ellipses to the surface brightness distribution of a galaxy. The important point with the fitting procedure FIT/ELL3 is that the center coordinates of the fitted ellipse are kept as free parameters. Any difference between the calculated ellipse center and the actual position of the nucleus is then giving an off-center distance of the nucleus.

The galaxy images had already been background-subtracted, cleaned from disturbing foreground stars, and calibrated from BC93 (where also all details concerning the photometry can be found). The pixel size of the digitized images corresponds to 40 µ, or 0.43", which has to be compared with the typical FWHM of 1.2" for the stellar images on the photographic plates. The position of a nucleus was simply taken as the center of the brightest pixel, resulting in a geometrical mean error of the nuclear position of 0.16". For the ellipse fitting the images were slightly smoothed with a running 55 pixel mean. This degree of smoothing was found experimentally to be optimal for our purposes.

Ellipses were then fitted to five isophotes in the surface brightness range 24-25 B arcsec^-2 with steps of = 0.25 mag, i.e. at the isophotal levels of 24, 24.25, 24.5, 24.75, and 25 B arcsec^-2. The fainter surface brightness boundary at 25 B arcsec^-2 was arbitrarily chosen to avoid the noisy outer parts of the galaxy images. The brighter surface brightness boundary at 24 B arcsec^-2, on the other hand, was dictated by the inclusion of faint dEs that have a surface brightness of 24 B arcsec^-2 already close to the center of the galaxy (underlying the nucleus). This simple and convenient procedure guarantees that all dwarfs are treated in a homogeneous way. We have also experimented with individually different surface brightness ranges within which to determine the nuclear position but found no difference, in the statistical results, to the present procedure.

For each isophotal level in the adopted surface brightness range we calculated the distance of the nucleus to the ellipse center as well as the position angle of the nuclear offset with respect to the major axis. Averaging over the five points in the surface brightness range we derived a mean off-center distance of the nucleus, , with a standard deviation, . To account for the differing sizes of the dwarf galaxies we have also calculated relative nuclear off-center distances by dividing by the "effective" (half-light) radius . All of these data are given in Table 1 as follows:

column (5): mean off-center distance of the nucleus, (in arcsec);

column (6): standard deviation of the nuclear displacement, (in arcsec);

column (7): relative nuclear off-center distance, .

Columns (1)-(4) of Table 1 are defined in Sect. 2 above.

The values in arcsecs can be transformed to linear distances by adopting a Virgo cluster distance. A convenient scaling is provided by 20 Mpc, where an angle of 1" just corresponds to 100 pc at the Virgo cluster.

In a number of cases the strong scatter, or generally inconsistent behaviour of the nuclear off-center distance in the surface brightness range 24-25 B arcsec^-2 was found to cast strong doubt on the calculated mean . A clear sign of an unreliable mean nuclear offset was also the inconsistency of the offset position angles for the different isophotal levels. A significant off-center distance is accompanied by a robust value for the position angle. Uncertain cases in this sense are flagged with a colon in columns (5) to (7) of Table 1 and they are shown with open symbols in Figs. 5-7 below.

© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000
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