We determined parameters that quantify the global deviations
from elliptical isophotes in Gunn r.
From the Fourier coefficient profiles sn(r) and cn(r)
intensity-weighted mean Fourier coefficients
We determined a characteristic value of c4(r), denoted c4, as the mean value of the three points around the extremum of c4(r). In case of no well-defined extremum, the mean value of the three points around the effective radius was used. This is the definition used by JF94 and JFK95a. We only looked for an extremum in the radius interval from to the radius where the uncertainty on exceeded . We calculated the uncertainty on c4 as half the min-max variation of the 3 points. A few of the galaxies had a minimum and a maximum in the c4(r)-profile of comparable amplitude. In these cases we still calculated c4 at the extremum with the largest amplitude, and if a tie, at the most regular one. Examples are R194 (p. ; c4 = -0.043) and R238 (p. ; c4 = -0.029). Both galaxies are boxy at low radii, and disky further out. For 4 of the 64 galaxies we did not determine c4, since it would be too uncertain ( ). These galaxies had no extrema and at or beyond the maximum radius used for the c4 determination.
In Figure we compare c4 with . The relation between them is (dashed line). JF94 found (dotted line). The discrepancy is likely due to the poorer spatial resolution of JF94, which affects c4 but not ; see also Sect. . That per se is smaller than |c4| is because is integrated over a larger range in r than just the 3 points around the extremum as c4 is. Some of the galaxies have quite different values of c4 and . For example, R188 (p. ) and R250 (p. ) have and , cf. Fig. (b). These two galaxies have a small c4(r) minimum at low radii and a large c4(r) maximum at large radii. Since is an intensity-weighted mean, is small for these galaxies, while c4 is large.
Properties of E and S0 Galaxies in the Clusters HydraI and Coma
Master's Thesis, University of Copenhagen, July 1997
Bo Milvang-Jensen (firstname.lastname@example.org)