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10.5 Uncertainties

There are a number of possible sources of uncertainty that enter into the derivation of distances from the Dn-sigma relation. These are:

(1) The uncertainty in the estimate of galactic absorption. This can be minimized using red bands (e.g., R, I, or H) for the photometry. The uncertainty is generally small, although in some directions (e.g., in Centaurus), an error of 0.05 mag in the B-band absorption estimate may arise.

(2) The uncertainty associated with assigning particular galaxies to a group. This can be evaluated by perturbing the algorithm used and noting the changes in distance estimates that arise. Assuming that redshift is the basis for the membership criterion, the error in recession velocity enters into the uncertainty but this is typically too small (<30 km s-1) to contribute significantly to the overall uncertainty.

(3) Perhaps the largest and most easily remedied uncertainty is associated with the precision of measurement of Dn and sigma. Diameter and velocity dispersion measurements for the more distant clusters are relatively poorly determined. The data of the 7S are such that for the most distant clusters, the errors of measurement contribute to the overall scatter in the Dn-sigma relation. Lucey et al. (1991a) have reported measurements of Dn and sigma in A2199 that differ systematically from those reported in the 7S work. Lucey et al. find dispersions that are 10% smaller and diameters that are 7.4% larger leading to an estimate of the distance to A2199 that is 20% smaller than that of the 7S. A2199 is one of the most distant clusters studied to date and exhibits the largest discrepancy of this type in the literature. As studies using the Dn-sigma method probe to greater distances, measurements of a quality that result in a reliable and reproducible distance indicator are required.

(4) The degree of physical uniformity of the sample of galaxies. This has been discussed in Sec. 10.2 where mass-to-light ratio, absolute magnitude and galaxy environment were considered. Other factors that could bias or add scatter to the Dn-sigma method include: the unknown distribution of intrinsic shapes, the degree of rotational support, the presence of additional subcomponents (e.g., independent cores, disks, or other isophote distortions), and possible dispersion anomalies at the core. Given the uncertain physical basis of the method, continuing searches for systematic effects are appropriate.

(5) The distribution of galaxies is not uniform and yet the treatment described in Sec. 10.2 assumes a correction for a bias which is based on a uniform distribution. The bias can work with either sign; on the near side of a concentration of galaxies the correction required acts to increase the estimated distances whereas on the far side the correction acts to decrease the estimated distances. Clearly this effect is potentially highly misleading in regions with large galaxy number density contrasts. An illustration of this is given in BFD. The size of the uncertainty introduced will depend on the distribution of galaxies in any given sample and will vary around the sky.

(6) Seeing can systematically bias the measurement of diameters. Dn is defined by the mean surface brightness it encloses, and as seeing reduces the mean surface brightness at all radii, seeing biases measurements of Dn to smaller values. Saglia et al. (1992) are investigating the magnitude of this effect. Although Lucey et al. (1991a) apply a seeing correction to their data on Abell 2199 and Abell 2634, the 7S did not make such a correction. The initial simulations of Saglia et al. (1992) indicate that in the regime where the seeing diameter is a substantial fraction of the half-light radius, say (Dseeing / Re) = 0.5, a substantial seeing correction is necessary amounting to approximately 4% when the true Dn is equal to Ae. Thus seeing can cause diameters to be under-estimated and therefore distances over-estimated.

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