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Astron. Astrophys. 333, 795-802 (1998)

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8. Cosmic expansion and cluster kinematics

Binggeli & Jerjen expected to find a `well-defined velocity-distance relation' based on their `fairly large' subsample of 43 objects with known velocities, if there were significant depth in the spatial distribution of Virgo dwarfs. They cited the lack of such a relationship based on their L -n and L - [FORMULA] `pseudo-distance' estimates, as evidence against the depth interpretation.

The most fundamental problem with their argument is that in order to generate relative distances based on each of two different scaling relationships, they have already assumed negligible depth when they estimate these relationships directly from the residuals with respect to the best-fitting curves to their data. The crucial point here is that should there be significant depth, the mean distance of their high-n objects must be lower than the mean distance of their low-n objects, due to Malmquist bias. The relative distance scales they construct for each relationship should therefore not be based on a best fit to data for Virgo galaxies, but on a curve defined by a best fit to data from either a sample of objects known to be at similar distances (e.g. Fornax-Cluster galaxies) and/or a sample of objects whose distances are known (e.g. Local-Group galaxies). In Fig. 8 the differential frequency of galaxies should increase monotonically with increasing n if their galaxy sample were unbiased. As this is not what is observed, we can conclude that their galaxy sample suffers from bias against high n objects. Should there be depth in the spatial distribution of their sample galaxies, the mean distance of their lower n objects must be greater than the mean distance of their higher n objects. Their residuals can, at best, therefore only yield meaningful relative distances for galaxies within very small ranges in n for which the degree of the Malmquist bias can be assumed to be constant.

[FIGURE] Fig. 8. A histogram of the number of galaxies in Binggeli & Jerjen's sample of 128 dwarfs per unit profile curvature, n, interval. The shaded regions represent that subsample of 43 objects with published radial velocities.

Furthermore, as already demonstrated in Sect. 3, the `pseudo-distances' derived by Binggeli & Jerjen for their Figs. 10 and 11, must indeed be highly inaccurate on account of the errors in their photometry. Also, they apply the [FORMULA] versus n and [FORMULA] versus [FORMULA] relationships to all early-type dwarfs indiscriminately, in the absence of e.g. colour information.

The existence of so many outliers (two of which are objects with negative radial velocities) on Binggeli & Jerjen's Figs. 10 & 11 is therefore not surprising. However, as previously suggested in YC95, there may well be significant line-of-sight substructure in the spatial distribution of Virgo galaxies, complicating the kinematics of the galaxy populations present. Significant spatial depth therefore need not necessarily imply the `quiet' velocity-distance relationship presumed by Binggeli & Jerjen.

We have been interested in the kinematics of the dwarf-galaxy populations in Virgo for a number of years now, and a major programme to measure large numbers of redshifts for early-type dwarf-candidates is already well underway. The Virgo galaxies targeted by Drinkwater et al. (1996) with the multi-fibre spectrograph on the United Kingdom Schmidt Telescope (UKST), were, on account of the observing constraints at the time, generally of high surface brightness. Consequently, most of them were found to be in the background. However, 8 objects were confirmed to be dwarf or intermediate early-type galaxies. In 1997, early-type objects of low surface-brightness were targeted by Drinkwater et al. (in preparation), again using the UKST, and 67 velocity measurements were obtained. Further measurements made in 1997 with a different telescope and and future ones (from two separate telescope-time allocations in 1998) will be presented in subsequent papers. A detailed investigation into the Virgo-dwarf velocity field will then be based on these new data.

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© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998