4. Binggeli and Jerjen's correlation analyses
Binggeli & Jerjen investigated the following four correlations: versus , versus , versus , and versus ; for Virgo galaxies. They observed rms scatters in these correlations of 0.92, 0.73, 0.76 and 0.85 mag. respectively, and asserted that: `A scatter of 0.7 mag. is what one can already get from the relation between the mean effective surface brightness and total magnitude'.
As is evident from Fig. 5 there is a significant and not necessarily linear scale error in their magnitude scale for galaxies that lie within the VPC survey area (corresponding to their Plates 17, 18 and 26 but with two objects on their Plate 4). The sense of this error is such that the luminosities of their fainter galaxies were over-estimated with respect to their brighter objects. In the case of the outlying fields their scale errors are almost certainly even larger as the only calibrators used were VCC galaxies with total-magnitude values taken from either the VCC or de Vaucouleurs & Pence (1979). As mentioned in Sect. 3, there are very large systematic errors in both of these sources of magnitudes. In fact the preliminary work of Young (1994 & 1997) finds that these sources over-estimate luminosities by about 0.7 mag. at the faint end.
As already demonstrated in Sect. 3, Binggeli & Jerjen's photometry was based on differentially zero-pointed plates (i.e. objects on each of the 13 different plates received different absolute calibrations). Furthermore, their values were not systemic ones (i.e. obtained by integrating Sérsic's function through to ), but those of Binggeli & Cameron (1993), which were obtained using a different extrapolation procedure and including the nuclear light contribution when present. The effects of both of these limitations in their reduction procedures would be to increase the observed scatters in the versus , the versus and the versus correlations. Of these three correlations, the first would be affected the most. This is because the term in the other two correlations can to a certain extent compensate for the errors in the values adopted (even if neither the measured nor the measured bear much resemblance to the actual values). Also, the versus correlation is the one most susceptible to increased scatter when, as by Binggeli & Jerjen, applied indiscriminately to objects of different stellar populations in the absence of galaxy-colour information.
We therefore find that Binggeli & Jerjen's dataset is useful only for investigating the versus correlation, assuming of course that Binggeli & Cameron's (1993) background subtraction procedures were adequate. We are therefore confronted with an observed scatter of 0.85 mag. in a scaling relationship based on a sample of 128 Virgo galaxies. Clearly, even if the measurement errors in the parameters and n introduced a random component as high as 0.30 mag., we are still left with a scatter of 0.80 mag. to explain. Binggeli & Jerjen attribute this remaining component mainly to intrinsic scatter, while we would attribute a large part of it to spatial depth.
© European Southern Observatory (ESO) 1998
Online publication: April 28, 1998