Total Magnitudes of Virgo Galaxies. II.
An Investigation into the m_p Scale of Volume I of Zwicky et al.'s

Catalog of Galaxies and Clusters of Galaxies
Christopher Ke-shih Young and Zheng-yi Shao, PASA, 18 (2), in press.

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Isophotal magnitudes

Isophotal magnitudes were generated for all 92 Sample M_I and M_II objects by integrating the best-fitting Sérsic profile parameters, as listed in Table 3 of Paper I or in the VPC, to isophotes of one's choice. B-band profile parameters were used when available. Otherwise, preference was given to B_J-band profile parameters over U-band ones. For most objects in Table 2 of Paper I however, only U-band parameters were available. In order to transform non-B-band parameters to B-band ones, it was necessary to work out

X=B_t-B_{J_t} or X=B_t-U_t as appropriate, and to add X to the extrapolated central surface brightness ( $\mu_{{B_J}_0}$ or $\mu_{U_0}$ respectively) before performing the integrations to the chosen limiting isophote. In the cases of the B-band profile parameters listed in Table 3 of Paper I, all luminosity excesses or deficits with respect to the best-fitting Sérsic model were taken into account by evaluating

$Y=B_{t}{\rm (integ.)} -B_{t}{\rm (syst.)}$ and adding Y to $\mu_{B_0}$ , after integration. The integrals to the limiting isophotes were performed numerically using the Compound Form of Simpson's rule and 2000 intervals spanning the range r=0 and the mean (i.e. azimuthally averaged) radius of the limiting isophote.

**Figure 1:** The differences between m_p and B_24.4 for the 92 Sample M_I and M_II galaxies, shown as a function of B_t in order to enable direct comparisons with Fig. 3. Objects listed in Volume II of the CGCG are plotted as ` $\circ$ ' symbols, whilst Volume I objects are plotted as `+' symbols if cluster members or ` x ' symbols if background objects. The dotted line represents the measured completeness limit of Volume I in B_t space ( $B_t \sim 14.7$ ).
$\begin{figure} \begin{center} \psfig{file=p2f1.ps,height=7.5cm,angle=-90} \end{center} \end{figure}$

In order to evaluate which limiting isophote would yield isophotal magnitudes most closely resembling the CGCG's m_p values, we measured both the mean

$m_{p}-B({\rm isophotal})$ offset and the scatter as a function of limiting isophote. Over the total-magnitude range

$11.5 \leq B_{t} < 14.5$ , it was found that using a limiting isophote of $\mu_{B}=24.5$ mag.arcsec^-2 minimised the mean

$m_{p}-B({\rm isophotal})$ offset to -0.005 mag. with a scatter of 0.163 mag.; whilst using a limit of $\mu_{B}=24.3$ mag.arcsec^-2 minimised the scatter to 0.159 mag. with a mean

m_p-B_24.3 offset of -0.025 mag. However, we have adopted the intermediate limiting isophote of $\mu_{B}=24.4$ mag.arcsec^-2, because as shown in Fig. 1, this offers a scatter of only 0.160 mag. and a mean

m_p-B_24.4 offset of only -0.01 mag. The choice of the bright-end limit to our B_t range avoids the scale error that is clearly visible brightward of $B_{t}\sim11.5$ in Fig. 1. Our faint-end limit on the other hand was necessitated by the CGCG's increasing incompleteness faintward of $B_t \sim 14.7$ as well as the CGCG's faint-end limit (which is responsible for the absence of data points in the upper right-hand corner of Fig. 1. The consistency of these results appears to confirm that m_p values are essentially B-band isophotal magnitudes (except at the bright and faint ends of the magnitude scale) and that no colour transformation is necessary. Note that there is no conflict with the main conclusion of Bothun & Cornell (1990) whose finding that `Zwicky magnitudes are not very isophotal in nature' was restricted to galaxies for which

$m_{p} \geq 14.0$ mag.

**Figure 2:** B_24.4 as a function of m_p for the 92 Sample M_I and M_II galaxies. Objects listed in Volume II of the CGCG are plotted as ` $\circ$ ' symbols, whilst Volume I objects are plotted as `+' symbols if cluster members or ` x ' symbols if background objects. The dashed lines represent the suggested m_p-to-B_24.4 transformations for Volume I objects over the ranges
$10.0 < m_{p} \leq 12.0$ mag. and

$14.7 \leq m_{p} \leq 15.6$ mag. (Equations 4 and 6 respectively). Note that the apparent scale error at the faint end must be real because the datapoints are concentrated away from the dashed-dotted line, which represents the CGCG's

$m_{p} \leq 15.6$ cut-off. The dotted line represents the estimated completeness limit of Volume I in B_24.4 space and is based on the approximation:

$B_{24.4} \sim B_{t}+0.3$ mag.
$\begin{figure} \begin{center} \psfig{file=p2f2.ps,height=7.5cm,angle=-90} \end{center} \end{figure}$

Should one wish to convert m_p values into B_24.4 ones over the whole magnitude range covered by the CGCG, one would need to consider the case shown in Fig. 2 in which B_24.4 is the dependent variable plotted as a function of m_p. Bright-end and faint-end transformations were derived here by fitting straight lines constrained to pass though the points (12.0,12.0) and (14.7,14.7) respectively. Both fits were unweighted² and based on Volume I objects only. The m_p-to-B_24.4 transformations obtained were:

for

$m_{p} \leq 12.0$ (with a scatter of 0.42 mag.):