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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Estimating B_t from m_p

**Figure 3:** The differences between m_p and B_t 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 dotted line represents the measured completeness limit of Volume I in B_t space (
$B_t \sim 14.7$ ), whilst the dashed-dotted line represents the CGCG's faint-end limit of

$m_{p} \leq 15.6$ mag.
$\begin{figure} \begin{center} \psfig{file=p2f3.ps,height=7.5cm,angle=-90} \end{center} \end{figure}$

The differences between the CGCG magnitudes and the B_t values of the dataset defined in Paper I are shown in Fig. 3. From this figure it is clear that there is a very large scale error at the bright end, which causes the CGCG to severely under-estimate the luminosities of objects brighter than

$B_{t}\sim11.5$ mag., by of the order of 1.0 mag. with respect to the B_t scale at

$B_{t} \sim 10.0$ mag., and more than 1.5 mag. at

$B_{t} \sim 9.0$ mag. Over the range

$11.5 \leq B_{t} < 14.5$ we find that the difference between the two magnitude scales is relatively constant with a mean m_p-B_t offset of 0.28 mag. However, the scatter of 0.27 mag. is relatively large and the distribution of data points with respect to the line defining the mean offset is certainly not Gaussian. In fact, it actually shows a tendency towards bimodality suggestive of significant systematic differences between the very natures of the m_p and B_t scales.

**Figure 4:** B_t 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 solid curve represents our suggested m_p-to-B_t transformation for Volume I objects (Equation 7), whilst the dashed curve represents Kron & Shane's suggested corrections to Volume I m_p values. Faintward of $B_t \sim 14$ , the two curves are barely distinguishable. The dashed-dotted line represents the CGCG's
$m_{p} \leq 15.6$ cut-off whilst the dotted line represents the measured completeness limit of Volume I in B_t space ( $B_t \sim 14.7$ ).
$\begin{figure} \begin{center} \psfig{file=p2f4.ps,height=7.5cm,angle=-90} \end{center} \end{figure}$

Should one wish to convert m_p values into B_t ones over the whole magnitude range covered by the CGCG, one would need to consider the case shown in Fig. 4 in which B_t is the dependent variable plotted as a function of m_p. An unweighted third-degree polynomial was found to be more than adequate here. The transformation equation obtained, which was based on Volume I objects only but applies to the entire magnitude range of Volume I of the CGCG (with a scatter of 0.45 mag.), was:

B_t= -110.39 + 26.194 m_p - 1.9231 m_p² + 0.048948 m_p³

(7)

As shown in Fig 4, this transformation is in excellent agreement with Kron & Shane's suggested corrections to Volume I m_p values at the faint end, though the agreement is less good elsewhere.

Next Section: Estimating m_p from B_t
Title/Abstract Page: Total Magnitudes of Virgo
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Contents Page: Volume 18, Number 2

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Estimating Bt from mp

Estimating B_t from m_p