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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Our galaxy samples and CGCG completeness

**Table 1:** Completeness of the CGCG within the VPC survey area as a function of B_t, see text for definitions of Galaxy-samples C_I and C_II
	Volume I			Volume II
B_t range	N^CGCG_{C_I}(B_t)	N^VPC_{C_I}(B_t)	completeness	N^CGCG_{C_II}(B_t)	N^VPC_{C_II}(B_t)	completeness
(mag.)	(objects)¹	(objects)²	(%)	(objects)¹	(objects)²	(%)
B_t < 14.0	57	57	100	11	11	100
$14.0 \leq B_t < 14.5$	16	16	100	3	4	75
$14.5 \leq B_t < 15.0$	9	12	75	4	4	100
$15.0 \leq B_t < 15.5$	10	14	71	2	4	50
$15.5 \leq B_t < 16.0$	17	25	68	0	0	N/A
$16.0 \leq B_t < 16.5$	10	41	24	0	8	0
$16.5 \leq B_t < 17.0$	2	51	4	0	9	0

overall total	121	216	56	20	40	50

Notes: (1) The number of CGCG-listed objects in Galaxy-sample C_I or C_II (where a subscript I denotes Volume I and a subscript II denotes Volume II). (2) The total number of VPC-listed objects in Galaxy-sample C_I or C_II including objects omitted from the CGCG (where a subscript I denotes the Volume I survey area and a subscript II denotes the Volume II survey area). This quantity is also the galaxy-sample size on which the corresponding completeness ratio is based.

The Virgo Photometry Catalogue (VPC) of Young & Currie (1998), which is complete to

B_J₂₅=18.0 mag. over the whole of its survey area of 23 deg.², can be used in order to investigate the completeness of Volume I of the CGCG to B_t = 17.0 as a function of B_t. It is however, only of limited use in investigating the completeness of Volume II of the CGCG, because most of the VPC survey area lies within the area of sky covered by Volume I. Note that no parts of the VPC survey area lie exterior to those [much larger] areas of sky covered by Volumes I and II of the CGCG and that all CGCG-listed objects lying within the VPC survey area are also listed in the VPC. For the purpose of studying the CGCG's completeness as a function of B_t, we required a large and complete galaxy sample including every object down to a specified limiting B_t value (that was considerably fainter than the faint-end limit of the CGCG) within a clearly defined area of the sky. Precise B_t values were not essential for every galaxy, and especially at the bright end (where the CGCG could be expected to be 100% complete) some B_t estimates of lower accuracy could be tolerated. However, for the purposes of investigating the CGCG's magnitude scale, only CGCG-listed objects with reliable photometry could be invoked. In order to make optimum use of the data available, we therefore defined two overlapping samples of galaxies for the area of sky covered by Volume I and a further two for the area of sky covered by Volume II: hereunder C_I & M_I and C_II & M_II respectively. Each Sample C was defined as the set of all galaxies to be used for the CGCG-completeness study, whilst each sample M was defined as the set of all galaxies to be used for the CGCG magnitude-scale studies. Each Sample C comprised all galaxies listed in the VPC (regardless of whether they are listed in the CGCG or not) which we found to be brighter than B_t=17.0; approximate B_t values having been derived for those objects lacking B_t measurements in the VPC or in Tables 2 and / or 3 of Paper I. For 10 Volume I objects; VPC 64, 99, 159, 171, 242, 379, 505 863, 878 & 953; B_{J_t} values are listed in the VPC but B_t values are not¹, and so the approximation:

$\begin{displaymath} B_{t} \sim B_{J_t} + 0.35(B-V) \end{displaymath}$

(1)

(with (B-V) set to 0.8 mag.) was used. For the outstanding high surface-brightness VPC objects for whom Young & Currie's (1998) B_J-band photometry was saturated, and for whom the VPC therefore does not list B_t or B_{J_t} values, rougher approximations were necessary. These were based on the B_J₂₅ (B_J-band isophotal magnitude measured to the

$\mu_{B_J} = 25.0$ mag.arcsec^-2 isophote) values listed in the VPC, but most of which were for the bright objects in question based on various sources of magnitude measurements external to the VPC (that are not necessarily of high accuracy and will be investigated in future papers in this series). For these galaxies, we obtained estimates of B_t from Equation 1 (also with (B-V) set to 0.8 mag.) and:

$\begin{displaymath} B_{J_t} \sim B_{J_{25}}-0.35 {\rm\hspace{1.5mm}mag.} \end{displaymath}$

(2)

(this latter offset being the VPC's mean B_J-band extrapolation). This was of course equivalent to:

$\begin{displaymath} B_{t} \sim B_{J_{25}} - 0.07 {\rm\hspace{1.5mm}mag.} \end{displaymath}$

(3)

and enabled the CGCG's completeness to be quantified as a function of B_t, as documented in Table 1. The galaxy VPCX 50 was also taken into consideration using Equation 3. The total number of VPC galaxies brighter than

$B_{t} \sim 17.0$ was found to be 256. Of these, 216 were found to lie within the area of the sky covered by Volume I of the CGCG, whilst only 40 were found to lie within the area covered by Volume II. Galaxies not listed in the CGCG were flagged and divided into would-be Volume I and would-be Volume II objects. The brightest sample object found to be omitted from Volume I is VPC 800 (

$B_t \sim 14.7$ ), whilst the brightest object omitted from Volume II is VPC 283 (

$B_{t} \sim 14.4$ ). Each Sample M on the other hand, comprised only of CGCG objects for which reliable B_t measurements are listed in the VPC or Tables 2 and / or 3 of Paper I. Note that not all of the objects listed in Table 3 of Paper I lie within the VPC survey area, but that all of these objects lie within the areas of sky covered by Volumes I and II of the CGCG. At the faint end, it was found that 34 galaxies for which B_t values are listed in the VPC correspond to CGCG objects. As all of the 58 objects listed in Tables 2 & 3 of Paper I are listed in the CGCG, the combined sample comprised of 92 galaxies in total, of which 90 were Volume I objects whilst only 2 were Volume II ones. For any galaxy of B_t < 17.0 then, the following rules determined which subset of each Samples C and /or M it belonged to; the overlap region between each Sample C and M being denoted $C \cap M$ , and subsets of C and M not overlapping with M and C respectively being denoted

$C \backslash M$ and

$M \backslash C$ respectively.
$\bullet$ Reliable B_t available from VPC or Tables 2 and / or 3 of Paper I?
NO: Member of

$C \backslash M$ .
YES: $\bullet$ Galaxy listed in CGCG?
NO: Member of

$C \backslash M$ .
YES: $\bullet$ B_t available from Table 3 of Paper I?
NO: Member of $C \cap M$ .
YES: $\bullet$ Galaxy outside VPC survey area?
NO: Member of $C \cap M$ .
YES: Member of

$M \backslash C$ . Bearing in mind that the brightest object found to be omitted from Volume I of the CGCG is of

$B_t \sim 14.7$ , on the basis of Table 1 we can say that Volume I of the CGCG is only about 70% complete over the range

$14.75 \leq B_{t} < 15.75$ . Furthermore, we find that late-type galaxies are heavily over-represented faintward of the CGCG's completeless limit. In fact, out of the 43 VPC galaxies for which

$14.5 \leq B_{t} < 16.5$ but which were omitted from the CGCG, only 4 are listed as irregulars, probable irregulars or spirals in the VPC and one as a BCD. Apart from a further 6 whose types are unknown, the remaining 32 are all early-type objects (29 ellipticals, 2 lenticulars and 1 probable lenticular). We take this to be evidence that Zwicky et al.'s selection criteria were heavily morphology dependent at the faint end, at least for Volume I. Unfortunately, our galaxy sample is not extensive enough to be able to confirm this finding with confidence for Volume II.

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Our galaxy samples and CGCG completeness