3 I-band photometry

The largest database on I-band photometry is that of [13, Caldwell & Coulson (1987, hereafter CC).] However, they list magnitude-mean V-I values instead of the traditional intensity-mean. [26, Gieren et al. (1998)] mention they add a correction of -0.03 mag to the magnitude-mean I to estimate the intensity-mean. However, by comparing some entries in Gieren et al.'s Table 3 to the data in CC it turns out that they actually added +0.03 mag.

In view of this, I decided to perform a literature study and to calculate whenever possible the intensity-mean $\mbox{$<I\gt$}$ magnitude, as well as the intensity-mean <V>-magnitude (all V magnitudes are on the Johnson system) for the same dataset as the available I-band data, from the original sources. The intensity-mean magnitude is calculated according to [38, Tanvir (1997):]

$$<m\gt\; = -2.5 \log \sum_{i=1}^{n} \,0.5 \,({\phi}_{i+1}-{\phi}_{i-1})\, 10^{-0.4\,m_i}$$ (1)

where ${\phi}_i$ and m_i are the phase and magnitude of the i-th epoch after folding with the period, and with ${\phi}_{n+1} = 1 +{\phi}_1$ and ${\phi}_0 = {\phi}_n$.

Johnson-I photometry was transformed to Cousins-I using the formula presented in CC. Washington photometry was transformed following [14, Coulson et al. (1985).] If necessary, the phases of the individual observations were calculated, and/or the phases ordered, in order to apply Eq. (1).

The intensity-mean <I>, and <V>-<I> are presented in Table 1. It contains 283 datasets for 189 stars. Also listed are the number of data points in the light curve used, the reference to the data, and the original photometric system (C = Cousins, J = Johnson, W = Washington). In three cases (l Car, $\beta$ Dor and S Nor) the data of [15, Dean et al. (1977)] and [16, Dean (1981)] were combined beforehand to calculate the intensity-means. The data in Table 1 does not contain all known I-band datasets, but is intented to contain all published datasets with photometry in the Cousins system, and all datasets in any system when no Cousins photometry exists, except datasets which contain very few (of order 5 or less) data points. When more than one entry exists for a star, the first one may be considered the "best'' one, which is a subjective balance between the original photometric system (Cousins being preferred over other photometric systems to avoid possible systematic effects due to the transformation) and the number of points in the light curve.

From this dataset I find that the difference magnitude-mean minus intensity-mean is 0.0070 $\pm$ 0.034 in the I-band taking all datasets; 0.0048 $\pm$ 0.033 taking the 193 datasets which contain $\ge$ 20 data points in the light curve and -0.0025 $\pm$ 0.036 taking the 41 datasets which contain $\ge$ 40 points in the light curve. The correction value of 0.03 used by [26, Gieren et al. (1998)] is therefore not confirmed.

One can ask the question if there are any systematic differences between the datasets. For example, there are 26 stars for which both original datasets in the Johnson and Cousins system are available, and with $\ge 10$ points in the light curve. The difference between the "transformed Johnson'' - "Cousins'' datasets is -0.007 $\pm$ 0.019 in <I>, and -0.004 $\pm$ 0.026 in <V> - <I>. There are 24 stars with (at least) 2 datasets in the Cousins system, and $\ge 10$ points in the light curve. The difference "first dataset - second dataset'' is 0.0009 $\pm$ 0.0120 in <I> and $-0.008 \pm$ 0.014 in $\mbox{$<V\gt - <I\gt$}$. This suggests that there are no systematic differences due to the transformation from the Johnson to the Cousins system, and among the different observations in the Cousins system themselves, and that the spread in <I> and <V>-<I> are consistent with the typical error quoted in a single observation which is of order 0.01 magnitude.

The intensity-mean <V> (only the "best'' dataset in the case of more than one entry) was also compared to the corresponding value listed in the Fernie et al. database. In 23 cases the difference was more than 0.03 mag. However, in 9 of those cases there are fewer than 10 points in the light curve and this difference is probably due to the poor sampling of the light curve. Since the <V> and <I> have been calculated from the same dataset, the <V>-<I> magnitude should still be reliable. In 13 other cases the difference in magnitude is between 0.03 and 0.052, which seems large but still acceptable. There is one odd case, and that is RW Cas where the difference in <V> is 0.101 mag and in <B>-<V> 0.1 magnitude. The [41, Welch (1997)] database indicates that the dataset of [33, Moffett & Barnes (1984)] is the largest single dataset for this star, and it was used by me, as it also is the only dataset containing I-data. From this datset I find <V> = 9.218, and <B>-<V> = 1.196. The Fernie et al. database lists <V> = 9.117 and <B>-<V> = 1.096. From the combined data set of [7, Berdnikov (1992, 1993)] with 63 points in the light curve I obtain <V> = 9.229 and <B>-<V> = 1.243, in agreement with the magnitudes from the [33, Moffett & Barnes (1984)] data. This leaves little doubt that the data used in the Fernie et al. database is in fact from [33, Moffett & Barnes (1984),] however listed with an off-set of 0.1 mag in <V> and <B>-<V>, possibly a typographical error. Table 2 contains data for which I-band data exists but no intensity-mean values could be derived. Two stars come from [, Arellano Ferro (1984)] who does not list the original individual observations. The values listed are in the Cousins system transformed from the original Johnson photometry. All the other stars are listed in CC but the original data could not be traced. Very likely there are in unpublished material quoted by CC. The values listed are magnitude-means on the Cousins system.

Table 3 lists the Type I HIPPARCOS Cepheids without I-band data.

  

Table 2: Cepheids without intensity-mean I-band data

  

Table 3: Cepheids without I-band data