The WFCAM multiwavelength Variable Star Catalog (Corrigendum)
^{1}
Departamento de Física Teórica e ExperimentalUniversidade Federal do Rio
Grande do Norte, 59072970
Natal, RN, Brazil
email: ferreiralopes1011@gmail.com
^{2}
Instituto de Astrofísica, Pontificia Universidad Católica de
Chile, Av. Vicuña Mackenna 4860,
7820436 Macul, Santiago, Chile
^{3}
Millennium Institute of Astrophysics, Santiago, Chile
^{4}
SUPA (Scottish Universities Physics Alliance) WideField Astronomy
Unit, Institute for Astronomy, School of Physics and Astronomy, University of
Edinburgh, Royal Observatory, Blackford Hill, Edinburgh
EH9 3HJ,
UK
^{5}
Gemini Observatory, Colina El Pino, Casilla 603, La Serena, Chile
Key words: stars: variables: general / infrared: stars / dust, extinction / stars: formation / techniques: photometric / errata, addenda
The multiplicative expression on the (see Sect. 3.1, Eq. (6)) variability indices does not properly correct for different numbers of epochs in different filters. The expression can be written in the following form: (1)where s>j. is the Bessel correction while 1 /n_{s} is the factor for the mean value. The first parameter (right side) is incorrect and introduces a bias related to n_{s} values when s> 2. Additionally the Bessel correction needs to be repeated for each additional correlation term, as we show below. Indeed, the weight of this bias must increase with both s and n_{s}. Therefore these indices must be replaced by following, (2)where Γ is given by, (3)where u_{ijs} is the ith epoch of filter j_{s}. This new index is the mean value of the correlations and it is not biased for n_{s}; additionally it reduces to for s = 2.
As discussed above, the analysis of for s> 2 in Fig. 5 is incorrect since the index is biased by the extra first term such that the index is relatively reduced in value at larger values of n_{s}. A corrected version is shown in Fig. 1, which shows the distribution of the unbiased variability indices () as a function of K magnitude. These indices present a similar range of values for different values of s. Additionally, we can observe that the centre of the distribution (m) decreases with increasing s, whilst the fullwidth at half maximum increases. This is caused by an asymmetry in the number of combinations that produce negative values compared to positive values with increasing s. Real correlated variations return positive values, whereas random or semicorrelated noise is much more likely to return negative values. This leads to a better discrimination between variable and nonvariable stars as s increases. For instance, we can select about 90% of the WFCAM Variable Stars Catalog in a sample 2.2 times smaller when s = 4 than that when s = 2.
Fig. 1 variability indices versus the Kband magnitude for the initial database, for three values of s: s = 2 (upper panel), s = 3 (middle panel), and s = 4 (lower panel) on the lefthand side, with histograms of each distribution on the righthand side. The red line marks a Gaussian fit and we record the fullwidth half maximum and centre in each righthand panel. 

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Fig. 2 Distribution of versus variability indices, for orders 2 (left) and 3 (right). The C1 and C2 sources are indicated by red and green circles, respectively. 

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The shape of the cutoff surfaces in Fig. 6 for is unbiased in the magnitude dimension, but the n_{s} dimension is biased by . The selections of variable star candidates were performed for as well as . and are unbiased and they may provide a complete selection of variable stars candidates. Meanwhile, the incorrect factor in for s> 2 does not provide a strong bias in our selection because the selection is performed using the cutoff surfaces which are modified to take the mean effect of the bias into account. However, indices
should be replaced by indices, since the surfaces can correct for the average bias factor but there is be an increased variance in that could be reduced by using .
Figure 2 shows the corrected plot of panchromatic variability indices versus flux independent (see Fig. 8). As expected, the overlap at large values of remains.
© ESO, 2015
All Figures
Fig. 1 variability indices versus the Kband magnitude for the initial database, for three values of s: s = 2 (upper panel), s = 3 (middle panel), and s = 4 (lower panel) on the lefthand side, with histograms of each distribution on the righthand side. The red line marks a Gaussian fit and we record the fullwidth half maximum and centre in each righthand panel. 

Open with DEXTER  
In the text 
Fig. 2 Distribution of versus variability indices, for orders 2 (left) and 3 (right). The C1 and C2 sources are indicated by red and green circles, respectively. 

Open with DEXTER  
In the text 