3. Variable stars

To select potential variables we employed three methods which are described in detail in Kaluzny et al. (1996). The overall quality of photometry discussed here is similar to the quality of data discussed in Paper I (see Fig. 1 (click here) in that paper). The new data set is, however, by a factor of 6 more extended with respect to the total number of measurements available for a given star. An additional advantage is the fact that on several nights the cluster was monitored continuously for 4-6 hours. In contrast, during the CTIO run the longest session on NGC 288 lasted only about 1.5 hours.

Nine certain periodic variables were identified. This sample includes 6 already known objects and 3 newly discovered variables. A finding chart allowing unambiguous identification of all variables is shown in Fig. 1 (click here).

  
Figure 2: The diagram for RR Lyr star V3. Circles and triangles correspond to moments of minimum and maximum light, respectively

  
Figure 3: Phased V light curves for NGC 288 variables

Table 1 (click here) lists some basic characteristics of the light curves of variables . The periods were determined using ANOVA statistic (Schwarzenberg-Czerny 1996). The light curves used for period determination were expanded by including data reported in Paper I. The time base of these combined light curves equals 5 years. The periods of all variables are firmly established. The period of V3 has been substantially revised in comparison with the value given in Paper I. Moreover, our data indicate the presence of some peculiarities in the light curve of V3. We found it difficult to phase all observations of V3 with the single ephemeris. Examination of the periodogram obtained with ANOVA algorithm (Schwarzenberg-Czerny 1996) reveals the presence of two peaks of comparable height near the frequency . Periodograms obtained for other variables show single peaks at frequencies corresponding to periods listed in Table 1 (click here). It is known that some RR Lyr stars show long-term amplitude modulation. This behavior is known as Blazhko effect (Blazhko 1907). In fact, the amplitude of V3 seems to be very stable, so it is not a Blazhko variable. Our data indicate instead the presence of some phase shifts in the light curve of V3. This is illustrated in Fig. 2 (click here) where we show the diagram for the moments of maxima and minima of light. The deviations were calculated using ephemerides:

The presented diagram can be interpreted as an evidence for increasing period of V3. However, more data are needed to clear up this problem.

The colors listed in Table 1 (click here) are based on a single exposure in the B-band and two bracketing exposures in the V-band. The mean V magnitudes were calculated by numerically integrating the phased light curves after converting them to an intensity scale. Table 1 (click here) gives also equatorial coordinates for variables . A transformation from rectangular to equatorial system was derived based on positions of 50 stars from the list provided kindly by Dr. Guo (Guo et al. 1993). These stars were identified in the outermost parts of the field covered by TEK3 camera. No transformation star could be located in the central part of the cluster. Therefore there is a possibility that the coordinates derived for variables from the central part of NGC 288 suffer from some systematic errors.

 

day h:m:sec

V3 RRc 0.4302 15.14 14.92 0.45 0.28 0:52:40.21 -26:32:28.8

V4 SX 0.07907 17.24 17.04 0.30 0.29 0:52:42.80 -26:34:45.4

V5 SX 0.05107 17.54 17.33 0.46: 0.16 0:52:44.98 -26:33:52.1

V6 SX 0.06722 17.28 17.01 0.41 0.30 0:52:42.40 -26:34:54.6

V7 SX 0.03996 17.92 17.88 0.06 0.28 0:52:41.39 -26:33:59.7

V8 SX 0.04653 17.78 17.74 0.06 0.28 0:52:44.27 -26:33:59.6

V9 SX 0.03937 17.52 17.49 0.05 0.29 0:52:42.88 -26:34:09.6

V10 EW 0.43875 - 19.09 0.38 0.61 0:52:47.86 -26:33:01.9

 

The phased light curves of stars are shown in Fig. 3 (click here). For V3 we plotted only measurements obtained between October 16, 1991 and November 7, 1991. Variables V8 and V9 joint the group of 4 other SX Phe stars identified previously in NGC 288. Object V10 is most probably a contact binary of W UMa type. Figure 4 (click here) shows a CMD of NGC 288 with marked positions of variables . The presented data are based on photometry obtained with the Swope telescope and TEK2 camera. All SX Phe stars occupy positions among blue stragglers. The contact binary V10 is located slightly above the main sequence. We note that only very few binary stars located below turnoffs of their host globular clusters are known for a moment (Mateo 1996). In fact, a prevailing fraction of binaries identified so far in globular clusters are blue stragglers. In contrast, a large fraction of eclipsing binaries known in old open clusters is located on the red side of main sequence (e.g. NGC 188, NGC 2243 and M 67). This apparent difference between globular and open clusters results likely from a selection effect favoring a discovery of only relatively brighter systems in globular clusters.

  
Figure 4: The color-magnitude diagram for NGC 288 with the positions of the variables . The contact binary V10 is marked with a filled square

3.1. Cluster membership of the variables

It was already shown in Paper I that SX Phe stars are likely members of the cluster. That conclusion was based on a good agreement between absolute magnitudes of these stars derived under the assumed cluster membership and absolute magnitudes calculated from the period versus luminosity relation as calibrated by McNamara (1995). The analogical procedure applied to variables V8 and V9 leads to the conclusion that they, too, are likely members of NGC 288.

We have applied the absolute brightness calibration of W UMa type binaries established by Rucinski (1995) to estimate M_V for the newly discovered contact binary V10. Rucinski's calibration gives M_V as a function of period, unreddened color (B-V)₀ and metallicity:

We adopted and E(B-V)=0.04 for NGC 288 (Zinn 1985). We obtained from Rucinski's calibration M_V=4.06 for V10. The formal error of this estimate, resulting purely from uncertainties in Rucinski's calibration, is about 0.3 mag. On the other hand we may estimate an absolute magnitude of the variable under assumed cluster membership. We adopted an apparent distance modulus of the cluster (Pound et al. 1987) and obtained for V10 M_V= 4.17. The fact that the above two estimates of M_V are consistent with each other supports the hypothesis that V10 is a member of NGC 288. We note also that the cluster location on the sky near the South Galactic Pole implies a small contamination of its field by the foreground stars.