3 Analysis and results

In this section we describe the search for new variable stars and analyse the new data on known variables. Frequency analysis was carried out using PERIOD98 (Sperl 1998), which calculates amplitude spectra and offers simultaneous least-squares fits of multiple frequencies, with corresponding amplitudes and phases. Following Breger et al. (1993), we require a peak in the amplitude spectra to have a signal-to-noise (S/N) ratio of at least 4 to be taken into consideration, the noise level being calculated in the residual amplitude spectrum in the region where the peak was found. We are aware that because of our relatively small data sets, the 4$\sigma$ criterion may not be strictly applicable and the suggested frequency solutions are often not unique due to poor spectral windows. The data are, however, sufficiently abundant to serve their purpose: to detect new variables and determine time scales and approximate amplitudes. Only for stars where the frequency solution gave a good fit to the data will this fit be shown.

The cluster colour-magnitude diagram (CMD), based on data from SBL, is shown in Fig. 2. The positions of the newly detected variable stars discussed below are indicated using the identification number of SBL, which we will also use in the discussion of the individual variables. The brightness and colours of the variables, following SBL, are outlined in Tables 2 and 3. These values are not averaged over the pulsational periods found below and may be slightly off depending on the amplitudes of the variations. We note that SBL found an average value of the reddening, E(B-V), of 0.466 mag, but values for individual stars could amount to as much as 0.7 magnitudes.

Figure 2: The colour-magnitude diagram of NGC6231, based on data from SBL. The positions of the detected variable stars are indicated. The dashed line is the $\delta$ Scuti instability strip from Breger (2000). The $\gamma$ Doradus stars are expected to be found near the cool border of the $\delta$ Scuti instability strip (Handler 1999), while the SPB and $\beta$ Cephei stars are found among stars brighter than V=12.

   

Table 3: New and confirmed bright variable stars in NGC6231, based on the 2000-data. Tentative frequency solutions are given, see Table 2 for explanations of the entries. $a_{\it b}$ is the (semi-) amplitude of the strongest frequency in the b-band.

SBL	BVF	Segg.	BL95	V	B-V	f1	f2	f3	f4	f5	f6	S/N	$a_{\it b}$	Notes
0226	20	253	31	9.580	0.165	14.9	1.7	4.5				13.8	6.9	$\beta$ Cep star
0268	26	282	158	9.752	0.168	8.4	2.6					6.9	3.1	$\beta$ Cep star
0275		249	19	11.888	0.244	1.65	0.74					14.2	12.8	new SPB?
0303	37	261	67	10.281	0.190	10.1	11.0	1.3	11.5	0.2	12.7	22.4	10.1	$\beta$ Cep star
0394	39	209		10.599	0.196	1.4	1.7					8.1	5.5	new SPB?
0456	36	104	127	10.174	0.226	3.1	3.9	0.1				10.4	7.7	new $\beta$ Cep star
0461	40	294A	89	10.745	0.210	0.4	0.5					10.4	5.9	new SPB?
0486	22	238	45	9.603	0.173	0.4	0.3	14.6	13.8	10.4		12.3	3.2	$\beta$ Cep star
0515	49		129	11.198	0.257	5.3	3.5	0.8	7.4			7.1	4.7	new $\beta$ Cep star?
0653	28	110	11	9.803	0.223	8.3	0.9					6.0	4.0	$\beta$ Cep star
0712	23	150	124	9.601	0.194	9.9	8.3	10.6				11.2	6.0	$\beta$ Cep star

3.1 The faint stars

For the faint-star data sets (1998-1999), we visually inspected all light curves for variability and thereby selected stars suitable for further investigation. For these stars we checked their position on the chip (close to a bright star, close to the edge, etc.), calculated amplitude spectra and compared overlapping data sets. Only stars for which the evidence for intrinsic variability was found convincing (and significant on the 4$\sigma$level) were taken as being variable and will be discussed below. For some of these stars, the evidence for variability is also present in the 2000-data, although these light curves have much higher noise levels (as they were optimised for the bright stars) and poorer sampling as a result of the acquisition of four-colour photometry - as illustrated in Fig. 3.

The detected faint variable stars, along with preliminary frequency solutions, are presented in Table 2. In Figs. 4-16 we show amplitude spectra and light curves for the variables. Of the light curves, we only show enough data to support our claim of variability, the amount depending on the time scales of the variations. For each variable star we briefly discuss the observed variations and, when possible, give a preliminary classification. However, data obtained more recently will lead to a more precise and definite classification and will be included in forthcoming papers.

One result from BVF is of great interest here. BVF suggest that all cluster stars between 14$^{\rm m}$ and 16$^{\rm m}$ are PMS stars. This is based on the fact that basically all stars in this magnitude range are found above the ZAMS, without following its shape. It is exactly in this magnitude range that we detect our new faint variable stars. We will, therefore, be cautious in discussing the evolutionary status of these stars, which should all be investigated in further detail - including determination of cluster membership. We will now discuss the new faint variable stars individually.

Figure 3: Comparison between the deep 1998 data (lower panel) and the 2000-data for one of the faint variable stars (SBL0455).

SBL0306 is a short-period variable star with an amplitude of a few mmag. The variability is clearly visible in the light curves (Fig. 4), but a part of the data is contaminated by bleeding from bright stars. The data are not sufficiently abundant to pin down a good frequency solution and the frequencies given in Table 2 do not describe the light curves very well. One frequency (9.8 cd^-1), however, is recovered in the 2000-data. The star is situated right in the $\delta$ Scuti instability strip and this, along with the periods and amplitudes, leads us to suggest that it is indeed a $\delta$ Scuti star.

Figure 4: Amplitude spectrum and V light curves of SBL0306. Data were obtained during 8 nights, of which 2 are shown.

SBL0332 is also clearly variable, with periods of the order of days and amplitudes of several hundredths of a magnitude. It is found at the cool side of the $\delta$ Scuti instability strip, but further to the red than expected for a $\gamma$ Doradus star. It could, in principle, be a $\gamma$ Doradus star affected by intracluster differential reddening, but two frequencies (above 4 cd^-1) are higher than what would be expected for a $\gamma$ Doradus star (below about 3 cd^-1, see e.g. Kaye et al. 1999). Four frequencies describe the variations well and the residual amplitude spectrum, shown as the insert in Fig. 5, is flat after pre-whitening with the four terms and the residual noise level is less than 1 mmag.

Figure 5: Amplitude spectrum and V light curves of SBL0332. The residual amplitude spectrum after pre-whitening with four frequencies is shown, on the same scale, in the insert in the upper panel. All data are shown.

SBL0417 was found to be a PMS star by SBL and we find that it is also variable. The variability is displayed in Fig. 6. Only one frequency can be found, but it does not describe the variability completely. If the variations are caused by pulsations, it could be a PMS $\gamma$ Doradus star, given the time scale of the variations of about a day. As this is known to be a PMS star, the variations may be irregular, but the present data set is not sufficiently abundant to determine this.

Figure 6: Amplitude spectrum and V light curves of SBL0417 - a variable PMS star. Four out of ten nights of data are shown.

SBL0432 is a short-period variable showing effects of beating between several frequencies (Fig. 7). The periodogram does not yield a clear-cut frequency solution, but indicates, along with the time series, that the variations occur on two time scales. As given in Table 2, we find three frequencies in the region 30-40 cd^-1 and two below 5 cd^-1. The star is found near the main sequence, in the $\delta$ Scuti instability strip, and the evidence that it is a $\delta$ Scuti star is rather convincing - especially considering the beating light curve, typical for a low-amplitude $\delta$ Scuti star. The additional presence of low-frequency variations makes it a very interesting object.

Figure 7: Amplitude spectrum and V light curves of SBL0432. The residual amplitude spectrum after subtracting the 5 terms in Table 2 is shown, on the same scale, as the insert in the upper panel. Two out of nine nights of data are shown.

SBL0455 was suggested to be a $\delta$ Scuti star in BL95. This is very clearly confirmed by our data, as shown in Fig. 8. The light curves suggest the presence of several frequencies (beating), which is confirmed by the frequency analysis. We find 3 frequencies, but more are probably present. The amplitude of the frequency at 18.9 cd^-1 apparently increased from 3.1 mmag in 1998 to 10.7 mmag in 2000, although this result should be taken with caution because of the much lower quality for the fainter stars in the 2000 data set. The star is positioned off the main sequence in the CMD: if it is a single star and a member of the cluster, it is a PMS star.

Figure 8: Amplitude spectrum and V light curves of the $\delta$ Scuti star SBL0455. Two out of nine nights of data are shown.

SBL0508 is variable (Fig. 9) on two time scales: about 4 days and 6-8 hours. The star is positioned to the cool side of the $\delta$ Scuti instability strip, off the main sequence. We find 3 frequencies with amplitudes between 4 and 12 mmag, but more data are needed on this object.

Figure 9: Amplitude spectrum and V light curves of SBL0508. Five out of nine nights of data are shown. The insert shows the residual amplitude spectrum, on the same scale, after subtracting three frequencies.

SBL0595 is a short-period variable with a typical $\delta$ Scuti type light curve. It is also found in the $\delta$ Scuti instability strip and it most likely belongs to this class. The amplitude spectrum is complicated and the light curve is somewhat noisy (Fig. 10) compared to the low amplitude of the variations. The variability is clearly present, but can be represented by several different frequency solutions. We find 3 frequencies near 40 cd^-1, but these merely indicate the time scale of the variations.

Figure 10: Amplitude spectrum and V light curves of SBL0595. Two out of 19 nights of data are shown.

SBL0598 shows relatively long-period variations (in the $\gamma$ Doradus range) and amplitudes of only a few mmag. Some of the light curves can be seen in Fig. 11. We find two frequencies which describe the light curve reasonably well. The star is positioned to the hot/blue side of the $\delta$ Scuti instability strip and it is probably not a cluster member, even given the significant amount of differential reddening present over the cluster (see SBL). SBL0598 is SAAO 2 - BL95 labels the foreground $\delta$ Scuti star with this number, but that bright foreground object is in fact SAAO 3.

Figure 11: Amplitude spectrum and V light curves of SBL0598. Note the low amplitude of the variations. Data were obtained on 20 nights, of which nine are shown.

SBL0628 shows variability on a time scale of days and with relatively high amplitude (Fig. 12). We attempted to fit the light curves with two frequencies, but the fit deviates from the light curves on several nights. The dominant frequency (1.2 cd^-1) is present in the D90 and D154 data individually, while for the secondary frequency two different aliases are highest in the two data sets. This star could be a $\gamma$ Doradus star, also considering its position in the CMD.

Figure 12: Amplitude spectrum and V light curves of SBL0628. Data were obtained on 20 nights, of which 9 are shown.

SBL0636 is variable on a very low level. Figure 13 shows that mmag variations are present, both in the data obtained with the D90 (middle panel) and with the D154 (lower panel). In the amplitude spectrum, the variations are not obvious, but fitting 3 frequencies ranging from about 2 to 9 cd^-1 leaves a clean residual in the amplitude spectrum, and the frequency solution seems to fit the light curves rather well. The star is situated in the area of the CMD where the $\gamma$ Doradus stars are expected to be, but only one of the frequencies is in the range expected for the $\gamma$ Doradus stars.

Figure 13: Amplitude spectrum and V light curves of SBL0636. The insert shows the pre-whitened data (3 frequencies) on the same scale. Data were obtained during 19 nights of which 2 are shown (in the upper panel one from the D90, in the lower panel one from the D154)

SBL0646 is very similar to SBL0636 with regard to amplitudes and frequencies of the variations. Both stars are also situated close to each other in the CMD. Light curves and the amplitude spectrum can be seen in Fig. 14. The middle panel has data from the D90, the lower panel data from the D154. We find 3 frequencies to be present between 2 and 4 cd^-1. This star might be a $\gamma$ Doradus star.

Figure 14: Amplitude spectrum and V light curves of SBL0646. Useful data were obtained during 14 nights, of which 2 are shown.

SBL1949 is a very faint star (V=18.28), but slow variations on a time scale of days are clearly present in the light curves, resulting in low-frequency peaks in the amplitude spectrum (Fig. 15). Two frequencies describe both the amplitude spectrum and the light curves fairly well.

Figure 15: Amplitude spectrum and V light curves of SBL1949. The insert shows the amplitude spectrum, on the same scale, after subtracting 2 frequencies. Data were obtained during 18 nights of which 10 are shown.

ASK0171 is clearly variable, but was not observed by SBL or BVF. The variations occur on a time scale of a day. We have no colour information on this star, but the V-magnitude is approximately 16$^{\rm m}$. It may be a $\gamma$ Doradus star based on the periods and the brightness, but colour data are clearly needed on this object. The star is too faint to have reliable photometry in the 2000 uvby data sets.

Figure 16: Amplitude spectrum and V light curves of ASK0171. Data were obtained during 16 nights of which 10 are shown.

Positions of all the faint variable stars in the colour-magnitude and colour-colour diagrams presented by SBL were checked using their photometry. Only the PMS star SBL0417 deviates from the majority of stars in these diagrams.

3.2 The bright stars

For the 2000-data optimised for the ninth magnitude stars, uvby photometry is available. One night from 2000 June yielded data of comparatively low quality and has been rejected. For the stars discussed below, there are thus 8 nights of data available in the analysis, covering in total about 300 datapoints per filter. In order to search for new variable stars, we visually inspected the light curves and calculated amplitude spectra for the different bands. A star was deemed worthy of further investigation if signs of variability could be seen in the light curves from the individual filters and/or when there was excess power at the same frequencies in the corresponding amplitude spectra. The relatively small amount of data resulted in a poor spectral window (which can be assessed from the dominant frequency near 15 cd^-1 in the upper panel of Fig. 17) and the suggested frequency solutions, given in Table 3 for the stars discussed below, should again be regarded as preliminary. All the stars discussed below, except SBL0275 for which no membership information is available, were classified as likely members of the cluster by BVF (from whom we have also adopted the spectral classifications). For the known $\beta$ Cephei stars we show, as an example, data for a single star only. For several of those stars, we find evidence for long-period variations superimposed on the faster $\beta$ Cephei pulsations. Such variations, which were also noticed by BS83, may well be real and should be investigated in further detail when more data are available.

SBL0226 (V945Sco, B1V + B1V) is a known $\beta$ Cephei variable and double-lined binary. We find three frequencies, of which the first and an alias of the third, match the two corresponding frequencies in BS83. However, these frequencies do not describe the light curves completely. The amplitude spectrum and examples of light curves, representative for the quality of data on the other known $\beta$ Cephei stars as well, are shown in Fig. 17.

Figure 17: Amplitude spectrum and b light curves of SBL0226.

SBL0268 (B2V + B2V) is also a known $\beta$ Cephei variable and a double-lined binary. We find two frequencies, one of which is the same as in BE85. Variations at higher frequencies are visible in all four filters, but are not detected in our data because of a too low S/N.

SBL0275 is a new SPB candidate. The star is situated very close to the ZAMS, possibly inside the SPB instability strip (to be verified at a later stage). The detected low-frequency variations are consistent with such a classification (see e.g. Pamyatnykh 1999). The evidence for the variability is shown in Fig. 18.

Figure 18: Amplitude spectrum and b light curves of SBL0275.

SBL0303 (B2IV) is a known $\beta$ Cephei variable and probable binary (García & Mermilliod 2001). It has several frequencies around 10 cd^-1, and of the five we detect in that region, four correspond to the frequencies (or their 1 cd^-1 aliases) from BS83. We find two peaks in the low-frequency region, of which one is close to a 1 cd^-1 alias of the single low-frequency found by BS83.

SBL0394 (B2IV-V) is a new SPB candidate. The low-frequency variation is clearly seen in Fig. 19, but aliases of the two frequencies listed in Table 3 can also fit the variation.

Figure 19: Amplitude spectrum and b light curves of SBL0394.

SBL0456 is, based on the position in the CMD and the shape of the light curves (Fig. 20), a new $\beta$ Cephei candidate. The frequency solution does not match the light curves completely; variations on a shorter time-scale than those listed in Table 3 may be present in the light curves, but the data presently available are insufficient to detect such variations.

Figure 20: Amplitude spectrum and b light curves of SBL0456.

SBL0461 (B1.5V) is a new SPB candidate. The long-period variations are visible in the light curves in Fig. 21, but should be checked with new and more abundant data.

Figure 21: Amplitude spectrum and b light curves of SBL0461.

SBL0486 (V964Sco, B1V(n)) is a known $\beta$ Cephei variable; BE85 find the three frequencies 11.3835, 14.7983 and 18.0741 cd^-1, of which we find aliases of the two first. We also find evidence for two low-frequency variations with periods around 3 days.

SBL0515 (B1V(n)) is variable with several frequencies in the range 3-8 cd^-1, but aliasing gives several possible frequency combinations. The frequencies and amplitudes suggest a $\beta$ Cephei classification, but this seems inconsistent with the position of the star in the CMD, as it is much fainter than the other $\beta$ Cephei stars. This could suggest that it is a non-cluster member, although BVF find it to be a likely member. It is a very interesting target, but new data are clearly needed.

Figure 22: Amplitude spectrum and b light curves of SBL0515.

SBL0653 (B1V) is a known $\beta$ Cephei variable. We find an alias of the BS83 oscillation frequency at 9.27 cd^-1. The low frequency variation at 0.9 cd^-1 is not stable: if we pre-whiten using aliases to the 8.3 cd^-1 frequency, the highest low-frequency peak is no longer located at 0.9 cd^-1 or aliases to this value. There is no indication of an oscillation at 16.4 cd^-1 as found by BS83.

SBL0712 (V920Sco, B1V(n)) is a known $\beta$ Cephei variable with 3-4 frequencies found around 9 cd^-1. A low-frequency variation of 1.69 cd^-1 (14.2 h) appears to be present just below the detection threshold, similar to what was found in BS83 ( $16.63\pm0.12$ h). García & Mermilliod (2001) list the star as a possible binary.

3.3 Possible variable stars and eclipsing binaries

Two possible $\beta$ Cephei stars from BE85 were in the field of our 2000-observations. In both cases variability is seen, but detections cannot be made at a significant level.

SBL0353 (S289, SB1) shows variability in the frequency region 10-15 cd^-1, but the amplitudes are below one mmag (b) and are not significant in our data. It is a possible $\beta$ Cephei star according to BE85, but more data are needed to confirm this. Similar variations are seen in all four filters, but in all cases with amplitudes below the detection threshold. If the variation is periodic it is in the frequency range 10 to 15 cd^-1 with amplitudes up to 1 mmag.

SBL0437 has a possible oscillation near 15 cd^-1 and perhaps also variations at low frequencies. It is a possible $\beta$ Cephei star according to BE85, but although our data confirm that variability may be present, the data currently available do not allow a detection at the 4$\sigma$ level in the amplitude spectrum.

No new detections of eclipsing binary systems result from the data, but parts of eclipses were observed for two known EBs.

SBL0505 (S224, SAAO100) is an eclipsing O9 IV binary (Levato & Morrell 1983, BL95) for which García & Mermilliod (2001) determine new orbital elements ( P=2.453087 d). We observed a rising and a descending branch of two individual minima, but could not determine the times of mid-eclipse from the data.

SBL0521 (S232, SAAO040) is a single-lined eclipsing binary (B0.5 V) observed spectroscopically by Levato & Morrell (1983) and García & Mermilliod (2001) and photometrically by BL95. We observed a part of an eclipse with an 0 $\stackrel{\rm m}{\textstyle .}$15 minimum at HJD 2451740.6702. The full primary eclipse is estimated to last more than 8 hours. A weaker minimum of 0 $\stackrel{\rm m}{\textstyle .}$05 on JD 2449500.51 was reported by BL95. The phase coverage is still insufficient to determine a period.

SBL0334 (S272, SAAO105) is a possible eclipsing binary for which BL95 observed a single sharp minimum of 0.05 mag. Their suggested period of 1.6 d is unlikely, as we have better than $90\%$ phase coverage for that period, but see no eclipses. A modulation of the light curve may be present, but the currently-available data are inconclusive.