4 Discussion

We turn now to a discussion of the nature of those stars identified as photometric variables, using the locations of these stars in the colour-magnitude diagram as a way of organising the discussion.

4.1 Stars below the cluster main sequence

We have found eight variables located below the cluster main sequence. In 7 cases, our light curves show only irregular variations and, except for one star (star K), the amplitudes of the variations are small (see Table 5). The available proper-motion membership probabilities for these stars confirm non-membership in the cluster (see Tables 1 and 2). Our data provide very limited information about the nature of the observed variability. However, at the suggestion of the referee, we have closely examined the light curves for indications of RS CVn behaviour. Magnetic activity causes many RS CVn systems to be variables, due to spots on the surface of the active star(s) that rotate in and out of view. This usually results in periodic photometric variability, with amplitudes ranging from hundredths to tenths of a magnitude, typically among stars with spectral type late-F to mid-K (e.g. Strassmeier 1992).

We do not observe periodic variability in the light curves of these stars. However, we cannot definitively exclude the possibility that these are background RS CVn systems, as spots on some RS CVn can be variable on timescales of days or even less than a single rotation period. Interestingly, we note that our light curve for star 2823 (S 845), while not strictly periodic, does show weak evidence for possible periodic behaviour (with a period of 2.9 days) for a portion of our lightcurve. Perhaps this is a field RS CVn with a rapidly evolving spot geometry. We note that our light curves for two other stars (stars 4795 and 4804) show some evidence for flaring (i.e. rapid, short-duration rises in brightness), but such flaring is evidently somewhat rare among RS CVn systems (e.g. Henry & Newsom 1996).

While no proper-motion membership information is available for the one periodic variable below the main sequence (star 2426, see Sect. 3.3), the observations of Orosz et al. (2002, in prep.) indicate that this star is an Algol-type binary and a non-member.

4.2 Stars on the cluster main sequence

In Sect. 3.3 we mentioned six stars situated on the cluster main sequence that show some evidence for periodic variability. If these tentative periods are upheld, they may be related to the stellar rotation periods (due to, e.g., starspot modulation). In addition, we have found another 21 stars on the cluster main sequence (not including the X-ray sources discussed in Paper I) whose light curves show non-periodic variations at a statistically significant level in at least one filter (Table 5). The amplitudes of variability exhibited by a few of these stars is remarkably large (few tenths of a mag; see Fig. 1). Our data do not shed much light on the nature of this variability. Perhaps the variations we observe have their origin in magnetic activity on the surfaces of these G and K stars.

Fifteen of these 27 stars are high-confidence variables, showing statistically significant variability in more than one filter. Of these, 11 are known proper-motion members of the cluster (see Sect. 3.2). As discussed in Sect. 3.2, photometric variability at the levels to which our survey is sensitive ($\sim$1-2%) is evidently rare among the main-sequence members of M 67, with an occurrence rate of at most a few percent in those observed by us.

   
4.3 Stars on the cluster binary sequence

Photometric variables on the cluster binary sequence are interesting because such variability can point the way to the discovery of interacting binary systems. If periodic, the observed variability may be related to the dynamics of the binary system. Three of the variables for which we found a photometric period are situated on the cluster binary sequence.

The two most notable variable stars on the cluster binary sequence in our observations are the two W UMa (contact binary) systems, stars 3665 and 2976, which have already been introduced in Sect. 3. The former (ET Cnc) was discovered by Gilliland et al. (1991) while the latter is newly discovered here. ET Cnc has a primary-eclipse depth in V of 0.16 mag, and a secondary-eclipse depth of 0.1 mag. The unequal eclipses in the observed light curve potentially indicate that the system is in poor thermal contact or is semi-detached (see also discussion in Paper I on the X-ray source W UMa S 1036).

We have discovered that star 2976 (S 757) is a strong candidate for being a W UMa system in M 67. Sanders (1977) gives this star a proper-motion membership probability of 95%. The most likely period from our time-series analysis is 0.1800 days, which we interpret as the half-period of 0.3600 days, assuming two eclipses of very similar depth. Spectroscopic radial-velocity measurements will be needed to confirm this period. Nonetheless, a period of 0.36 days places this star on the W UMa period-colour relation (e.g. Rucinski 1993) very well, given its (B-V) colour of 0.61. We note that Sandquist & Shetrone (2001) have also recently reported detection of eclipses in this star with a period of $P \sim 0.4$ days.

The discovery of this new W UMa variable brings the total number of such contact binaries in M 67 to four. We can estimate the frequency of W UMa systems in M 67 by comparing this number to the number of proper-motion cluster members from, e.g., the study of Girard et al. (1989). The Girard et al. study includes 367 proper-motion members (probability $\ge$75%) among stars with V<15.5 in a region $34' \times 42'$ about the cluster centre. This yields a W UMa frequency of 4/367 = 1.1%, which is consistent with the contact-binary frequency in other Galactic open clusters of $\sim$1% (Rucinski 1998). We note that while the new W UMa discovered by us is contained in the Girard et al. study, one of the three previously known systems is not (ET Cnc is a bit too faint with V=15.8), even though it is within the spatial boundaries of that study. And the spatial area of the present study is somewhat smaller than that of the Girard et al. study. As noted by Rucinski (1998), a detailed accounting of contact-binary statistics is made difficult because of these differences in depth and spatial coverage of different studies. Even so, the W UMa frequency in M 67 is evidently of order 1%.

Figure 5: V-band light curve for the spectroscopic binary, star 4619 (S 1508).

In addition to these two contact binary systems, we have also discovered periodic variability in another star on the cluster binary sequence, star 2703 with a period of 3.6 days. While our data permit us to say little about this star, its location in the colour-magnitude diagram and its periodic light curve make this a prime candidate for follow-up spectroscopic monitoring. Perhaps the observed photometric period corresponds to the binary orbital period. No membership information is presently available for this star.

Four stars (3348, 3780, 4415, 4654) situated on the cluster binary sequence did not evince periodic variability in our data, but nonetheless showed statistically significant variability. Star 4415 (S 1506) is a proper-motion member and was monitored by Mathieu et al. (1986) for radial-velocity variations, but no indication of binarity was found ($\sigma=1$ km s^-1 in 8 observations spanning 2 years); perhaps this is a wide binary. Star 4654 (S 1492) is a proper-motion non-member, and in any case its photometric variability is only significant in one filter. The other 2 stars, both of which are "high-confidence" variables, deserve spectroscopic follow-up to determine if they are interacting binary systems. Star 3780 (S 1264b) is a proper-motion member, but we note that its photometry might be affected by the presence of a close neighbor. Star 3348 does not presently possess cluster membership information.

Figure 6: V-band light curve for the giant star 4859.

Finally, we have found four stars (3578, 4337, 4341, 4619) showing statistically significant variability that are also known spectroscopic binaries (R. Mathieu, private communication). Star 4337 (S 1224b) has an orbital period of 12.44 days and an eccentricity of 0.03. Star 4341 (S 1224a) has an orbital period of 726 days, and an eccentricity of 0.3. For star 3578 (S 2209a) no orbital solution has yet been derived. The light curves of these three stars show no evidence for periodicity on the orbital or pseudo-synchronous periods (Hut 1981). However, we caution that our photometry for these stars may be contaminated by close neighbors. Star 4619 (S 1508), situated at the cluster turnoff, was found by Mathieu et al. (1990) to be a spectroscopic binary with an orbital period of 25.9 days and an eccentricity of 0.44. The BVI light curves of this star do not show evidence for periodic variability on the spectroscopic orbital period or the pseudo-synchronous period of 11.2 days. This star's V-band light curve is shown in Fig. 5.

4.4 Giant stars

Five of the variables reside on the red giant branch of the cluster colour-magnitude diagram. These variables show relatively low levels of variability, with rms $\sim$0.02 mag. We note that for three of these five stars, the observed variability is statistically significant in only one of the filters observed (i.e. they are not "high-confidence" variables). For the other giant stars included in our observations, we can place 3$\sigma$ upper limits on variability of $\sim$0.015 mag, based on the limiting photometric precision of our photometry for the brightest sources.

Star 3775 (S 1264a) is a spectroscopic binary, and should be monitored further to study any possible connection between the binary orbit and photometric variability. While a "high-confidence" variable, we caution that our photometry is suspect due to the presence of a close neighbor. Mathieu et al. (1986) monitored the giants 3726 (S 1279), 4039 (S 1293), and 3949 (S 1305), but found no evidence for radial-velocity variations ( $\sigma \leq 0.5$ km s^-1in about 15 observations spanning more than 10 years, for all three stars). Thus we consider it unlikely that the variability, if real, is related to binarity. Henry et al. (2000) found a large fraction of low-amplitude ($\sim$0.01 mag) photometric variables among a sample of 187 G ($\sim$25%) and K ($\sim$50%) giants. For the group of giants of type earlier than K2 - which includes our four variable giants - they exclude both radial pulsation and rotational spot-modulation as the origin of the brightness variations. Henry et al. suggest that non-radial, g-mode pulsations most likely give rise to the variability.

Interestingly, star 4859, the other high-confidence variable on the giant branch, shows a peculiar light curve, with rapid, short-duration dips (Fig. 6). Unfortunately, being situated in the far outskirts of the cluster, no membership information is available for this star.

4.5 Blue stragglers

Two of the blue stragglers in M 67 not detected in X-rays show statistically significant photometric variability in our data. Photometric variability among blue stragglers is particularly interesting in light of the uncertain evolutionary status of these objects. Photometric variability may be a clue to the presence of a binary companion (e.g. in the case of the eclipsing blue straggler S 1082, see Goranskij et al. 1992; van den Berg et al. 2001) or may provide information on the stellar structure of the stars (in the case of oscillations, see discussion in Gilliland & Brown 1992).

Star 3905 (EX Cnc or S 1284) is a spectroscopic binary that shows low-amplitude photometric variations with a period of $\sim$1.3 hours first discovered by Gilliland et al. (1991), Gilliland & Brown (1992), and Simoda (1991). The B and V light curves we obtained during the highly sampled run 4 show a similar behaviour. These short-timescale variations are probably related to the star's position within the $\delta$ Scuti instability strip and not to the orbital period of 4.2 days (Milone & Latham 1992a).

Star 3858 (S 1263) was monitored spectroscopically by Milone & Latham (1992b), but no orbit was determined. Gilliland et al. included this star in their search for solar-analog oscillations, but observed an rms scatter of only 0.005 mag. Simoda (1991) similarly found no evidence for photometric variability, but Kim et al. (1996) do report a high dispersion in the light curve of this star. The light curves that result from our observations also display a large scatter (up to 0.03 mag), and this variability is statistically significant in all three bands. While our results and those of Simoda and Kim et al. can be explained in terms of sensitivity differences of the studies, the Gilliland et al. result suggests that the variability observed by us and by Kim et al. does not persist at all times.