Variable stars in the open cluster NGC 6791 and its surrounding field
Key Words.:Stars: starspots – Stars: statistics – Stars: variables: general – binaries: eclipsing – novae, cataclysmic variables – open clusters and associations: individual: NGC 6791
Aims:This work presents a high–precision variability survey in the field of the old, super metal–rich open cluster NGC 6791.
Methods:The data sample consists of more than 75,000 high–precision CCD time series measurements in the band obtained mainly at the Canada–France–Hawaii Telescope, with additional data from S. Pedro Mártir and Loiano observatories, over a time span of ten nights. The field covers an area of arcmin.
Results:We have discovered 260 new variables and re-determined periods and amplitudes of 70 known variable stars. By means of a photometric evaluation of the membership in NGC 6791, and a preliminary membership based on the proper motions, we give a full description of the variable content of the cluster and surrounding field in the range 16 23.5. Accurate periods can be given for the variables with 4.0 d, while for ones with longer periods the limited time–baseline hampered precise determinations. We categorized the entire sample as follows: 6 pulsating, 3 irregular, 3 cataclysmic, 89 rotational variables and 61 eclipsing systems; moreover, we detected 168 candidate variables for which we cannot give a variability class since their periods are much longer than our time baseline.
Conclusions:On the basis of photometric considerations, and of the positions of the stars with respect to the center of the cluster, we inferred that 11 new variable stars are likely members of the cluster, for 22 stars the membership is doubtful and 137 are likely non–members. We also detected an outburst of about 3 mag in the light curve of a very faint blue star belonging to the cluster and we suggest that this star could be a new U Gem (dwarf nova) cataclysmic variable.
|Authors||Nr. of variables||IDs||Notes|
|Kaluzny & Rucinski ((1993)) (KR93)||17||V1–V17||V15B7|
|Rucinski, Kaluzny & Hilditch ((1996)) (RK96)||5||V18–V21 and B8|
|Mochejska et al. ((2002)) (M02)||47||V22–V67 and B4||B4 was previously catalogued by|
|Kaluzny & Udalski ((1992)) as|
|a blue star, but not as variable.|
|Mochejska et al. ((2003)) (M03)||7||V68–V74|
|Kaluzny ((2003)) (K03)||4||V75–V78|
|Bruntt et al. ((2003)) (B03)||19||V79–V100||V85V76; V56V96; V77V88|
|Mochejska et al. ((2005)) (M05)||14||V101–V114|
|Hartman et al. ((2005))||10||V115–V124||Plus 7 suspected variables|
The photometric precision achieved by several ongoing transiting planet searches allows us to extend the census of variable stars down to very low amplitudes and faint magnitudes in selected sky regions. Variable stars are an important source of astrophysical information: from observations of them we are able to test several theories (e.g., evolutionary and pulsational models). Since all stars in an open cluster have essentially the same age, chemical composition and distance, the study of variables which are cluster members can put more severe constraints on the physical parameters. Comparisons can also be made between the variable stars of the cluster and those of the surrounding field.
In this paper, we present the study and the classification of 260 new variable stars that we found in the field of the open cluster NGC 6791, while for 70 already known variables we compare our results with the previous ones. NGC 6791 (= 19 20 53; = +37 46′18″), is a rich and well studied open cluster. It is thought to be the one of the oldest and probably the most metal-rich cluster known in our Galaxy. Its age is estimated to be about 8–9 Gyrs (Carraro et al., (2006); King et al., (2005); Chaboyer, Green, & Liebert, (1999); Stetson et al., (2003); Kaluzny & Rucinski, (1995)); however, the white dwarf cooling sequence indicates a different value, i.e., 2.4 Gyr (Bedin et al., (2005)). The most recent estimates of its metallicity are [Fe/H]=+0.39 (Carraro et al., (2006)), [Fe/H]=+0.47 (Gratton et al., (2006)), and [Fe/H]=+0.45 (Anthony-Twarog et al., (2006)). In this work we adopt for NGC 6791 a distance modulus mag and a reddening =0.09 mag (Carraro et al., (2006)). The cluster is thus located at about 4.1 kpc from the Sun.
Because of its extreme characteristics, NGC 6791 has been the target of many surveys (see Table 1 for a list of publications). Taking into account the fact that in four cases the same stars have two identification numbers (V15B7, V56V96, V76V85 and V77V88) and counting also the stars B4 and B8, the total number of known variable stars in the field of NGC 6791 to date was 123 (plus 7 suspected variables, proposed by Hartman et al., (2005)).
In Sect. 2 below we describe our observations, in Sect. 3 we give details about the methods we employed in the search for variable stars, which are themselves presented in Sect. 3.2. In Sect. 4 we describe the properties of the variable stars, focusing our attention on probable cluster members and some additional peculiar cases. The entire catalogue of variable stars is reported in an Appendix.
2 Observations and data reduction
We surveyed NGC 6791 to detect the transits of extrasolar planets (Montalto et al., (2007)). The campaign covered 10 consecutive nights (from July 4, 2002 to July 13, 2002) and it was characterized by the continuous monitoring of the target on each clear night. Therefore, in addition to the planetary transit search, we could get access to the full variability content at 4.0 d, both for the cluster and the surrounding field. Three telescopes were used:
The Canada–France–Hawaii Telescope (CFHT) in Hawaii equipped with the CFHT12k detector, composed of 12 CCDs of 4128 2048 pixels and covering a field of about 0.32 deg. Owing to the large number of bad columns, data from chip 6 could not be used, so we could get data over a 0.29 deg field;
The San San Pedro Mártir (SPM) 2.1–m telescope equipped with the Thomson 2k detector and covering a field of about arcmin;
The Loiano 1.5–m telescope equipped with BFOSC + the EEV 13001348B detector and covering a field of arcmin.
Table 2 gives details about the length of the observing nights while Figure 1 shows the field of the CFHT survey and the edges of the Loiano and SPM surveys. The coordinates of the edges of our fields are also listed in Tab. 2. The field of the SPM observations is entirely included within chip 9 and the field of the Loiano observations partially covers chips 2, 3, 4, 8, 9 and 10 of CFHT (see Fig. 1). The luminosities of the new variables range from =23.2 mag to mag (near 1 mag above the turn–off); brighter stars are saturated. The calibration of the CFHT, Loiano and SPM data have been performed by using the Kaluzny & Rucinski photometry ((1995)). More details on the data reduction procedure can be found in Montalto et al. ((2007)).
|19 20 258||19 20 363||19 19 237|
|19 21 304||19 21 104||19 22 580|
|37 41′226||37 43′154||37 36′67|
|37 53′427||37 50′31||38 4′212|
3 The identification of variable stars
The intensive monitoring of NGC 6791 allowed us to obtain tens of thousands of photometric time series for stars located in, close to, and far away from the cluster center. We have analysed 73331, 6055, and 2152 light curves obtained from the CFHT, Loiano and SPM telescopes respectively. The CFHT, Loiano and SPM time series are composed of about 250, 60 and 170 datapoints, respectively. The observations, intended to detect photometric transits, were performed in the band only.
3.1 The search for variable candidates
To search for variable stars, we calculated the best “sinusoid plus constant” fit for all light curves (Vanicek, (1971); Ferraz-Mello, (1981)). We evaluated the goodness of the fit by calculating parameters related to the reduction of the initial variance obtained by introducing the periodic term. These parameters are the reduction factor (Vanicek, (1971)) and the coefficient of spectral correlation (Ferraz-Mello, (1981)).
Owing to the huge number of light curves, we need one or more parameters to discover the variability. Toward this goal, we considered the parameter defined as , where is the maximum value of (i.e., the one corresponding to the frequency of the best-fit sinusoid in the Ferraz-Mello method). If a star does not show variability the introduction of a sinusoid does not improve the fit and then is close to zero (no variance reduction) and ; on the other hand, a sine-shaped variability strongly reduces the variance ( close to 1) and hence . The purpose was to use the parameter as a tracer of variability for short-period (i.e., intranight) variability.
To search for long–period variability, we introduced a second parameter, more sensitive to the night–to–night variations. We calculated the mean magnitude and the standard deviation on each night, and after that we calculated the parameter defined as:
where is the peak–to–peak difference and is the mean of the over all nights.
To test the capability of the and parameters to detect variable stars, we prepared a sample containing two types of light curves: 7722 artificial constant light curves (see Montalto et al., (2007) for details) and 70 light curves of already known variable stars which are included in our CFHT field. In Fig. 2 we plot vs. for the light curves of constant stars (small points) and of variable stars (large points). The variable stars are substantially apart from the constant stars and most have . The variable stars with and superposed on constant stars are mostly EA–type stars or irregular stars (e.g., cataclysmic variables). Among variables (i.e., large dots in Fig. 2), the stars with small have short periods ( d), while stars with large have long periods. Therefore, we can conclude that the combination of the and parameters is a good tracer of variability.
To detect the variable stars in our sample of 82,000 light curves we first selected in an automatic way all the stars with , according to the test described above. We thereby reduced the huge initial sample to 6,500 stars. After the calculation of the amplitude spectrum of their time series, we adopted as a second selection criterion a signal–to–noise ratio (S/N) greater than 4.0 around the highest peak in the amplitude spectrum. This procedure allowed us to reduce our sample to 900 stars, i.e., 1.1% of the whole initial sample. Further checks have been made by examining the light curves of a random sample of stars with , large and 3.5S/N4.0, but we did not find any additional variables.
Our approach allowed us to detected hundreds of stars showing peaks in their power spectra at 1.00 cd, at 0.05 cd, or at =0.6 cd. The first two spurious periodicities are common and can be ascribed to small misalignments in the mean magnitudes from one night to the next or recurrent drifts (caused by small color effects, for example) in the intranight light curves. We suggest that the latter one is probably a photometric artefact occurring in some particular cases of blended stars, or stars close to CCD edges, or bad pixels. They have been considered as not reliable enough to infer a physical light variability. In our opinion, only the combination of automatic procedures and visual inspection allowed us to identify the three classes (=1.00 d, =1.6 d, 10 d) of spurious variables in the huge number of 82,000 light curves. In particular, we note that the identification of the whole sample of eclipsing binaries has been confirmed by the application of the box fitting technique (BLS, Kòvacs et al. (2002)), used by Montalto et al. ((2007)) to detect planetary transits.
At the end of the variable star identification, we were left with 330 cases to be characterized. Since we rejected about 2/3 of the sample selected by means of the parameters, we are confident we have not applied overly strict constraints in the candidate selection.
3.2 The cross check with previous surveys of NGC 6791
When comparing our field of view with those of other surveys, we found that 81 known variable stars are included. The CFHT survey failed to detect 45 known variable stars: seventeen stars (V22, V24, V26, V28, V30, V35, V36, V47, V50, V57, V61, V63, V64, V102, V103, V104, V105) are outside the CFHT field of view; 4 stars (V71, V106, V113 and V120) lie between two chips; 23 stars (V1, V6, V13, V19, V33, V39, V45, V49, V54, V56V96, V65, V66, V67, V69, V70, V72, V73, V74, V77V88, V78, V81, V97 and V112) are saturated; and the V76 data are useless.
Among the 81 known variable stars that we have observed, not all of them display variability in our sample: 4 stars (V10, V18, V21, V32) are previously classified as long-period detached eclipsing variables and we did not observed eclipses. We are not able to confirm the period of 15.24 days for V68 (M03), likely because of our shorter time baseline and the small amplitude of this variable (about 0.003 mag in –band, M03). Finally, we cannot confirm the variability of six stars (V20, V79, V84, V98, V99, V116) and of the seven suspected variables found by H05, since our data do not show any trace of variability.
Among the sample of the stars missing from the CFHT field, we identified 22 stars in the Loiano and SPM data sets (V6, V13, V19, V20, V33, V45, V54, V56V96, V65, V66, V67, V70, V71, V73, V74, V76V85, V77, V78, V81, V97, V106 and V113). However, owing to the smaller signal–to–noise ratio (S/N), the small number of datapoints and (in the case of the Loiano data) the limited survey time, we could only confirm the variability of stars V56V96, V66 and V76V85.
Throughout this paper we use the existing names for the already known variables; to identify the new ones discovered in our survey we used the five–digit number assigned by the DAOPHOT package followed by the number of the chip which the star belongs to. Accurate astrometry is provided to identify the stars on the sky. Moreover, all light curves of the variables will be available on CDS.
4 The variable star content of NGC 6791 and its surrounding field
The CFHT measurements are quite precise, thus the light curves are generally very well defined for 4 d. On the other hand, the periods and the shapes are uncertain for 4 d, since the observations only covered 2.5 cycles or less. We refer to Montalto et al. ((2007)) for a full description of the photometric errors. In order to evaluate the precision in the study of the variable stars, we calculated the standard deviations of the Fourier least-squares fits (truncated at the last significant term for the given star) for the 138 light curves having very good phase coverage. The precision was found to be better than 0.010 mag in 73 cases (53%), and better than 0.020 mag in a total of 122 cases (88%), as expected for stars ranging from 16.0 to 22.5. The discussion based is mostly on the CFHT data, which are by far the most numerous, precise and homogeneous; however, for some variables we have used data from Loiano and SPM in a very profitable way. As an example, only the longitude spread of the three observatories allowed us to derive the periods of the eclipsing binaries 00645_10, V107, V12, V109 and of the rotational variable 03079_9.
To proceed in the definition of the variable star content of NGC 6791 and its surrounding field, we calculated the power spectra of the data for all the 330 candidate variables by using the least-squares iterative sine-wave search (Vanicek, (1971)) and the Phase Dispersion Minimization (Stellingwerf, (1978)) methods. Differences have been examined and resolved. The separation into different classes of variable stars has been made on the basis of the light curve parameters (period, amplitude, Fourier coefficients) and standard photometric values (, , ), when available. The period estimates have been refined by means of a least–squares procedure (MTRAP, Carpino (1987)) and appropriate error bars have also been calculated. At the end of the process we get six pulsating stars with d, three irregular variables, three cataclysmic variables (CVs), 31 detached or semi–detached eclipsing binaries, 29 contact binaries, 90 rotational variables, 167 stars showing clear night-to-night variability on timescales too long for periods to be determined over our 9.2–d baseline. We adopt preliminary membership probabilities based on proper motion measurements kindly provided to us by K. Cudworth (private communication) for 35 stars. Moreover, for three new variable stars we adopted membership probabilities based on proper motions performed by Bedin et al. ((2006)) (hereafter B06, see Figure 3).
For the other stars, we consider their position in color–magnitude diagrams (CMDs), and their distance from the center of the cluster to infer whether they belong to the cluster (for EW–Type stars we also utilize the -- relation of Rucinski ((2003)). Toward this end, we plotted the radial distribution of all stars in Fig. 4. We see that at a distance of 10′ from the center of the cluster, the stellar density becomes near constant (about 21 star/arcmin). Thus, we adopt the value of 10′ as the external limit of the cluster and we consider “likely non-members” the variables located farther from the cluster center.
4.1 Pulsating variables
The main characteristics of our variables are listed in Tab. 3 and their light curves are shown in Fig. 5. The classification as High–Amplitude Delta Sct (HADS), SX Phe, RRc or RRab stars is based on the parameters of the Fourier decomposition (Poretti, (2001)). In all cases, the Fourier parameters are on the progressions described by the different classes. We note that our period for V123 is quite different from that given by H05 (0.107 d). Error bars on the periods are in the range 1–6 d.
Both RR Lyr variables are too faint to belong to NGC 6791. Since they have =17.21 (03653_3) and =18.28 (00345_1), their distance moduli greatly exceed that of the cluster.
This is also true for the very faint and short-period stars 00311_7 (=23.17) and 00224_10 (=21.72); therefore, it is more likely that they are Pop. II stars. On the other hand, using the relation given by McNamara ((2000)), we get distance moduli of 14.50 and 13.78, respectively, for V123 and 01497_12. These distance moduli and the distance from the cluster center (12′ and 22′, respectively) suggest that they do not belong to the cluster, though they are not very far from it. Therefore, they are probably Pop. I stars and hence High Amplitude Scuti stars.
Moreover, there are several variables whose light curves are very similar to those of Cepheid variables; the Fourier decomposition of some light curves (in particular the large amplitude ones, i.e., 00913_5, 01659_8, V46 and 01431_10, but also 01606_11, 02285_10, 00122_4 and 03056_3) yields parameters typical for Cepheid light curves. However, most of these variables are quite faint and the Period–Luminosity relation for Cepheids (Tammann et al., (2003)) yields distances in the range 39-171 Kpc. It is difficult to say whether these stars are nearby rotational variables (see below) in the Milky Way or very distant pulsating variables. For our present purposes, these stars have been included among the rotational variables listed in the Appendix.
The puzzling nature of all these apparently distant stars (i.e., the Cepheid-like ones, the RR Lyr and the faint SX Phe variables discussed above) deserves further investigation by means of spectroscopic and/or kinematic data.
4.2 Irregular variables
Table 3 also lists three irregular variables: these stars lie on the middle Main Sequence and are all located less than 3′ from the cluster center; thus we suggest that they belong to the cluster. V92 and V83 were previously defined as “periodic variables” by B03. Indeed, we noticed fast variability in our light curves (Fig. 6), but, more noticeably, the mean magnitude is also changing from night to night. The long periods given by M03 are not able to explain either the short- or the longer-timescale variability; actually, we could not detect any periodic term. We also detected no trace of periodicity in V93 (Fig. 6); we suspect that the periods given by M05 and B03 are spurious, since they are close to 1.0 d (0.99 and 0.94 d, respectively) and they could be produced by the irregular fluctuations.
We can conjecture that these variables are eruptive variables observed in a quiescent phase, in which rapid and/or slow changes with smaller amplitude can be observed; they resemble the case of V15 (see Sect. 4.3). We have no reliable indications about the membership probabilities.
4.3 Cataclysmic variables
As regards V15: M03 and M05 detected variability over the range of 3 mag and observed outbursts of about 0.5-1.0 mag; from our side, we could see a 0.15–mag variability in our light curves (Fig. 6), corresponding to the quiescent phase. V15 is very probably a NGC 6971 member, since the Cudworth proper-motion membership probability is very high (98%).
Both the position of the faint blue star 06289_9 in the two-colour diagram and the shape of its light curve (Figure 7) strongly suggest that this star could be a new cataclysmic variable (U Gem-type, dwarf nova). Moreover, we know that this object is a cluster member (see Figure 3). The star shows an outburst of about 3 mag and, though we did not observe the entire brightening, we would highlight that the magnitude was still increasing on the first night; thus we are able to say that the maximum brightness was reached immediately after.
We can estimate the orbital period, , and the recurrence time, , from the decay time, = [days mag] and the amplitude, (Warner, (1995), equations 3.5, 3.1, respectively). Assuming for and the values 3.330.50 d and 2.870.31 mag respectively, we find =2.541.41 h and =13.910.6 d. However, our light curve (Fig. 7) seems to rule out values shorter than 8 d.
The variable B8 shows a large-amplitude light curve (Fig. 7) over a quite short 7 d time span. The cataclysmic nature of B8 has been confirmed spectroscopically by Kaluzny et al. ((1997)) who also notes that B8 exhibits red colour while in a low state.
Following the same procedure used for 06289_9 and assuming =1.30.3 d mag for B8, we find =2.971.63 h and =11.48.5 d. The value is compatible with the 7 d periodicity (Fig. 7). A membership probability is not available for B8. However, using the equations 3.3 and 3.4 after Warner ((1995)), we obtain =8.060.68 mag and =4.970.42 mag. In turn, these values give two estimates for the distance modulus of B8, i.e., 13.82 0.68 mag and 14.20 0.42 mag. We note that the first is in agreement with the distance modulus of the cluster. Kaluzny et al. ((1997)) assumed that B8 belongs to the cluster, finding =5.2 mag and =7.6, i.e., values very similar to ours. B8 is located at 4′ from the center, and we can only conclude that the membership of this star is very probable.
4.4 Contact binaries
The simplest cases of eclipsing systems are the contact binaries (also named W UMa systems); they show short periods and continuous variability and therefore can be easily recognized and classified. We detected 29 of these variable stars; they have 0.40 days and very well defined light curves. The complete list and the light curves are reported in the Appendix. Tab. LABEL:ewbel lists the stars likely belonging to NGC 6791 (see above); their light curves are shown in Fig. 8. The very short periods and the secondary minima occurring at indicate binaries with circular orbits, as is also the case for stars with small amplitudes (in 7 cases we have amplitudes less than 0.20 mag: V3, V4, V5, V8, V23, V40 and 01441_8). The average error bar on the period estimates is of the order of 4–5 d.
However, we note that the stellar surfaces are not homogeneous since the maxima are often at different heights. Therefore, binarity and activity are probably combined here. In particular, the shape of the light curves of V4 (comparing RK96, M02 and our data) and V7 (comparing K93 and our data) have changed a lot; we suppose that stellar spots strongly modify the light curves. Proximity effects are also responsible for the large amplitudes observed for 01434_3 (Fig. 8, last panel) and 00766_5. We also found different periods for V118 (0.306321 d) and V124 (0.320143 d) compared to H05.
As for membership, the probabilities provided by Cudworth are 78%, 98% and 98% for V3, V4 and V5, respectively. Indeed, they are very close to the cluster center (45, 21 and 28, respectively).
We suggest that 01441_8, V118, V8, V117 and V7 are also contact binaries belonging to NGC 6791. To further verify this hint, we calculated their distance by using the -- relation given by Rucinski ((2003)); they turn out to have distance moduli (13.28, 13.28, 13.48, 13.28 and 13.18, respectively) very similar to that of the cluster (13.35).
Moreover, these stars are located at similar angular distances from the cluster center (62, 72, 71, 72 and 63, respectively). Figure 9 shows how the distance modulus of the cluster is in better agreement with those of the stars we proposed as cluster members than with those of the previously known members. Their positions in the CMDs (Fig. 10, filled circles) are similar to those of stars in the sample with 7.5 whose parallaxes have been determinated by HIPPARCOS (Rucinski, (2003)). We also note that most of the cluster members are near the turnoff point.
4.5 Eclipsing variables
In the cases of detached or semi–detached eclipsing binaries the classification and membership tasks are different from the case of contact binaries. Tab. LABEL:tabea lists the systems for which we could determine periods; their light curves are shown in Fig. 11. We still have short-period cases where we can reconstruct the complete light curve, as for the classical examples of Lyr variables (V29, 01558_5 and 00331_3). V9 is a more complicated Lyr system in which spots produce maxima with different heights. Indeed, it has been classified as an RS CVn variable by M05 and B03; they also observed a “shift of the modulation wave” from 1995 to 2002.
We note that our period for V119 is quite different from that given by H05 (0.1133 days); the new period makes this star an intermediate case between semi–detached and contact systems. Error bars on the periods in Tab. LABEL:tabea are d for 1.0 d, d for 2.0 d and a bit larger for 3.0 d.
Some variables show very sharp eclipses and out-of-eclipse variability due to different levels of stellar activity (05736_9, 00645_10, V109, 01393_1, V11 and V107; for the period of the latter star we prefer the longer of the two values given by M05).
In many cases we observed one eclipse only and we cannot give any value for the period, unless it has been given in the previous studies, as for the cluster member V80 (86% on the basis of the Cudworth membership probability). We also note that the amplitude we observed in V80 is much larger than that reported by B03.
To establish the membership of these eclipsing systems is not an easy task, since binary effects should be taken into account when considering colors and magnitudes. However, on the basis of the distance from the cluster center and their position in the CMDs, we can argue that V60, 02461_8 (both single-event eclipsing binaries), 05736_9, V29 and 00645_10 are very probable members. This hint is corroborated by the membership probabilities for V60 and 02461_8, which are 91% and 88% respectively.
The special cases of V9 and B4 deserve attention. V9 is the binary closest to the center and its membership probability is 82%. However, it looks a very evolved object in the CMD; its period (3.2 d) and activity (see above) are also more typical for a Main Sequence star. Therefore, its membership is very doubtful.
The Cudworth membership probability for B4 is only 40%, but in the CMDs B4 belongs to a little “clump” of very blue stars. This location is in agreement with the results of Liebert et al. ((1994)) and therefore B4 is likely a blue extanded horizontal–branch star belonging to NGC 6791. The star is classified by M02 and M03 (who consider it a non–member) as an eclipsing binary, but we note that the light curve could also result from a rotational modulation.
Other possible members are: V107, 00331_3, V109 and V11, considering that they are within 64 radius from the cluster center. The location in the CMDs of the eclipsing binaries belonging to NGC 6791 is shown in Fig. 10 (triangles).
4.6 Rotational variables
We found 89 variables whose light curves are characterized by small amplitude (usually less than 0.10 mag) and continuous variability. It is difficult to ascribe such variability to contact binaries undergoing grazing eclipses, since they should be less numerous than those having partial eclipses, since grazing eclipses occur only for a particular orientation of the orbital plane. Our hypothesis is that in most cases this variability results from spots carried by the stellar rotation; under this hypothesis, a large variety of light curves can be produced. Of course, we cannot rule out that a small fraction of these light curves might be actually generated by grazing eclipses.
The complete list of the rotational variables and their light curves is given in the Appendix. Here we discuss some examples. If the inclination of the rotational axis causes the progressive disappearance of the largest spots, the light curve displays continuous variation, which could be sine shaped in the simplest cases (a fraction of the spots is always visible; it can also produce Cepheid–like variability, as in the 001606_1 case, Fig. 12), or with a standstill (the hot or cold spots totally disappear; 00513_2 in Fig. 12) or, more commonly, it can be distorted by other spots besides the largest ones (00471_12 in Fig. 12). In cases of very active stars, a secondary wave also occurs (01175_5 in Fig. 12). Since the second wave often covers less than half of the period, these rotational variables can be distinguished from eclipsing binaries; we also note that the amplitude ratio between the first and second waves can be very different.
Also in the three cases in which the full amplitude is larger than 0.10 mag (V2, 02006_1 and 07483_9) rotational effects explain the observed features better than eclipses. For example, the light curves of V2 (=0.273 d) and 01298_5 (=0.586 d; see Fig. 12) show typical eclipsing binary behaviour, but the amplitudes, the periods, and, mainly, the asymmetries are more typical of a rotational effect. The case of 02270_11 is different (Fig. 12). Its light curve is very similar to that of a contact binary, but it does not repeat exactly, and unusual scatter is observed through the cycle. We also note that this non-repetitive behaviour of the light curves, due to the spot activity, is the reason why several variables stars show residual standard deviations higher than expected.
Our periods for V34, V37 and V38 are approximately half of those given by M02, since these authors classified these variables as ellipsoidal ones; the large amplitudes (0.18, 0.06 and 0.13 mag) are more in favour of a variability resulting from large spots, rather than the purely geometrical effect of tidally distorted stars. We also note that V37 did not show any flare activity similar to that reported by M02 during our survey. We have also revised the classification of V16, considered an eclipsing binary by M02 and M03.
We count 33 rotational variables in the 10′–circle (i.e., 0.105 star/arcmin) centered on the cluster, while we have 56 variables in the remaining 924–arcmin area (i.e., 0.061 star/arcmin). We have color indices ( and/or ) for 48 stars; 33 of them have a radial distance less than 10′ from the cluster center. We can confirm the membership for 6 stars having proper motion membership: V16, V38, V42, V48, V53 and 03079_9. We have no photometric indices for V41; however, it is at only 2′ from the cluster center and its Cudworth probability membership is 77%. Therefore, we consider V41 a member. For V14 we have the opposite situation because this star is at 1′ from the cluster center and its positions in the CMDs agree very well with a membership, but the proper motion measurements rule out that it can be a cluster member (0%) (see Figure 13, V14 is displayed as a starred dot). As mentioned by M03, the positions of V17 in the CMDs are unusual. Other variables located below the subgiant branch like V17 were found in the open cluster M67 (Mathieu et al., (2003)) and in the globular cluster 47 Tuc (Albrow et al., (2003)). Probably these objects (named “red stragglers” or “sub-subgiant branch stars”) are the result of some kind of mass exchange between the members of a binary system.
Putting the rotational variables without proper motion measurements on the CMDs we could infer that 8 stars are located on or close to the MS (represented with filled circles in Fig. 13); thus we suggest that these 8 stars belong to the cluster as well. Among the variables at greater distances, for three stars (01149_2, 01122_4 and 00513_2, all located between 11′ and 13′) the membership is doubtful, since their position in the CMDs is unclear. The other stars show apparent magnitudes and/or color indices too discrepant to be considered active MS stars belonging to NGC 6791.
When considering the variables without color indices, only two (V41 and 01874_2) are at less than 10′from the cluster center. We know that V41 is a probable cluster member (membership probability 77%), but, at the moment, we have no valid reason to consider the other star as a member.
Table LABEL:rotbel lists the rotational variables we suggest as cluster members. The error bars on the period are d for 1.0 d, d for 1.02.0 d, d for 2.05.0 d; periods longer than 5.0 d are tentative. Figure 13 shows the CMDs with the rotational variables belonging to the cluster (Tab. LABEL:rotbel) clearly indicated. We rejected as cluster members 16 stars out of 32 located within 10′ from the cluster center; i.e., we considered them to be stars of the Galactic field. We note that the resulting density of the Galactic field (0.051 star/arcmin) superimposed on the cluster is in good agreement with that of the surrounding galactic disk field (0.061 star/arcmin, see above), especially considering that Poisson statistics supply uncertainties around 0.01 on the density values.
The stellar rotation and the activity level are both expected to be small for single stars as old as NGC 6791. Therefore we suggest that the rotational variables belonging to the cluster are likely short–period binaries, whose rotational velocity and activity level have been enhanced by the tidal synchronization.
4.7 Long-period variables
We detected numerous stars having different mean magnitudes on the different nights. Their behaviours are more diversified than those of the stars we considered as spurious on the basis of their close similarities. The resulting power spectra are dominated by terms at very low frequencies, corresponding to periods often much longer than 10 d. These periods cannot be evaluated in a precise way, being comparable or, more frequently, longer than our time baseline. Therefore, we can only argue that these stars are variables, either in a periodic or in an irregular way. Since we detected many spotted stars, it is quite obvious to think that most of these long-period variables are spotted stars having a rotational periods longer than 10 d. The mean amplitude of these stars is about 0.02 mag, except for 5 stars whose amplitude exceeds 0.1 mag.
Among the long-period variables, we used the Cudworth probabilities to establish the membership of 18 stars. In order to roughly estimate the membership of the remaining long-period variables we checked their locations in the CMDs, in the cases where at least one color is available. We suggest that 5 stars are likely members of NGC 6791: 02138_8, 01610_9, 04392_3, V75 and 02268_10 (see Figure 14). They lie along the MS or the red-giant branch and, furthermore, they are all located at distances smaller than 85, from the cluster center. Looking at the position of the variable V76 V85 (memberships: 97%) in both CMDs, we suggest that this star could be similar to the “sub-subgiant branch” star V17. In Figure 15 we show its light curve and those of the 5 stars that we suspect to belong to the cluster. Table LABEL:lptab lists the long-period variables we suggest as cluster members; the entire sample is listed in the Appendix.
Our wide-field survey of NGC 6791 for the planetary-transit search allowed us to discover 260 new variable stars. When considering the membership probabilities given by Cudworth and B06, 13 of them belong to the cluster and one star (09831_9) is not member. On the basis of the distances from the cluster center and the positions in the CMDs, we suggest that another 11 stars are likely members, for 22 stars the membership is doubtful, and 137 stars are likely non-members. No photometric or kinematic data are available for 76 stars.
The variable star content of the cluster is very similar to that of the surrounding Galactic environment: in both samples we find rotational variables, contact and eclipsing systems. Contact binaries and rotational variables belonging to the cluster have the same characteristics as those located in the surrounding Galactic field. No evidence of pulsating variables has been found in NGC 6791, but this is not surprising, since it is a very evolved cluster and stars located in the instability strip or hotter pulsators have already left the MS.
The discovery of the new cataclysmic variable 06289_9 in addition to B8 and V15 adds another peculiarity to NGC 6791, making it unusual among the open clusters.
Acknowledgements.We are grateful to Kyle Cudworth kindly providing us with preliminary cluster membership probabilities. We also acknowledge Prof. Antonio Bianchini for his suggestions about the characteristics of the candidate cataclysmic variable and Giovanni Carraro for his useful comments. We thank the referee, Dr. J. Kaluzny, for his detailed report and useful comments. This work was funded by COFIN 2004 “From stars to planets: accretion, disk evolution and planet formation” by MIUR and by PRIN 2006 “From disk to planetary systems: understanding the origin and demographics of solar and extrasolar planetary systems” by INAF.
Appendix A List of identified variables
This Appendix includes the full list of the identified variables, separated according to our classification:
Into the tables, for each star we give the name (a five–digit number followed by the chip number which the star belongs), coordinates, photometric data (always the mag, color when available), informations about the variability (, period, amplitude), distance from the center (in arcmin) and finally the numerical value of the Cudworth’s membership probability (reported in the column ’Memb.’).
In most cases, when membership probabilities were not available, in the same column the label “m” means that we retain the star belonging to the cluster, while ’m?’ and “nm” mean “uncertain membership” and “likely non–member” respectively. The label “nd1” means that no photometric data are available to advance hypothesis about the membership, but the star is located nearer than 10′ from the center of the cluster. Finally “nd2” means that no photometric data are available and the star is located further than 10′ from the center; in this case we strongly suggest that the star does not belongs to the cluster.
|V29||EB||19.354796||37.751386||20.00||1.23||1.61||k||69.012||0.43662||0.22||m||4.9||Light curve distortion|
|at maximum light|
|V107||EA||19.355068||37.761553||17.97||0.93||1.00||k||64.433||3.27||0.24||m?||5.0||Minima at the very|
|beginning of the night.|
|01731_10||EA||19.357813||37.672819||19.27||0.67||0.80||k||64.783||0.34||nm||9.1||Minimum at the very|
|beginning of the night.|
|01740_7||EA||19.330623||37.638774||21.30||69.007||0.33||nd2||14.8||Maybe another minimum|
|02045_12||EA||19.381420||37.712211||17.16||68.030||0.26||nd2||24.0||Other minimum at 63.39|
|02241_11||EA||19.371472||37.827819||19.21||68.823||0.53||nd2||17.0||Maybe another minimum|
|00346_5||EA||19.365356||37.929481||20.16||65.014||0.17||nd2||15.5||Other minimum at|
|at 68.410. Short in time.|
|00631_12||EA||19.375473||37.649140||17.92||68.753||0.30||nd2||20.9||Minimum at the very|
|beginning of the night.|
|01511_10||EA||19.357145||37.689907||19.74||1.45||1.86||k||0.50||nm||8.1||Two Minima at night extrema.|
|V80||EA||19.351799||37.791061||17.90||0.94||k||67.607||4.631||0.10||86||2.9||Shallow eclipse ?|
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