Mon. Not. R. Astron. Soc. (2004) doi:10.1111/j.1365-2966.2004.08418.x

Variable stars in the field of the old open cluster NGC 188

X. B. Zhang, L. Deng, X. Zhou and Y. XinNational Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China

Accepted 2004 September 20. Received 2004 September 20; in original form 2003 December 3

ABSTRACTWe report the results of a new time-series charge-coupled device (CCD) photometry survey ofvariable stars in the field of the old open cluster NGC 188. In a 1◦ field covering the cluster,a total number of 27 variable stars, including eight new variables, were detected during thissurvey. The periods, the classifications as well as the membership of the newly discoveredvariables are discussed. Among those, two are definite member stars and one is a probablemember star of the cluster. They are all W UMa binaries. Thus the total number of W UMastars belonging to the cluster is increased to 10. A peculiar variable (V26 = GSC 4619−450)is found from the field. It is very likely a new large-amplitude β Cephei-type variable with apulsating period of about 0.1331 d. Revised basic data are given for the known variables in theprogramme field. The period of V8 is refined as 5.2096 d. The variability of V11 is confirmedby this observation. It is suggested to be a very probable FK Com-type variable with a periodof about 1.2433 d. Finally, the relative frequency of the occurrences of W UMa stars and thedistribution in the cluster are discussed. The result supports the hypothesis of mass segregationin NGC 188.

Key words: binaries: eclipsing – stars: variables: other – open clusters and associations:individual: NGC 188.

1 I N T RO D U C T I O N

This work is a contribution to the on-going BATC (Beijing–Arizona–Taipei–Connecticut) programme of searching for short-period variables in open clusters based on the wide-field charge-coupled device (CCD) survey. The main goal of this programmehas been described by Zhang et al. (2002, hereafter Paper I).

NGC 188 is an intensively studied old open cluster partly becauseof its richness of W UMa binaries and other types of variable stars.Early in the 1960s, there were four W UMa stars known in thecluster (Hoffmeister 1964; Efremov et al. 1964). Kaluzny & Shara(1987) discovered seven more variables, including three new WUMa systems in the cluster through a CCD photometric survey. In2000, we obtained wide-field time-series CCD photometry of thecluster and discovered eight new variables (Paper I), including aW UMa and an Algol-type eclipsing binary that are identified ascertain members of the cluster. This makes the number of W UMastars in NGC 188 to be eight. Very recently, Kafka & Honeycutt(2003) reported the discovery of a number of new faint variables inthe central area of NGC 188 through photometric monitoring of thecluster with the WIYN 3.5-m telescope.

In addition to the eight certain variables reported in Paper I, wehave detected several probable variable candidates from the 2000observations. In 2002, improved new time-series CCD photometrywas undertaken for NGC 188. The aim was to check the variabilityof these probable variable candidates and to search for more newvariables in the field of NGC 188, so that the catalogue of variable

stars can be made as complete as possible. In this paper, we shallpresent the results of the new CCD photometry. Sections 2 and 3describe the observations, data reduction and variability analysis.A colour–magnitude diagram for the cluster is shown and brieflydiscussed in Section 4. In Section 5, the variability and classificationof the variables are discussed one by one. Finally, a summary is givenin Section 6.

2 O B S E RVAT I O N S A N D DATA R E D U C T I O N

The observations were carried out at the Xinglong Station of theNational Astronomical Observatories of the Chinese Academy ofSciences on five nights between 2002 November 26 and 30. The datawere collected using the 60/90-cm Schmidt telescope equipped witha 2k × 2k Aerospace Ford CCD Camera. The photometer provides afield of view of about 1◦, with an image scale of 1.67 arcsec pixel−1.Two filters, a BACT i (centred at 6660 Å, bandwidth = 490 Å) anda BATC e (centred at 4920 Å, bandwidth = 350 Å), were used al-ternately during the observations. The exposure times were set as120 s for the i-band and as 300 s for the e-band images. Useful datawere recorded during 4–5 h on each night, amounting to a total of23 h of monitoring. In total, we got 289 frames of NGC 188, in-cluding 146 i-band and 143 e-band images. The average deadtimebetween two successive frames was about 5 min.

The preliminary data reduction was made using an automatedpipeline routine, which uses point spread function (PSF) fitting pho-tometry based on the DAOPHOT II (Stetson 1987). The results show

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that the average limiting magnitude for this survey was about i =17.2 mag. This corresponds to R ≈ 17.3 mag according to the cali-bration of mR = mi + 0.104 ± 0.055 from Zhou et al. (2003). Thesignal-to-noise ratio (S/N) of all stars with i � 18.0 mag, however,was large enough to detect variables with light variation magni-tudes larger than 0.05 mag. Following Paper I, we extracted thelight curves for all objects with i � 18 mag measured in the fieldfrom the data set. An absolute magnitude calibration was done; andthe time for each measurement was transformed into HJD time.

3 S E A R C H I N G F O R VA R I A B L E S TA R S

The sequences of measurements obtained in both the i and e filterswere used to search for variable stars in the cluster field. Two meth-ods were applied to select the potential variable candidates. First,we picked up the stars whose light curves show large deviationscompared with all other stars of similar magnitudes. In this waymore than 200 candidates were selected for further analysis. Then,a modified Stetson’s method (Stetson 1996), which is demonstratedin Zhang et al. (2003), was applied to check the intrinsic variabil-ity of these stars. The variability indices were calculated for allthe potential candidates. Stars with small values of variability in-dex were treated as spurious variables, and those showing noisy,chaotic light variations were rejected from the variable sample. Af-ter that, the number of the variable candidates decreased to about40. Furthermore, a detailed visual examination of the light curvesfor each candidate was made on an individual basis. As a result, atotal of 24 certain variables were identified from the previous candi-date list. Among these 24 stars, 16 are the known variables from theprevious work, the remaining eight objects being newly discoveredvariable stars. Three known variables (V7, V9 and V10) discoveredby Kaluzny & Shara (1987) and Kaluzny (1990) were not collectedinto the above variable sample. We then went back to check the dataset and the images. V9 and V10 were indeed detected, but their lightcurves did not show large enough variability systematically. As forV7, we found that it was located near a bad pixel strip on the CCDframes, so that it was not identified in most of the frames duringphotometry extraction. No reliable measurements can be made forthis star. However, these three variables are still included in the vari-able catalogue for completeness. The light curves of V9 and V10were extracted directly from the data for further discussion. Thebasic data of V7 were quoted from Paper I.

We also cross-checked the data table of Kafka & Honeycutt (2003)and ours for coincidences. Except for the three well-known variablesV1, V2 and V3, none of the variables found by Kafka & Honeycuttare confirmed in our catalogue. The reason for such a discrepancy isthat either they are too faint or their amplitudes are too low. Table 1lists the rectangular and equatorial coordinates of all the variablesobserved in the programme field. Temporary identification numbers,V20 through V27, are given to the eight new variables following thename sequence of Paper I. For a cross-identification, the ID numbersfor stars, which can be found in the catalogue of Dinescu et al.(1996), are also listed. Fig. 1 shows a rough finding chart, on whichthe X and Y coordinates (in pixels) of the variables correspond tothe data given in Table 1. All the variables are indicated by theirID numbers. On the finding chart, the ring III defined by Sandage(1962) is plotted as a solid circle, which illustrates the rough edgeof the cluster field.

The basic data of the variables are listed in Table 2. The data ofthe brightness and colour in maximum light as well as the amplitudeof each variable are determined from the phased light curves. Theperiods of the newly discovered variables are determined with a

Table 1. Coordinates of the variables in the field of NGC 188.

ID IDa X Y α(2000) δ(2000)

V1 967.61 1235.03 00:46:54.16 85:21:44.0V2 991.01 1047.60 00:47:33.52 85:16:24.7V3 765 1116.57 1001.01 00:50:27.93 85:15:08.8

V4 766 1133.18 1037.92 00:50:50.30 85:16:12.3V5 764 1026.22 1029.57 00:48:22.72 85:15:55.2V6 978.07 1019.32 00:47:16.63 85:15:35.8

V7 931.16 964.65 00:46:14.22 85:14:00.1V8 1361 1158.35 1102.88 00:51:24.42 85:18:03.7V9 583 867.03 841.21 00:44:52.39 85:10:25.5

V10 1127.59 878.40 00:50:44.85 85:11:39.4V11 632 892.04 918.26 00:45:22.74 85:12:38.7V12 407 1210.60 840.25 00:52:37.89 85:10:35.0

V13 1526 1153.68 1341.41 00:51:15.22 85:24:51.6V14 813.79 274.46 00:44:10.23 84:54:13.6V15 1221 1600.60 1318.29 01:01:50.81 85:24:00.6

V16 1219 1623.82 1312.66 01:02:23.46 85:23:49.5V17 1910 434.01 1533.20 00:33:49.00 85:29:22.7V18 1845.95 1330.15 01:07:39.88 85:23:59.7

V19 1908.55 944.06 01:08:31.90 85:12:53.9V20 1335 1044.54 1083.41 00:48:46.61 85:17:27.8V21 1378 1101.38 1220.20 00:50:02.98 85:21:23.3

V22 660.09 1590.80 00:39:11.02 85:31:28.9V23 1056.38 223.65 00:49:22.52 84:52:58.2V24 336.80 224.93 00:34:05.41 84:51:59.4

V25 1534.95 181.10 00:59:32.46 84:51:40.7V26 1944.07 50.32 01:08:01.27 84:47:25.0V27 91.67 27.97 00:29:20.75 84:45:45.2

aFrom Dinescu et al. (1996).

program based on the PDM method (Stellingwerf 1978). The revisedperiods given for the known eclipsing binaries are generally derivedthrough a classic O–C analysis of their minimum light timings. Ina few cases, period analysis for some stars (such as V8 and V12)are rather complicated, which will be discussed in Section 5. Theclassifications of the variables are given mainly according to thebehaviours of their light variations. This will be discussed furtherin the next section in connection with the locations in the colour–magnitude diagram (CMD).

4 T H E C M D O F T H E C L U S T E R A N DM E M B E R S H I P O F T H E VA R I A B L E S

In general, the result of a proper-motion study is the most im-portant criterion to discuss the cluster membership for a star. ForNGC 188, a very recent proper-motion study has been contributedby Dinescu et al. (1996). They gave a large table with the data ofproper motions and membership probabilities for stars in the field ofthe cluster. Thirteen variables discovered in this work can be foundin their catalogue, whose proper-motion membership probabilities(PMPs) adopted from Dinescu et al. (1996) are listed in Table 2.No PMP data are available for the other 14 stars. In this case, weshall discuss the membership of the variable stars based on both theproper-motion data and the spatial locations and the positions onthe colour–magnitude diagram (CMD).

In Fig. 2, we present a radial density profile of stars in the field ofNGC 188. The density profile is constructed with an i image withthe best seeing and highest signal-to-noise ratio. We calculate the

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Variable stars in field of NGC 188 3

Figure 1. A rough finding chart for the variables in the field of NGC 188 – north is up and east is to the left.

average density of stars for each 20-pixel (33-arcsec) wide annulusaround the centre of the cluster. Only stars brighter than 18 mag inthe i band are taken into account. Inspection of the density profileshows that the angular radius of the cluster is at least 10 arcminand very probably extends to 15–20 arcmin. This agrees with theresult we have suggested in Paper I through the CMD examinationof stars in different regions of the field. Based on the density pro-file, we can estimate the number of member stars of the cluster. Ifwe take the average density of stars with i � 18 mag at distancer � 20 arcmin as the background, the value is about 2 × 10−4

arcsec−1. Then, out of about 720 stars identified within the centralregion (r � 10 arcmin), there would be approximately 500 memberobjects. That is to say, about 70 per cent of stars in the central partof NGC 188 could be members of the cluster.

With the two-colour photometry data, an i versus e − i CMD ofthe cluster is formed. It is shown in Fig. 3, in which stars in the centralpart of the cluster are denoted by plus signs, and those outside thecluster are in tiny dots. To indicate the turn-off and the giant branchof the CMD of the cluster, an isochrone fitting is made, as shownby the solid line in the figure. To do that, an interstellar reddeningE(B − V ) = 0.09 (Sarajedini et al. 1999) and a distance modulusof (m − M)0 = 11.43 (von Hippel & Sarajedini 1998) are adopted.The variable stars identified in the programme field are denoted bytheir ID numbers. Their locations in the CMD are indicated usingthe data from Table 2.

As indicated in the finding chart, two stars, V20 and V21, arelocated in the very central part of the cluster and have very high

PMPs. They are certainly members of the cluster. V22 should be abackground field star as shown in the CMD.

V23, classified as a W UMa system, is located in the extendedpart of the cluster. In the CMD, its position is almost on the binarysequence of the cluster. It is very likely a member of the cluster,though no PMP data are available for the star.

The other four stars, V24–V27, are located very far fromthe cluster centre and are very likely field stars. As for the 19known variables (V1–V19), their cluster membership is identifiedfollowing the previous studies (Kaluzny & Shara 1987; Paper I). Asa result, 15 (V1–13, V20 and V21) out of the 27 variables couldbe members of NGC 188 with high probability, and one (V23) is aprobable cluster object.

5 P E R I O D S , L I G H T C U RV E S A N DC L A S S I F I C AT I O N O F T H E VA R I A B L E S

5.1 The known variables

Among the 19 known variables in the field of NGC 188, 13 stars(V1–V7, V13–15 and V17–19) were classified as W UMa bina-ries. During this observation, good light curves were recorded forall these stars except V7. The measurements for V7 are very poorand no more information can be drawn for the star from this survey.The basic data for V7 given in Table 2 are quoted from Paper I.From the measurements, we derived a number of new times of min-ima for the 12 known W UMa binaries by using the K-W method

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Table 2. Basic data of the variables in the field of NGC 188.

Star imax emax (e − i)max Ai Ae T 0(HJD) Period Type PMP Memb.

V1 16.16 16.81 0.65 0.45 0.36 1605.0219 0.289 7446 W UMa yesV2 16.08 16.74 0.66 0.75 0.73 1604.0391 0.306 9522 W UMa yesV3 15.32 15.89 0.57 0.72 0.85 1604.0391 0.306 9522 W UMa 88 yes

V4 15.23 15.81 0.58 0.42 0.46 1604.3231 0.342 456 97 W UMa 36 yesV5 15.53 16.21 0.68 0.30 0.34 1605.0516 0.585 9835 W UMa 94 yesV6 15.70 16.23 0.53 0.20 0.19 2605.0222 0.330 4319 W UMa yes

V7a 15.70 0.57 0.328 1916 W UMa yesV8 12.80 13.44 0.64 0.20 0.17 5.2096 RS CVn 1 yesV9 14.64 14.30 0.66 97 yes

V10 17.04 17.72 0.68 yesV11 13.48 14.24 0.76 0.05 0.05 1.2433 FK Com 100 yesV12 14.46 14.89 0.43 0.63 1605.2429 2.8136 EA 98 yes

V13 15.46 15.98 0.52 0.20 0.14 2607.0887 0.360 5843 W UMa 76 yesV14 17.12 18.31 1.19 0.52 0.56 2605.0182 0.278 5467 W UMa noV15 12.61 12.95 0.34 0.12 0.10 2605.0041 0.321 4957 W UMa 0 no

V16 13.49 13.60 0.11 0.61 0.496 94 RRd 0 noV17 14.77 15.29 0.54 0.43 0.44 2607.1130 0.316 4920 W UMa 0 noV18 16.85 17.31 0.46 0.23 0.24 2605.0052 0.288 7089 W UMa no

V19 15.91 16.44 0.53 0.39 0.39 1811.2954 0.307 2132 W UMa noV20 13.96 14.40 0.44 0.27 0.11 2606.0472 0.685 86 EB 95 yesV21 15.31 15.76 0.45 0.14 0.16 2606.1072 1.172 54 W UMa 100 yes

V22 13.94 15.50 1.56 0.07 0.12 0.470 42 Pul. noV23 16.21 16.69 0.48 0.34 0.36 2607.1152 0.386 3448 W UMa noV24 13.89 14.12 0.23 0.13 0.15 0.236 26 RR no

V25 14.49 14.97 0.48 0.28 0.36 2605.0779 0.354 1034 W UMa noV26 13.24 13.18 −0.06 0.33 0.54 0.133 31 β Cep noV27 15.60 16.05 0.45 0.26 0.43 0.330 23 Pul. no

aPaper I.

Figure 2. Radial density profile of stars in the field of NGC 188.

(Kwee & van Woerden 1956). Along with the minimum times pre-viously published (Kaluzny & Shara 1987; Kaluzny 1990; Paper I),a classic O–C period analysis was made using the method of leastsquares. New periods and ephemerides were determined for the 12W UMa systems as given in Table 2. With the revised periods, phasedlight curves for the 12 known variables are formed and shown inFig. 4.

In addition to the 13 known W UMa stars, we have also detectedthe variabilities of four other known variables, V8, V11, V12 and

V16. They are all members of the cluster showing special properties.Their light curves are shown in Fig. 5.

V8 is one of the most interesting variables of NGC 188 discoveredby Kaluzny & Shara (1987). In the CMD of the cluster, its positionis far above the turn-off point of the cluster. It was first suggestedto be an FK Com (Kaluzny 1990) and later classified as an RS CVnstar (Mazur & Kaluzny 1990; Paper I). This star has been observedmany times before, but, even so, its period is still very uncertain.Adding our new measurements in the i band to the previous data setof Paper I, we are able to compile a large data set of the star in boththe BATC i and e bands. This enables us to determine the periodwith higher reliability. By using the PDM code, the new value isderived as 5.2096 d. With this period, well-defined i- and e-bandlight curves of V8 are formed, as shown in Fig. 5. The completelycovered light curves reveal that V8 could be very likely an RS CVnstar rather than an FK Com-type variable.

The variability of V11 (I-116, Sandage 1962) was discovered byKaluzny (1990). According to its position in the CMD, Kaluzny(1990) suggested that this variable could be an eclipsing binarycontaining a red giant and an upper main-sequence star. However,no more information about the star are known. In the present study,the variability of V11 is confirmed by the well-covered light curvesin both the i and e bands. The amplitude of its light variation (0.08mag) is much smaller than that assumed by Kaluzny (1990). Tryingwith the PDM code, we got a probable period of 1.2433 d. The lightcurves do not show any eclipse-like behaviour. In the CMD, we findthat it is just located on the red giant branch. We suggest that V11is very likely an FK Com variable.

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Variable stars in field of NGC 188 5

Figure 3. The i/e − i colour–magnitude diagram for NGC 188.

V12 is an Algol-type eclipsing binary in the cluster. In the 2000observations, we detected only one completely covered eclipse andfailed to determine its period. During this survey, we recorded anew eclipse-like event. Combining the new i-band light curve withprevious data, a probable period of 2.8136 d is derived.

V16 is a field variable discovered during the 2000 photometricmonitoring. It was identified as an RRd-type pulsating star. Themain period is revised as 0.496 94 d in the present study.

V9 and V10 were found with light variations by Kaluzny & Shara(1987). Because of the low amplitudes of their light variations, theperiods as well as classifications for the two stars still remain un-known. In Fig. 6, we just present their real-time i- and e-band lightcurves. The two stars show somewhat light variations, but no clearconclusions could be drawn from the observations. Unlike Kaluzny& Shara (1987), we find that in our i versus e − i CMD of the cluster,V10 is not located on the subgiant branch but on the main sequence.This implies that V10 could not be an FK Com-type variable asstated by Kafka & Honeycutt (2003).

5.2 The newly discovered variables

There are a total of eight new variables discovered in the field ofNGC 188 during this survey. Two of these stars are definite membersand one is a probable member of the cluster. The light curves of alleight new variables are shown in Fig. 7. The periods of these starsare determined by using the PDM code. According to the behaviourof their light curves, three of the eight new variables were classifiedas W UMa stars, one as an EB-type eclipsing binary, one as a β Cepvariable and three as pulsators with uncertain types.

V20. This star is a certain member of the cluster. It presents anobvious EB-type light curve in the i band with an amplitude of0.27 mag. In the e band, it shows a shallower and much distortedlight curve with an amplitude decreasing to about 0.11 mag. Inthe CMD, its position is about 0.6 mag above the turn-off, veryclose to the area of blue stragglers in the cluster. An orbital pe-riod of 0.6859 d is assigned to this variable. The star could beclassified as a W UMa system, though its physical nature mustbe very complicated. Further observations of this star are stronglyrecommended.

V21. This is a typical W UMa system of the cluster. The star pos-sesses EW-type light curves in both the i and e bands, and in theCMD it is located almost on the cluster binary branch. It must be avery important object, as an outstandingly long orbital period sys-tem. At about 1.1725 d, the period of V21 is the longest among allthe W UMa stars in NGC 188 to date. More attention should be paidto this star.

V22. A certain background field star. The light curve shows that itis a pulsating variable rather than an eclipsing binary. A period of0.4704 d is derived.

V23. A typical W UMa binary with a period of 0.3863 d. It isprobably a member star of the cluster though no PMP data areavailable. If this is the case, it will be the eleventh W UMa starfound in the cluster.

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Figure 4. Phased i and e light curves of 12 known W UMa stars in the field of NGC 188.

V24. A field pulsating variable with a period of 0.2363 d. The am-plitude of light variations are of 0.13 mag in the i band and 0.15 magin the e band. The colour index at the maximum light is derived ase − i = 0.23. It looks like a δ Scuti star.

V25. A field variable star presenting a typical EW-type light curve.An orbital period of 0.3541 d is determined. It could be a contactbinary system.

V26 (GSC 4619−450). This is a bright field variable star of specialinterest. The light curves show that it is a typical pulsating variablewith very short period (about 3.2 h) and very large amplitude (0.33mag in i band and 0.54 mag in e band). From the colour index ofabout e − i = −0.12 obtained at the maximum light, we estimate

that V26 could be a very early B-type star. Taking all these factsinto account, we suggest that V26 could very likely be a β Cephei-type variable. However, comparing with other β Cephei variables,we find that the amplitude of its light variation is unusually large.Further observations will be made on this variable.

V27. This is a field star with definite light variability. Analysis ofthe light curves reveals that it is likely a pulsating rather than othertype of variable, though the classification is not certain. A period ofabout 0.3302 d is obtained.

6 C O N C L U S I O N S A N D D I S C U S S I O N

In summary, we have reported a new time-series CCD photom-etry on the old open cluster NGC 188 undertaken in 2003. The

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Variable stars in field of NGC 188 7

Figure 5. Phased i-band light curve of four variables: V8, V11, V12 and V16.

Figure 6. Real-time light curves of V9 and V10.

two-colour photometric survey resulted in the discovery of eightnew variables in the field of the cluster, including two definite mem-ber stars. Thus, there are to date a total number of 27 variables foundin the field, of which 15 are members of the cluster.

Most of the variables in the cluster are W UMa stars. The numberof the W UMa systems in NGC 188 is now 10. Considering a sampleof stars located within a radius of r � 10 arcmin from the centreof the cluster, and brighter than i = 18 mag, we find 720 stars; bysubtracting field stars fitted by star density profile, we can derivethat 500 could be cluster members (Section 4). With these data, theaverage relative frequency of occurrence of the W UMa stars in thecluster could be estimated to be about 1/72 to 1/50. This value isclose to and slightly larger than that determined for some other oldopen clusters such as M67, Be39 and Cr261 (Mazur et al. 1995). Itseems that we have approximately obtained a complete sample ofW UMa stars in this cluster. In Fig. 8 we plot the distribution of thecumulative density of the W UMa stars in the cluster. The cumulativedensities were calculated as the average values of the occurrence ofW UMa stars in each area of a series of concentric circles with aradius interval of 1 arcmin. For comparison, the cumulative density

contribution for all the stars detected in the cluster field is alsoillustrated. It is clear that these binary stars are strictly centrallyconcentrated. This result agrees with the expectation for a clusterundergoing mass segregation.

As far as the formation and evolution of W UMa stars in openclusters are concerned, our results suggest that special attentionshould be paid to three stars in NGC 188 (V11, V12 and V21).V11 is identified as an FK Com-type star in the cluster. Is it formedfrom a W UMa progenitor after coalescence? V12 is a detached orsemidetached binary system. Though its orbital period is relativelylong, could it evolve into contact through angular momentum loss(AML)? V20 is very likely a new W UMa system in the cluster witha period obviously longer than those of the others. Is it an examplebridging the contact and non-contact binaries through AML evolu-tion? NGC 188 has been shown to be an important cluster, whichmay provide significant insights into the formation and evolutionof W UMa systems. To answer the questions raised above, moreobservations on the cluster are needed.

Moreover, NGC 188 seems to be projected against a field pop-ulated with various kinds of variable stars. We have noted some

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Figure 7. Phased i and e light curves of the eight newly discovered variable stars in the field of NGC 188.

interesting variables among the field stars. V16 is an RRd star iden-tified by our previous work (Paper I). The new observations do notprovide more information for the star. V26 is a newly discoveredfield variable star with peculiar nature. The behaviour of its lightcurve, pulsating period and spectral type of the star suggest that it isvery likely a β Cephei-type variable. However, the amplitude of itslight variation is larger than that for most of the β Cephei variables.In comparison with BW Vul, a well-known variable that has the

largest amplitude of light and radial velocity variations among theknown β Cephei stars (Sterken, Pigulski & Liu 1993), V26 possessesa remarkably larger amplitude of light variation and shorter pulsat-ing period; the difference of light variation amplitude between thetwo different colours is more obvious. It seems that this star couldbe a very interesting example of the β Cephei class. If that is thecase, more observations on this variable are strongly recommended.In Fig. 9, we present the diagram of variations of the e − i colour

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Variable stars in field of NGC 188 9

Figure 8. The cumulative density profile of the W UMa systems foundin NGC 188 (solid line). The dotted line illustrates the cumulative densityprofile for all stars in the field, compressed by 40 times for clarity.

Figure 9. The variations of the e − i colour index versus phase for theβ Cep variable V26.

index. It would be helpful to understand the pulsating nature of thisstar.

AC K N OW L E D G M E N T S

This research is supported by the Chinese National Science Foun-dation (CNNSF) through grant 10173013. The authors are gratefulto the referee for valuable comments.

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