arXiv:1211.3541v1 [astro-ph.GA] 15 Nov 2012 7 ig1,NC76,NC79,adNC7788 NGC and Glushkova, E.V. 7296, NGC 7261, Berkeley NGC 96, Berkeley 12, clusters King 97, open of study Photometric ..Leonova, S.I. o.Nt .Ato.Soc. Astron. R. Not. Mon. cetd21 eebr0.Rcie 02Dcme 0 nori in 00; December 2012 Received 00. December 2012 Accepted lseslctdtwr h esu prlam ekly96 Berkeley arm: spiral Perseus ( the toward located and clusters 136, NGC 20, (2010)). King al. 19, et (Glushkova King this 7245 18, in NGC King OCLs six 13, of King and parameters region: physical photometry open main CCD of the BVRI distributions estimated age obtained and already space We Perseus the clusters. the on of investigation based of arm program spiral a dev We out small. carry still and is oped kpc 2 with above OCLs distances investigated heliocentric ob- the of CCD number photometric the from However, evaluated col servations. and easily Galac- distances, be of ages, can investigation their excesses the because properties, in disk role tic important (OCLs most clusters determi- the or Open play arms distance. spiral corotation inner the of of nation location unan- the remain as questions such many swered, and disk, structure Galactic the the of of study evolution the in progress important Despite INTRODUCTION 1 ig1 ( 12 King b ⋆ 78( 7788 c 1 4 3 2 l aut fPyis oooo ocwSaeUiest,Mos University, State Moscow Lomonosov Physics, of Faculty pca srpyia bevtr,RsinAaeyo Sci of Academy Madingle Russian Cambridge, Observatory, Astrophysical of Special University Astronomy, of State Moscow Institute Lomonosov Institute, Astronomical Sternberg 0 = -al [email protected] E-mail: 103 = 03RAS 2013 hssuyi ocre ihaohrsml fsxopen six of sample another with concerned is study This ◦ . l 1,NC79 ( 7296 NGC 91), 116 = ◦ . 72, l 116 = b ◦ . = 43, − ◦ . b 2 12, ◦ . = 2 9,Bree 7( 97 Berkeley 09), − ..Vlasyuk V.V. b l 0 = 1 ◦ . 000 101 = 78). , 2 − ⋆ 0 1– , ◦ . ..Zabolotskikh, M.V. 3,NC76 ( 7261 NGC 13), ◦ . ?? 88, epresent We ABSTRACT h esu prlam hs aa opeetdwith complemented data, These arm. spiral Perseus the rm2AS aebe sdt eemn h gs itne,an distances, ages, the determine to used been E have 2MASS, from y,2410 Myr, e 7 ig1,NC76,NC79,adNC7788 NGC and 7296, NGC 7261, NGC 12, King 97, ley Kn 2;10Mr 2830 Myr, 160 12); (King ntems nevl f[.–.] 1416,ad[.–.]slrmse,re masses, solar 12 King [1.5–1.7] 97, and words: Be [1.4–1.6], Key clusters [1.3–1.5], of of function intervals mass mass the the in in gaps found We 7788). c 0 pc, ( 21)Pitd5Spebr21 M L (MN 2018 September 5 Printed (2013) B b l − . = 24 106 = V − ± o hs lses 0Mr 3180 Myr, 40 clusters: these for ) 4 − +220 ◦ . 4 0 ◦ 0,adNGC and 60), . 200 VR BV n ..Rastorguev A.S. and , . 66, 3mg(G 26;ad10Mr 2750 Myr, 160 and 7296); (NGC mag 03 l aay pncutr n soitos niiul ekly9,Ber 96, Berkeley individual: associations: and clusters open : c 0 pc, 104 = b c 0 = I c . ◦ 77 . C htmtyi h ed fsxGlci pncutr toward clusters open Galactic six of fields the in photometry CCD ◦ . 38), our 04, ne,NzniAky,Krca-hresa eulc 35 Republic, Karachai-Cherkessian Arkhyz, UK Nizhnii 0HA ences, CB3 Cambridge, Road, y el- ± nvriy nvriesyp.1,Mso,199 Russia 119992 Moscow, 13, pr. Universitetsky University, ) ia om21 eebr00 December 2012 form ginal o,199 Russia 119992 cow, 0 2 . − +160 6mg(ekly9) 0Mr 2490 Myr, 70 97); (Berkeley mag 06 150 ..Koposov, S.E. h olwn nomto npooer ftecutr un- clusters the of study. photometry der on information following the r UBV h cluster the E 1 Helfer & Jennens K-giants, five of photometry photoelectric ac obe to tance tr ntecutrfield. cluster the in excess tric exclu- 2006) al. et (Skrutskie sively. Catalog Source Point 2MASS E ayfo .2t .9mg(ieeta ednn) Haug reddening). (differential photoelectric mag measured 0.69 to (1970) 0.52 from vary f17sas ekr 16)dtrie h lse age cluster the determined (1968) Fenkart t stars, 147 of c 0 pc, ( ( 5 = http://www.univie.ac.at/webda ≈ U B UBV ekly96. Berkeley h ED aaaeo pnsa clusters star open on database WEBDA The ekly97. Berkeley G 7261. NGC ig12. King − − 0Mr distance Myr, 10 . antdso 0sasaddrvdtecutrdistance cluster the derived and stars 10 of magnitudes p n h oorexcesses colour the and kpc 3 . E V 88 B ( 1 = ) 0 = ) B antdsfr3 tr n on h lse dis- cluster the found and stars 30 for magnitudes ± − r r − +440 0 V 2 = . 1 1 = . A . 380 0and 00 oa ady(94 bandphotoelec- obtained (1984) Pandey & Mohan 0mag. 50 9mg(G 21;20Mr 2450 Myr, 280 7261); (NGC mag 09 , T 0 = ) 2 E . tl l v2.2) file style X . 9kcadisclu excess colour its and kpc 49 c 0 pc, ae on Based p,isage its kpc, 8 2 ars 20)eautdtedsac to distance the evaluated (2008) Tadross e i 18)maue photoelectric measured (1984) Rio Del , . 3 5mg using mag, 75 E ..Spiridonova, O.I. . ( r 54 U − +220 20p,adclu excesses colour and pc, 3230 = − 210 ± UBV B 0 J 0 = ) . c 0 pc, 3mg(ekly9) 250 96); (Berkeley mag 03 , UBV H t − +180 htgahcmagnitudes photographic . 170 JHK ≈ and , . 3mg Using mag. 73 49 E 0 y,adcolour and Myr, 200 ( c 0 pc, antdso four of magnitudes ± B oorexcesses colour d s n G 7788 NGC and , 0 − K antdsfrom magnitudes . 2mg(NGC mag 02 . S V 51 17Russia 7147 spectively. 0 = ) E magnitudes ± ( 4 B 1 0 B iyz UBV . contains − 5mag 05 . 8and 68 V − +190 to ) ke- 170 2 E.V. Glushkova et al.

≈ (1975) found the cluster age t 200 Myr, distance r = 2200 Table 1. Log of observations pc, metal abundance [Fe/H] = −0.7, and colour excess − E(B V ) = 0.48 mag. Hoag et al. (1961) obtained pho- Date Object X Exposure time, s toelectric UBV photometry for 28 stars and photographic B, V , Rc, Ic UBV photometry for 53 stars; Eggen (1968) measured UBV photoelectric magnitudes for two stars; Kubinec (1973) mea- Aug. 27, 2003 NGC 7788 1.05 300, 300, 300, 300 60, 30, 30, 30 sured photographic BV magnitudes for seven stars. NGC 7790 1.07 300, 100, 100, 100 NGC 7296. Based on ∆a and BV R CCD photome- Aug. 29, 2003 NGC 7296 1.01 300, 300, 300, 300 try for about 140 stars, Netopil et al. (2005) determined the 300, 300, 300, 300 cluster age t ≈ 100 Myr, distance r = 2930 pc, and colour 30, 30, 15, 15 excesses E(B −V ) = 0.15±0.02 and E(V −R) = 0.00±0.02 NGC 7790 1.06 300, 100, 100, 100 mag. Oct. 15, 2009 NGC 7790 1.06 300, 150, 150, 150 NGC 7788. Haug (1970) measured photoelectric UBV King 12 1.05 300, 300, 300, 300 magnitudes of five stars; Becker (1965) measured photo- 30, 30, 30, 30 graphic UBV magnitudes of 113 stars; and Frolov (1977) NGC 7788 1.05 300, 300, 300, 300 found photographic BV magnitudes of 67 stars. −−, 30, 30, 30 NGC 7790 1.06 300, 150, 150, 150 The clusters Be 96, King 12, NGC 7261, and NGC 7788 NGC 7790 1.09 300, 150, 150, 150 were studied by means of photographic and photoelectric Oct. 16, 2009 NGC 6940 1.05 300, 150, 150, 150 photometry down to V-band limiting magnitudes of 14.5– Berkeley 96 1.05 300, 300, 300, 300 16.5 mag. According to the estimates reported by the above 30, 30, 30, 30 authors and by Dias et al. (2002) for NGC 7788, the dis- Berkeley 97 1.04 300, 300, 300, 300 tances to all these clusters exceed 2 kpc. Hence the pub- 30, 30, 30, 30 lished colour- diagram (CMD) isochrone fits in- NGC 7790 1.05 300, 150, 150, 150 volved only the upper parts of the main sequences of the NGC 7296 1.06 300, 300, 300, 300 clusters studied whose physical parameters could therefore 30, 30, 30, 30 be determined with large errors. Berkeley 97 was studied us- NGC 7790 1.05 300, 150, 150, 150 NGC 7790 1.09 300, 150, 150, 150 ing only JHKS data, also down to a shallow limiting magni- NGC 7790 1.10 300, 150, 150, 150 tude. The only published color-magnitude diagram of NGC Oct. 18, 2009 NGC 7790 1.06 300, 150, 150, 150 7296 is based on CCD photometry and goes down to a V- Berkeley 97 1.06 300, 300, 300, 300 band limiting magnitude of 16.8 mag. CCD data is known NGC 7790 1.05 300, 150, 150, 150 to be often fraught with systematic errors and we therefore King 12 1.07 300, 300, 300, 300 decided to repeat the observations of this cluster. We also NGC 7790 1.08 300, 150, 150, 150 wanted to verify a very small value E(V −R) = 0.00 derived Oct. 19, 2009 NGC 7790 1.05 300, 150, 150, 150 by Netopil et al. (2005). All these factors justify our choice NGC 7790 1.10 300, 150, 150, 150 of the six open clusters listed above. Nov. 18, 2009 NGC 7790 1.05 300, 150, 150, 150 Berkeley 97 1.06 400, 400, −−, −− Berkeley 97 1.06 400, 400, −−, −− Berkeley 96 1.09 300, 300, 300, −− 2 OBSERVATIONS AND DATA REDUCTION 1.12 30, 30, 30, 30 NGC 7790 1.07 300, 150, 150, 150 We observed six open clusters in the Johnson/Kron–Cousins broadband BV RcIc using the Zeiss–1000 telescope at the Special Astrophysical Observatory of the Russian Academy several times for each night as a photometric standard, and of Sciences equipped with a photometer based on an EEV the NGC 6940 cluster was used once as a photometric stan- 42–40 2K × 2K CCD. The pixel size, readout noise, and gain dard (see Table 1). The standard magnitudes for stars in the − − were equal to 13.5 µm, 4e , and 2.08e per ADU, respec- fields of NGC 7790 and NGC 6940 were taken from Stetson’s ′′ tively. The scale and field of view were equal to 0. 207/pixel database 2. The ranges of magnitudes and colours for about ′ ′′ ′ and about 7 , and 0. 238/pixel and about 8 during the 2003 250 standard stars in the cluster field are 12.7

c 2013 RAS, MNRAS 000, 1–?? Photometry of open star clusters 3

Figure 1. V –band images of the clusters studied (exposure time 300 s). The common orientation of all frames (except for NGC 7296) relative to the equatorial coordinate system is indicated by the arrows on the image of NGC 7788. The image size is near 8′× 8′ (7′× 7′ for NGC 7296).

− − − (V Ic)= ϕ(v i)+ ξ(V −Ic), of (V Rc) colour was used only for the stars without B magnitudes. The averages of the median coefficients were where b, v, r, and i are the magnitudes in the instrumental ε = −0.073 ± 0.005, ρ = −0.125 ± 0.012, µ = 1.211 ± 0.010, ± ± system and B, V , Rc, and Ic are the magnitudes in the stan- ψ = 0.803 0.010, and ϕ = 0.875 0.007 for the observations dard system. The formula for the V magnitude as a function done in 2003 and ε = −0.076 ± 0.003, ρ = −0.131 ± 0.005,

c 2013 RAS, MNRAS 000, 1–?? 4 E.V. Glushkova et al.

µ = 1.208 ± 0.006, ψ = 0.910 ± 0.006, and ϕ = 0.877 ± 0.003 narrow “tails”, because only one frame in each band was for the observations done in 2009 (the rms deviations are taken with the exposure 300 s, and no averaging was per- given as the errors). We used mean values to recalculate the formed; the same is seen for σ(V −Ic) (Berkeley 96). zero points ξV1 , ξV2 , ξ(B−V ), ξ(V −Rc), and ξ(V −Ic) for the We compared the derived magnitudes and colours with times of observations of the standard clusters. The differ- published photometry and show the magnitude and colour ences in the ψ coefficients are presumably due to the changes differences in Fig. 3. Our photometric data are in good agree- in the photometer layout mentioned above. ment with all other photoelectric data - see plots for Be 96 As shown in Table 1, the standard clusters NGC 7790 and King 12, “star” symbols on the plots for NGC 7261 and and NGC 6940, and all program clusters were observed at NGC 7788. In contrast, the comparison of our CCD photom- the same air mass X. This explains why we did not estimate etry with photographic values reported elsewhere exhibits the coefficients. In the cases where NGC 7790 was rather wide spread, as shown by the “dot” symbols on the observed twice, before and after the program cluster, we cal- plots for NGC 7261 and NGC 7788. We also found system- culated the zero points of the transformation expressions by atic differences of approximately 0.2 ± 0.05 mag in V and a linear interpolation between zero point values calculated 0.1 ± 0.05 mag in (V − Rc) between our values and those from the standard cluster. Weighted mean V magnitudes derived by Netopil et al. (2005) for NGC 7296. Differences and (B − V ), (V − Rc), and (V − Ic) colours were computed in the (B − V ) colours show the systematic trend from 0.1 and published only for those stars in the fields of the six pro- to 0.25 mag. However, 32 common stars identified in the gram clusters, for which the magnitudes and colours derived APASS catalogue show small negative differences of about from different frames and reduced to the standard system −0.07 ± 0.03 mag in V and −0.04 ± 0.02 mag in (B − V ), differ by less than 0.1 mag. This value (0.1 mag) seems to be respectively. the typical magnitude error for the faintest measured stars To estimate the cluster distance, age, and colour excess and, at the same time, close to 3σ-variance of magnitudes toward the cluster, we built the following colour–magnitude measured on different frames. The final values of the errors diagrams (CMD) for each program cluster: (V, B − V ), in the magnitudes and colours were calculated as the rms (V,V − Rc), and (V,V − Ic) – from our data, and (J, J − errors of the weighted mean on all frames (taking into ac- H), (Ks, J − Ks) – from the 2MASS catalogue. The faint count the errors in the aperture corrections and the errors stars with colour errors exceeding 0.05 mag were excluded introduced by the transformation from the instrumental sys- from our consideration. We then fit each CMD to a solar- tem to the standard one). However, if the rms deviation of metallicity isochrone by Girardi et al. (2002) using the the magnitude or colour calculated on all frames exceeded method developed by Koposov et al. (2008). In this method the rms error of the weighted mean, this rms deviation was we superimposed the isochrone on the colour–magnitude di- taken as the final error. agram in such a way that the corresponding plot for the ra- The results of the photometric study of the clusters dial density distribution exhibits a peak for the stars lying Berkeley 96, Berkeley 97, King 12, NGC 7261, NGC 7296, in the vicinity of the isochrone (the distance in the colour and NGC 7788 are presented in Tables 4, 5, 6, 7, 8, and 9, index for such stars is less than 0.05 mag) and an almost respectively. Tables 4–9 are available in the electronic form flat distribution for all other stars (supposed field stars). only and are accessible at the CDS website 3 and at the The centers of clusters were found from density maps built Sternberg Astronomical Institute website 4. In this paper, using data from the 2MASS PSC. We considered the po- we list a sample of few lines of Table 4 only as an exam- sition of the maximum of the density peak as the center ple. Tables 5–9 have the same layout. The tables include of the cluster, and the distance from the cluster center, at the equatorial coordinates α and δ in degrees at the epoch which the star density in the cluster region becomes flat on J2000, V magnitudes and (B − V ), (V − Rc), and (V − Ic) the radial density distribution and equal to the density of colours and their errors σV , σ(B−V ), σ(V −Rc), and σ(V −Ic) field stars, as the cluster radius. In this way we evaluated for individual stars. We used 99.999 in all cells where the the distance, colour excess, and age for each cluster on each corresponding values are not available. CMD. To convert the colour excesses found from different colour–magnitude diagrams to the colour excess E(B − V ) and to calculate the distance modulus, we used the follow- · − 3 RESULTS AND DISCUSSION ing relations: AKs = 0.670 E(J Ks) (Dutra et al. (2002)) and AV = 3.08 · E(B − V ), E(V − Rc) = 0.61 · E(B − V ), 3.1 Determination of Physical Parameters E(V − Ic) = 1.35 · E(B − V ), E(V − J) = 2.25 · E(B − V ), and E(V − H) = 2.57 · E(B − V ) (He et al. (1995)). We derived V magnitudes and (B−V ), (V −Rc), and (V −Ic) Figures 4-9 present the V − (B − V ), V − (V − Rc), colours for the stars in the fields of Berkeley 96, Berkeley 97, − − − − King 12, NGC 7261, NGC 7296, and NGC 7788. In Fig. 2, V (V Ic) (or R (R Ic), see explanations below), and J − (J − H) colour–magnitude diagrams, on which the the error in the magnitude, σV , and the errors in the colours, corresponding isochrones are plotted (solid lines). σ(B−V ), σ(V −Rc), and σ(V −Ic), are plotted against the V magnitude for each cluster; the numbers on each plot indi- For each cluster, Table 2 gives the refined coordinates cate the number of stars. In most cases, the errors do not of the center, αJ2000 and δJ2000, the cluster diameter d in − exceed 0.10 mag; the magnitude limit is 20-21.5 mag, de- arcminutes, the age t in Myr, the colour excesses E(B V ), − pending on the band. The colour plots for NGC 7261 show and the true distance moduli (m M)0 determined from each CMD and recalculated using the relations above. On the whole, the parameters derived from different colour– 3 http://cdsarc.u-strasbg.fr/ magnitude diagrams agree well, although for some clusters 4 http://ocl.sai.msu.ru/ we can see small differences in E(B − V ) values estimated

c 2013 RAS, MNRAS 000, 1–?? Photometry of open star clusters 5

Berkeley96 Berkeley97 King 12 NGC7261 NGC7296 NGC7788 0.10 σ 1235 888 706 782 808 777 V

0.05

0.00 σ 712 624 462 418 633 440 (B−V)

0.05

0.00 σ 1034 775 677 761 711 762 (V−R)

0.05

0.00 σ 1167 743 640 761 672 654 (V−I)

0.05

0.00 10 14 18 10 14 18 10 14 18 10 14 18 10 14 18 10 14 18 22 V, mag

Figure 2. Errors in the magnitudes, σV , and in the colours, σ(B−V ), σ(V −Rc), and σ(V −Ic), versus V magnitude for the program clusters (from left to right) Berkeley 96, Berkeley 97, King 12, NGC 7261, NGC 7296, and NGC 7788; the numbers on top of each plot indicate the number of stars; all values along the horizontal and vertical axes are given in magnitudes. separately from optical and infrared data. We suppose that NGC 7788, we include data from both Loktin et al. (2001) these differences can be due to greater contamination of and Dias et al. (2002), because Loktin et al. (2001) deter- the infrared CMDs by field stars as compared to optical mined the distance moduli, and Dias et al. (2002) included data, and to the uncertainties of color excess transforma- these distances in his catalogue. Table 3 shows that only tions used. The final values of mean colour excesses and the in the case of the King 12 cluster our parameters are in true distance moduli, along with their rms deviations, are good agreement with those obtained in the previous study listed in Table 3. All CMDs yield approximately the same by Mohan & Pandey (1984). For the remaining five clusters age estimates for each cluster, so we did not put any er- investigated in this study, the physical parameters have been rors for the ages, which generally depend on the isochrones considerably improved. used. We could not derive the cluster parameters from the (Ks, J − Ks) diagram for NGC 7788, because of the large dispersion of stars in this CMD. 3.2 Mass Function Let us compare our parameters with those from the For three clusters – Berkeley 97, King 12, and NGC 7788 literature. Table 3 contains the colour excesses E(B − V ), – we noticed gaps on their main sequences on all CMDs true distance moduli (m − M)0, distances r in parsecs, and built from our BVRcIc CCD photometry. To verify these logarithms of the age lgt from this paper and different pub- gaps, we extracted r and i data from the IPHAS survey lished sources. For the clusters King 12, NGC 7261, and (Drew et al. (2005)) and transformed these values from the

c 2013 RAS, MNRAS 000, 1–?? 6 E.V. Glushkova et al.

∆V, mag ∆(B−V), mag Berkeley 96 0.4 0.2 0.0 −0.2 King 12 −0.4 0.2 0.0 −0.2 NGC 7261 −0.4 0.2 (Hoag et al.) 0.0 −0.2 NGC 7261 −0.4 0.2 (Fenkart) 0.0 −0.2 NGC 7788 −0.4 0.2 (Haug; Frolov) 0.0 −0.2 NGC 7788 −0.4 0.2 (Becker) 0.0 −0.2 NGC 7296 −0.4 0.2 (Netopil et al.) 0.0 −0.2 NGC 7296 −0.4 0.2 (APASS) 0.0 −0.2 −0.4 10 12 14 16 10 12 14 16 18 V, mag

Figure 3. Differences of magnitudes, ∆V (left), and colours, ∆(B − V ) (right), for common stars in this paper and Del Rio (1984) in the field of Berkeley 96; in this paper and Mohan & Pandey (1984) in the field of King 12; in this paper and Hoag et al. (1961) (symbol “star” – photoelectric photometry, symbol “dot” – photographic photometry), Fenkart (1968) in the field of NGC 7261; in this paper and Haug (1970) (symbol “star”), Frolov (1977) (symbol “dot”), Becker (1965) in the field of NGC 7788; in this paper and Netopil et al. (2005) (symbol “star” – ∆(B − V ), symbol “dot” – ∆(V − R)) in the field of NGC 7296; in this paper and the APASS catalogue in the field of NGC 7296. The V magnitude is along the horizontal axis on all plots; the dashed line corresponds to zero magnitude and colour differences.

SDSS system into Cousins R, I magnitudes using empiri- ficial stars (most of them are faint) does not exceed 10% cal colour transformations by Jordi et al. (2006). We then of the total population. Images with artificial stars are then built colour–magnitude diagrams (R, R − Ic) using both our processed using the same algorithm. The portion of restored photometric data and those derived from IPHAS. Figures stars in each interval of magnitudes gives us the complete- 5, 6, and 9 include these two CMDs. For each cluster, the ness value in the same magnitude intervals. We used the gap on the main sequence is situated at the same values of least of the two values obtained by V and Ic images accord- magnitudes and colours on both diagrams – (R, R − Ic) and ing to Sagar & Richtler (1991). This method makes it pos- (Riphas, (R − I)iphas). We used solar-metallicity evolution- sible to find the real PDLF with errors less than 3% in each ary tracks and isochrones by Girardi et al. (2002) to evaluate magnitude interval where the completeness is more than 0.5. the mass intervals (in solar-mass units) that correspond to The members of each cluster were selected by photometric these MS gaps: [1.3–1.5] for Berkeley 97, [1.4–1.6] for King criteria using (V,V − Ic) diagrams. We built the PDLF for 12, and [1.5–1.7] for NGC 7788. stars inside the cluster radius and for the field stars, and corrected both functions for the incompleteness factor and Present-day luminosity and mass functions for these for the area difference. The resulting PDLF is the difference three clusters were built by star counts for all stars fainter between the cluster PDLF and the field stars PDLF. than those at the MS turn-off. To evaluate the completeness of our photometric data, we used the method described by To convert the luminosity function into the mass Sagar & Richtler (1991). Artificial stars were added to our function, we used stellar evolutionary tracks and solar- initial images in the B and Ic filters. The fraction of arti- metallicity isochrones by Girardi et al. (2002). Fig-

c 2013 RAS, MNRAS 000, 1–?? Photometry of open star clusters 7

Figure 4. Colour–magnitude diagrams for Berkeley 96. The diamonds mark the positions of stars on the diagram; the solid lines indicate the corresponding isochrones. All values along the horizontal and vertical axes are given in magnitudes. The size of the region for which the diagram was constructed is 3′.

12 12 12 12 8

10 14 14 14 14

12 16 16 16 16 J V V R R_iphas

14

18 18 18 18

16

20 20 20 20

18 0.5 1.0 1.5 2.0 0.4 0.6 0.8 1.0 1.2 1.4 0.4 0.6 0.8 1.0 1.2 1.4 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.5 1.0 1.5 (B-V) (V-R) (R-I) (R-I)_iphas (J-H)

Figure 5. Colour–magnitude diagrams for Berkeley 97. The diamonds mark the positions of stars on the diagram; the solid lines indicate the corresponding isochrones. All values along the horizontal and vertical axes are given in magnitudes. The size of the region for which the diagram was constructed is 4′. ures 10, 11, and 12 show the MFs for clusters Berkeley 97, The gaps on each plot are plotted according to main se- King 12, and NGC 7788. The values of the power law expo- quence gaps on the colour-magnitude diagrams. The escape nent (logarithmic mass function slope) – α was calculated by point on Fig. 11 and Fig. 12 corresponds to the deficiency or the χ2 solution for linear regression without taking into ac- the absence of stars in the gaps. There is no such point on count escape points in the case of King 12 and NGC 7788. Fig. 10 although a main sequence gap can be clearly seen in

c 2013 RAS, MNRAS 000, 1–?? 8 E.V. Glushkova et al.

8 8 6

10 10

10 10 8

12 12

12 12 10 14 14

14 14 J V V R 12

16 16 R_iphas

16 16 14 18 18

18 18

20 20 16

20 20

22 22 18 0.5 1.0 1.5 2.0 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 (B-V) (V-R) (R-I) (R-I)_iphas (J-H)

Figure 6. Colour–magnitude diagrams for King 12. The diamonds mark the positions of stars on the diagram; the solid lines indicate the corresponding isochrones. All values along the horizontal and vertical axes are given in magnitudes. The size of the region for which the diagram was constructed is 5′.

Figure 7. Colour–magnitude diagrams for NGC 7261. The diamonds mark the positions of stars on the diagram; the solid lines indicate the corresponding isochrones. All values along the horizontal and vertical axes are given in magnitudes. The size of the region for which the diagram was constructed is 7′. the case of Berkeley 97. It can be explained by the insuffi- 4 CONCLUSIONS cient subtraction of field stars. Such gaps and breaks in MF plots may be due to a discontinuity in the process of star We used our optical BVRcIc CCD observations to obtain the formation inside the cluster. V magnitudes and (B − V ), (V − Rc), and (V − Ic) colours for a large number of stars in the fields of six open clusters: Berkeley 96, Berkeley 97, King 12, NGC 7261, NGC 7296,

c 2013 RAS, MNRAS 000, 1–?? Photometry of open star clusters 9

Figure 8. Colour–magnitude diagrams for NGC 7296. The diamonds mark the positions of stars on the diagram; the solid lines indicate the corresponding isochrones. All values along the horizontal and vertical axes are given in magnitudes. The size of the region for which the diagram was constructed is 8′.

10 10 10 10 8

12 12 12 12 10

14 14 14 14 12 J V V R R_iphas

16 16 16 16 14

18 18 18 18 16

20 20 20 20 18 0.5 1.0 1.5 2.0 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 (B-V) (V-R) (R-I) (R-I)_iphas (J-H)

Figure 9. Colour–magnitude diagrams for NGC 7788. The diamonds mark the positions of stars on the diagram; the solid lines indicate the corresponding isochrones. All values along the horizontal and vertical axes are given in magnitudes. The size of the region for which the diagram was constructed is 4′. and NGC 7788 (see electronic Tables 4-9). For each cluster, the ages, distances, and colour excesses of the clusters un- we constructed optical and infrared (based on 2MASS data) der study (Table 3). colour–magnitude diagrams with the Padova isochrones su- perimposed (Figs. 4-9). We used this technique to derive We found three clusters – Berkeley 97, King 12, and NGC 7788 – to have gaps on their main sequences. Indepen- dent data extracted from the IPHAS (Drew et al. (2005))

c 2013 RAS, MNRAS 000, 1–?? 10 E.V. Glushkova et al.

Table 2. Cluster parameters determined from optical and infrared data

Berkeley 96 Berkeley 97 King 12 NGC 7261 NGC 7296 NGC 7788

h m s h m s h m s h m s h m s h m s αJ2000 22 29 49 22 39 28 23 53 01 22 20 07 22 28 01 23 56 38 ◦ ′ ′′ ◦ ′ ′′ ◦ ′ ′′ ◦ ′ ′′ ◦ ′ ′′ ◦ ′ ′′ δJ2000 +55 23 47 +58 59 51 +61 56 45 +58 07 41 +52 19 22 +61 24 02 d 3′ 4′ 5′ 7′ 8′ 4′ t,Myr 40 250 70 160 280 160 E(B − V ), mag V, B − V 0.50 0.72 0.54 1.00 0.22 0.49 V, V − Rc 0.58 0.85 0.57 0.93 0.24 0.52 V, V − Ic 0.53 0.75 0.51 0.86 0.19 0.49 J, J − H 0.55 0.79 0.47 0.78 0.28 0.47 Ks,J − Ks 0.56 0.72 0.44 0.83 0.25 −− (m − M)0, mag V, B − V 12.71 12.08 12.05 12.16 12.18 12.39 V, V − Rc 12.39 11.86 11.83 12.35 11.97 12.09 V, V − Ic 12.89 12.13 12.19 12.41 11.98 12.30 J, J − H 12.23 11.76 11.96 12.16 11.72 12.03 Ks,J − Ks 12.31 11.71 11.85 12.21 11.92 −−

Table 3. Comparison of our cluster parameters with published data

E(B − V ), mag (m − M)0, mag r,pc lg t Source

+440 Berkeley 96 0.54 ± 0.03 12.51 ± 0.28 3180−380 7.60 this paper 0.68 13.61 5300 Del Rio (1984) +220 Berkeley 97 0.77 ± 0.06 11.91 ± 0.19 2410−200 8.40 this paper 0.75 11.28 1800 ± 85 7.30 Tadross (2008) +180 King 12 0.51 ± 0.05 11.98 ± 0.15 2490−170 7.85 this paper 0.52 − 0.69 11.98 2490 ± 85 Mohan & Pandey (1984) 0.59 12.034 7.037 Loktin et al. (2001) 0.59 2378 7.037 Dias et al. (2002) 0.59 11.88 7.12 Kharchenko et al. (2005) +160 NGC 7261 0.88 ± 0.09 12.26 ± 0.12 2830−150 8.20 this paper 0.48 11.7 2200 8.3 Jennens & Helfer (1975) 1.00 12.55 3230 7.0 Fenkart (1968) 0.969 11.280 7.670 Loktin et al. (2001) 0.969 1681 7.670 Dias et al. (2002) +190 NGC 7296 0.24 ± 0.03 11.95 ± 0.16 2450−170 8.45 this paper 0.15 ± 0.02 12.33 ± 0.2 2930 ± 350 8.0 ± 0.1 Netopil et al. (2005) +220 NGC 7788 0.49 ± 0.02 12.20 ± 0.17 2750−210 8.20 this paper 0.283 12.030 7.593 Loktin et al. (2001) 0.283 2374 7.593 Dias et al. (2002) 0.48 11.87 7.48 Kharchenko et al. (2005)

catalogue confirmed these features on colour-magnitude di- 2.5 agrams for these three clusters. We built the luminosity func- α = −2.27 ± 0.59 tion and the mass function for these clusters and found the 2 features on the MF plot. 1.5 M) ∆

N/ 1 ∆ log(

ACKNOWLEDGMENTS 0.5

We used the WEBDA database operated at the Institute for 0 Astronomy of the University of Vienna and developed by E.

−0.5 Paunzen and J.-C. Mermilliod; 2MASS data, which is a joint −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 log(M ) project of the University of Massachusetts and the Infrared center Processing and Analysis Center/California Institute of Tech- Figure 10. nology, funded by NASA and NSF; the APASS database, lo- Mass function of Berkeley 97. cated at the AAVSO website 5; and the Virtual observatory resource 6 developed at Sternberg Astronomical Institute 5 http://www.aavso.org/apass 6 http://vo.astronet.ru c 2013 RAS, MNRAS 000, 1–?? Photometry of open star clusters 11

Table 4. Photometric data for Berkeley 96

αJ2000, deg δJ2000, deg V σV B − V σ(B−V ) V − Rc σ(V −Rc) V − Ic σ(V −Ic) 337.446900 55.392340 11.200 0.003 0.326 0.005 99.999 99.999 99.999 99.999 337.567690 55.446010 16.511 0.027 0.806 0.014 0.525 0.026 0.990 0.024 337.378080 55.451410 18.611 0.028 1.145 0.062 0.722 0.036 1.314 0.040 337.374210 55.451490 19.292 0.023 1.394 0.036 0.926 0.016 1.720 0.049 ......

2.5 Girardi L., Bertelli G., Bressan A., et al., 2002, A&A, 391, 195 α = −2.04 ± 0.42 2 Glushkova E.V., Zabolotskikh M.V., Koposov S.E. et al., 2010, Astronomy Letters, 36, 14 1.5 Hardie R.H., 1964, Photoelectric Reductions in the book M) ∆

N/ 1

∆ Astronomical Techniques, ed.W. A. Hiltner, University of

log( Chicago, p. 178. 0.5 Haug U., 1970, A&AS, 1, 35

0 He L., Whittet D.C.B., Kilkenny D, and Spencer Jones J.H., 1995, A&AS, 101, 335 −0.5 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Hoag A.A., Johnson H.L., Iriarte B., et al., 1961, Publ. US. log(M ) center Nav. Obs., 17, 345 Jennens P.A., Helfer H.L., 1975, MNRAS, 172, 681 Figure 11. Mass function of King 12. Jordi K., Grebel E.K. and Ammon A., 2006, A&A, 460, 339 Kharchenko N.V., Piskunov A.E., Roser S. et al., 2005, 2.5 A&A, 438, 1163 2 α = −2.69 ± 0.41 Koposov S.E., Glushkova E.V. and Zolotukhin I.Yu., 2008, A&A, 486, 771 1.5 Kubinec W.R., 1973, Publ. Warner Swasey Obs., 1, No. 3 M) ∆

N/ 1 Loktin A.V., Gerasimenko T.P. and Malysheva L.K., 2001, ∆

log( Astron. Astrophys. Trans., 20, 607 0.5 Mohan V., Pandey A.K., 1984, Ap&SS, 105, 315 Netopil M., Paunzen E., Maitzen H.M., et al., 2005, Astron. 0 Nachr., 326, 734

−0.5 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Del Rio G., 1984, A&AS, 56, 289 log(M ) center Sagar R., Richtler T., 1991, A&A, 250, 324 Skrutskie M.F., Cutri R.M., Stiening R., et al., 2006, AJ, Figure 12. Mass function of NGC 7788. 131, 1163 Stetson P.B., 1987, PASP, 99, 191 Tadross A.L., 2008, MNRAS, 389, 285 (Moscow State University). We thank L.N. Berdnikov, O.V. Vozyakova, and A.K. Dambis for valuable advice and the anonymous referee for useful comments.

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7 www.astro.iag.usp.br/.wilton/clusters.txt (2012)

c 2013 RAS, MNRAS 000, 1–??