A&A 372, 477-494 (2001)
DOI: 10.1051/0004-6361:20010441

Photometric study of the double cluster $\vec h$ & $\mathsf{\chi}$ Persei[*]

A. Marco - G. Bernabeu

Dpto. de Física, Ingeniería de Sistemas y Teoría de la Señal, Universidad de Alicante, Aptdo. de Correos 99, 03080, Alicante, Spain

Received 20 July 2000 / Accepted 28 January 2001

Abstract
We present $uvby\beta$ CCD photometry of the central region of the double cluster h & $\chi $ Persei. We identify $\approx$350 stars, of which 214 were not included in Oosterhof's catalogue. Our magnitude limit V=16.5 allows us to reach early F spectral type and obtain very accurate fits to the ZAMS. We derive reddening values of $E(b-y) = 0.44\pm0.02$ for h Persei and $E(b-y) = 0.39\pm0.05$ for $\chi $ Persei. From the ZAMS fitting, we derive distance moduli $V_{0}-M_{V} = 11.66\pm0.20$ and $V_{0}-M_{V} = 11.56\pm0.20$ for h and $\chi $ Persei respectively. These values are perfectly compatible with both clusters being placed at the same distance and having identical reddenings. The shift in the main-sequence turnoff and isochrone fitting, however, show that there is a significant age difference between both clusters, with the bulk of stars in h Persei being older than $\chi $ Persei. There is, however, a significant population of stars in h Persei which are younger than $\chi $ Persei. All this argues for at least three different epochs of star formation, corresponding approximately to $\log t = 7.0, 7.15$ and 7.3[*].

Key words: techniques: photometric - Galaxy: open clusters and associations: individual: h Persei, $\chi $ Persei - stars: evolution - emission-line, Be-formation


1 Introduction

Photometric studies of open clusters are extremely useful to determine the physical properties of star members. Even though modern spectroscopic techniques allow the observation of large numbers of stars in a relatively short time, the stellar population of most clusters is still too vast for an in-depth study. Among photometric systems, the uvbyH$\beta $ system is the most appropriate for the study of early-type stars, since it has been designed to provide accurate measurements of their intrinsic properties.

This is the first in a series of papers dedicated to the study of the B-star population of Galactic open clusters. B-type stars are sufficiently bright to allow very accurate narrow-band photometry and at the same time numerous enough to provide a statistically significant population (unlike the brighter but very rare O-type star).

  \begin{figure} \par\includegraphics[width=6.5cm,clip]{10127.fig1.ps}\hspace*{1mm} \includegraphics[width=6.5cm,clip]{10127.fig2.ps}\end{figure} Figure 1: a),b). Schematic maps of the observing region in NGC 884 and NGC 869. The size of the dots represents relative brightness of stars in the field. North is down and East left in all fields.

The double cluster h & $\chi $ Persei is one of the richest young open clusters accessible from the Northern hemisphere, and therefore it is well documented in the literature. An extensive photographic study was carried out by Oosterhoff (1937); MK spectral types for cluster members were determined by Bidelman (1943), Johnson & Morgan (1955), Schild (1965, 1966, 1967) and others; optical photometry in various systems was carried out by Johnson & Morgan (1955), Wildey (1964), Schild (1965), Crawford et al. (1970b), Waelkens et al. (1990), and others; infrared photometry was obtained by Mendoza (1967) and Tapia et al. (1984). A study of the membership probability of 3086 stars brighter than B=15.5 magnitudes within an area of 50 arcmin radius centered on h & $\chi $ Persei was carried out by Muminov (1983) on the basis of proper motion and photometric (V-(B-V); V-(U-V); (U-B)-(B-V)) criteria. There is no general agreement on the distance moduli and the ages of both clusters. Crawford et al. (1970b) conclude, on the base of $uvby\beta$ photometry, that both clusters have nearly the same age and distance, the distance modulus being $11.4\pm0.4$ mag. Balona & Shobbrook (1984), however, correct this value for evolutionary effects and adopt a distance modulus of 11.16 for both clusters. On the other hand, Tapia et al. (1984) find confirmation of a previous suggestion by Schild (1967) that h Persei is younger and closer than $\chi $ Persei, with distance moduli of 11.7 and 12.0, respectively. Doom et al. (1985) show that in the OB association Per OB1 the low mass stars formed first, the most massive stars being (10-20) Myr younger than the low mass ones. In an attempt to improve these values, we present in this paper deep $uvby\beta$ photometry of the double open cluster h & $\chi $ Persei. Given the nearness of these clusters, our magnitude limit (V=16.5) allows us to reach early-F main sequence stars. This is $3\:{\rm mag}$ deeper than the previous study by Crawford et al. (1970b) and allows us a very accurate fit to the Zero Age Main Sequence (ZAMS) and hence precise determination of the astrophysical parameters of the clusters.
 

 
Table 1: Log of the observations taken at the 1.0-m JKT on December 11th and December 22nd 1997 for two frames.
Cluster Frame Central Star Coordinates (1950)
h Persei #1 1057 $\alpha=2{\rm h}$ 15m 32.67s $\delta=+56\hbox{$^\circ$ }54\hbox{$.\mkern-4mu^\prime$ }20\hbox{$.\!\!^{\prime\prime}$ }49$
$\chi $ Persei #2 2227 $\alpha=2{\rm h}$ 18m 27.70s $\delta=+56\hbox{$^\circ$ }55\hbox{$.\mkern-4mu^\prime$ }02\hbox{$.\!\!^{\prime\prime}$ }08$
Filter   Exposure Times (s)  
  $[V \leq 10]$   [$V \geq 16$]
u 60 300 1200
v 22 110 450
b 7 40 150
y 6 30 120
$\rm H\beta_{narrow}$ 50 250 1000
$\rm H\beta_{wide}$ 6 30 120


2 Observations

Observations of the central region of h & $\chi $ Persei were obtained at the 1-m Jacobus Kapteyn Telescope (JKT), located at the Observatorio del Roque de los Muchachos, La Palma, Spain on the nights of 10-22 December 1997. The telescope was equipped with the $1024 \times 1024$ TEK 4 chip CCD and the four Strömgren uvby and the narrow and wide H$\beta $filters. Pixel size was $0\hbox{$.\!\!^{\prime\prime}$ }331$ in such a way that the whole field covered by each frame was $5\hbox{$.\mkern-4mu^\prime$ }6 \times 5\hbox{$.\mkern-4mu^\prime$ }6$. Even though both clusters are actually more extended than the area covered by our frames ($\sim$ $18\hbox{$^\prime$ }$ across considering the outermost regions), our images are centered on the central region of both clusters, where member star density is much higher.

We took two frames covering the whole of the central region of each cluster (central coordinates are displayed in Table 1). Figures 1a,b show plots of the observed fields in h & $\chi $ Persei respectively. The dot sizes are indicative of the relative instrumental y magnitude. Each cluster was observed using three different exposure times in each filter (Table 1), so that the widest range of magnitudes possible was observed with good signal-to-noise ratio. Standard stars were observed in the clusters h & $\chi $ Persei, NGC 6910, NGC 2169 and NGC 1039 using the intermediate exposure time.

Throughout this paper the numbering system used will be that of Oosterhoff (1937). For those stars that were not observed by Oosterhoff (1937), a new system has been adopted. New stars in h Persei are listed after a "4'' prefix, while new stars in $\chi $ Persei are listed starting with a "7'' prefix. Coordinates in each frame for these newly catalogued stars are given in Table 2.

It is worth noting that our sample is representative of the star population, except in the sense that it contains almost exclusively main-sequence stars (and some giants of the earlier spectral types). Most of the brightest member stars are far away from the central region. This has no bearing on the determination of the main cluster parameters (such as reddening and distance), but can influence the study of the system age. For this reason, we have supplemented our data with observations of a number of members brighter than V=11 taken from Johnson & Morgan (1955) and Crawford et al. (1970b).

   
3 Reduction procedure

The reduction of all frames was carried out using the IRAF[*] routines for the bias and flat-field corrections. The photometry was obtained by PSF fitting using the DAOPHOT package (Stetson 1987) provided by IRAF. The atmospheric extinction corrections were performed using the RANBO2 program, which implements the method described by Manfroid (1993). It has been shown that the choice of standard stars for the transformation is a critical issue in $uvby\beta$ photometry. Transformations made only with unreddened stars introduce large systematic errors when applied to reddened stars, even if the colour range of the standards brackets that of the programme stars (Manfroid & Sterken 1987; Crawford 1994). Our data cover a very wide range of spectral types and hence a wide range of intrinsic colours. Moreover, during this campaign several clusters with different interstellar reddenings were observed.

 

 
Table 3: Standard stars with their catalogued values and spectral types taken from the literature.
Number V b-y m1 c1 $\beta $ Spectral Type
h Persei  
837 14.080 0.393 0.000 0.918 2.801  
843 9.320 0.277 -0.050 0.166   B1.5V
867 10.510 0.393 0.161 0.375 2.613  
869         2.700  
935 14.020 0.362 -0.004 0.854 2.802  
950 11.290 0.318 -0.048 0.214 2.642 B2V
960         2.767  
978 10.590 0.305 -0.039 0.177 2.643 B2V-B1.5V
982         2.796  
1015 10.570 0.225 0.033 0.741   B8V
1078 9.750 0.316 -0.065 0.167 2.610 B1V-B1Vn
1181 12.650 0.372 -0.034 0.379 2.718  
$\chi $ Persei  
2133         2.676  
2139 11.380 0.255 -0.033 0.196 2.649 B2V
2147 14.340 0.406 -0.050 1.002 2.863  
2167 13.360 0.352 -0.056 0.627 2.752  
2185 10.920 0.283 -0.049 0.406 2.700 B2Vn
2196 11.570 0.250 -0.006 0.210 2.670 B1.5V
2200         2.721  
2232 11.110 0.292 -0.105 0.207 2.651 B2V
2235 9.360 0.316 -0.088 0.150 2.611 B1V
2251 11.560 0.302 -0.042 0.349 2.709 B3V
NGC 2169  
11 10.600 0.084 0.065 0.541 2.698 B8V
15 11.080 0.130 0.109 0.944 2.864 B9.5V
18 11.800 0.115 0.105 0.912 2.872 B9.5V



   
Table 4: Standard stars with their catalogued values and spectral types taken from the literature (continued Table 3).
Number V b-y m1 c1 $\beta $ Spectral Type
NGC 6910  
7 10.360 0.670 -0.160 0.110 2.612 B0.5V
11 10.900 0.770 0.420 0.430 2.555  
13 11.720 0.660 -0.140 0.220 2.647 B1V
14 11.730 0.590 -0.100 0.220 2.652 B1V
15 12.220 0.590 -0.110 0.330 2.679  
17 12.660 0.670 -0.120 0.310 2.659  
18 12.810 0.750 -0.140 0.290 2.680  
19 12.920 0.640 -0.120 0.380 2.662  
20 12.980 0.610 -0.130 0.420 2.692  
NGC 1039  
92 11.960 0.303 0.138 0.481 2.678  
96 9.740 0.086 0.176 0.973 2.890  
97 11.820 0.144 0.198 0.900 2.855  
102 10.760 0.151 0.194 0.894 2.848  
105 11.220 0.176 0.204 0.796 2.817  
109 10.030 0.066 0.152 1.013 2.916  
111 9.950 0.055 0.163 1.021 2.908  

The data are taken from Crawford et al. (1970b) and Johnson & Morgan (1955) for h & $\chi $Persei, Perry et al. (1978) for NGC 2169, Crawford et al. (1977) for NGC 6910 and Canterna et al. (1979) for NGC 1039. Spectral types, when available, are taken from Schild (1965) and Slettebak (1968) for h & $\chi $ Persei, Perry et al. (1978) for NGC 2169, Morgan & Harris (1956) and Hoag & Applequist (1965) for NGC 6910 and Canterna et al. (1979) for NGC 1039.


In order to cover the whole range of programme stars, we selected our standard stars in the same clusters under investigation. A preliminary list of standard stars was built by selecting a number of non-variable non-peculiar candidate stars in h & $\chi $ Persei, NGC 2169, NGC 6910 and NGC 1039, observed with the same Kitt Peak telescopes and instrumentation used to define the uvby Crawford & Barnes (1970a) and H$\beta $ Crawford & Mander (1966) standard systems, so that there is no doubt that the photometric values are in the standard systems. Since the original observations of h& $\chi $ Persei by Crawford et al. (1970b) do not include V values, we used values given by Johnson & Morgan (1955), which were also taken with the same instrumentation, for the V transformation.

The list of adopted standard stars and their photometric data to be used in the transformations are given in Tables 3 and 4.


 

 
Table 5: Catalogue of 41 standard stars observed and transformed to the Crawford-Barnes uvby and the Crawford-Mander $\rm H\beta $ standard systems. The internal rms errors of the mean measure in the transformation of each star are given in Cols. 8 to 11 in units of 0.001 mag. Columns 12 to 16 give the difference $D=\rm standard$ value minus transformed value, in units of 0.001 mag. N is the number of measures of each standard star in the transformation in V, (b-y), m1, c1. The number of measures in $\beta $ is one for each standard star in the transformation.
Star V (b-y) m1 c1 $\beta $Nuvby $\sigma_{V}$ $\sigma_{b-y}$ $\sigma_{m_{1}}$ $\sigma_{c_{1}}$ DV D(b-y) Dm1 Dc1 $D_{\beta}$
h Persei  
869 - - - - 2.724- - - - - - - - - -024
837 14.095 0.411 -0.031 0.907 2.7893 006 009 024 024 -016 -019 032 011 012
843 9.330 0.319 -0.151 0.240 -1 - - - - -010 -042 101 -074 -
867 10.572 0.376 0.177 0.379 2.6665 006 008 013 025 -063 016 -015 -005 -053
935 14.051 0.411 -0.076 0.856 2.7816 018 007 018 038 -031 -049 073 -003 021
950 11.297 0.337 -0.079 0.221 2.6301 - - - - -007 -019 031 -007 012
960 - - - - 2.727- - - - - - - - - 040
978 10.646 0.328 -0.070 0.194 2.6345 016 013 016 023 -056 -023 031 -017 009
982 - - - - 2.779- - - - - - - - - 017
1015 10.573 0.223 0.029 0.677 -2 037 023 006 030 -003 003 005 064 -
1078 9.775 0.317 -0.043 0.138 2.6113 008 021 042 036 -025 -002 -021 030 -001
1181 12.655 0.352 -0.008 0.338 2.7036 022 022 044 030 -006 020 -025 041 015
$\chi $ Persei  
2133 - - - - 2.658- - - - - - - - - 018
2139 11.351 0.298 -0.097 0.235 2.6412 011 024 030 007 029 -043 064 -039 008
2147 14.359 0.392 -0.083 1.022 2.7835 023 034 051 051 -019 013 033 -020 080
2167 13.364 0.347 -0.080 0.616 2.7336 012 008 012 024 -004 005 025 011 019
2185 10.926 0.275 -0.018 0.412 2.6883 008 013 038 044 -006 008 -031 -006 012
2196 11.549 0.304 -0.066 0.246 2.6326 012 013 023 023 021 -052 056 -034 038
2200 - - - - 2.707- - - - - - - - - 014
2232 11.052 0.238 -0.029 0.177 2.6394 013 013 041 035 058 054 -077 030 012
2235 9.365 0.311 -0.071 0.131 2.5753 012 015 046 039 -005 005 -016 018 036
2251 11.563 0.297 -0.028 0.367 2.6896 009 011 027 030 -004 004 -013 -018 020
NGC 2169  
11 10.538 0.076 0.061 0.545 2.7191 - - - - 062 008 004 -004 -021
15 11.023 0.122 0.092 0.939 2.8561 - - - - 057 008 017 005 008
18 11.733 0.053 0.260 0.813 2.8831 - - - - 067 062 -155 099 -011
NGC 6910  
7 10.320 0.667 -0.150 0.092 2.6522 011 004 012 016 041 003 -011 018 -040
11 - - - - 2.639- - - - - - - - - -084
13 11.681 0.619 -0.082 0.211 2.6612 004 023 038 004 039 041 -058 009 -014
14 11.730 0.569 -0.053 0.201 2.6782 004 028 040 018 001 021 -048 019 -026
15 12.193 0.609 -0.134 0.359 2.6982 007 006 014 002 027 -019 024 -029 -019
17 12.635 0.700 -0.149 0.294 2.6882 008 010 025 040 025 -030 029 017 -029
18 12.816 0.755 -0.132 0.296 2.7052 014 004 006 048 -006 -005 -009 -006 -025
19 12.897 0.610 -0.065 0.402 2.7092 025 035 037 047 023 031 -056 -022 -047
20 12.920 0.619 -0.118 0.446 2.7302 016 001 019 006 060 -009 -013 -026 -038
NGC 1039  
92 11.928 0.282 0.150 0.520 2.7091 - - - - 032 021 -012 -039 -031
96 9.703 0.063 0.219 0.976 2.8871 - - - - 037 023 -043 -003 003
97 11.782 0.129 0.215 0.934 2.8381 - - - - 038 015 -017 -034 017
102 10.724 0.150 0.193 0.893 2.8511 - - - - 036 001 001 001 -003
105 11.166 0.167 0.232 0.971 2.8321 - - - - 054 009 028 -175 -015
109 10.034 0.040 0.178 1.018 2.9601 - - - - -004 026 -026 -005 -044
111 9.900 0.025 0.249 0.964 2.9271 - - - - 050 030 -086 057 -019



The following uvby transformation equations from the instrumental to the standard system together with the standard errors on the coefficients are obtained using the equations by Crawford & Barnes (1970a), where the coefficients have been computed following the procedure described in detail by Grønbech et al. (1976):

$\displaystyle V =11.269 +0.091(b-y)\,+\,y_{{\rm i}}\pm0.003 ~~~\pm0.007$     (1)


$\displaystyle (b-y) = 0.636 + 1.070(b-y)_{{\rm i}}\pm0.008 \,\,\pm0.008$     (2)


$\displaystyle m_{1} =-0.523 + 1.009m_{1{\rm i}} - 0.206(b-y)\pm0.008 ~~~\,\pm0.015 ~~~~\, \pm0.009$     (3)


$\displaystyle c_{1} = 0.543 + 1.019c_{1{\rm i}} + 0.257(b-y)\pm0.004 ~\,\pm0.004~~\,\,\pm0.007$     (4)

where the index "i'' stands for instrumental magnitudes.

The transformed values for the 41 standard stars are given in Table 5, together with their precision and deviation with respect to the published standard values. Table 6 shows the mean catalogue minus transformed values for the standard stars and their standard deviations, which constitute a measure of the accuracy of the transformation. From the mean differences between catalogue and transformed values, it is clear that there is not a significant offset between our photometry and the standard system. Since the individual differences for a few stars seem to be rather large, an attempt was made to improve the transformation by removing these stars from the standard list. We find however that the transformation coefficients and their precision do not improve significantly.

The H$\beta $ instrumental system and transformation equations were computed following the procedure described in detail by Crawford & Mander (1966). The transformation coefficients are a=3.514 and b=1.059. Transformed values and their differences with respect to the mean catalogue values are given in Table 5. The mean difference is -0.003 with a standard deviation 0.031, which, as in the case of the uvby transformation, indicates that there is no significant offset with respect to the standard system.

4 Results

4.1 Membership and reddening

We have obtained $uvby\beta$ CCD photometry for more than 350 stars in the fields of h & $\chi $ Persei. The magnitude limit $V\approx 16.5$ allows us to identify 214 stars that were not catalogued by Oosterhoff (1937). Even though all of them are listed in Table 2 some of them are so faint that the number of counts was not enough to reach a good signal-to-noise ratio in all the filters. Therefore these stars are discarded from our sample.

  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig3.eps}\end{figure} Figure 2: V- (b-y) diagram for all stars in the field of h Persei. Open squares represent stars considered as members while filled squares are non-members. Filled circles are stars catalogued as Be stars. Open circles are supergiant and giant stars not observed by us and taken from the study of Crawford et al. (1970b).

To assess the membership of a star, we look at its position in the V-(b-y)and V-c1 diagrams. We find that in both diagrams the vast majority of the stars fall along a very well defined main sequence. Inspection of these photometric diagrams reveals that a number of stars do not fit well the main sequence loci in both diagrams. Those objects are considered as non-members unless they are catalogued as Be stars (see Figs. 2-5). Indeed Be stars have colours differing from those of non-emission B stars due to additional reddening caused by the circumstellar envelope and tend to have redder (b-y) and lower c1 values than normal B stars (Fabregat et al. 1996). In addition, the M4.5Iab supergiant star RS Per (2417) is considered to be a cluster member.

There is a smaller number of stars whose position is displaced with respect to the main sequence in only one of these diagrams. For these stars we calculate the free reddening indices [m1], [c1] and [u-b]:

[m1]=m1+0.32(b-y) (5)


[c1]=c1-0.20(b-y) (6)


[u-b]=[c1]+2[m1] (7)

and use the $\beta - [u-b]$ diagram to roughly evaluate their spectral classification (See Fig. 6). We find that stars 867, 969, 1084 and 1138 in h Persei and stars 2376, 7029 and 7081 in $\chi $ Persei have spectral types not corresponding to their photometric positions. We consider these objects as non-members. As the c1 index is less affected by extinction than the (b-y) colour, the V-c1 diagram provides a more secure diagnostic than the V-(b-y) diagram. Therefore, stars whose position only deviates from the main sequence in the V-(b-y) plane could be affected by differential extinction. In $\chi $ Persei, the only case is star 2370. Since Muminov (1980) gives it a relatively low membership probability (0.38), we have excluded this star from further analysis. In h Persei, we have stars 911, 1072 and 1257. The membership probability is low for 911 and 1257 (0.15 and 0.36 respectively according to Muminov 1980). So we consider them as likely non-members of the cluster. Star 1072, on the other hand, has much higher probability, 0.78 (Muminov 1980), and we consider it a cluster member. Other stars, 2185, 2140 and 2311 in $\chi $ Persei have positions in the V-c1 diagram deviating sligthly towards brighter V. The membership probability is high for 2185 and 2140 (0.76 and 0.98 respectively in Muminov 1980). We consider 2185 and 2140 as members.
  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig4.eps}\end{figure} Figure 3: V- c1 diagram for all stars in the field of h Persei. Open squares represent stars considered as members while filled squares are non-members. Filled circles are stars catalogued as Be stars. Open circles are supergiant and giant stars not observed by us and taken from the study of Crawford et al. (1970b).

The case for 2311 is not so clear, but since it is likely to be an eclipsing binary (Krzesinski & Pigulski 1997), we will not use it for the determination of the cluster parameters, though it may well be a member (Vrancken et al. 2000). A similar situation occurs with the stars 859, 869, 926 and 1000. In h Persei we consider as non-member the star 859, because of its low membership probability (0.07; Muminov 1980), and as members stars 869, 926 and 1000 because of their higher probabilities (0.74, 0.60 and 0.99 respectively; Muminov 1980). In Tables 8 and 9 we present the resulting values for V, (b-y), m1, c1 and $\beta $ and their precisions, together with the number of observations for member stars of h & $\chi $ Persei respectively. In Tables 10 and 11, we list the stars identified as non-members in the fields of h & $\chi $ Persei respectively together with their photometric data. Finally in Tables 12 and 13, we give the photometric data for Be star members of h & $\chi $ Persei respectively.
  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig5.eps}\end{figure} Figure 4: V - (b-y) diagram for all stars in the field of $\chi $ Persei. The open squares are considered as members and the filled squares as non-members. The filled circles are stars catalogued as Be stars. Open circles are supergiant and giant stars not observed by us and taken from the study of Crawford et al. (1970b).


 

 
Table 6: Mean catalogue minus transformed values for the standard stars and their standard deviations in V, (b-y), m1, c1 and $\beta $.
DmV Dm(b-y) Dmm1 Dmc1 $D_{m{\beta}}$
0.014 0.003 -0.005 -0.004 -0.003
0.033 0.027 0.049 0.044 0.031



  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig6.eps}\end{figure} Figure 5: V- c1 diagram for all stars in the field of $\chi $ Persei. Theopen squares are considered as members and the filled squares as non-members. The filled circles are stars catalogued as Be stars. Open circles are supergiant and giant stars not observed by us and taken from the study of Crawford et al. (1970b).


  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig7.eps}\end{figure} Figure 6: $[u-b] - \beta $ diagram for all stars whose position deviates from the main sequence in only one of the photometric diagrams. The thin lines represent the loci of main-sequence B stars (left), the main sequence A-stars (bottom right) and the main sequence F-stars (top right). Open squares represent stars from the field of h Persei and while filled circles are from the field of $\chi $ Persei.

From the list of member stars we select those falling in the range of B-type stars in the V-(b-y) and V-c1 diagrams. From this subset we remove all Be stars and all early B stars which deviate strongly from the ZAMS. We also exclude stars 869, 926, 976, 1000, 1072, 2140 and 2185 because, in spite of appearing as likely members in the photometric diagrams, they have positions deviating slightly from the average loci of stars with the same spectral type. For all the remaining B stars we calculate individual reddenings. We follow the procedure described by Crawford et al. (1970b): we use the observed c1 to predict the first approximation to (b-y)0 with the expresion (b-y)0=-0.116+0.097c1. Then we calculate E(b-y)=(b-y)-(b-y)0 and use E(c1)=0.2E(b-y) to correct c1 for reddening c0=c1-E(c1). The intrinsic color (b-y)0 is now calculated by replacing c1 by c0 in the above equation for (b-y)0. Three iterations are enough to reach convergence in the process. The final average values of reddening are $E(b-y) = 0.44\pm0.02$ for h Persei and $E(b-y) = 0.39\pm0.05$ for $\chi $ Persei. These values are consistent, within the errors, with both clusters having the same reddening in their central region.

In the E(b-y) - V diagrams (see Figs. 7 and 8) we notice that the scatter of individual reddenings is quite small in both clusters, confirming the result obtained by Crawford et al. (1970b) of homogeneous reddening across the central region. With the aid of these values we calculate the intrinsic colours and magnitudes of the candidate members of both clusters, listed in Table 14.

 

 
Table 7: Photometric data and spectral type for bright members of h & $\chi $ Persei taken from the literature. The fifth column indicates whether the star is inside the area covered by our observations (In) or more distant from the central region (Out).
h Persei
Number V (b-y) c1 E(b-y) Position Spectral Type
3 7.400 0.244 0.051 0.360 Out B2Ib
339 8.850 0.288 0.071 0.410 Out B1IV
612 8.410 0.255 0.070 0.380 Out B1II
1162 6.660 0.443 0.101 0.560 In B2Ia
1187 10.820 0.348 0.212 0.460 In B2IV
1899 8.530 0.289 0.138 0.400 Out B2II
1781 9.210 0.267 0.145 0.380 Out B1IV
$\chi $ Persei
2227 8.050 0.328 0.111 0.440 In B2II
2361 8.750 0.351 0.108 0.460 Out B0.5III
2541 9.150 0.292 0.146 0.400 Out B2II
2589 7.440 0.574 0.860 0.610 Out A2Iap?
2621 7.000 0.512 0.455 0.590 Out B8Ia


Since none of the stars in the sample, except RS Per, is in a late evolutionary state (all stars earlier than B3 deviate from the main sequence, but none seems to have a luminosity class higher than III), we have added to our colour-magnitude plots all the stars brighter than V=11 taken from Johnson & Morgan (1955) and Crawford et al. (1970b), which, as shown in Sect. 3, are on the same system as our observations. Values of V (Johnson & Morgan 1955), (b-y), c1, individual E(b-y), position in the clusters (Crawford et al. 1970b) and spectral type (Schild 1965; Slettebak 1968) are given in Table 7. A few of these stars are inside the area covered by our observations but were saturated in some of our frames.

As we can see from the values of individual reddening, the h Persei stars outside the inner 5.6 arcmin have reddenings lower that the average calculated for the inner 5.6 arcmin, and therefore they lie to the left of the rest of the members in the V-(b-y) diagram. This is due to the fact that the (b-y) colour is more affected by reddening than the c1 index. Their position in the V-c1 diagram agrees well with the rest of the cluster, because this index is very little affected by reddening.

In $\chi $ Persei three stars outside the central region have reddenings higher than the average for the central region, and therefore they lie to the right of the rest of the stars in the V-(b-y) plane. Once more their position in the V-c1 diagram is compatible with the rest of the cluster. We conclude that the analysis of the V-c1 diagram yields much firmer results than the analysis of the V-(b-y) diagram, as the actual position of each star in the latter is modified by the difference between its individual reddening and the average value for the central region.

  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig8.eps}\end{figure} Figure 7: Individual values of E(b-y) calculated using Crawford's et al. (1970b) procedure against V magnitude for h Persei members in the B spectral type range.


  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig9.eps}\end{figure} Figure 8: Individual values of E(b-y) calculated using Crawford's et al. (1970b) procedure against V magnitude for $\chi $ Persei members in the B spectral type range.

4.2 Spectral classification

Given the paucity of spectroscopic studies of cluster members, we decided to estimate the spectral types for all members observed by us. Since our objects cover a wide range of spectral types, we use different procedures depending on the intrinsic photometric values. Following Napiwotzki et al. (1993), we select stars with $(b-y)_{0} \leq 0.00$ (corresponding to $T_{\rm eff} \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\dis... ...finterlineskip\halign{\hfil$\scriptscriptstyle ...K) and use the temperature calibration based on the dereddened [u-b] index, given by Napiwotzki et al. (1993):

\begin{displaymath}\Theta \equiv \frac{5040\:{\rm K}}{T_{\rm eff}} = 0.1692 + 0.2828[u-b] - [u-b]^{2}. \end{displaymath} (8)

Once the temperature of the star is known, we derive an approximate value for the gravity $\log g$ by means of the grids of Moon & Dworetsky (1985). For the hottest stars ( $T_{\rm eff} \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\dis... ...skip\halign{\hfil$\scriptscriptstyle ...), only a rough estimate of $\log g$ is derived from the theoretical grids of Lester et al. (1986).

For stars with $0.00 \leq (b-y)_{0} \leq 0.04$ (corresponding to $8500\:{\rm K} \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\d... ...finterlineskip\halign{\hfil$\scriptscriptstyle ...K), we use the parameters

a0 = 1.36(b-y)0 + 0.36m0 + 0.18 c0 - 0.2448 (9)

and

\begin{displaymath}r^{*}=0.35c_{1} - 0.07(b-y) -(\beta -2.565) \end{displaymath} (10)

to derive both $T_{\rm eff}$ and $\log g$ from the grids of Moon & Dworetsky (1985).

Finally, for stars with $(b-y)_{0} \geq 0.04$, we derive $T_{\rm eff}$ and $\log g$ directly from c0 and $\beta $ by using the grids of Moon & Dworetsky (1985).

As a last step, we derive approximate spectral types by correlating the estimated $T_{\rm eff}$ and $\log g$ with the average values for each spectral type from Kontizas & Theodossiou (1980) and Allen (1973). The estimated spectral types are listed in Table 14. The validity of this approximation is confirmed by the fact that, for all the stars which have a spectroscopic spectral classification, our estimate is consistent with the spectroscopic determination with an uncertainty of $\pm1$ subtype. The only exception is the star 1116, for which we give a spectral type B2, while a spectral type B0.5V is given by Schild (1965). We note that, based on Geneva photometry, Waelkens et al. (1990) found that none of the stars classified as B0.5 in h Persei seems to be any hotter than other stars classified as B1 or B1.5, showing that the spectral classification of some stars is uncertain.


 

 
Table 10: Photometric data for non-members of h Persei.
Number V b-y m1 c1 $\beta $ $\sigma_{V}$ $\sigma_{b-y}$ $\sigma_{m_{1}}$ $\sigma_{c_{1}}$ $\sigma_{\beta}$ Nuvby $N_{\beta}$
859 10.726 0.352 -0.126 0.311 2.642 0.018 0.015 0.024 0.021 0.004 5 2
865 13.276 0.663 0.538 0.283 2.577 0.015 0.012 0.021 0.023 0.013 4 3
867 10.572 0.376 0.177 0.379 2.671 0.006 0.008 0.013 0.025 0.007 5 2
886 15.346 0.749 -0.054 0.644 2.614 0.009 0.019 0.031 0.033 0.006 3 2
911 11.359 0.287 -0.033 0.235 2.671 0.013 0.010 0.015 0.009 0.010 4 2
969 13.017 0.945 0.100 0.490 2.624 0.008 0.017 0.039 0.016 0.019 5 3
1015 10.573 0.222 0.030 0.677 - 0.037 0.023 0.006 0.031 - 2 0
1023 12.567 0.413 0.197 0.266 2.659 0.021 0.016 0.030 0.018 0.005 5 3
1047 12.039 0.268 0.062 0.168 2.705 0.012 0.010 0.029 0.015 0.004 5 3
1054 13.831 0.623 0.111 0.506 2.606 0.017 0.010 0.021 0.045 0.026 6 3
1084 15.940 0.510 0.022 0.552 2.797 - - - - - 1 1
1099 13.179 0.436 -0.042 0.957 2.834 0.014 0.017 0.022 0.031 0.005 6 3
1100 14.060 0.562 0.094 0.677 2.761 0.030 0.041 0.102 0.084 0.018 6 3
1138 12.710 1.222 0.439 0.500 2.614 0.015 0.021 0.055 0.049 0.031 3 2
1155 12.518 0.400 -0.009 0.616 2.769 0.016 0.027 0.055 0.032 0.023 6 3
1167 14.028 0.571 0.129 0.398 2.628 0.032 0.020 0.054 0.044 0.013 6 3
1184 12.113 0.317 0.061 0.183 2.712 0.013 0.031 0.062 0.047 0.008 4 2
1189 13.810 0.639 0.147 0.579 2.615 0.016 0.012 0.069 0.165 0.027 4 2
1194 14.598 1.025 0.233 0.398 2.618 0.025 0.017 0.068 0.075 0.013 2 2
1238 15.324 0.743 0.003 0.510 2.656 - - - - - 1 1
1257 10.326 0.403 0.029 0.139 2.654 0.020 0.018 0.029 0.021 0.004 2 2
1272 13.406 1.007 0.179 0.457 2.604 0.016 0.023 0.030 0.015 0.028 2 2
4001 15.302 0.722 -0.001 0.512 2.650 0.012 0.003 0.011 0.054 - 3 1
4002 15.446 1.006 0.049 0.333 2.623 - - - - - 1 1
4007 15.838 0.721 -0.081 0.598 2.689 - - - - - 1 1
4014 16.044 0.701 -0.002 0.483 2.610 - - - - - 1 1
4019 16.135 0.801 -0.122 0.527 2.585 - - - - - 1 1
4021 16.162 0.782 -0.033 0.393 2.615 - - - - - 1 1
4040 16.400 0.459 -0.107 1.140 2.818 0.007 0.030 0.007 0.005 - 2 1


For the vast majority of the stars in the sample, we derive gravities compatible with their being main-sequence objects. Among the F and late A stars the scatter in the derived gravities is rather larger than among B-type stars, probably reflecting the larger errors associated with fainter magnitudes. For almost all of the stars at the low temperature end, we derive low gravities ( $\log g \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displays... ...\offinterlineskip\halign{\hfil$\scriptscriptstyle ...). Among the stars later than F0, only 7097 (F4), 7108 (F2) and 7091 (F2) give $\log g \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displays... ...\offinterlineskip\halign{\hfil$\scriptscriptstyle .... The situation completely reverses for the hot stars. On the whole A0-F0 range, only star 856 (A7) has a value of $\log g$ that stands out as being particularly lower than that of all other stars. Among B stars, where the gravity determination is probably more reliable, a few stars have $\log g \approx 3.5$, and could be evolved. These are 1198 (B9), 1020 (B8), 1179 (B6) and 1232 (B3). From their atmospheric parameter calculations, Vrancken et al. (2000) find that B1 and B1.5 stars classified as main-sequence have gravities corresponding to higher luminosities. In particular, they find $\log g = 3.4$ for the star 2311 (B2III), for which we obtain $\log g \approx 3.5$. This would imply that also the star 2255 (B2) and the star 2246 (B1), for which we estimate a similar gravity, are giants.

 

 
Table 11: Photometric data for non-members of $\chi $ Persei.
Number V b-y m1 c1 $\beta $ $\sigma_{V}$ $\sigma_{b-y}$ $\sigma_{m_{1}}$ $\sigma_{c_{1}}$ $\sigma_{\beta}$ Nuvby $N_{\beta}$
2087 13.315 0.463 0.002 1.119 2.851 0.003 0.029 0.045 0.048 0.013 3 3
2093 14.863 0.566 -0.060 0.951 2.831 0.025 0.012 0.038 0.022 0.036 3 2
2097 12.943 0.339 -0.058 0.476 2.699 0.018 0.020 0.028 0.030 0.006 6 4
2098 14.221 0.440 -0.040 1.144 2.891 0.012 0.031 0.044 0.051 0.012 4 3
2107 13.894 1.023 0.171 0.480 2.604 0.011 0.016 0.026 0.060 0.010 3 2
2127 14.961 0.666 0.016 0.491 2.612 0.026 0.020 0.019 0.039 0.004 3 2
2158 15.515 0.586 -0.025 0.870 0.000 - - - - - 1 0
2188 15.070 0.525 -0.036 1.010 2.861 0.018 0.037 0.056 0.029 0.018 3 2
2198 13.487 1.143 0.451 0.365 2.608 0.001 0.008 0.056 0.041 0.023 2 4
2202 13.300 0.500 0.142 0.337 2.629 0.023 0.025 0.027 0.019 0.013 3 3
2216 14.253 0.967 0.161 0.435 2.568 0.024 0.017 0.009 0.043 0.010 2 2
2281 15.110 0.599 -0.004 0.936 2.749 0.029 0.026 0.045 0.009 0.005 2 2
2315 13.754 0.404 -0.064 1.031 2.833 0.013 0.012 0.024 0.022 0.027 5 4
2329 12.762 0.543 0.111 0.714 2.657 0.018 0.022 0.046 0.050 0.005 6 4
2345 13.092 0.202 0.191 0.307 2.759 0.015 0.029 0.065 0.051 - 3 1
2356 15.104 0.651 -0.001 0.568 2.692 0.013 0.052 0.105 0.055 0.029 3 2
2365 13.701 0.524 0.072 0.430 2.620 0.033 0.035 0.063 0.038 0.018 6 4
2370 14.042 0.248 0.111 0.775 2.843 0.055 0.063 0.131 0.090 0.027 6 4
2376 13.481 0.526 0.080 0.665 2.717 0.023 0.034 0.081 0.039 0.030 6 4
2381 13.003 0.525 0.278 0.389 2.584 0.017 0.022 0.039 0.041 0.014 6 4
2397 14.161 0.625 0.036 0.502 2.649 0.029 0.023 0.072 0.032 0.041 5 4
7013 15.320 0.698 -0.005 0.551 2.601 - - - - 0.041 1 2
7025 13.292 0.480 -0.011 0.793 2.777 - - - - - 1 1
7029 16.166 0.484 -0.061 0.686 2.839 - - - - - 1 1
7035 15.677 0.874 -0.161 0.598 2.596 - - - - - 1 1
7044 16.040 0.809 -0.110 0.440 2.610 - - - - - 1 1
7071 15.601 0.608 0.004 0.751 2.719 0.002 0.005 0.005 0.064 0.043 2 2
7081 15.899 0.564 0.002 1.233 2.812 - - - - - 1 1
7082 12.856 0.357 0.102 1.063 - - - - - - 1 0
7101 15.912 0.431 0.024 1.188 2.907 0.042 0.011 0.016 0.036 2 1  


   
4.3 Distance modulus determination

We have estimated the distance modulus to h & $\chi $ Persei by using both: (a) the $\beta $ index calibration of Balona & Shobbrook (1984) and (b) by fitting the observed V0 vs. (b-y)0 and V0 vs. c0ZAMS to the mean calibrations of Perry et al. (1987).


  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig10.eps}\end{figure} Figure 9: Absolute magnitude MV against intrinsic colour (b-y)0for h Persei members. The thick line represents the ZAMS from Perry et al. (1987). Three isochrones corresponding to $\log t = 7.0, 7.15$ and 7.30are labelled with their respective $\log t$. Filled circles are supergiant stars not observed by us and taken from the study of Crawford et al. (1970b). Open squares are stars in our sample previously catalogued as having high rotational velocity (Slettebak 1968).


  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig11.eps}\end{figure} Figure 10: Absolute magnitude MV against intrinsic colour c0for h Persei members. The thick line represents the ZAMS from Perry et al. (1987). Three isochrones corresponding to $\log t = 7.0, 7.15$ and 7.30are labelled with their respective $\log t$. Filled circles are supergiant stars not observed by us and taken from the study of Crawford et al. (1970b). Open squares are stars in our sample previously catalogued as having high rotational velocity (Slettebak 1968).

(a) Since the Balona & Shobbrook calibration is only valid for B-type stars, we select only those stars that we used for the reddening determination, calculate their intrinsic photometric indices adopting the average reddening for each cluster, and derive MV from c0 and $\beta $. For each star, we obtain the distance modulus V0 - MV, and finally we calculate the distance modulus for each cluster as the average of its members. The values obtained are listed in Tables 15 and 16.

For h Persei, we find an average $V_{0} - M_{V}= 11.4\pm0.5$, where the uncertainty represents only the standard deviation of the individual measurements and does not include the errors derived from the uncertainty in the photometric indices or the calibration itself. When these are taken into account, the determinations for all individual stars are compatible with the average value, but for the possible exception of star 880.


 

 
Table 12: Photometric data for Be stars of h Persei.
Number V b-y m1 c1 $\beta $ $\sigma_{V}$ $\sigma_{b-y}$ $\sigma_{m_{1}}$ $\sigma_{c_{1}}$ $\sigma_{\beta}$ Nuvby $N_{\beta}$
922 9.528 0.363 -0.188 0.220 2.600 0.008 0.004 0.015 0.008 - 2 1
1161 10.148 0.383 -0.047 0.085 2.559 0.019 0.021 0.046 0.036 0.001 5 2
1268 9.355 0.339 -0.019 0.032 2.624 0.008 0.001 0.008 0.019 - 2 1



 

 
Table 13: Photometric data for Be stars of $\chi $ Persei.
Number V b-y m1 c1 $\beta $ $\sigma_{V}$ $\sigma_{b-y}$ $\sigma_{m_{1}}$ $\sigma_{c_{1}}$ $\sigma_{\beta}$ Nuvby $N_{\beta}$
2088 9.117 0.367 -0.161 0.071 2.544 - - - - - 1 1
2165 10.053 0.342 -0.114 0.075 2.483 0.018 0.019 0.033 0.016 0.011 4 3
2242 10.956 0.321 -0.076 0.300 2.552 0.010 0.016 0.030 0.021 0.015 5 3
2262 10.538 0.343 -0.110 0.126 2.542 0.005 0.012 0.012 0.014 0.020 5 3
2284 9.673 0.330 -0.034 -0.074 2.426 0.013 0.017 0.070 0.072 0.019 3 2
2371 9.204 0.260 0.040 0.370 2.585 0.022 0.053 0.135 0.513 0.016 3 2


The average value for $\chi $ Persei is $V_{0} - M_{V}= 12.1\pm0.2$. There are several stars that deviate considerably from the cluster mean, namely 2296, 2091 and 2251, some of which have very large uncertainties in MV. Removing these stars does not significantly change the average value for V0 - MV.

  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig12.eps}\end{figure} Figure 11: Absolute magnitude MV against intrinsic colour (b-y)0for $\chi $ Persei members. The thick line represents the ZAMS from Perry et al. (1987). Three isochrones corresponding to $\log t = 7.0, 7.15$ and 7.30are labelled with their respective $\log t$. Filled circles are supergiant and giant stars not observed by us and taken from the study of Crawford et al. (1970b). Open squares are stars in our sample previously catalogued as having high rotational velocity (Slettebak 1968).


  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig13.eps}\end{figure} Figure 12: Absolute magnitude MV against intrinsic colour c0for $\chi $ Persei members. The thick line represents the ZAMS from Perry et al. (1987). Three isochrones corresponding to $\log t = 7.0, 7.15$ and 7.30are labelled with their respective $\log t$. Filled circles are supergiant and giant stars not observed by us and taken from the study of Crawford et al. (1970b). Open squares are stars in our sample previously catalogued as having high rotational velocity (Slettebak 1968).

(b) Fitting the theoretical ZAMS is not only intrinsically more accurate, but also makes use of all the stars in the sample. This is important, because when the A and F stars are well fit to the ZAMS, it can be seen (Figs. 9-12) that all early B stars deviate significantly from the ZAMS.

We fit individually data from both clusters and derive best fit distance moduli of $V_{0}-M_{V} = 11.56\pm0.20$ for $\chi $ Persei and $V_{0}-M_{V} = 11.66\pm0.20$ for h Persei (the error indicates the uncertainty in positioning the theoretical ZAMS and its identification as a lower envelope). We see that the two values are, within the errors, identical, and that the values derived by using the Balona & Shobbrook calibration, with their larger errors, are compatible with them. We therefore come to the conclusion that both clusters are indeed at the same distance.

As a further test, we plot in Figs. 13 and 14 the combined V0-(b-y)0 and V0-c0 diagrams for stars in both clusters. Points in these diagrams represent average values for the photometric index, taken over an interval of 0.5 mag, displaced by the individual distance modulus found for each cluster. It is obvious that both clusters fit the same ZAMS, confirming that the distance modulus are basically identical.

4.4 Age determination

(a) We first derive the age of both clusters on the basis of the data of our sample. It is well known that a number of giant stars in h & $\chi $ Persei have rotational velocities considerably higher than the average for field stars of the same spectral type and also that some of these are Be stars (Slettebak 1968; Waelkens et al. 1990; Denoyelle et al. 1994). Such stars can occupy positions in the photometric diagrams that differ considerably from those of non-peculiar stars of the same spectral type. For this reason, no Be stars have been included in our plots. Similarly, three supergiants binaries and four possible binary candidates in the clusters observed by Abt & Levy (1973) have also been excluded.

By comparing Figs. 13 and 14, it is obvious that the dispersion in the location of evolved stars in the MV-(b-y)0 diagram is an artifact introduced by differential reddening, since it disappears completely in the MV-c0diagram. This again confirms that the latter must be preferred as the reference colour-magnitude plot.

Also plotted in Figs. 9-14 are isochrones computed with the evolutionary models of Schaller et al. (1992) for a log age of 7.00, 7.15 and 7.30 respectively (Meynet et al. 1993). The metallicities adopted are X=0.68, Y=0.30 and Z=0.020 (Schaller et al. 1992). The isochrones have been transformed from the LogT-LogL plane to the uvby system after Torrejón (1996). The data clearly show that the main-sequence turnoff in h Persei occurs at a later spectral type than in $\chi $ Persei, which indicates that, contrary to previous speculations, h Persei is actually older than $\chi $ Persei.

In spite of this it is clear from Fig. 10 that the brightest stars in h Persei are substantially younger than the rest of the cluster, with some of them falling on the $\log t=7.0$ isochrone. This effect cannot be due to the fact that some of the stars are fast rotators. In Figs. 9-12 stars with high rotational velocities have been identified (1133 in hPersei and 2296 and 2299 in $\chi $ Persei, Slettebak 1968). Most of the stars falling on the $\log t=7.0$ isochrone have low measured rotational velocities. Morever Meynet & Maeder (2000) have shown that a $\log t=7.3$ isochrone for high rotational velocity stars is almost identical to a $\log t=7.2$ isochrone without rotation and therefore a variation in $\log t$ of 0.3 dex is too high to be explained by high rotation alone.

(b) In order to verify our conclusions, we have included data for a few stars brighter than V=11 taken from the literature, (see discussion in Sect. 4.1). For consistency, their unreddened photometric values have been calculated with the average reddening obtained for the central region of both clusters, since we have already shown that this has little bearing on the MV-c0 diagram.

Inclusion of brighter stars in the H-R diagram of h Persei corroborates our original finding. All the earliest stars are consistent with $\log t=7.0$ or even younger, with the brightest supergiant stars even suggesting $\log t=6.8$ (See Fig. 10).

This two-branch age distribution, with most stars being compatible with $\log t=7.3$ and all the massive stars indicating $\log t=7.0$ or younger is clearly not due to the presence of binaries or high rotational velocity stars.

The presence of stars with high rotation results in an apparent age dispersion (Meynet & Maeder 2000) and not in the separation into two branches. We note that massive stars from both the central region and the outskirts of the cluster display this effect without any obvious age separation, i.e., the younger age of massive stars does not seem to be related to their spatial distribution.

A similar situation can be observed in $\chi $ Persei (see Fig. 12). Two of the brightest stars seem to be younger than the rest of the cluster and fit the $\log t=7.0$ isochrone. In this case, however, dispersion due to effects such as rotation cannot be ruled out, specially since not all bright stars seem younger than the bulk of the cluster.

 

 
Table 14: Intrinsic photometric values and approximate spectral classification for all members (h Persei members on the left column, $\chi $ Persei members on the right). Unless otherwise indicated in the text, luminosity class is always taken to be V.
Number V0 (b-y)0 c0 Spectral Type Number V0 (b-y)0 c0 Spectral Type
820 11.281 -0.090 0.497 B6 2085 9.648 -0.088 0.179 B3
821 13.600 0.096 0.965 A8 2091 10.022 -0.029 0.270 B3
832 12.325 -0.089 0.829 A0 2092 13.086 0.027 1.004 A2
836 13.883 0.008 0.754 A3 2094 10.189 -0.088 0.184 B2
837 12.203 -0.029 0.819 A0 - - - - -
842 11.250 -0.105 0.485 B7 2108 12.936 -0.046 0.872 A0
843 7.438 -0.122 0.152 B1 2109 13.340 0.059 1.005 A5
844 13.700 0.059 1.025 A8 2111 11.787 -0.024 0.608 B7
845 12.872 -0.046 0.934 A0 2114 9.369 -0.082 0.184 B2
848 13.203 -0.024 1.030 A2 2116 11.826 -0.028 0.618 B8
854 12.348 -0.035 0.973 A1 2123 13.376 0.021 1.044 A2
856 13.699 0.078 1.077 A7 2124 13.462 0.074 1.019 A5
857 13.017 -0.015 0.990 A0 2133 10.521 -0.073 0.293 B3
864 8.035 -0.145 0.095 B2 2139 9.661 -0.074 0.201 B1
875 13.719 0.093 0.929 A5 2147 12.682 0.002 0.944 A0
876 10.823 -0.066 0.352 B3 2149 12.456 -0.005 0.760 B9
879 9.686 -0.114 0.197 B2 2167 11.687 -0.043 0.538 B6
880 11.137 -0.041 0.404 B3 2170 13.621 0.064 1.031 A5
885 13.870 0.038 0.963 A5 2174 13.638 0.047 1.036 A7
892 9.324 -0.100 0.217 B1 2175 12.878 -0.030 0.952 A0
893 10.072 -0.077 0.404 B4 2179 12.462 -0.049 0.910 A0
896 10.597 -0.105 0.368 B5 2193 13.725 0.049 0.970 A5
898 12.660 -0.037 0.879 A0 2194 11.804 -0.050 0.608 B8
901 13.010 -0.015 0.973 A0 2196 9.872 -0.086 0.168 B2.5
907 10.482 -0.092 0.331 B3 2200 11.011 -0.087 0.397 B5
909 13.296 0.123 1.026 A7 2206 13.913 0.092 0.936 A7
914 13.310 0.030 1.099 A3 2209 13.719 0.034 1.063 A5
917 12.883 -0.067 0.935 A1 2211 11.273 -0.090 0.474 B7
923 11.152 -0.117 0.349 B5 2214 14.097 0.081 0.898 A7
924 13.281 0.037 1.010 A3 2215 13.869 0.092 1.034 A5
929 8.414 -0.118 0.137 B2 2219 13.746 0.111 0.870 A7
930 10.485 -0.079 0.336 B5 2223 12.341 0.001 0.974 A1
934 12.753 0.000 0.889 A0 2224 12.169 -0.024 0.624 B8
935 12.159 -0.029 0.768 B9 2229 9.666 -0.095 0.160 B2
936 8.503 -0.115 0.118 B1 2232 9.377 -0.157 0.090 B2
939 10.371 -0.074 0.306 B3 2235 7.688 -0.079 0.053 B1
941 13.325 -0.011 0.979 A1 2239 12.543 -0.023 0.776 B9
945 12.904 -0.053 0.942 A1 2240 12.359 -0.105 0.681 A0
946 12.526 -0.001 0.962 A1 2241 11.913 -0.071 0.669 B9
947 13.936 0.077 0.878 A7 2245 10.820 -0.101 0.341 B5
948 13.741 0.037 0.968 A3 2246 8.259 -0.108 0.034 B1
949 13.812 0.043 0.904 A5 2249 13.472 -0.009 1.002 A2
950 9.405 -0.104 0.133 B2 2251 9.886 -0.093 0.289 B4
952 10.180 -0.098 0.306 B3 2253 10.956 -0.102 0.427 B7
955 13.889 0.090 1.008 A8 2254 13.595 0.057 0.983 A5
956 10.662 -0.077 0.426 B5 2255 9.015 -0.102 0.096 B2
959 10.966 -0.086 0.431 B6 2258 12.271 -0.061 0.804 B9
960 11.823 -0.080 0.648 B9 2260 12.300 -0.014 0.769 B9
963 9.129 -0.117 0.144 B1 2261 12.857 -0.051 0.930 A0
965 10.703 -0.075 0.388 B5 2267 11.547 -0.103 0.429 B7
966 12.354 -0.068 0.830 A0 2268 11.945 -0.054 0.591 B8
970 12.511 -0.044 0.795 B9 2269 11.427 -0.088 0.480 B7
971 12.568 -0.061 0.917 A0 2270 12.476 -0.012 0.847 A0
978 8.754 -0.112 0.106 B2 2275 11.409 -0.038 0.411 B6
979 12.354 -0.031 0.829 A0 2277 13.271 -0.022 0.999 A2
980 7.824 -0.130 0.106 B1.5 2283 12.963 -0.018 0.913 A0
982 12.027 -0.068 0.702 B9 2286 13.048 -0.014 0.975 A1
985 10.226 -0.103 0.325 B4 2294 12.481 -0.068 0.733 B9



 
Table 14: continued.
Number V0 (b-y)0 c0 Spectral Type Number V0 (b-y)0 c0 Spectral Type
986 10.697 -0.115 0.313 B5 2296 6.816 -0.110 0.018 B1.5
987 12.743 0.018 0.988 A3 2297 11.266 -0.051 0.398 B5
988 10.857 -0.118 0.377 B6 2299 7.447 -0.118 -0.01 B1
990 12.537 -0.083 0.759 A0 2300 13.921 0.062 0.664 -
991 9.535 -0.094 0.180 B2.5 2301 10.257 -0.108 0.258 B5
992 8.060 -0.116 0.121 B1.5 2307 13.518 0.034 0.968 A5
997 9.194 -0.102 0.173 B2 2309 11.107 -0.128 0.403 B7
999 11.462 -0.102 0.509 B8 2311 7.713 -0.106 0.152 B2
1004 8.957 -0.106 0.149 B2 2314 12.883 -0.039 0.994 A1
1007 13.683 0.007 1.021 A5 2317 13.328 -0.002 1.011 A2
1014 11.034 -0.116 0.400 B7 2319 11.415 -0.118 0.471 B8
1017 13.899 0.074 0.947 A8 2323 12.541 -0.050 0.842 A0
1018 13.761 0.039 1.046 A5 2324 12.212 -0.087 0.744 A0
1020 11.879 -0.070 0.585 B8 2331 12.508 -0.063 0.873 A0
1021 11.105 -0.089 0.513 B8 2332 12.901 0.031 0.910 A2
1025 13.859 0.075 0.943 A5 2335 12.729 0.015 0.968 A2
1028 12.886 -0.039 0.944 A1 2338 11.933 -0.045 0.633 B9
1030 14.156 0.137 0.859 A7 2349 11.138 -0.126 0.362 B7
1031 13.324 0.012 0.992 A3 2350 11.699 -0.068 0.447 B7
1034 13.254 0.023 0.940 A3 2352 10.655 -0.092 0.326 B6
1038 13.678 0.073 1.021 A5 2355 13.897 0.040 0.799 A5
1041 9.165 -0.119 0.136 B2.5 2358 12.631 -0.071 0.781 A0
1049 12.005 -0.036 0.590 B7 2359 12.205 -0.078 0.713 B9
1050 14.110 0.113 0.921 A7 2362 13.769 0.025 0.988 A3
1052 13.334 -0.004 1.052 A2 2363 12.243 -0.083 0.773 A0
1053 12.721 -0.098 0.771 A0 - - - - -
1056 12.779 -0.012 0.969 A0 2379 10.541 -0.129 0.232 B5
1058 11.729 -0.050 0.609 B8 2392 9.075 -0.114 0.099 B2
1059 12.836 -0.005 1.031 A1 2401 13.781 0.148 0.987 A5
1064 12.721 -0.040 0.820 A0 2407 12.647 -0.064 0.761 A0
1066 11.253 -0.066 0.467 B7 2410 12.533 -0.064 0.709 A0
1077 11.900 -0.061 0.618 B9 2414 12.192 -0.106 0.812 A2
1078 7.883 -0.123 0.050 B2 2416 13.636 -0.014 0.910 A3
1079 13.747 0.030 0.689 A2 7014 14.210 0.168 0.815 F0
1080 9.259 -0.104 0.109 B2.5 7015 14.253 0.154 0.833 A7
1081 12.428 -0.054 0.793 A0 7016 14.026 0.106 0.925 A5
1083 11.496 -0.070 0.486 B7 7017 14.486 0.206 0.7047 F3
1085 8.534 -0.114 0.048 B1.5 7021 14.594 0.274 0.708 F4
1091 13.986 0.064 0.888 A7 7023 14.383 0.234 0.755 A8
1093 11.594 -0.051 0.486 B7 7024 14.329 0.184 0.772 A8
1095 11.743 -0.062 0.532 B8 7027 14.036 0.185 0.863 F0
1096 13.186 0.024 1.031 A3 - - - - -
1105 12.107 -0.051 0.719 B9 7037 14.618 0.240 0.565 -
1106 12.212 -0.041 0.728 B9 7038 13.466 0.024 1.065 A2
1108 12.037 -0.047 0.716 B9 7045 13.975 0.166 0.676 F0
1109 9.080 -0.100 0.110 B3 7046 14.260 0.065 1.041 A8
1110 11.569 -0.081 0.515 B8 7047 14.425 0.182 0.821 A7
1116 7.360 -0.089 0.042 B2 7048 14.058 0.120 0.994 A5
1117 13.877 0.078 0.905 A8 7049 14.804 0.266 0.621 -
1118 12.193 -0.054 0.751 B9 7052 14.386 0.189 0.646 A7
1121 11.841 -0.052 0.595 B8 7054 14.392 0.198 0.701 F2
1122 10.332 -0.074 0.321 B6 7062 13.425 0.008 0.959 A2
1126 10.803 -0.096 0.230 B5 7064 14.255 0.127 0.896 F0
1128 10.261 -0.079 0.252 B5 7066 14.248 0.093 0.834 -
1129 11.038 -0.049 0.419 B7 7067 14.597 0.212 0.710 F5
1130 12.582 -0.029 0.801 A0 7068 14.233 0.138 0.840 A8
1132 6.548 -0.099 -0.00 B2 7070 14.441 0.218 0.724 F0
1133 7.095 -0.073 0.001 B1 7077 14.421 0.189 0.821 F0
1145 12.894 -0.016 0.937 A2 7080 14.182 0.197 0.872 A7



 
Table 14: continued.
Number V0 (b-y)0 c0 Spectral Type Number V0 (b-y)0 c0 Spectral Type
1147 12.719 0.033 0.910 A3 7083 13.889 0.053 0.909 A7
1152 12.909 -0.008 0.970 A1 7084 11.529 -0.063 0.452 B7
1163 13.240 0.065 0.962 A7 7085 14.197 0.106 0.682 A7
1175 12.636 -0.013 1.017 A1 7086 7.684 -0.134 -0.00 B2.5
1179 11.003 -0.054 0.376 B6 7088 14.823 0.329 0.503 -
1180 12.937 -0.042 0.754 A2 7091 14.535 0.317 0.604 F2
1181 10.763 -0.088 0.250 B5 7092 13.162 -0.011 0.962 A2
1185 11.286 -0.039 0.407 B7 7093 14.337 0.151 0.686 F0
1190 13.527 0.018 1.046 A3 7096 14.310 0.179 0.702 A8
1191 12.821 -0.014 0.837 A0 7097 14.442 0.329 0.549 F4
1192 13.037 0.014 1.148 A3 7099 14.428 0.210 0.729 F2
1198 11.912 -0.041 0.615 B9 7104 14.086 0.083 0.861 A7
1202 10.231 -0.088 0.268 B5 7105 14.406 0.172 0.896 F0
1203 12.018 -0.038 0.723 B9 7108 14.766 0.251 0.554 F2
1206 12.754 -0.005 0.900 A1 7109 14.408 0.174 0.797 F0
1213 12.730 -0.034 0.854 A0 7116 14.334 0.207 0.781 F0
1218 13.997 0.090 0.940 A7 7118 14.216 0.069 0.820 A8
1222 13.747 0.079 1.007 A5 7122 13.204 0.037 0.821 A3
1232 9.391 -0.102 0.114 B3          
1240 14.013 0.065 0.895 A7          
1251 13.626 0.046 1.034 -          
1260 12.296 -0.006 0.726 A0          
1262 12.531 -0.062 0.907 A0          
1265 12.462 -0.085 0.814 A0          
1267 12.530 0.002 0.698 A0          
1281 12.159 -0.015 0.839 A0          
4009 14.050 0.247 0.776 A8          
4011 14.084 0.092 0.798 A7          
4012 14.108 0.264 0.739 F2          
4013 14.131 0.163 0.875 A8          
4016 14.171 0.183 0.696 F2          
4017 14.205 0.118 0.782 F0          
4018 14.216 0.187 0.934 A8          
4023 14.266 0.119 0.858 F0          
4025 14.309 0.125 0.622 F0          
4029 14.438 0.224 0.936 A7          
4030 14.438 0.208 0.693 -          
4036 14.480 0.163 0.630 F0          
4037 14.493 0.232 0.660 F0          
4042 14.538 0.203 0.733 F0          



 

 
Table 15: Individual intrinsic data for B stars in h (right) and $\chi $(left) Persei. The colour excess E(b-y) has been calculated using Crawford's et al. (1970b) procedure. The absolute magnitudes have been calculated by using the calibration (based on the $\beta $ index) by Balona & Shobbrook (1984). The error in MV has been computed using the formula by Balona & Shobbrook (1984). See text for details.
Number E(b-y) MV $\sigma_{M_{V}}$ V0-MV Number E(b-y) MV $\sigma_{M_{V}}$ V0-MV
2085 0.401 -1.747 0.509 11.333 843 0.419 - - -
2091 0.452 -4.392 0.471 14.147 864 0.401 -2.224 0.298 10.259
2094 0.400 -1.858 0.252 12.003 876 0.456 -0.953 0.140 11.776
2111 0.424 -0.419 0.029 12.061 879 0.423 -2.051 0.273 11.737
2114 0.406 -2.223 0.131 11.521 880 0.477 -1.539 0.169 12.676
2116 0.419 -0.334 0.230 12.037 892 0.435 -2.015 0.542 11.339
2133 0.405 -1.401 0.263 11.858 893 0.440 -1.037 0.254 11.109
2139 0.413 -2.326 0.164 11.888 896 0.415 -1.384 0.405 11.981
2167 0.411 -0.377 0.103 11.972 907 0.432 -1.222 0.345 11.704
2194 0.397 -0.391 0.438 12.164 929 0.424 -2.647 0.120 11.061
2196 0.404 -2.135 0.252 11.947 930 0.444 -0.888 0.120 11.373
2200 0.380 -0.841 0.136 11.893 936 0.429 -2.673 0.090 11.176
2211 0.370 -0.916 0.365 12.276 939 0.453 -1.221 0.382 11.592
2224 0.422 -0.107 0.335 12.138 950 0.439 -2.533 - 11.938
2229 0.396 -2.228 0.312 11.870 952 0.428 -1.465 0.125 11.645
2232 0.339 -2.383 0.502 11.978 956 0.438 -0.919 0.087 11.581
2235 0.422 -3.839 0.968 11.387 959 0.428 -0.954 0.371 11.920
2241 0.370 0.109 0.388 11.892 963 0.425 -2.331 0.027 11.460
2245 0.372 -1.520 0.106 12.419 965 0.443 -0.844 0.493 11.547
2246 0.395 -3.555 0.904 11.794 978 0.434 -2.534 0.085 11.288
2251 0.385 -1.004 0.211 10.912 980 0.415 -2.788 0.280 10.612
2253 0.362 -0.496 0.426 11.572 985 0.421 -1.156 0.113 11.382
2255 0.395 -3.201 0.287 12.196 986 0.410 -1.280 0.078 11.977
2267 0.361 -0.300 0.199 11.972 988 0.401 -0.814 0.152 11.671
2268 0.395 -0.382 0.511 12.306 991 0.445 -2.224 0.131 11.759
2269 0.371 -0.560 0.280 12.068 992 0.428 -2.310 - 10.370
2275 0.429 -0.689 0.599 11.931 997 0.437 -2.023 0.146 11.217
2296 0.394 -3.855 0.825 10.652 1004 0.435 -2.327 0.107 11.284
2297 0.417 -1.003 0.108 12.153 1014 0.400 -0.442 0.386 11.476
2299 0.390 -3.860 0.292 11.308 1021 0.417 -0.085 0.254 11.190



 

 
Table 16: Individual intrinsic data for B stars in h (right) and $\chi $(left) Persei. The colour excess E(b-y) has been calculated using Crawford's et al. (1970b) procedure. The absolute magnitudes have been calculated by using the calibration (based on the $\beta $ index) by Balona & Shobbrook (1984). The error in MV has been computed using the formula by Balona & Shobbrook (1984). See text for details (continued Table 15).
Number E(b-y) MV $\sigma_{M_{V}}$ V0-MV Number E(b-y) MV $\sigma_{M_{V}}$ V0-MV
2301 0.373 -1.185 0.371 11.516 1041 0.423 -2.199 0.406 11.364
2309 0.338 -0.935 0.123 12.266 1078 0.428 -3.191 0.035 11.074
2319 0.341 -0.590 0.299 12.214 1080 0.441 -2.284 0.102 11.543
2324 0.346 -0.095 0.091 12.496 1085 0.437 -2.839 0.090 11.373
2338 0.400 0.253 0.180 11.638 1109 0.445 -2.172 0.269 11.252
2349 0.344 -0.896 0.104 12.232 1116 0.463 -3.056 - 10.416
2350 0.395 -0.711 0.114 12.389 1122 0.451 -0.819 0.149 11.151
2352 0.382 -1.013 0.268 11.702 1126 0.438 -1.146 0.430 11.949
2359 0.358 0.487 0.144 11.855 1128 0.453 -1.487 0.330 11.748
2379 0.354 -1.367 0.157 12.064 1129 0.467 -0.642 0.175 11.680
2392 0.382 -2.142 0.383 11.250 1132 0.458 -4.037 - 10.585
2414 0.320 0.424 - 12.069 1133 0.484 - - -
7084 0.399 - - - 1179 0.466 -1.232 0.077 12.235
7086 0.372 -3.240 0.165 11.001 1181 0.444 -1.216 0.224 11.979
- - - - - 1202 0.442 -1.132 0.109 11.363
- - - - - 1232 0.443 -2.456 0.110 11.847



  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig14.eps}\end{figure} Figure 13: Absolute magnitude MV against intrinsic colour (b-y)0for h & $\chi $ Persei members. The ZAMS and isochrones are as in figures for the individual clusters. Data points represent averages taken over 0.5 mag intervals for each cluster. Filled squares are datapoints for h Persei, while open squares are datapoints for $\chi $ Persei.

5 Discussion

We find that the reddening and distance moduli to h & $\chi $ Persei are consistent with both clusters being placed at the same distance. However, the later main-sequence turnoff of h Persei indicates that this cluster is older than $\chi $ Persei, as far as a single age determination is meaningful. From isochrone fitting, we find that the bulk of stars in h Persei fit an age of $\log t = 7.30$, while in $\chi $Persei no star seems to be old enough to lie on the $\log t = 7.30$ isochrone. However, all the earliest stars in h Persei deviate clearly and strongly from the rest of the cluster with some stars falling along the $\log t=7.0$ isochrone and the brightest objects being even younger (probably as young as $\approx$ $\log t=6.8$).

Almost all the stars in $\chi $ Persei are consistent with $\log t=7.10-7.15$, though two of the brightest stars could be slightly younger ( $\log t=7.00$). The low age of the few brightest members of hPersei is the reason why previous authors attributed a younger age to h Persei than to $\chi $ Persei (Tapia et al. 1984; Schild 1967). On the other hand, the age of most stars in $\chi $ Persei corresponds approximately to the average between the two branches in h Persei, which explains why other authors have given the same age for both clusters (Crawford et al. 1970b). The presence of at least two branches in the H-R diagram for h Persei strongly suggests two star formation epochs, the younger one corresponding to the more massive stars.


  \begin{figure} \par\includegraphics[width=6.7cm,clip]{10127.fig15.eps}\end{figure} Figure 14: Absolute magnitude MV against intrinsic colour c0for h & $\chi $ Persei members. The ZAMS and isochrones are as in figures for the individual clusters. Data points represent averages taken over 0.5 mag intervals for each cluster. Filled squares are datapoints for h Persei, while open squares are datapoints for $\chi $ Persei.

Since the age of the bulk of $\chi $ Persei does not correspond to any of the two isochrone fits in h Persei (which we find to be at the same distance), the evidence points to several stages of star formation in the region.

This effect can be observed both when we consider only the stars covered by our observations (which are all relatively close to the main sequence) and also when the brighter members taken from the literature (in a later evolutionary stage and not necessarily belonging to the central region) are included. Since we have excluded any star that could be suspect of binarity or any pecularities, and the MV-c0 is not significatively affected by reddening, we may conclude that the age spread is real.

Our distance determination is consistent with some of the higher values found in literature (except those which give a different and larger distance to $\chi $ Persei). We derive our distance by fitting the ZAMS to stars much fainter than in previous work. As indicated by Vrancken et al. (2000), the lower distance moduli measured by Crawford et al. (1970b) and Balona & Shobbrook (1984) are due to their use of only the brightest stars. As can be seen in our HR diagrams, all stars earlier than $\approx$B3 deviate considerably from the ZAMS. This is again in agreement with the results of Vrancken et al. (2000), who find that all the stars in their sample of B1 and B2 stars are giants, even though some of them were previously classified as main-sequence.

From our data, we find no new Be stars in h & $\chi $ Persei. This is not the last word on this issue, because many catalogued Be stars do actually show a $\beta $ index that does not indicate emission in our data. Since our census of B stars in the areas observed is complete, we can calculate the fraction of Be stars with respect to total number of B stars. In h Per, we find 3 Be stars among 74 B stars, which means an abundance $N_{\rm Be}/N_{{\rm B + Be}}$ (supergiants excluded) of 4%. In $\chi $ Persei, we find 6 Be stars out of 53 B stars, representing an abundance of 11%. Given the scatter in ages in h Per and the small number of Be stars, we cannot derive any conclusions about the effect of cluster age on Be abundance.

6 Conclusions

We derive reddening and distance values consistent with the idea that h Persei and $\chi $ Persei are placed at the same distance. From the ZAMS fitting, we derive an approximate distance modulus $V_{0}-M_{V}=11.6\pm0.2$ for both clusters. The ages of the two clusters seem to be, however, different. There is evidence for two massive star populations in h Persei, fitting the $\log t=7.0$ and $\log t=7.3$isochrones, with the more massive stars being younger. The age spread in $\chi $ Persei is, on the other hand, negligible, with all stars fitting the $\log t=7.10-7.15$ isochrone. We interpret these data as favouring the idea that both clusters belong to a single star forming region in which at least three different star formation stages have taken place.

Acknowledgements

We would like to thank the Spanish CAT panel for allocating observing time to this project. AM would like to thank Dr. J. Fabregat for his help with the observations and Dr. J. M. Torrejón for making available the theoretical isochrones transformed to the MV/c0 and MV/(b-y)0 spaces. The authors gratefully acknowledge an anonymous referee for his/her very valuable comments.

References

 

Copyright ESO 2001