3 Results

3.1 Physical parameters of NGC 2539

We present the color-color diagram (Fig. 3) and the color-magnitude diagrams (Fig. 4) from the UBVI photometric data.

Figure 3: Color-color diagram of the open cluster NGC 2539. Solid and dashed lines denote the unreddened and reddened empirical ZAMS by Sung & Bessell (1999), respectively. Open circles: cluster members, star symbols: spectroscopic binaries and crosses: non-members, classified by Joshi & Sagar (1986), Clariá & Lapasset (1986) and Mermilliod & Mayor (1989). Dots are stars with unknown membership.

Figure 4: Color-magnitude diagrams of the open cluster NGC 2539. Thick lines denote the empirical ZAMS by Sung & Bessell (1999). Thin and dashed lines represent the theoretical isochrones for Z=0.019 by Girardi et al. (2000). From upper to the lower, the isochrones represent $\log t ($yr) = 8.7, 8.8 and 8.9, respectively. Symbols are the same as in Fig. 3.

In order to determine more accurate physical parameters of this cluster, we used cluster members with high priorities. Joshi & Sagar (1986) identified cluster members based on their positions in the color-color and color-magnitude diagrams and their spatial distributions in the sky. Clariá & Lapasset (1986) judged memberships of a few red giants by examining interstellar extinctions and luminosity classes, and Mermilliod & Mayor (1989) by measuring radial velocities. We estimated the interstellar reddening value $E(B-V)=0.06 \pm 0.03$ from the empirical zero-age main sequence fitting in the color-color diagram, with the assumption of E(U-B)/E(B-V) = 0.72. Another reddening value $E(V-I) = 0.08 \pm 0.03$ was calculated by the adoption of E(V-I)/E(B-V) = 1.25(Dean et al. 1978). Solid and dashed lines in Fig. 3 denote the unreddened and reddened zero-age main sequences by Sung & Bessell (1999) for solar metal abundance.

We determined the distance modulus of $(V-M_{V})_{0}=10.2 \pm 0.1$ and the cluster age of $\log t ($yr) = 8.8 from the zero-age main sequence and theoretical isochrone fitting in two color-magnitude diagrams of (B-V) vs. V and (V-I) vs. V as shown in Fig. 4. We assumed the total extinction value of $A_{V}=3.1 \times E(B-V)$ and made use of the theoretical isochrones with Z=0.019 calculated by Girardi et al. (2000).

In Table 2, we compare our results with the previous ones.

 

 

Table 2: Physical parameters of the open cluster NGC 2539.

Reference	E(B-V)	(V-MV)0	Age( $\times 10^{8}$yr)	[Fe/H]
Pesch (1961)	$0.10 \pm 0.05$	10.6	--	--
Clariá & Lapasset (1986)	$0.08 \pm 0.02$	$9.8 \pm 0.5$	$6.4 \pm 0.8$	(+0.24 $\pm$ 0.06) $_{\rm DDO}$
				(+0.2 $\pm$ 0.1)$_{\rm CM}$
				(-0.2 $\pm$ 0.1) $_{\rm MT_{1}}$
Joshi & Sagar (1986)	$0.08 \pm 0.02$	$10.1 \pm 0.3$	5.4	--
Lapasset et al. (2000)	0.06	10.42	6.3	--
Our study	$0.06 \pm 0.03$	$10.2 \pm 0.1$	6.3	--

Our values are generally similar to other ones; especially they are in good agreement with the recent values by Lapasset et al. (2000).

3.2 Variable stars in NGC 2539

We examined light variations of 583 stars using a total of 581 time-series CCD frames. Seven new variable stars were discovered. Position of variable stars, which are arbitrarily labeled from V1 to V7, are marked as open circles in Fig. 1. Two of them, V1 and V2, were identified as pulsating stars from their light curves. We estimated pulsating periods of V1 using the multiple frequency analysis by Kim & Lee (1996). Figures 5 and 6 show the power spectra and light curves of V1, respectively.

Figure 5: Power spectra of V1. The upper panel shows spectral window. The dominant pulsating frequency of V1 is 18.032 cycles/day.

Figure 6: Light variations of V1. The solid lines represent synthetic curves made by amplitudes and phases of two frequencies, f1=18.032 cycles/day and f2=0.240 cycles/day.

From the bottom panel of Fig. 5, we detected a pulsation frequency of f₁ = 18.032 cycles/day (0.055 day). Another frequency of f₂ = 0.240 cycles/day seems to be caused by daily variations, maybe the flat-field problem of our observation system (Sung et al. 2001); this might be the reason that a little large dispersions are shown in phase diagrams of $V2 \sim V7$ (Fig. 7).

Figure 7: Light curves of V2 to V7. Data points are differently marked for each observing night. Mean error bars are shown at the left bottom in each panel.

The period of another pulsating variable V2 was determined to be $0\hbox{$.\!\!^{\rm d}$ }352$ from the phase-match technique. Its light curve is shown in Fig. 7 together with five eclipsing binary stars from V3 to V7. Positions of two pulsating variables in the color-magnitude diagram are marked by star symbols in Fig. 8. Considering the positions, pulsating periods and amplitudes, we classify V1 as a $\delta$ Scuti star and V2 as a $\gamma$ Doradus star. But it should be noted that V2 might be a field star having larger reddening value of $\Delta E(B-V) \ge 0.2$ than the cluster members, because this star is cooler and fainter than the cool edge of $\gamma$ Doradus instability strip (Handler 1999).

The light curves of five eclipsing binary stars V3$\sim$V7 are shown in Fig. 7. These stars are represented by open circles in the color-magnitude diagram of Fig. 8. V5 shows the primary and secondary minima which are clearly discernible in spite of large dispersions of data points in the out-of-eclipse phase. Considering the position of V6 in the color-magnitude diagram, we think that V6 is a field star, as Clariá & Lapasset (1986) insisted. Basic parameters of seven new variable stars are summarized in Table 3.

Figure 8: Positions of seven new variable stars in the color-magnitude diagram of the open cluster NGC 2539. The thin line represents the empirical ZAMS by Sung & Bessell (1999). The thick dotted and solid bars indicate $\delta$ Scuti (Breger 1979) and $\gamma$ Doradus instability strip (Handler 1999), respectively. Two pulsating stars are marked by star symbols and five eclipsing binary stars by open circles.

   

Table 3: Basic parameters of seven new variable stars in the open cluster NGC 2539.

ID $_{\rm OURS}$	ID $_{\rm BDA}$	$\langle$ V $\rangle$	B-V	Period	$\Delta V_{\max}$	Epoch	Type	membership
V1	113	13 $.\!\!^{\rm m}$213	0 $.\!\!^{\rm m}$255	0 $.\!\!^{\rm d}$055	$\sim$0 $.\!\!^{\rm m}$02	2451597.1575	$\delta$ Scuti	--
V2	-	14 $.\!\!^{\rm m}$290	0 $.\!\!^{\rm m}$577	0 $.\!\!^{\rm d}$352	$\sim$0 $.\!\!^{\rm m}$04	2451585.13	$\gamma$ Doradus	field (?)
V3	-	15 $.\!\!^{\rm m}$652	0 $.\!\!^{\rm m}$739	0 $.\!\!^{\rm d}$292	$\sim$0 $.\!\!^{\rm m}$25	2451591.025	Eclipsing binary	--
V4	-	14 $.\!\!^{\rm m}$584	0 $.\!\!^{\rm m}$749	0 $.\!\!^{\rm d}$340	$\sim$0 $.\!\!^{\rm m}$13	2451596.06	Eclipsing binary	--
V5	329	14 $.\!\!^{\rm m}$301	0 $.\!\!^{\rm m}$581	0 $.\!\!^{\rm d}$945	$\sim$0 $.\!\!^{\rm m}$13	2451617.99	Eclipsing binary	--
V6	133	11 $.\!\!^{\rm m}$050	1 $.\!\!^{\rm m}$603	1 $.\!\!^{\rm d}$964	$\sim$0 $.\!\!^{\rm m}$07	2451630.07	Eclipsing binary	field
V7	338	12 $.\!\!^{\rm m}$527	0 $.\!\!^{\rm m}$250	0 $.\!\!^{\rm d}$700	$\sim$0 $.\!\!^{\rm m}$04	2451629.15	Eclipsing binary	--

ID $_{\rm BDA}$: Identification from the open cluster database by Jean-Claude Mermilliod (http://obswww.unige.ch/webda).

Until a few years ago, $\gamma$ Doradus stars were considered to be young objects from the fact that they were discovered in several open clusters with ages less than 250 Myr such as NGC 2516 (age  $\sim$  137 Myr, Zerbi et al. 1998), M 34 (age  $\sim$  250 Myr, Krisciunas & Patten 1999), M 45 (age  $\sim$  74 Myr, Martín & Rodríguez 2000) and NGC 2301 (age  $\sim$  250 Myr, Kim et al. 2001b). No $\gamma$ Doradus candidates were detected in the Hyades cluster with age of about 600 Myr (Krisciunas et al. 1995). Our result, no $\gamma$ Doradus stars in NGC 2539 with the cluster age of 630 Myr, is consistent with this suggestion by Krisciunas & Patten (1999). However, recent photometric survey discovered a few $\gamma$ Doradus candidates in open clusters with older ages than 250 Myr ; one in M 44 (age  $\sim$  730 Myr, Martín & Rodríguez 2002), one in Mel 111 (age  $\sim$  450 Myr, Martín 2000) and two in NGC 6633 (age  $\sim$  430 Myr, Martín 2002). Eyer et al. (2002) concluded that recent studies do not show a clear relationship between age and the incidence of $\gamma$ Doradus stars.