DETECTION OF A SECOND-GENERATION BINARY IN THE GLOBULAR CLUSTER ω CENTAURI

Eclipsing binaries play an important role in astrophysics. They are excellent tools for the study of star formation and stellar structure, in determining the physical properties of stars, and for testing the theories of stellar evolution. We can obtain their absolute physical parameters such as mass, radius, and luminosity from their combined photometric and spectroscopic solutions. Such studies lay the observational basis for the theories of stellar structure and evolution. Globular cluster eclipsing binaries are powerful tools for distance determination and are of great importance to the dynamic evolution of globular clusters. It was initially thought that eclipsing binaries are totally absent in the globular cluster environment. However, our thinking has been enormously changed by new discoveries in the past 20 years. More than one hundred eclipsing binaries have been discovered in globular clusters with the widespread use of the CCD detectors and of methods to extract photometric information from crowded images.

Twenty-six years ago, Renzini & Buzzoni (1986) pointed out that globular clusters are the best examples of simple stellar populations, assemblies of stars born at the same time and sharing homogeneous chemical composition. However, recent photometric and spectroscopic studies significantly challenged this traditional paradigm, causing a change in our understanding. In a recent high-resolution spectrum analysis involving a sample of 1958 stars in 19 galactic globular clusters, Carretta et al. (2009) convincingly showed that each globular cluster is composed of multiple stellar generations, with the coexistence of both first- and second-generation stars. Gratton et al. (2001, 2004) also found that globular clusters are actually made of multiple stellar populations.

ω Centauri, with an age of 16 ± 3 Gyr (Noble et al. 1991), is the most luminous and massive globular cluster in the Milky Way. This cluster has been extensively studied; many optical surveys have been carried out in order to search for variable stars in this cluster, which has a small heliocentric distance (=5.2 kpc and 1 pc = 3.26 lt-yr) (Harris 1996, 2010 edition). Indeed, over 400 variables have been discovered in this cluster, making it the most variable rich globular cluster in the Milky Way. Johnson et al. (2009) showed that there are at least four peaks in the metallicity distribution function, ranging from [Fe/H] = −1.75 to −0.75. Nearly half a century ago, Woolley (1966) was the first to claim that ω Centauri is a complex cluster composed of several populations. This has been supported by the more recent photometry and spectroscopy observations. Recently, Bedin et al. (2004) found two (and possibly more) separate sequences of the main sequence in the cluster. This cluster is considered to be the nucleus of a nucleated dwarf galaxy which has been completely destroyed by the Galactic tidal field (Bekki & Norris 2006).

So far, there have been more than 30 EA-type binaries discovered in globular clusters. V78 of ω Centauri was once assumed to be the first EA-type binary discovered in globular clusters. However, from their radial velocity analysis, Geyer & Vogt (1978) found that V78 is not a member of the ω Centauri cluster. As globular clusters are very dense with thousands of member stars, it is difficult to observe the EA-type binaries. Only a few globular cluster EA-type binaries such as NJL 5, V209, and OGLEGC 18 in ω Centauri (Helt et al. 1993; Kaluzny et al. 2007; Thompson et al. 2001) have had photometric solutions and physical parameters determined. NV364, with a period of 0.84724 days, is one of the 18 EA-type binaries in the globular cluster ω Centauri. It was first discovered near the outer region of the cluster by Kaluzny et al. (2004) during a photometric survey for variable stars in the field of this cluster. Since no detailed photometric analysis has been carried out for this binary, we analyze the B and V passband light curves (LCs) collected from Kaluzny et al. (2004) and estimate its physical parameters by the LC program of the Wilson–Devinney (W–D) code. We also calculate the distance modulus of NV364 using the luminosity–color relation with optical (BV) observations. The ages of the binary components are obtained based on the mass–radius relation. These results should be considered preliminary because of the lack of spectroscopic data.

ω Centauri was observed during the interval from 1999 February 6–7 to 2000 August 9–10 using the 1.0 m Swope telescope at Las Campanas Observatory by the Kaluzny group (Kaluzny et al. 2004) under the Cluster AgeS Experiment (CASE) project.⁵ The data were collected on 59 nights and revealed 117 new variables, including 35 SX Phe variables, 26 binaries, and 17 RR Lyrae stars. On the basis of their observations, we analyze the LCs of one EA-type binary NV364. The ephemeris used to calculate the phases of NV364 is

$$\begin{equation} {\rm Min.\, I}=2451306.7344+0.84724E. \end{equation} \tag{ 1 }$$

This is the first time photometric solutions of the binary system NV364 have been obtained. We delete some of the photometric data that have large errors (mostly in the B band). The 2003 version of the W–D program (Wilson & Devinney 1971; Wilson 1990, 1994; Wilson & Van Hamme 2003) is used to model the BV LCs. The iterations are made in mode 2, which corresponds to the detached configuration. Bellini et al. (2009) determined (B − V) as 0.113 and the membership probability as 93% for NV364. Adopting an interstellar reddening of E(B − V) = 0.12 for ω Centauri following Harris (1996; 2010 edition), we derive (B − V)₀ = −0.007 for NV364. The color index of the system is mostly provided by the primary component, and the effective temperature of the primary is normally fixed by the color index of the system. Therefore, we fix the (B − V)_{0, 1} of the primary component at a value of −0.007. We adopt a metallicity of [Fe/H] = −1.53 (Harris 1996; 2010 edition) and expect log g to lie between 4.0 and 4.5. Using the program provided by Worthey & Lee (2011), we calculate the effective temperature of the primary component T₁ = 9383 ± 94 K and 9429 ± 94 K corresponding to the values of log g and the above (B − V)_{0, 1}. As the photometric solution is sensitive to the temperature ratio but fairly insensitive to the actual value of T₁ (Yakut & Eggleton 2005), we adopt an average value of T₁ = 9406 ± 94 K. So, the primary component of NV364 has radiative-equilibrium envelope. The bolometric albedo and the gravity-darkening coefficient of the primary are set as A₁ = 1.0 and g₁ = 1.0. The bolometric and bandpass limb-darkening coefficients of the primary are also fixed (van Hamme 1993). The previous parameters of the secondary component can be fixed based on the value of the effective temperature of the secondary component T₂.

The adjustable parameters are the mass ratio q, the effective temperature of the secondary component T₂, the monochromatic luminosity of the primary component in each band L₁, the orbital inclination i, and the dimensionless potentials of the two components Ω₁ and Ω₂. First, we should obtain the mass ratio q. To determine an accurate value of the mass ratio q, the respective parameters are set free until a convergent solution is obtained at the minimum value of residuals, ΣW(O − C)² (Figure 1). The final photometric solutions are listed in Table 1, where Ω_in is the inner Roche lobe potential. The comparison between observed and theoretical LCs is shown in Figure 2.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Because of the large metallicity spread found for stars in the cluster, we also use a metallicity of [Fe/H] = −1.0 to determine the effective temperature of the primary component and obtain T₁ = 9405 ± 94 K. Based on our analysis, we find that the additional solution results of this metallicity value are almost the same as previous solutions. Therefore, we do not list the results of our additional solutions and adopt the results using [Fe/H] = −1.53 as the final solution.

We should confirm if NV364 is a member of the globular cluster ω Centauri before we determine the physical parameters of NV364. Therefore, we calculate the distance modulus of NV364 using the luminosity–color relation with optical (BV) observations. We adopt the same equation as Bilir et al. (2008):

$$\begin{equation} M_v=a(B-V)_0+c. \end{equation} \tag{ 2 }$$

In order to calibrate the coefficients of the equation, we select six EA-type binaries in the globular cluster ω Centauri, each with a membership probability that is higher than 97%. They are listed in Table 2. Their absolute magnitudes M_v are obtained assuming interstellar absorption A_v = 0.372 (where A_v ∼ 3.1E(B − V), E(B − V) = 0.12; Harris 1996 (2010 edition)). The predicted coefficients and their uncertainties are obtained by means of the least-square fitting. The values are a = 1.36606 ± 0.70196 and c = 2.18119 ± 0.20144, respectively. Then, we derive the absolute magnitude M_v = 2.17 ± 0.21 mag for NV364. Consequently, the distance modulus of NV364 is (m − M) = 14.05  ±  0.21, which is in agreement with the value of the distance modulus of the globular cluster ω Centauri, 13.94 (Harris 1996; 2010 edition). Therefore, NV364 is a member of the globular cluster ω Centauri.

Based on the apparent distance modulus in the V band of ω Centauri, (m − M)_v = 13.94 (Harris 1996, 2010 edition), we estimate the physical parameters of NV364 using the W–D program, which follows Kepler's third law (the same method used in Liu et al. 2011).

First, we calculate the V-band absolute magnitude of NV364 using the relation $M_{v_{{\rm max}}}=m_{v_{{\rm max}}}-A_v-(m-M)_v$. $m_{v_{{\rm max}}}$ is the maximum magnitude appearing at phase 0.25 or phase 0.75 when both surfaces of the two components face us. Then, we calculate bolometric correction of NV364. We use the program provided by Worthey & Lee (2011) to calculate the bolometric correction, obtaining BC_V = −0.208 mag and −0.222 mag, corresponding to the values of log g= 4.0 and 4.5. Adopting an average value of BC_V = −0.215 mag, we obtain the absolute bolometric magnitude of NV364, M_bol = 1.763 mag. Second, we use the LC program of the W–D code to estimate the combined absolute bolometric magnitude, which can be compared with the result in the previous step. The LC program can derive the absolute bolometric magnitude M_bol of each component from the period, semimajor axis, and other parameters determined from photometric solutions. The semimajor axis is the only variable here. Each time we input the semimajor axis, we obtain a set of absolute bolometric magnitudes of the primary and secondary because we determine the radii of the two components based on the value of the semimajor axis. Subsequently, we obtain the luminosities of the two components based on the Stefan–Boltzmann law. Last, we can obtain the absolute bolometric magnitudes of the two components based on the connection between the absolute bolometric magnitude of a star and its luminosity. Then, we combine them to determine the total value and compare that value with the observed absolute bolometric magnitude of the system until we find the right semimajor axis. The relation between the semimajor axis and the combined absolute bolometric magnitude of the two components is shown in Figure 3. According to the figure, we find that when the semimajor axis is 5.43 R_☉, the absolute bolometric magnitudes of the primary and secondary components are 2.09 and 3.22 mag, respectively, obtaining M_{bol, max} = 1.7616 mag. This is consistent with the observed value within the error range. The gained physical parameters of NV364 are listed in Table 3, where the errors are derived from the uncertainty of q.

Zoom In Zoom Out Reset image size

Table 3. Physical Parameters of NV364

Parameters	Values	Errors
M1 (M☉)	1.60	±0.06
M2 (M☉)	1.40	±0.02
R1 (R☉)	1.30	±0.01
R2 (R☉)	1.03	±0.01
A (R☉)	5.43	±0.04
Lbol1 (L☉)	11.59	±0.22
Lbol2 (L☉)	4.09	±0.24
log g1 (cgs)	4.41	±0.01
log g2 (cgs)	4.56	±0.01
Mbol1 (mag)	2.09	±0.01
Mbol2 (mag)	3.22	±0.02
Mbol (mag)	1.7616	±0.0052
$m_{v_{{\rm max}}}$ (mag)	16.29	Assumed

Download table as:  ASCIITypeset image

The B and V LCs of NV364 have been analyzed using the W–D program. The final solutions show that NV364 is a well-detached binary system; the primary and secondary components of NV364 fill 69.7% and 62.1% of their inner Roche lobes, respectively. There is no mass transfer between them. The effective temperatures of the primary and secondary components are 9406 K and 8185 K, corresponding to respective spectral types A0 and A5. Both appear to be early-type stars in the early stage of their evolution. Using the luminosity ratios from photometric solutions, we can obtain the observed visual magnitudes of the components from the B and V magnitudes of NV364. We obtain V₁ = 16.971  ±  0.006, B₁ = 17.048  ±  0.006, V₂ = 17.933  ±  0.015, and B₂ = 18.138  ±  0.016, where the errors represent the respective uncertainties in the solutions. The positions of the eclipsing components in the ω Centauri color–magnitude diagram (CMD; Noble et al. 1991) are shown in Figure 4. They are located between the blue straggler region and the blue horizontal branch. Both are bluer than the main-sequence stars in ω Centauri, suggesting that they are younger and more metal rich. From the physical parameters of the two components, we find that they both obey the mass–luminosity relation of normal main-sequence stars,

$$\begin{equation} M_{{\rm bol}}=4.6-10\lg (M/M_\odot). \end{equation} \tag{ 3 }$$

At the same time, the surface gravity of the primary component is log g = 4.41 cgs, and that of the secondary component is log g = 4.56 cgs. Drilling & Landolt (2000) derived the surface gravity log g = 4.14 cgs for main-sequence A0-type stars and log g = 4.29 cgs for main-sequence A5-type stars. Though the two components are not located in the main-sequence region in the CMD of ω Centauri, they are early-type normal main-sequence stars.

Zoom In Zoom Out Reset image size

We have obtained the masses and radii of the two components using the LC program of the W–D code, 1.60 M_☉, and 1.30 R_☉ for the primary component and 1.40 M_☉ and 1.03 R_☉ for the secondary component. Both components are normal main-sequence early-type stars and their masses and radii are known. We can use the equations

$$\begin{equation} t_{{\rm MS}}=\frac{3.37\times 10^9}{(M/M_\odot)^{2.122}}, \end{equation} \tag{ 4 }$$

$$\begin{equation} \frac{t}{t_{{\rm MS}}}=0.941(r_m-0.39)^{0.814} \quad {\rm for} \quad r_m < 1.0, \end{equation} \tag{ 5 }$$

$$\begin{equation} \frac{t}{t_{{\rm MS}}}=0.77(r_m-0.588)^{0.434} \quad {\rm for} \quad r_m > 1.0, \end{equation} \tag{ 6 }$$

and

$$\begin{equation} r_m=\log (R_1/R_2)/\log (M_1/M_2) \end{equation} \tag{ 7 }$$

derived from Yıldız (2011) to calculate their ages. Where r_m = 1.74 for NV364, we find that the ages of the primary and secondary components are 1.02 and 1.35 Gyr, respectively. As it is generally assumed that binary components are formed at the same time, we adopt an average value of 1.19 Gyr for the two components. The age of ω Centauri is 16 ± 3 Gyr (Noble et al. 1991), and the first-generation stars in ω Centauri formed nearly at the same time as the cluster. The two components are much younger than the first-generation stars. They formed much later; hence, we conclude that NV364 is a second-generation binary.

We discuss two possibilities to address the question, "How can second-generation stars form in the globular cluster ω Centauri"? The first is that the second-generation stars could have formed from gas ejected from field stellar populations that surrounded globular clusters which formed within a dwarf galaxy environment (Bekki & Norris 2006; Bekki et al. 2007). There, globular clusters may be formed by the mixing of pristine gas ejected from the numerous massive field asymptotic giant branch stars formed earlier in the dwarf galaxy; later on, the dwarf galaxy is dynamically destroyed by the Galactic tidal fields to become the Galactic halo components. The second possibility is suggested by D'Ercole et al. (2008). They showed that the second-generation stars are formed in the innermost region of a globular cluster, where the gas lost by the first-generation stars collects in a cooling flow. The initial mass of first-generation stars needs to provide large enough recycled stellar mass to form a substantial amount of second-generation stars. Following the hydrodynamic simulations, in the N-body initial conditions second-generation stars are concentrated in the inner region of the globular cluster.

If our results are confirmed, NV364 will be the first second-generation binary to be identified in globular clusters. The presence of a second-generation binary system in ω Centauri is evidence of multiple populations of this cluster. There is a possibility that ω Centauri could be the nucleus of a nucleated dwarf galaxy. Since the binary NV364 is not in the center of ω Centauri but rather is at the edge, we would suggest that the first possibility of how the second-generation stars form is more likely to be right. That is to say, ω Centauri at first would be a nucleated dwarf galaxy later completely destroyed by the Galactic tidal field so that only its nucleus is now observed (Bekki & Freeman 2003). Because of the lack of the spectroscopic data, these results should be considered preliminary. In the future, we hope to obtain the spectroscopy data to determine more accurate physical parameters; we also aim to derive the Na abundance and [O/Na] ratio of NV364 to improve our results.

This work is partly supported by the Chinese Natural Science Foundation (Nos. 11133007, 10973037, 10903026, and 11003040) and by the West Light Foundation of the Chinese Academy of Sciences. We are grateful for the photometric data of the CASE project. We also thank the anonymous referee for very positive comments and helpful suggestions.