The Spectroscopic Orbits of Three Double-lined Eclipsing Binaries: I. BG Ind, IM Mon, RS Sgr

BG Ind (also HD 208496 = HR 8369 = SAO 247247) is listed as a possible eclipsing binary in the fourth edition of the Bright Star Catalogue (Hoffleit & Jaschek 1991), while Manfroid & Mathys (1984) confirmed the eclipsing nature of BG Ind and established an orbital period of 1.464047 days from its photometric observations. The first spectral analysis of the system by Andersen, Jensen & Nordström (1984) showed that HD 208496 is a double-lined eclipsing binary with F3V spectral type. Kholopov et al. (1987) designated it as BG Ind in the 68th Name-list of Variable Stars and classified it as EA (Eclipsing Algol).

Although it is a bright system, due to its southern declination, there are only a few studies discussing the nature of the system. van Hamme & Manfroid (1988) analyzed the system with ground-based photometric light curves in Strömgren $uvby$ bands. Using the two radial velocities (RVs) given earlier by Andersen et al. (1984), van Hamme & Manfroid (1988) were able to estimate the mass and radius of the component stars as 1.41$M_{\odot}$ and 2.22$R_{\odot}$, 1.20$M_{\odot}$ and 1.60$R_{\odot}$, for the primary and secondary, respectively. BG Ind was also observed by the Hipparcos satellite (Perryman et al. 1997). The Hipparcos light curve shows that the magnitude of the system at maximum brightness is $V_{max}=6.11$ mag and the depth of the primary eclipse is 0.25 mag.

The variability of IM Mon (also HD 44701 = HIP 30351 = SAO 133189) was discovered by Gum (1951), who published the first photometric light curve. The light curve of the system obtained by Gum (1951) is asymmetric with scatter and implies a system consisting of two detached components sufficiently close to each other to exhibit proximity effects. Gum (1951) analyzed the light curves without spectroscopic information and gave the relative dimensions of the component stars. Sanyal & Sinvhal (1964) presented new photometric observations of IM Mon. Their light curves in B and V filters show the same asymmetry as seen in the light curve of Gum (1951). According to Sanyal & Sinvhal (1964), the scatter seen in the light curve of IM Mon is not random but systematic due to intrinsic variability of the cooler component.

The first spectroscopic observations of the system were made by Pearce (1951). Analyzing 18 spectra, Pearce (1951) gave the spectroscopic orbital elements for the first time and the absolute dimensions of the components. According to the analysis of Pearce (1951), IM Mon consists of two main sequence stars with spectral types of B4 and B7 and masses of 6.8M_⊙ and 4.5M_⊙ for the primary and secondary, respectively. Cester et al. (1978) gave the updated light curve elements using the photometric data of Gum and Sanyal & Sinvhal (1964). The most recent V-band photometric observations of IM Mon were made by Shobbrook (2004), which were not attemped to be solved. Our present study attempts to obtain precise orbital elements of the system to study the components in more detail, especially the secondary components which was so called responsible for the scatter in the light curve.

RS Sgr (also HD 167647 = HIP 89637 = SAO 209959) is bright southern eclipsing binary. Roberts (1901) confirmed the variability of the system and determined the first times of minimum light. In the recent orbital period study of RS Sgr by Cerruti & de Laurenti (1990), the orbital period of the system is given as 2.41568311 days. The spectroscopic studies of the system were started in the beginning of 20th century. The latest spectroscopic study related to RS Sgr was made by Ferrer & Sahade (1986). Analyzing 46 spectra of the system, Ferrer & Sahade (1986) gave the spectroscopic orbital elements and masses of the components using the orbital inclination given by Baglow (1948). The latest study of the absolute dimensions of the components were given by Cerruti & de Laurenti (1990). According to the analysis of Cerruti & de Laurenti (1990), RS Sgr consists of two main sequence stars with spectral types of B5 and A2, masses of 7.18M_⊙ and 2.41M_⊙, radius of 5.11R_⊙ and 4.10R_⊙, for the primary and secondary, respectively. Here, we re-study the system spectroscopically.

Relatively sharp lines of the components of BG Ind allow measurements of Doppler shifts of the spectral lines by simple Gaussian fittings. However, a selection of spectral order plays an important role for a reliable RV measurement since the spectral features of the components must be far enough away from each other to avoid blending. For this reason, among the 89 spectral orders available in each of our échelle spectrum we selected the wavelength region 6050–6150 Å (the absolute order number: 93) where the Ca I (6102.723Å) lines of the components are strong enough for reliable RV measurement (see Fig. 1). The Gaussian fitting to the lines was performed using the splot task of IRAF. In case of blending of lines at near conjunction times (see Table 1), deblend function was used to fit two Gaussians to the blended lines. However, at times when the spectral feature of one of the component star is behind the other or very strongly blended at the conjunction time, the RV of the former was not measured. The laboratory wavelength of Ca I line used for the determination of the V_γ velocity are taken from the NIST database (Ralchenko et al., 2008). The heliocentric correction are applied to all RVs measured before using them in the orbital solution. The final RVs are given in Table 1.

van Hamme & Manfroid (1988) have determined the orbital period of BG Ind as 1.464069 days from a set of light curves obtained at different epochs. This orbital period was assumed to be reliable and used during our analysis of orbital solution.

With the RVs obtained from the Gaussian fitting, pure Keplerian orbital solution was obtained by least-squares fitting. The orbital period was kept fixed, while the eccentricity $e$, longitude of periastron $\omega$, velocity semi-amplitudes $K_{1,2}$, systemic velocity $V_{\gamma}$ and conjunction time have been converged in the least-squares solution. After a few attempts, the eccentricity is found to be very small ($e$=0.002) compared to its uncertainty (0.007). Therefore, the final feasible spectroscopic orbit was adopted assuming a circular orbit. The adopted orbital parameters are given with uncertainties in Table 4. The theoretical Keplerian orbital fitting to the O-C residuals is shown in Fig. 4.

Our spectra of IM Mon confirm its early spectral type (B5V) reported in SIMBAD database. Apart from the Balmer lines, the most prominent lines in the spectra are He I lines and the Mg II line at 4481 Å. Among the He I lines, 6578 Å and 5875 Å are relatively stronger than the rest. The region where the He I 5875 Å line is located includes telluric lines of water vapor (H₂O) which strongly blends with the stellar line. Therefore, the He I 6675 Å line have been chosen for reliable RV measurements. The spectral region of He I 6678 Å line is given in Fig. 2 with orbital phase indicated for each spectrum.

From the component spectral lines in Fig. 2, it can be seen that the line profiles of the components are broadened primarily by the rotation. Thus, the blending of the lines for this close binary are relatively frequent during the orbital motion. We, therefore, used two-dimensional cross-correlation technique (the code TODCOR). The algorithm of TODCOR was developed by Zucker & Mazeh (1994) and has been efficiently applied to multiple-component spectra of late-type double-lined spectroscopic binaries (Latham et al. 1996; Metcalfe et al. 1996, among others) and more recently to short-period early-type binaries (Gonzáles & Lapasset 2003; Southworth & Clausen 2007). Basically, TODCOR calculates two-dimensional cross-correlation function (CCF) from one observed and two template spectra in re-binned log $\lambda$ space and then locates the maximum of the CCF. We re-binned our observed and template spectra so that each pixel corresponded to 1.6 kms^-1. The template spectrum of each component was synthetically produced using the appropriate model atmosphere grids of Kurucz (1993). The atmosphere parameters (log$g$, T_eff) of the components were adopted assuming the primary is B4V and the secondary is B7V spectral type as estimated by Pearce (1951). The projected rotational velocity of the components were determined by comparison of the synthetically broadened spectral lines with the observed spectra. The RVs of the components were computed from the 2-dimensional CCFs with the highest score which is formed by combining the one dimensional CCFs of the shifted and rescaled template spectra with the observed one. The RVs measured are presented in Table 2.

Using the RVs determined by TODCOR routine, the orbital solution was performed by least-squares orbital fitting. The orbital period of $P$$=$1.1902424 days, which was taken from the web page “Up-to-date Ephemerides of Eclipsing Variables” provided by Kreiner (2004), was fixed while the velocity semi-amplitudes $K_{1,2}$, systemic velocity $V_{\gamma}$ and the conjunction time were converged in the least-squares solution. As in the analysis of BG Ind, the Keplerian orbital solution of IM Mon was first made by converging the eccentricity ($e$) and the longitude of periastron ($\omega$) parameters. Once the eccentricity is found to be negligible, we adopted circular orbit in following orbital fittings. The radial velocities of the secondary component at phases $\phi$$=$0.07, 0.56 and 0.44 could not be measured due to strong blending. We also did not use the radial velocities of the components at phases near conjunction ($\phi$$=$0.91, 0.07 for primary, $\phi$$=$0.41 for secondary star) to avoid the Rossiter-McLaughlin effect (Rossiter, 1924) seen at the eclipsed star’s line profiles due to rotation. The adopted orbital parameters from the least-square fitting are listed in Table 4 and the orbital fitting to RVs is shown in Fig. 5.

Along the optical spectrum of RS Sgr, relatively strong neutral He lines of the primary component indicate the early spectral type status of the component. Weaker light contribution of the secondary component as well as its later spectral type (Ferrer & Sahade, 1986) avoid detection of the lines of the cooler component. We found that Mg II (4481 Å) lines of both component are the most suitable lines for reliable RV measurements.

Applying Gaussian fittings to the individual lines and the use of deblend function of IRAF when the individual lines are blended, as it was done in the case of BG Ind, allowed us to measure RVs of the components which are given in Table 3.

The least-square orbital solution has been applied to the RVs in Table 3. During the orbital fitting, the orbital period of the systems given by Kreiner (2004) while other orbital elements such as conjunction time T₀, eccentricity $e$, longitude of periastron $w$, velocity semi-amplitudes K_1,2 and the systemic velocity V_γ were converged. In every iteration the eccentricity of the orbit was found to be zero. Therefore, we assumed the circular orbit in our final adopted solution. The spectroscopic orbital elements of RS Sgr found in our analysis are given in Table 4 together with their uncertainties.