Wide binary stars with non-coeval components

1 Introduction

The formation of binary stars basically follows two scenarios: fission of rotating molecular gas clouds during gravitational collapse and inelastic collisions of stars during the formation of young star clusters (Tutukov and Cherepashchuk 2020). Capture of a component from the field stars is not ruled out in principle either, though it should be relatively rare. Capture occurs when two stars pass close to each other in the presence of a scattering medium that can absorb excess kinetic energy, leaving the two stars bound. This medium could be a third star, a circumstellar disk, or the stars themselves if the collision is close enough to cause tides to rise and fall. Capture in the presence of a third body and “tidal capture” requires a high stellar density, which is atypical for field stars.

Capture in the presence of a stellar disk may play some role in the formation of wide systems, because the capture cross section must on the order of the size of the disk, leading to the formation of systems with large semi-axis of about 100 AU. Clarke and Pringle (1991) considered the possibility of a large, massive protostellar accretion disk playing a role in the formation of binary stars by enabling the capture of a passing star within a dense star-forming region. It was found that capture rates are too low to play a major role in all known star-forming environments, particularly when the probability of prior disk dispersal by the more frequent high-velocity interactions is considered.

An indicator of the capture could be the difference in the ages of the components. It is evident, in particular, that in evolutionary-wide systems (i.e., systems with no matter transfer between components today or in the past) with components of the same age, a less massive component cannot appear to be more evolved.

Our previous attempt to find pairs with non-coeval components was by estimating the durations of preMS and main sequence (MS) stages for stars of different masses. In particular, we looked for wide pairs in which a very low-mass secondary component (with mass m 2 and duration of preMS stage τ preMS ( m 2 ) ) is already an MS star, and, massive primary (with mass m 1 and duration of preMS + MS stages τ MS ( m 1 ) ) is still an MS star. We have found three candidates with τ preMS ( m 2 ) > τ MS ( m 1 ) , and the results can be found in Malkov (2000).

The aim of this study is to use another approach to find non-coeval pairs among visual binaries. For an indication of non-coevality, we compared spectral classes and masses of the components estimated from the spectral classification.

The structure of this article is as follows: Section 2 describes our sample selection, Section 3 describes our observations for the first three objects and spectral data reductions. Data analysis is described in Section 4, and the results are discussed in Section 5. Section 6 summarizes this article.

2 Sample selection

The general method of this work is to apply the simple idea of finding non-coeval pairs among visual binaries. For an indication of non-coevality, we compared spectral classes and masses of the components estimated from spectral classification. Applying this idea to the Sixth Catalog of Orbits of Visual Binary Stars, ORB6 (Hartkopf et al. 2001), we found 13 systems in which less massive component looks more evolved, and consequently, the components are probably non-coeval (Malkov 2020).

We have made a search for additional data on these 13 systems in ORB6 (Hartkopf et al. 2001), the Catalog of Stellar Spectral Classifications (Skiff 2014), the Multiple Star Catalog (MSC; Tokovinin 2018), and the SIMBAD database. The parameters of three systems presented in this article are shown in Table 1.

3 Observations and data reduction

Three of these 13 systems have been observed with the Southern African Large Telescope’s (SALT; Buckley et al. 2006, O’Donoghue et al. 2006) High Resolution Spectrograph (HRS; Barnes et al. 2008, Bramall et al. 2010, Bramall et al. 2012, Crause et al. 2014). The HRS is a thermostabilized double-beam echelle spectrograph, with the entire optical part housed in a vacuum to reduce the influence of temperature variations and mechanical interference. The blue arm of the spectrograph covers the spectral range 3,735–5,580 Å, while the red arm covers the spectral range 5,415–8,870 Å. The spectrograph is equipped with two fibers (object and sky fibers) and can be used in low (LR, R ≈ 14,000 – 15,000 ) medium (MR, R ≈ 40,000–43,000 ), and high (HR, R ≈ 67,000–74,000 ) resolution modes. For our observation, HRS was used in MR, with both the object and sky fibers having a diameter of 2.23 arcsec. Both the blue and red arm CCDs were read out by a single amplifier with a 1 × 1 binning. All additional details of observations are summarized in Table 2. In general, each star was observed once, but in the case of HD 101379, three spectra were obtained, whereas for both HD 156331 and HD 160928, only one spectrum was obtained. Exposures were selected in such a way that they accumulated a signal-to-noise ratio (SNR) of more than 150 in the spectral range 4,300–8,800 Å. Unfortunately, the sensitivity of HRS drops rapidly to a bluer of 4,300 Å and the final SNR in this spectral region is extremely difficult to predict.

During a weekly set of HRS calibrations, three spectral flats and one spectrum of ThAr lamp were obtained in this mode, resulting in an average external accuracy of 300 m  s − 1 . The method of analysis, described in Section 4, needs to use spectra corrected for sensitivity curve. For this reason, spectra of spectrophotometric standard from the list of Kniazev (2017)^[1] were observed and used during HRS data reduction.

Primary reduction of the HRS data, including overscan correction, bias subtractions, and gain correction, was done with the SALT science pipeline (Crawford et al. 2010). Spectroscopic reduction of the HRS data was carried out using the standard HRS pipeline and our own additions, which are detailed in Kniazev et al. (2019).

4 Spectral data analysis

Analysis of totally reduced HRS spectra was performed using fbs (Fitting Binary Stars; Kniazev et al. 2020), a dedicated software package developed by our team for stellar spectra analysis and used by us in different studies (Berdnikov et al. 2019, Gvaramadze et al. 2019, Kniazev 2020, Gvaramadze et al. 2021). fbs software analyses spectra of stars assuming that the observed spectrum consists of spectra of two components of the binary system. The program fits observed spectrum with spectra of two components using a library of high resolution theoretical stellar spectra, and determines the radial velocities and stellar parameters ( T eff , log g , sin i and [Fe/H]) for each component of the binary system. In clear cases of binary stars, the package uses two model spectra with individual velocities and stellar parameters. As an output, the software produces velocities and stellar parameters for both components. The current version of this software employs different stellar models (Coelho 2014, Husser et al. 2013, Hubeny and Lanz 1995).

It was noted in Kniazev (2020) that the output errors of fbs software could underestimate the real errors of analysed data. Unfortunately, since each reduced échelle spectrum is about a hundreds of thousands points length, finding a global minimum of the function as shown in Kniazev et al. (2020) is a very time-consuming process. For that reason, Monte-Carlo simulations or the use of Markov chain Monte Carlo methods is not a real way to estimate errors. It is easier to estimate the accuracy of the method by comparing results of fbs with previously published data (e.g., Kniazev et al. 2020), or by treating each obtained spectrum of the same object as an independent one, modelling each with fbs, and studying the output result as the statistical sample (Kniazev 2020).

Table 3 and Figure 1 show the results of our fbs modeling for obtained spectra. Since three spectra were obtained for HD 101379, each spectrum was analyzed independently with fbs and the presented parameters and their errors are average values for this star. We also repeated the same analysis with the stellar models of Coelho (2014) (Coelho in Table 3) and Husser et al. (2013) (Phoenix in Table 3), convolving them to match the HRS MR instrumental resolution. These results are also presented in Table 3. Finally, after comparing these results, we use errors for each parameter in this work, as shown in the last row of Table 3.

Figure 1

The results of the fbs fit all stars in this work: HD 101379 (top), HD 156331 (middle), and HD 160928 (bottom). Each panel consists of two sub-panels: the top one shows the result of the fit in the spectral range 3,900–8,870 Å. The observed spectrum is shown in black. Both found components are shown in blue and orange, respectively, with their sum shown in red. The bottom one shows the difference between the observed spectrum and its model in black, altogether with errors propagated from the HRS data reduction (continuous dark blue line). Gray vertical areas mark the spectral ranges that were excluded from the fit for different reasons, mainly due to bands of lines from the Earth atmosphere. Only blue spectra for HD 156331 and HD 160928 are shown for more details.

5 Parameters of the studied systems

The parameters of three systems observed with SALT are shown in Figure 2 and presented in Tables 1 and 3. Absolute magnitudes of the components M V are calculated from parallax and visual brightness (Table 1), as well as weight in V band and interstellar reddening E ( B − V ) values (Table 3).

Figure 2

HD 101379, HD 156331, and HD 160928 systems on the HRD. The solid curves represent the main sequence, subgiant, and giant sequences (blue, gray and red, respectively), while the dashed blue curve represents ZAMS (Straižys 1992). Green circles and black squares represent primary (more luminous) and secondary components of the binaries, respectively, with uncertainty bars. Coelho and Phoenix stellar modelsare shown in the top and bottom panels, respectively.

We can see from Figure 2 that the more massive (and more luminous) components of HD 101379 and HD 160928 appear more evolved than the less massive ones. It should be added that according to MSC (Tokovinin 2018), HD 101379 (= The Washington visual double star catalog (WDS) 11395-6524 = HIP 56862) is in fact a quadruple system, where HD 101379 A is a spectroscopic binary SB1 and HD 101379 B is an eclipsing binary.

On the contrary, the secondary (less massive) component of HD 156331 is more evolved than the primary (Figure 2), and consequently, it is a good candidate for the wide binary with non-coeval components. It is an indication of the non-coevality of the components, and consequently, we can assume that this system could be formed by a capture.

In addition, another assessment can be made. HD 156331 was included in our list of pairs with probably non-coeval components (Malkov 2020) because the spectral classification of the components, F8III+B9V, given in WDS (Mason et al. 2001), corresponds to masses of 1.76 and 2.58 (hereafter in solar mass), respectively, and hence the less massive component looks more evolved. The values of T eff and log g obtained in this work for this system (Table 3, Phoenix library) rather indicate the spectral types F5III+A7IV, which correspond to masses of 1.51 and 1.82, respectively. The difference in the masses has decreased, but the situation has not changed qualitatively. Here, we use the scales SpT – T eff – log g – mass from Straižys (1992), and the typical mass error value when estimating it from the spectral type is 0.1.

However, the assumption that HD 156331 B has luminosity class = IV (subgiants) or V (main sequence) contradicts its position on the HRD (Figure 2). The star is located well below zero age main sequence (ZAMS). According to WDS (Mason et al. 2001), the components of HD 156331 have the same brightness in the V-band (which is contrary to our weight values in Table 3), but even under this assumption, the absolute magnitude of HD 156331 B “rises” only to a value of M V = 3.13 mag and the star remains under ZAMS.

In his detailed study of several fast visual binaries, based on speckle interferometry Tokovinin (2017), in particular, found orbital elements and calculated dynamical parallax for HD 156331 ( ϖ dyn = 14.2 mas ), which turned out to be different from the Hipparcos value ( ϖ HIP = 16.9 mas ). Recent Gaia observations rather confirm the latter value ( ϖ Gaia = 16.7 mas , see Table 1 and note that the parallax is given with a fairly high accuracy of 3%). However, even relying on dynamical parallax will only make the components brighter by about 0.3 mag, and HD 156331 B will still remain under ZAMS, as shown in Figure 2.

Our values of HD 156331 components’ radial velocities (Table 3) are quite consistent with the radial velocity difference of ∼ 30 km s − 1 near the periastron, predicted by Tokovinin (2017). On the contrary, components’ magnitude difference found by Tokovinin (2017) corresponds to WDS values rather than the values found in this article and presented in Table 3.

Finally, it should be noted that the formal errors derived from the separation of the spectra of the parameters of the components significantly underestimate the real ones. Moreover, the output parameters can be correlated (e.g., log g and V sin i ), so the analysis of the position of the components on the HRD must take into account the errors of the total brightness, and of the magnitude difference, as well as errors and a possible correlation of the obtained temperatures.

As a result, the HD 156331 system requires further observation and analysis.

6 Conclusion

We have studied several stars from our preliminary list of candidates for wide pairs with non-coeval components and discovered that the less massive component of HD 156331 is probably more evolved than the more massive. We can assume that this system could be formed by a capture. To prove the non-coevality, one needs a detailed investigation of this and other candidates.