Abstract

The kinematics of 237 chromospherically active binaries (CABs) were studied. The sample is heterogeneous with different orbits and physically different components from F to M spectral-type main-sequence stars to G and K giants and supergiants. The computed U, V, W space velocities indicate that the sample is also heterogeneous in velocity space. That is, both kinematically younger and older systems exist among the non-evolved main sequence and the evolved binaries containing giants and subgiants. The kinematically young (0.95 Gyr) subsample (N= 95), which is formed according to the kinematical criteria of moving groups, was compared with the rest (N= 142) of the sample (3.86 Gyr) to investigate any observational clues of binary evolution. Comparing the orbital period histograms between the younger and older subsamples, evidence was found supporting the finding of Demircan that the CABs lose mass (and angular momentum) and evolve towards shorter orbital periods. The evidence of mass loss is noticeable on the histograms of the total mass (Mh+Mc), which is compared between the younger (only N= 53 systems available) and older subsamples (only N= 66 systems available). The orbital period decrease during binary evolution is found to be clearly indicated by the kinematical ages of 6.69, 5.19 and 3.02 Gyr which were found in the subsamples according to the period ranges of log P≤ 0.8, 0.8 < log P≤ 1.7 and 1.7 < log P≤ 3, respectively, among the binaries in the older subsample.

Introduction

Chromospherically active binaries (CAB) are the class of detached binary systems with spectral types later than F characterized by a strong chromosphere, transition region and coronal activity. Enhanced emission cores of Ca ii H and K lines, and sometimes in the Balmer Hα line are primary indicators of chromospheric activity and are often accompanied by photometric variability due to star-spots. The first published CAB catalogue by Strassmeier et al. (1988) contained the classical RS CVn systems defined by Hall (1976) and the BY Draconis-type binaries defined by Bopp & Fekel (1977). The 168 CAB in the first catalogue have been increased to 206 in the second catalogue (Strassmeier et al. 1993). The third catalogue has not yet been published but Eker has privately continued to collect CABs and the unpublished list of Eker, which was the main data base for this study, nowadays contains about 280 CABs.

At the first attempt, Eker (1992), was unsuccessful in breaking up the sample of 146 CABs into kinematically distinct subsamples. Containing F to M spectral types and luminosity classes V to II, the already heterogeneous sample of the CABs was also found to be heterogeneous in the sense that kinematically younger and older systems exist among evolved binaries with at least one component of a giant or a subgiant, and among unevolved main-sequence binaries. The Hipparcos data (Perryman et al. 1997) were not available to Eker (1992). However, Aslan, Özdemir & Ískender (1999), who used the Hipparcos proper motions and parallaxes of 178 CABs, also found no clues to non-homogeneity in the velocity dispersions. Aslan et al. (1999) concluded that there are no significant differences between the subsamples of RS CVn binaries, although there are some indications of the main-sequence RS CVn binaries having smaller velocity dispersions, indicating younger ages.

The increased size of the sample of the CABs together with the greatly improved astrometric data (parallaxes and proper motions) provided by Hipparcos (Perryman et al. 1997) motivated us to restudy the kinematics of CABs in a similar manner to Eker (1992). As soon as the U, V, W space velocities and dispersions were produced, the (γ)-shaped concentration in the velocity space near the location of the local standard of rest (LSR) on the (U, V) plane was immediately noticed. It was soon realized that this concentration was formed by young binaries belonging to moving groups (MGs).

MGs are kinematically coherent groups of stars that share a common origin, and thus offer a better way of compiling subsamples of CABs that are the same age. Eggen (1994) defined a supercluster as a group of stars gravitationally unbound but sharing the same kinematics occupying extended regions in the Galaxy. Therefore, a MG, unlike the well-known open clusters, can be observed all over the sky. The determination of the possible members of MGs among binaries and single stars has been carried out by Eggen (1958a,b, 1989, 1995), Montes et al. (2001a) and King et al. (2003).

Consequently, our initial intention of studying the kinematics of the CAB subsamples in a similar manner to Eker (1992) was changed and the whole sample was divided into two groups, with the first group containing the possible MG members chosen by the kinematical criteria originally defined by Eggen (1958a,b, 1989, 1995) and the second group the rest of the sample. Picking out the possible MG members from the whole sample of the CABs which are known to be young made it possible to form kinematically young and old subsamples. After studying the kinematics and determining the average ages, the histograms of the total mass (Mh+Mc), period, mass ratio and orbital eccentricity were compared between the two subsamples as much as the available data permitted. This new system of investigation using kinematical data made it possible to discover new observational clues to binary evolution confirming that detached CABs also lose mass and angular momentum. The angular momentum loss and period decrease were predicted for systems with tidally locked short periods (Demircan 1999). Apparently, binary evolution with orbital angular momentum loss also exists among systems with unlocked long periods. Due to limited space, our investigation into mass-loss rates and associated rates of orbital period decrease will be handled in a forthcoming study.

Data

The 237 systems were selected from the 280 CABs in the unpublished list of Eker. The criteria of selection is the possession of complete basic data (proper motion, parallax and radial velocity) allowing computation of the space velocity of a binary system with respect to the Sun. The selected systems are listed in Table 1 with the columns showing order number, the most common name, HD and Hipparcos cross reference numbers, celestial coordinates [International Celestial Reference System (ICRS) J2000.0], proper motion components, parallax and radial velocity. The basic data were displayed with associated standard errors (s.e.s). The reference numbers in the end column are separated into three fields with semicolons to indicate from where the basic data were taken. The two or more reference numbers in a field separated by commas indicate subfields if there is more than one reference to any basic data.

1

Hipparcos astrometric and radial velocity data of the CABs.

1

Hipparcos astrometric and radial velocity data of the CABs.

Parallaxes and proper motions

The parallaxes and the proper motions in Table 1 were taken mainly from the Hipparcos and Tycho Catalogues (ESA 1997) and the Tycho Reference Catalogue (Hog et al. 1998). Among the 237 systems in Table 1, only 15 (6.3 per cent) binaries do not have Hipparcos parallaxes. Most of the Hipparcos parallaxes have relative errors that are much less than 50 per cent (σπ/π≪ 0.5). Only 14 systems (5.9 per cent) in our list have σπ/π > 0.5. Care was taken not to use parallaxes less than the two-sigma detection limit of Hipparcos which is 1.94 mas (σ= 0.97 mas) (Perryman et al. 1997). It was therefore decided to discard the parallax measurement of five systems (IN Com, HD 122767, RT CrB, V832 Her and AT Cap) and treat them as the other 15 binaries without a trigonometric parallax. However, the other nine systems with σπ/π > 0.5 (V764 Cen, RV Lib, HD 152178, V965 Sco, CG Cyg, RS Umi, RU Cnc, SS Cam, V1260 Ori) were kept in the main list as their parallaxes are bigger than the detection limit.

For the systems without trigonometric parallaxes, a published parallax of any kind was preferred. Among the 20 systems (15 with no π, five below the detection limit) only the six systems (HP Aur, HZ Com, HD 71028, HD 122767, V846 Her and V1430 Aql) were found without any published parallaxes so that spectroscopic parallaxes were estimated for them from their spectral types and luminosity classes.

The Hipparcos and the Tycho catalogues usually give an associated uncertainty for all of the parallax and the proper motion component measurements. However, there are six systems in the list without an uncertainty at the proper motion components. ‘No errors quoted’ may imply something odd about the star. One possibility is that there were no errors because none could be established. Alternatively, it could be a simple omission or that there were too few data to permit a s.e. estimation. Following an optimistic approach, we have preferred to adopt the average uncertainties of Perryman et al. (1997); 0.88 mas yr−1 in μα cosδ and 0.74 mas yr−1 in μδ, for Hipparcos stars that are brighter than nine magnitudes. However, the uncertainty of 5.5 mas yr−1 in the proper motion components for HP Aur was taken from Nesterov et al. (1995). Similarly, the 2.5 mas yr−1 uncertainty is taken from Bakos, Sahu & Nemeth (2002) for the ξ Uma B and CM Dra systems.

Nevertheless, the major contribution in the propagated errors for the U, V, W space velocities comes from the parallax uncertainty. The largest errors must thus be associated with the nine systems (3.8 per cent in the list) with σπ/π > 0.5. In order to see their effect, the average propagated uncertainty of those nine systems were computed with δU=± 7.16, δV=± 11.09 and δW=± 6.94 km s−1. However, there is a large intrinsic spread in the Galactic space motions (U, V, W) so that even such large uncertainties imposed by several individual motions appear to be unimportant. For the sake of statistical completeness, however, the missing s.e.s of 15 spectroscopic parallaxes were completed.

Sparke & Gallagher (2000) state that if interstellar absorption and reddening do not introduce problems, then luminosities of main-sequence stars can often be found to within 10 per cent, leading to uncertainties of 5 per cent with respect to distance. The giant branch is almost vertical and thus the best hope for determining luminosity is within 0.5 in the absolute magnitude, and hence the distance to 25 per cent. Working on the safe side, the subgiants were assumed to be as giants and thus an uncertainty of 25 per cent was assigned for the missing s.e.s of eight giants and four subgiants. The missing s.e.s of three systems (IM Vir, HP Aur, HZ Com) with dwarf components were found with a 5 per cent uncertainty as per the suggestion of Sparke & Gallagher (2000). With a median distance of 98 pc, the current sample of the CABs contains nearby systems and so interstellar absorption and reddening could be ignored. Moreover, the CABs are so popular and well-studied systems that we are confident we can apply the rules of Sparke & Gallagher (2000) for estimating the missing s.e.s of 15 (6.3 per cent in the list) spectroscopic parallaxes. IM Vir and HZ Com are within 60 pc and so within a distance of a 287 pc, only the error of HP Aur could be doubted. This, however, will not effect the statistics of the whole sample. The average propagated errors at U, V and W for

these 15 systems were computed as δU=± 5.49, δV=±4.55 and δW=± 3.81 km s−1, respectively, which are smaller than the propagated errors of nine systems with σπ/π > 0.5, but bigger than the average propagated errors of the whole sample : δU=±3.43, δV=±2.92 and δW=±2.42 km s−1.

Finally, after filling in the missing information in Table 1, the average s.e.s for the proper motion components are 0.62 mas yr−1 in μα cos δ and 0.43 mas yr−1 in μδ and the average relative uncertainty of the parallaxes (σπ/π) is 14.7 per cent.

Radial velocities

Unlike the proper motions and the parallaxes, which were mostly taken from the Hipparcos and the Tycho catalogues, the radial velocities were collected one by one from the literature. Moreover, unlike single stars with a single radial velocity, the binaries and the multiple systems need the radial velocity for the mass centre of the system (γ). That is, numerous radial velocity measurements are needed just for computing the orbital parameters together with the velocity of the mass centre of a system. Fortunately, the CABS are popular and so reliable orbital parameters have already been determined for many systems. However, there are 21 systems in our list (Table 1) which are known to be binaries but do not yet possess determined orbital elements. For such systems, the mathematical mean of the measured radial velocities was adopted as the centre of mass velocity and then the standard deviation from this mean was taken to be the error estimate. Alternatively, there are many systems with multiple orbit determinations but most of these multiple orbit determinations are not independent. That is, the data used in the previous determination were also used or considered in the later study which gives the most improved orbital elements. In such cases, it was preferred to use the value of (γ) and its associated error from the most recently determined orbit unless the most recent study gives unexpectedly large associated errors. There are rarely systems with independently determined orbital parameters but in those cases the weighted mean of the systemic velocities (γ) and the weighted mean of the associated errors were used. These systems are listed with their multiple reference numbers separated by commas after the second semicolon in the last column of Table 1.

Different authors prefer to give different kinds of uncertainties associated with the published parameters of the orbit. In order to maintain consistency, these different types of uncertainties have been transformed into standard errors as most of our data are already expressed with the s.e.s. With the exception of the probable error (p.e.), the other uncertainties (i.e. mean error, s.e., rms error and σ) indicate the same confidence level and thus can be transferred directly. However, when transforming the p.e.s to the s.e.s, the relationship of p.e. = 0.675 rms.e. was used.

Galactic Space Velocity Components

The Galactic space velocity components (U, V, W) were computed together with their errors by applying the algorithm and the transformation matrices of Johnson & Soderblom (1987) to the basic data; celestial coordinates (α, δ), proper motion components (μα, μδ), radial velocity (γ) and the parallax (π) of each star in Table 1, where the epoch of J2000 coordinates were adopted as described in the ICRS of the Hipparcos and the Tycho catalogues. The transformation matrices use the notation of the right-handed system. Therefore, U, V and W are the components of a velocity vector of a star with respect to the Sun, where U is directed toward the Galactic Centre (l= 0°, b= 0°); V is in the direction of the Galactic rotation (l= 90°, b= 0°); and W is towards the north Galactic pole (b= 90°). The computed uncertainties are small and the averages are δU=±3.43, δV=±2.92 and δW=±2.42 km s−1. By inspecting the space velocity vectors graphic, only 18 (7.6 per cent) systems with a space velocity uncertainty of >±15 km s−1 were found. If those systems were removed from the sample, the average uncertainties of the components would be reduced to δU=±2.4, δV=±2.0 and δW=±1.8 km s−1. Thus, most of our sample stars have uncertainties that are very much smaller than the dispersions calculated.

The space distribution

Before discussing the velocity dispersions and kinematical implications, it was decided to inspect the space distribution of the sample of the CABs. Therefore, the Sun-centred rectangular Galactic coordinates (X, Y, Z) corresponding to the space velocity components (U, V, W) were calculated. The computed coordinates are given in Table 2. The projected positions on the Galactic plane (the X, Y plane) and on the plane perpendicular to it (the X, Z plane) are displayed in Fig. 1.

2

Kinematic data of the CABs.

2

Kinematic data of the CABs.

1

The space distribution of sample stars on the Galactic plane, and one other of two perpendicular planes. X, Y and Z are directed towards the Galactic Centre, Galactic rotation and the North Galactic Pole.

1

The space distribution of sample stars on the Galactic plane, and one other of two perpendicular planes. X, Y and Z are directed towards the Galactic Centre, Galactic rotation and the North Galactic Pole.

Fig. 1 indicates that, with a median distance of 98 pc, the current sample of the CABs contains relatively close systems, which can be considered as being contained within the Galactic thin disc. They can also be accepted as being almost homogeneously distributed in all directions as they are seen from the Sun.

Galactic differential rotation correction

The high level of accuracy of the U, V, W velocities motivated us to investigate the effect of the differential Galactic rotation on the U, V, W velocities. The effect of the Galactic differential rotation is proportional to the distance of stars from the Sun in the Galactic plane, that is, the W velocities are not affected in the first approximation which assumes stars are on the Galactic plane. As all of the systems are relatively nearby, the first-order corrections described in Mihalas & Binney (1981) was smaller than the uncertainties of the U and V velocities by Eker (1992) for the 146 CABs (which are also in the present list). Nevertheless, there was no harm in applying the correction even if it is negligible, as Eker (1992) explained.

As the largest uncertainty of the input data appears to be with the parallax measurements, the uncertainty in the distance contributes most to the uncertainties of the U, V, W velocities when compared with the contributions of proper motions and radial velocities. With the greatly improved astrometric data of Hipparcos giving reliable parallax measurements of up to 500 pc, the uncertainties in the (U, V, W) space motions are greatly reduced (by nearly five times) compared with the data used by Eker (1992).

Using the space distribution in the X, Y plane shown in Fig. 1, the first-order Galactic differential correction contributions to the U and V space motions were computed as described in Mihalas & Binney (1981). Then, star by star, they were compared to the uncertainties of the U and V motions computed. It was not unexpected to see 128 of the stars (54 per cent) in our list with Galactic differential rotations bigger than the uncertainty of the U component of the space velocity. The effect on the V component is small, and thus there are only three CABs with the effect being bigger than the uncertainty in V. Nevertheless, it seems evident that first-order Galactic differential rotation correction is necessary for most of the stars in our sample. Therefore, a first-order correction of Galactic differential rotation was applied to all of the stars in the present sample. The corrected U, V, W values are given in Table 2, together with the propagated s.e.s.

Thick disc and halo binaries

The number of metal-poor binaries in our sample was also determined by using the kinematical parameter f= (1/300)(u2+ 2.5 v2+ 3.5 w2)1/2 suggested by Grenon (1987) and Bartkevicius, Lazauskaite & Bartasiute (1999). Here, the u, v, w velocities represent a space velocity with respect to the LSR. The (U, V, W) velocities are obtained by adding the velocity of the Sun with respect to the LSR to the (u, v, w) velocities of stars with respect to the Sun. The values of (U, V, W)= (9, 12, 7) km s−1 (Mihalas & Binney 1981) were used in this transformation. Statistically, stars with f≤ 0.35 belong to the thin disc, stars with 0.35 < f≤ 1.00 belong to the thick disc and stars with f > 1 belong to the halo. Consequently, the vast majority (92 per cent) of our sample are thin disc stars. The thick disc stars are less, comprising about 7 per cent of CABs in our sample. Only one binary star, HD 149414 is a halo star according to its space motions (kinematic). The spectroscopic metal abundance ([m/H]=−1.40 dex) of this star given by Latham et al. (1988) confirms the classification based on kinematical criteria. The Hipparcos parallax of this star gives a distance of 48 pc, and so it appears to be a halo binary in the solar neighbourhood. This binary has a long period (133 d) and a eccentric orbit (Mayor & Turon 1982). It is interesting that Buser, Rong & Karaali (1999) and Siegel et al. (2002) found that 6 per cent of the solar neighbourhood stars belong to the thick disc population, which is an almost identical ratio to our sample of the CABs.

Discussion

General outlook

The distribution of the corrected U, V, W velocities on the (U, V) and (W, V) planes is displayed in Fig. 2. At first glance, the general look of the current (U, V) diagram (Fig. 2a) appears to have similar characteristics to the (U, V) diagram of Eker (1992) of the same sample but with fewer stars (146) and a much lower level of accuracy. Quantitatively speaking, the average motion of the current sample with respect to the Sun is (U, V, W) = (−13.5, −19.7, −8.1) km s−1 with a dispersion of (37.3, 26.0, 19.4) km s−1 with respect to the LSR; indeed close to the values of Eker (1992), i.e. (U, V, W) = (−10, −20, −7) km s−1 and dispersions of (37, 27, 23) km s−1. Later, Aslan et al (1999) also studied the kinematics of the 178 CABs using the Hipparcos astrometric data. The shape and the distribution characteristics of the (U, V) diagram of Aslan et al (1999) has a similar appearance to the mean motion of (U, V, W) = (−11.8, −20.5, −6.4) km s−1 relative to the Sun and (35.8, 22.4, 18.2) km s−1 dispersions in the space velocities with respect to LSR.

2

Velocity dispersions of the sample of the CABs (a) on the U, V plane and (b) on the W, V plane. The velocities are heliocentric. The position of the LSR is marked by +.

2

Velocity dispersions of the sample of the CABs (a) on the U, V plane and (b) on the W, V plane. The velocities are heliocentric. The position of the LSR is marked by +.

The similar appearance, the similar mean velocity and the similar distribution of the current sample on (U, V) does not seem to display any advantage (i.e. of increased accuracy and numbers) over the previous studies. However, as soon as our first (U, V) diagram was produced, the γ-shaped concentration of the (U, V) velocities near the LSR (see Fig. 2a) was noticed. Such a concentration of kinematically young systems is not noted by either Eker (1992) or Aslan et al (1999). However, the γ-shaped concentration is very clear in Fig. 2(a). The concentration of the young systems is also noticeable on the (W, V) plane (Fig. 2b) but is spherical in shape.

Containing F to M spectral-type main-sequence stars, together with evolved G and K giants and even supergiants, the studied samples of CABs seems to be very heterogeneous. Alternatively, the orbital periods of the binaries in the sample range from fractions of a day to >300 d. This may mean that there are different evolutionary paths (Plavec 1968; Thomas 1977) indicating different ages existing among the stars in the sample. As Eker (1992) investigated and Aslan et al (1999) announced, there could be no significant kinematical differences between the subsamples of the CABs with the exception of an indication that the main-sequence RS CVn systems tend to have smaller velocity dispersions implying smaller ages.

The difficulty of separating kinematically young and old populations in just the velocity space is obvious. The dispersions increase with age but there are always some stars left near the LSR. It is therefore not safe to pick stars randomly near the LSR and then to make a kinematically young group with them. The classical approach would be to form the subgroups according to certain objective criteria at first, and then to investigate and to compare the dispersions among the subgroups.

However, the concentration of velocities around (U, V) = (17, −8), (U, V) = (−4, −26), (U, V) = (−37, −14) and (U, V) = (0, 0) km s−1 perhaps reflects some kind of group motions of the stars in the solar vicinity. Eggen (1958a,b, 1989, 1995) and Montes et al. (2001a) discuss the possible MGs (Local Association, Ursa Major, Castor, IC 2391 and Hyades), which might cause the concentration of space velocities as described above. Therefore, as a first step before examining the classical subgroups, it was decided to determine the MG members of our sample and then investigate if the γ-shaped concentration is caused by them. Moreover, membership of one of the known MGs would be an objective criterion to discriminate the kinematically young population of the present sample of the CABs.

Members of MGs among CABs

The kinematical criteria originally defined by Eggen (1958a,b, 1989, 1995) for determining the possible members of the best-documented MGs are summarized by Montes et al. (2001a,b). Basically, there are two criteria as follows.

  • The proper motion criterion, which uses the ratio (τ/ν) as a measure of how the star turns away from the converging point, where the ν and the τ values are the orthogonal components of the proper motion (μ) of a test star. The component ν is directed towards the converging point and τ is perpendicular to it on the plane of the sky. A test star becomes a possible member if (τ/ν) < (0.1/ sin λ), where λ is the angle corresponding to the arc between the test star and the converging point.

  • The radial velocity criterion, which compares the observed radial velocity (γ, the centre of mass velocity) of the test star to the predicted mean radial velocity Vp=VT cos λ, where VT is the magnitude of the space velocity vector representing the MG as a whole. The test star is a possible member if the difference between γ and Vp is less than the dispersions of the radial velocities among the stars in the MG.

Fulfilling one of the criteria makes the test star a possible member. Fulfilling both criteria, however, does not guarantee membership. This is because there is always a possibility that the same velocity space is occupied by the MG members and the non-members. Further independent criteria implying a common origin and same age as the member stars may be investigated in order to confirm the true membership.

The parameters of the five best-documented MGs and the possible membership criteria of each of them have been summarized in Table 3. The criteria have been applied one by one to all stars in our sample of the CABs and 95 systems out of 237 were found to be satisfying at least one of the criteria for one of the MGs in Table 3. Those potential candidates are marked on Table 2 indicating the number of criteria fulfilled (‘1’ means only one criterion, ‘2’ means both criteria were satisfied) and the name of the MG involved. Some previously known members are also marked on a separate column as a consistency check.

3

Parameters of the best-documented MGs and possible membership criteria.

3

Parameters of the best-documented MGs and possible membership criteria.

After all of the possible MG members were determined, the sample was divided into two groups. The one which contains the possible MG members is called ‘MG’ and, the other, which contains the rest of the sample is named ‘field stars’. The (U, V) diagrams of these groups are compared in Fig. 3. The γ-shaped concentration which

3

Distribution of (a) possible MG members and (b) field stars on the (U, V) diagram.

3

Distribution of (a) possible MG members and (b) field stars on the (U, V) diagram.

was noticed on the (U, V) diagram of the whole sample (Fig. 2a) shows itself more clearly in Fig. 3(a) after the removal of any stars which fail to be possible members of any of the five MGs in Table 3. The smooth distribution (Fig. 3b) with a larger dispersion of the field stars is also clear on comparison with the whole sample (Fig. 2a) and the possible MG members (Fig. 3a). Comparison of these two groups in the (W, V) diagram are displayed in Fig. 4.

4

Distribution of (a) possible MG members and (b) field stars on the (W, V) diagram.

4

Distribution of (a) possible MG members and (b) field stars on the (W, V) diagram.

The kinematical differences between the two groups of CABs can be shown numerically if their mean motions and dispersions are compared. The ‘MG’ has a mean motion of (U, V, W) = (−16.9, −13.5, −7.6) km s−1 with dispersions of (20.6, 9.8, 12.8) km s−1 while the ‘field stars’ appear with a mean motion of (U, V, W) = (−11.2, −24.0, −8.4) km s−1 and dispersions of (45.4, 32.9, 22.9) km s−1. According to Wielen (1977), σU= 20.81, σV= 9.76, σW= 12.74 km s−1 velocity dispersions indicate a kinematical age of 950 Myr, which is slightly bigger than the known ages of the MG given in Table 3. This is because the dispersion of stars was computed with respect to the LSR. However, the true age would be less if the true dispersion point of each group is considered. Taking into consideration that some of the possible MG members are not really members, then this age can be treated as an upper limit. Alternatively, the kinematical criteria for forming the ‘MG’ group includes only a limited number of young binaries and thus there can be binaries left in the ‘field stars’ that are younger than 950 Myr. Thus, this age (950 Myr) cannot be considered as a lower limit for the ‘field stars’ which are found to have 3.86 Gyr age from the dispersions. There can be stars much younger and older than this average age among the ‘field stars’.

On careful inspection of Figs 3(b) and Fig. 4(b), one may notice the distinct holes left in the centres of the distributions after the possible MG members are removed. This confirms the point implied by the term ‘possible’, and suggests that a substantial amount of the MG stars are really not MG members. Any individual systems older than the common age of the MG could be selected out as non-members with their ages being predicted by stellar evolution, but this process does not guarantee removing all of the non-members as there is still a possibility that a field star, with a similar age to the MG, occupies the same velocity space fulfilling the kinematical criteria to be a possible member. Nevertheless, our prime concern is to divide the current sample of the CABs into two distinct age groups in order to compare the physical parameters and then investigate the reasons behind and noticeable differences. Although both the ‘MG’ and ‘field stars’ are not very homogeneous as regards the two different ages, we found current grouping satisfactory for this study.

Comparing ‘field stars’ and ‘MG’

The physical parameters of the CABs are listed in Table 4. The columns are self explanatory and indicate the spectral type, SB (indicating single- or double-lined binary or whether within a multiple system), orbital period, eccentricity, mass ratio, mass of the primary, mass function and radii of components. The data were collected primarily from the same literature where the radial velocities were taken.

4

Physical parameters of the CABs.

4

Physical parameters of the CABs.

With the intention of compiling binaries according to the known evolutionary stages of luminosity classification, the whole sample was divided into three groups. The first group is called ‘G’ which contains binaries with at least one component being a giant. A giant classification in the spectral type, if it exists, or otherwise, with one of the radii being six solar radii or bigger, were accepted as criteria to form the ‘G’ group. The group of the subgiants, ‘SG’, were formed from the rest of the sample with a similar criterion; a subgiant classification in the spectral type, or at least one component being bigger than two solar radii. After forming the giants and subgiants, the rest of the sample is called ‘MS’ (main sequence). All three groups contain almost equal numbers of MGs and field stars.

In the first step, the mass and period distributions among those three groups were studied. The result confirms the common knowledge that massive systems are likely to be found in the G group and the less massive systems are likely to be found among the MS group (thus it is not displayed). However, it is of interest to display the period distribution (Fig. 5) among the G, SG and MS systems. The SG group shows nearly a normal distribution with a peak at 6 d and a range of orbital periods ranging from 0.79 to 50 d. The G group prefers not only the more massive systems but also the systems with the longest orbital periods. According to Fig. 5, systems containing a giant star prefer an orbital period of 10 d or longer and

5

Histogram of the period distribution among binary systems containing MS, SG and G groups. All groups contain almost equal numbers of younger MGs and older field binaries.

5

Histogram of the period distribution among binary systems containing MS, SG and G groups. All groups contain almost equal numbers of younger MGs and older field binaries.

rarely shorter periods. Notice the sharp decrease in the short-period binaries in the G group. The MS systems are mostly <10 d, with a shortest period of 0.476 533 d. Our sample does not have many shorter periods because CABs are detached systems. Much shorter periods are common among the contact (W UMa) and semicontact (β Lyrae) binaries. It is interesting to note that the range of MS periods covers a reasonably large range of the most preferred G group periods with a smooth decrease. This decrease may well be due to the selection effect that main-sequence long-period systems are harder to be noticed than long-period binaries with a giant or two. However, a similar selection effect cannot be true for the decrease in the G systems towards the shorter periods.

Fig. 6 compares the orbital period distributions between the kinematically younger (MG) and older (field) populations in our sample. Both groups have about the same range of orbital periods. However, the younger MG group shows a smoother distribution, without a distinct peak, contrasting with the older population, which shows a Gaussian peak at 11.3 (log P= 1.053) d. Initially, the composition rates of the G, SG and MS systems in both groups were investigated. There are 88 systems in the younger population in Fig. 6(a), which is composed of 34 per cent G, 24 per cent SG and 42 per cent MS systems. Alternatively, there are 127 of the stars in the older population in Fig. 6(b), which is composed of 43 per cent of G, 25 per cent of SG and 32 per cent of MS systems. There is not much difference in the distributions of the subgroups between the two groups. Therefore, the periodic preferences of the subgroups (G, SG and MS) alone can not explain the differences seen between Figs 6(a) and (b). Nevertheless, the decrease in the number of systems in the longer and shorter periods in field stars (the older sample) may affect binary evolution.

6

Comparison of period histograms of (a) MGs and (b) field stars.

6

Comparison of period histograms of (a) MGs and (b) field stars.

According to Demircan (1999), mass loss from a binary is associated with momentum loss causing a decrease in the semimajor axis of the orbit. A shrinking orbit forces the orbital period to decrease. Fig. 6 appears to support this scenario. This is because, assuming that field stars had a similar period distribution to MGs at the origin when they were younger, the decrease in the longer period systems could be interpreted using the above prediction. However, the number of short-period systems that do decrease appears to contradict the scenario. That is, normally one expects to count more systems with shorter periods among the older binaries if orbital periods decrease during evolution. However, it should not be forgotten that the binaries in our sample are all detached systems. Apparently, the period decrease and radius increase in the evolution changed those short-period systems into contact or semicontact form, and thus they are no longer in our sample and we see their number decreasing relative to the original population. Therefore, the decrease in the short-period systems in Fig. 6(b) also supports the prediction of period decrease in the binary evolution.

By comparing the period histograms of the G, SG and MS systems between the MGs and the field stars, Fig. 7 also presents evidence of decreasing orbital periods during binary evolution. It is noticeable that the histogram of the G systems for the field stars shows a sharp peak at 20 (log P= 1.3) d. There is a sharper decrease towards the shorter periods. Such a sharp decrease is not visible in the young population (G systems of MGs). This sharp decrease could be caused by the missing systems which are no longer on the list; due to evolution they became contact or semicontact systems. The shifting of the peak of the normal distribution towards the shorter periods as evidence of the orbital period decrease is clearly visible when comparing the G groups; and perhaps even among the SG. Nevertheless, the opposite, that is the peak of the distribution of the field (MS) systems appears to be at longer periods with respect to the peak of the MG (MS) systems. However, considering the fact that evolving into contact or semicontact configurations is most likely among the short-period MS systems than the G systems, it could thus be normal to see the peak moving towards the longer periods in the MS systems. The MS systems causing a peak at around the 1-d period in the MG group must have evolved to contact or semicontact configurations so that the number of such systems appears to be less in the field stars. Therefore, the peak appears to have moved towards the longer periods for field (MS) binaries.

7

Comparison of period histograms of subgroups between MGs and field binaries. G, at least one component is giant; SG, subgiant; and MS, both components on the main sequence.

7

Comparison of period histograms of subgroups between MGs and field binaries. G, at least one component is giant; SG, subgiant; and MS, both components on the main sequence.

One may ask why the peak of field (MS) binaries indicates a shorter period than the peak of field (G) binaries if evolution to contact configuration is effective for up to 10 d, which is indicated by the histogram of the field (G) binaries. Here, we must remember that neither the younger (MG) nor the older (field) groups are very homogeneous. There could be older binaries among the possible MG members, so they are referred to as being possible, and there could be many young binaries among the field stars. The kinematical criteria only select possible MG members. It is possible that unselected stars could be young systems but not satisfy the MG criteria. This complication, however, is not to such a degree that despite this heterogeneous nature, the period shortening effect of the binary evolution is perceptible on our histograms. It is a challenge for future studies to select the older systems from the possible MG members and select the younger systems from the field stars for a better comparison of the younger and the older groups of binaries.

Orbital periods decreasing with age are confirmed by the kinematical data. The older population (field stars) has been divided into three period ranges (Table 5) and the space velocity dispersions and kinematical ages were calculated for the short- (log P≤ 0.8), intermediate- (0.8 < log P≤ 1.7) and the long-period (1.7 < log P≤ 3.0) systems. The increase in the dispersions, implying older ages, towards the shorter periods appears to support the period histograms, that is, the orbital period decrease must occur during binary evolution.

5

Kinematical ages of period subgroups in field stars.

5

Kinematical ages of period subgroups in field stars.

The period decrease due to angular momentum loss requires that the total mass of the binaries must be decreasing through the magnetically driven winds in the CAB components (Demircan 1999). The distribution of binaries with respect to total masses (Mh+Mc) in MG and field binaries are compared in Fig. 8. The expectation was to be able to see the peak of the older group moving towards the smaller values with respect to the peak of the younger group. However, the opposite is presented in Fig. 8. In contrast to the peak points, the tails of the histograms support the prediction of a total mass decrease for the binaries. Indeed, the gradual decrease of the tail in the young MG stars changed to a sharper decrease in the field stars towards the massive systems. That is, the big mass systems in the young population changed to smaller mass systems in the older population. Similarly, sharp number decrease of the younger population (MG) towards the less massive systems changed to a rather gradual decrease in the older population (field stars). Both indicates a decrease in mass in binary evolution. However, the heterogeneity and the evolution into contact or semicontact configurations complicates the histograms, making the interpretation of the peaks more difficult. Therefore, in Fig. 9 the young and old groups of Fig. 8 are separated to compare the G, SG and MS systems. The decrease in the total mass, and therefore the shifting of the peak of the distribution towards the smaller masses, becomes noticeable in the comparisons of the G and SG systems but not very clear in the MS systems. However, it may be interesting to note that the low-mass tail of the MS systems of field stars is longer compared with the tail of the MS systems of MGs.

8

Comparison of the total mass (Mh+Mc) histograms of (a) MGs and (b) field stars.

8

Comparison of the total mass (Mh+Mc) histograms of (a) MGs and (b) field stars.

9

Comparison of total mass histograms of subgroups. G, at least one component is giant; SG, subgiant; and MS, both components on the main sequence.

9

Comparison of total mass histograms of subgroups. G, at least one component is giant; SG, subgiant; and MS, both components on the main sequence.

Fig. 10 compares the eccentricity histograms of the MGs and the field stars. The field stars have a slightly higher peak at e= 0 (circular orbits) but high-eccentricity orbits exist at a similar level in both populations. Circularization of binary orbits is expected to be faster at shorter period orbits. As both groups contain long-period orbits, it is normal to see eccentric orbits in both groups. However, it is interesting to see a decrease in the relative number for the slightly eccentric orbits (e∼ 0.1) in the field stars.

10

Comparison of eccentricity histograms between MGs and field binaries.

10

Comparison of eccentricity histograms between MGs and field binaries.

In order to compare the mass ratio between MGs and field binaries, the mass ratio histograms in Fig. 11 were produced. The mass ratio q=M2/M1, where M1 is the primary mass and M2 < M1, is defined for Fig. 11. The difference is clear, in that the peak at q= 1 decreased and the number of low-mass ratio binaries increased among the field stars. This is expected because during binary evolution the mass ratio of q= 1 must decrease towards the smaller values. Owing to the problems defining the mass ratio (M2/M1 or Mh/Mc) and the changing role and temperature of the components during binary evolution (a hotter component in the MS may become cooler as it evolves to a subgiant and a giant), interpretation of Fig. 11 is not easy. Therefore, only the possible decrease of the mass ratio through the evolution from MGs to field binaries is pointed out here.

11

Comparison of the mass ratio (q=M2/M1, where M1 is the primary mass and M2 < M1) histograms between MGs and field binaries.

11

Comparison of the mass ratio (q=M2/M1, where M1 is the primary mass and M2 < M1) histograms between MGs and field binaries.

Acknowledgments

This research has been made possible by the use of the SIMBAD data base, operated at CDS, Strasbourg, France, and the ARI data base, Astronomisches Rechen-Institut, Heidelberg, Germany. Thanks to D. Latham for providing private communications. We would like to thank, TUBITAK, Turkish Research Council and the Research Foundation of Çanakkale Onsekiz Mart University for their partial support on this research. Finally, we would like to thank the anonymous referee for his/her valuable comments.

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Appendix

Appendix A: References To Table 1

Author notes

Visiting Astronomer, Istanbul University Science Faculty, Department of Astronomy and Space Sciences.