Kinematics of W UMa-type binaries and evidences on the two types of formation

The kinematics of 129 W UMa binaries is studied and its implications on the contact binary evolution is discussed. The sample is found to be heterogeneous in the velocity space that kinematically younger and older contact binaries exist in the sample. Kinematically young (0.5 Gyr) sub-sample (MG) is formed by selecting the systems which are satisfying the kinematical criteria of moving groups. After removing the possible MG members and the systems which are known to be members of open clusters, the rest of the sample is called Field Contact Binaries (FCB). The FCB has further divided into four groups according to The orbital period ranges. Then a correlation has been found in the sense that shorter period less massive systems have larger velocity dispersions than the longer period more massive systems. Dispersions in the velocity space indicates 5.47 Gyr kinematical age for the FCB group. Comparing with the field chromospherically active binaries (CAB), presumably detached binary progenitors of the contact systems, the FCB appears to be 1.61 Gyr older. Assuming an equilibrium in the formation and destruction of CAB and W UMa systems in the Galaxy, this age difference is treated as empirically deduced lifetime of the contact stage. Since the kinematical ages of the four sub groups of FCB are much longer than the 1.61 Gyr lifetime of the contact stage, the pre-contact stages of FCB must dominantly be producing the large dispersions. The kinematically young (0.5 Gyr) MG group covers the same total mass, period and spectral ranges as the FCB. But, the very young age of this group does not leave enough room for pre-contact stages, thus it is most likely that those systems were formed in the beginning of the main-sequence or during the pre-main-sequence contraction phase.


INTRODUCTION
The low mass contact binaries, popularly known as W Ursae Majoris stars, are easily recognized by their eclipsing light curves with equal (or nearly equal) minima as wide as to touch one another. With a small orbit implied by a short orbital period less than a day, the binary components fill their Roche lobes so that the dumbbell-shaped stars touch each other at the inner Langrangian point. The W UMa ⋆ E-mail: sbilir@istanbul.edu.tr † Visiting Astronomer, Istanbul University Science Faculty, Department of Astronomy and Space Sciences systems have spectral types ranging from late A to middle K and they are located near or just above the main sequence. The strong tidal interaction synchronized their rotation thus the period of rotation is equal to the orbital revolution. The rapid rotation and convective atmospheres are primary causes to their observed chromospheric and coronal emissions as well as to the presence of large starspots which are the manifestations of strong, dynamo-generated magnetic activity.
The rapid rotation and quickly changing radial velocity, on the other hand, is a serious obstacle to obtain a reliable radial velocity from the highly broadened and blended spectral lines of numerous W UMa systems. Therefore, forming a complete sample for studying galactic space motions and kinematics of W UMa stars is limited with the availability of the radial velocity measurements. From the identified 374 W UMa binaries (Kukarkin et al. 1971;van't Veer 1975) in the 3rd General Catalog of Variable Stars (GCVS), Guinan & Bradstreet (1988) were able to collect only 34 systems with a measured center of mass velocity. The number of stars classified as EW (eclipsing binaries of W UMa type) increased to 561 in the 4th edition of GCVS. But there were only 78 systems available with complete physical parameters which were studied statistically by Maceroni & van't Veer (1996). Only 37 out 78 had spectroscopic mass ratio determined from the radial velocities. Finally, Aslan et al. (1999) counted 125 W UMa binaries in the Hipparcos Catalogue, but there were only 34 binaries from which the space motions can be computed. The revised 4th edition of GCVS now contains 751 W UMa. Thanks to the dedication of David Dunlap Observatory (DDO), where 54 per cent of current radial velocities came from, and Dominion Astrophysical Observatory (DAO) with 20 per cent contribution, and the improvements of spectroscopic techniques for measuring radial velocities that a total of 129 W UMa systems were collected for this study. Nearly four times the number and the improved accuracy of data justified us to repeat previous attempts of studying kinematics of W UMa binaries.
With a small sample of less accurate data, Guinan & Bradstreet (1988) estimated a kinematical age of 8-10 Gyr for W UMa systems. If this age is compared to the ∼ 5 Gyr average age of chromospherically active binaries (CAB), classical RS CVn and BY Dra systems (Eker 1992), W UMa stars appear two times older. Nevertheless, this age of W UMa binaries was found consistent with the theory of contact binary formation from the detached binary progenitors, presumably from the short period (P < 5 days) RS CVn binaries, by a mechanism involving angular momentum loss and orbital period decrease previously suggested by Huang (1967), Mestel (1968), Okamoto & Sato (1970), van't Veer (1979) and Vilhu & Raunen (1980). But, according to the space velocities and dispersions computed by Aslan et al. (1999), W UMa binaries cannot be older than RS CVn systems. This means that W UMa binaries could not have evolved from detached binaries unless the time to reach contact stage is very short.
With no pre-contact stage, there is an opposing theory which predicts the formation of contact binaries directly by a fission process (Roxburgh 1966) at the end of the premain sequence contraction. Considering the brief lifetime of the contact stage (0.1 < tcontact < 1 Gyr) estimated by Guinan & Bradstreet (1988), this theory would fail to produce older populations of W UMa binaries unless the angular momentum of contact binaries is conserved. However, with the conservation of the orbital angular momentum, this theory would refuse the formation of the contact binaries from the detached binary progenitors.
Apparently, an empirical evidence implying whether the total orbital angular momentum is conserved or not within the evolutionary time scale is extremely important to reveal the actual working model. Inspired by the predictions of Demircan (1999), Karataş et al. (2004) presented such an evidence recently from the kinematics of CAB sample containing RS CVn and BY Dra stars. The evidence of orbital period decrease, connected to mass and angular momentum loss, was shown by comparing the total mass (M1 + M2) and period histograms between the kinematically younger (age 0.95 Gyr) and the older (age 3.86 Gyr) CAB sub samples. The orbital period decrease was also indicated by the fact that the shorter orbital period systems were found older than the longer orbital period systems. According to a preliminary investigation of Demircan et al. (2004), the period decrease is exponential in time so that the active detached binaries, up to about 5 days orbital period, could change into contact form within less than about 5 Gyr. Therefore, the formation of W UMa stars from detached binaries is evidently occurring. Nevertheless, this does not mean this is the only mechanism to form contact binaries. It may still possible that a limited fraction W UMa systems, possibly the very young ones, may be forming by the fission process.
In the present work, the kinematics of W UMa binaries is studied and its implications on the contact binary evolution is discussed. The present sample has been found heterogeneous like the CAB sample in a sense that there are younger (∼ 1 Gyr age) and older (∼ 6 Gyr age) W UMa binaries covering the same range of spectral types and orbital periods. The evidence of mass and angular momentum loss causing orbital period decrease during contact binary evolution has been investigated for a preliminary step as done by CAB sample by Karataş et al. (2004) by comparing the total mass (M1 + M2) and period histograms between the younger and the older sub samples.

DATA
Among the 751 recorded W UMa binaries in the recently revised 4th edition of GCVS, 129 systems were found to have radial velocities. After compiling the rest of the basic data (parallaxes and proper motions), the sample is listed in Table 1, which is self explanatory, with the columns: order number, name, HD and Hipparcos reference numbers, celestial coordinates (ICRS 2000), proper motions, parallaxes and radial velocities. The associated standard errors are given besides the related parameter. The reference numbers in the last 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 indicate the sub fields, that is, there are multiple references.

Parallaxes and proper motions
The parallaxes and the proper motions in Table 1 were mostly taken from the Hipparcos and Tycho Catalogs (ESA 1997) and the Tycho Reference Catalog (Hog et al. 1998). The parallax and the proper motion components of three stars (TX Cnc, EE Cet, BL Eri) were taken from Roese & Bastian (1988). Among the 129 systems in Table 1, the 25 binaries do not have any trigonometric parallax, and the 12 binaries have a large relative uncertainty (σπ/π > 0.5) in the parallax measurements. Considering the fact that Hipparcos measurements are reliable up to 500 pc (two-sigma detection limit σ ≈ 1 mas, Perryman et al. 1997), we decided to discard the parallaxes of five (AQ Tuc, TY Pub, XZ Leo, AG Vir, RZ Com) systems since their measured parallaxes indicate a distance further than 500 pc. These five stars and ER Ori, which were erroneously listed with a negative parallax, are treated like the other 25 systems without a trigonometric parallax. For them, the photometric parallaxes, which were determined from the period-colorbrightness relation M (V ) = −4.44 log P +3.02(B−V )o+0.12 by Rucinski (2004), were used. The photometric parallaxes were calculated with the corrections of the interstellar absorption, which were computed from the color excess as AV = 3.1E(B − V ). Since all systems were assigned a spectral type, the color excesses were available together with their observed colors.
The Hipparcos and Tycho catalogues usually give an associated uncertainty for all of the parallax and the proper motion component measurements. However, there are 18 systems in the list without an uncertainty at the proper motion components. With an optimistic approach, we have   Gatewood 1995 preferred to adopt an average uncertainty 2.5 mas yr −1 for them, which were determined by Hog et al. (2000) for the Hipparcos stars in general. On the other hand, Rucinski (2004) estimated that the absolute magnitudes computed by the period-brightness relation of W UMa systems are within the accuracy of ±0.25 mag. Therefore, a corresponding 12.5 per cent uncertainty for the photometric parallaxes were taken. Recent investigations, both visual and spectroscopic, indicated the presence of additional components for some W UMa binaries. Trigonometric parallaxes are frequently wrong for those systems as for the brighter systems with large uncertainties in the parallaxes. We have not preferred to introduce additional uncertainties into the published data. However, for the reader is who want to estimate the bias introduced by such multiple system, the W UMa's with additional components are marked in the last column of Table 5 and are shown by empty symbols in the figures.

Radial velocities
All W UMa binaries have circular orbits. Thus the center of mass velocity can be obtained simply by fitting a sine curve to the measured radial velocities. However, except for the four systems (TW Cet, RZ Tau, TY Pup, AK Her), all W UMa stars in our list had well determined orbital parameters so that the center of mass velocities (γ) were available with uncertainties. The center of mass velocities and the associated standard errors were listed in Table 1 with their sources. If there was more than one source available, the data in the latest source is taken since previous radial velocities were used in the later determined orbital parameters. Nevertheless, we have found the three systems (V523 Cas, AG Vir, V566 Oph) with multiple orbits which were determined independently from the independent data sets. For them, the weighted mean of the systemic velocities (γ) and the weighted mean of the associated errors are adopted. Only the four systems (TW Cet, RZ Tau, TY Pup, AK Her) had measured center of mass velocities but uncertainties were not available. Their uncertainties were estimated from the scatter of component velocities on the radial velocity curve. All different types of errors have been transformed to standard errors for the sake of consistency.

Sky and space distributions
There exist no program similar to that of DDO, which contributed 54 per cent of radial velocities, in the southern hemisphere, where the number of observatories already relatively less so there is a strong bias in the sky distribution of the present W UMa systems. The celestial coordinates (α, δ) are plotted in Fig. 1a that the bias is obvious as there are 103 systems (80 per cent) in the northern and 26 systems (20 per cent) in the southern hemisphere. Unfortunately, the bias is unavoidable because 1) The present work is established on the accumulated data in the literature and it is not vise to wait for another unknown period without a clue how southern systems will be increased. 2) Eliminating some northern systems to establish isotropy is not feasible since it would greatly reduce the statistical significance of the sample. Due to the angle (63 • ) between the celestial equator and the galactic plane, distribution of the sample in the galactic coordinates ( Fig. 1b) appears to be less effected by the bias. Nevertheless, this is only an illusion because un-isotropy would not change by changing the coordinate system. In order to inspect the space distributions of the present W UMa sample, the Sun centered rectangular galactic coordinates (X towards Galactic center, Y Galactic rotation, Z north Galactic Pole) were calculated. The (X, Y , Z) space coordinates are given in Table 2. The projected positions on the Galactic plane (X, Y plane) and on the plane perpendicular to it (X, Z plane) are displayed in Fig. 2. The bias on the prime reference frames (X − Y , X − Z, and Y − Z) are not that obvious as Fig. 1a. Having 69 systems with X < 0 and 60 system with X > 0, the Y − Z plane shows the least bias. Having 65 and 44 systems the northern and southern Galactic latitudes, Galactic plane (X − Y ) shows the strongest bias ( Fig. 2) but still it is not obvious as Fig.  1a.
With a median distance of 137 pc, the sample contains relatively nearby systems and it can be considered within the Galactic thin disc. Occupying almost the same space in the Solar neighborhood, the CAB sample , had a smaller median distance (98 pc) than W UMa sample. Thus, we were curious to compare space dispersions of the present W UMa sample and CAB sample. In order to avoid complications of far distant members, the space dispersions of both samples within 300 pc are calculated.  Indeed, with the space dispersions of δX = ±78, δY = ±90, and δZ = ±87 pc, the W UMa sample seems a little more dispersed than the CAB sample with the space dispersions of δX = ±77, δY = ±75, and δZ = ±73 pc.
Considering the fact that CAB's being on average brighter than the less common W UMa's, it has been expected the opposite, since CAB's would be visible at longer distances. Obviously, the observational selection is more affected by the easy recognition of W UMa's rather than the higher absolute brightness of CABs. Apparently, the less bright contact binaries were identified and studied more than the CAB's in similar distances.

Galactic space velocities
Galactic space velocity components (U , V , W ) were computed by applying the algorithm and the transformation matrices of Johnson & Soderblom (1987) to the basic data: celestial coordinates (α, δ), proper motion components (µα, µ δ ), 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 International Celestial Reference System (ICRS) of the Hipparcos and the Tycho Catalogues. The transformation matrices use the notation of the right handed system. Therefore Uncertainties of (U , V , W ) space velocity components have been computed by propagating the uncertainties of the input data (proper motions, parallax and radial velocity) by the algorithm also by Johnson & Soderblom (1987). The arithmetic mean of the uncertainties for (U , V , W ) are: δU = ±5.52, δV = ±4.67 and δW = ±3.75 km s −1 . By inspecting the individual errors of space velocity vec- tors (S = √ U 2 + V 2 + W 2 ), we have found only 11 (8.5 per cent) systems with the errors bigger than ±20 km s −1 . If those systems were removed from the sample, the averages would reduce to δU = ±4.04, δV = ±3.12, and δW = ±2.68 km s −1 . Thus, it can be claimed confidently that most of the sample stars have the velocity uncertainties smaller than the velocity dispersions calculated. However, in comparison with the CAB sample , the average uncertainties of the present W UMa sample appear nearly two times bigger. Obviously, this is the result of the lower accuracy of W UMa radial velocities because of shorter orbital periods and higher rotation rates.
Having relatively less accurate space velocities, we were curious to check the effect of the differential Galactic rotation. Thus, the first-order Galactic differential rotation contributions to the U and V components were computed as described in Mihalas & Binney (1981). The W velocities are not affected in this first order approximation. We have found 27 stars (21 per cent) with the contribution from the Galactic differential rotation being greater than the uncertainty of the U component of the space velocity. The effect on the V component is rather small that the effect of Galactic differential rotation was found smaller than the uncertainties in V . Nevertheless, the Galactic differential rotation correction was applied to all of stars in the present sample. The corrected U , V , W are given in Table 2, together with the propagated standard errors.
There is no direct way to estimate how the un-isotropic sky distribution (bias shown in Fig. 1a) effects the W UMa space velocities. However, since present sample contains only nearby systems within the Galactic thin disc and since first order Galactic differential rotation correction were applied, the bias seems to be minimized perhaps disappeared in the space velocity distribution. This is because the velocity distribution present W UMa sample has a great resemblance to the velocity distribution of the CAB sample ) which were considered homogeneously and isotropically distributed in the solar neighbourhood. Distribution of the space velocity components on the U − V plane is displayed in Fig. 3a.
In order to display reliability of computed U , V , W velocities, Fig. 3b shows error bars some selected systems as 1) five system which are the most distant, 2) five systems with the biggest space velocity vector (S), 3) five systems which are the most dispersed on the U − V diagram. It is also clear on Fig. 3b that propagated uncertainties, even the extreme cases as above, appear smaller than the dispersion thus the space velocities (U , V , W ) and their dispersion can be considered realible. Nevertheless, in order to minimize the contribution of the space velocity errors, the dispersion were calculated with respect to the LSR rather than arithmetic mean of the space velocities. The position of the LSR is obtained by subtracting the Sun's velocity (U, V, W )⊙ = (9, 12, 7) km s −1 by Mihalas & Binney (1981) from the frame of (U , V , W ) velocities.

Population analysis
As in the CAB sample , we have used the parameter fK = (1/300)(1.0u 2 + 2.5v 2 + 3.5w 2 ) 1/2 to determine the possible metal poor binaries kinematically as suggested by Grenon (1987) and Bartkevicius, Lazauskaite, & Bartasiute (1999). Here, the u, v, w velocities represent space velocity components with respect to the LSR. Statistically, the stars fK ≤ 0.35 belong to the thin disc, the stars with 0.35 < fK ≤ 1.00 belong to the thick disc. The stars with fK > 1 belong to the halo population.
According to fK analysis, the vast majority (93 per cent) of our sample are thin disc stars. The possible thick disc members are found to be 7 per cent in the current sample. The thick disc candidates are FU Dra, AP Dor, RW Dor, FG Hya, OU Ser, AU Ser, V921 Her, V2357 Oph, and VZ Psc. Spectroscopic metal abundances of W UMa stars appear unachievable due to fast rotation and blendings in their spectra. Photometric indices are also entirely unreliable due to the elevated magnetic activity of the W UMa systems. Nevertheless, photometric metal abundance of BW Dra has been determined by Marsakov & Shevelev (1995) Marsakov & Shevelev (1995) according to the revised Yale isochrones ages (Green, Demarque, & King 1987). If those metal abundances and isochrone ages are correct, with the fK kinematic value of 0.33, BW Dra appears as a star which belongs to the thick disc population although it's fK value is little less than the lower limit. Karataş et al. (2004) had found 7 per cent of CAB binaries are possible members of the thick disc population. It is indeed interesting that the same percentage of thick disc W UMa binaries confirmed in this study coincides with nearly the same ratio, 6 per cent of solar neighborhood stars in general belongs to the thick disc population which were found by Buser, Rong, & Karaali (1999)

Kinematics of contact binaries
Having only the main sequence components from the spectral types A to K, the present sample of W UMa binaries appear less heterogeneous than the CAB binaries with the components F to M spectral types of all combinations of the luminosity classes from V to II. Having orbital periods from 1 days to several hundred days, the CAB sample is also considered heterogeneous ) regarding to the period ranges since different orbital periods may represent different evolutionary paths (Plavec 1968, Thomas 1977. But, with a very limited range of short orbital periods (0.22 < P < 1.13 days), the W UMa sample can be claimed homogeneous in a sense that all binaries with main sequencecomponents are in the contact stage. However, the velocity distribution of W UMa sample on the U − V plane (Fig.  2) appears heterogeneous as the CAB sample, that kinematically younger and older sub systems occupy the same velocity space. With the dispersions of 36.5, 26.2, 19.5 km s −1 at U , V , and W velocity components, it is possible to assign a 4.43 Gyr kinematical age to the whole sample according to the kinematical tables of Wielen (1982). Karataş et al. (2004) assigned 3.86 Gyr age to the field CAB binaries. Thus, even before selecting out possible moving group (MG) members, which indeed seems to exist from the appearance of Fig. 3, the W UMa sample is little older than the CAB sample. Guinan & Bradstreet (1988) investigated whether correlations exist between the space velocities and the physical properties of the W UMa systems, such as orbital period (P ), mass ratio (q), system type (A or W), filling factor (f ), ultraviolet excess, and metallicity index. A weak correlation appeared possible in the sense that the space velocities tend to increase with decreasing orbital period. Also, a weak correlation appeared as binaries with large f (over-contact) tend to have higher space velocities. But, no correlation had been found between the space velocities and the mass ratio, the space velocities and the binary type (A or W), the space velocities and the metallicity index.
In order to search kinematically different sub groups, here we have preferred to divide the whole sample into two sub samples according to a criterion, then to compare their U − V diagrams. The preliminary criteria and the U − V diagrams are summarized and displayed in Fig. 4. W UMa binaries with spectral types later than F7 tend to have larger dispersions ( Fig. 4a and b) than W UMa's of earlier spectral types. This could be explained by the fact that the later spectral types on the H-R diagram contain older systems since evolution into the main-sequence and the duration on the main sequence is longer. However, it is indeed extraordinary that kinematically young and old systems (small and large dispersions) may well exist in both groups. Thus, this criterion fails to provide kinematically homogeneous sub samples.
W UMa stars are classified into A-or W-type systems from their light curves and radial velocity curve (Binnendijk 1970). The W-type systems are those like W UMa itself in which the hotter component (the star eclipsed at the primary minimum) is the smaller and the less massive. Comparison of the U − V diagram between the A-and W-type in Fig. 4 confirms the Guinan & Bradstreet (1988) that both  groups are indistinguishable kinematically, that younger and older systems are equally likely to exist in both sub groups of A or W.
If a few high dispersion binaries are removed from the small mass ratio systems, then both sub groups ( Fig. 4e and f) of mass ratio criterion will be indistinguishable kinematically. Like the two criteria before, the mass ratio criterion also fails to distinguish younger and older systems homogeneously.
The degree of over-filling (f ) of the inner critical equipotential surface is an important parameter which may indicate a stage of an evolution for a contact binary which would coalesce into a single star. FK Com is believed by some to be the product of binary star coalescence (Bopp & Rucinski 1981, Bopp & Stencel 1981. The value of over-filling factor f , which depends on how it is defined, changes from the minimum, when the system is just in contact, to the maximum when components fillout their outer critical envelopes. Different authors define f differently, e.g. Guinan & Bradstreet (1988) define f as 1 ≤ f ≤ 2, but Maceroni & van't Veer (1996) define f as 0 ≤ f ≤ 1. Using the same definition as Maceroni & van't Veer (1996), we have found 109 systems with (f ). The systems with smaller f are compared to the systems with large f on the U − V diagram ( Fig. 4g and h).
The systems with larger f values seem to have larger dispersions, so they appear kinematically older than the systems with smaller f . Although this is a natural consequence of the theory of coalescence into a single star, and it may appear to confirm Guinan & Bradstreet (1988), with a careful look at the U − V diagrams ( Fig. 4g and h) one may notice the two sub groups are not really homogeneous. Kinematically older and younger systems appear to exist in both groups.
In order to make a direct comparison to the Fig. 9 of Guinan & Bradstreet (1988), the space velocities (s = √ u 2 + v 2 + w 2 ) in our sample is plotted against the f values in Fig. 5. According to this presentation, the high velocity stars may well exist at low or high values of f . Thus it can be concluded that f criterion, like the criteria before (spectral type, binary type (A or W), mass ratio) is not a good criterion to differentiate kinematically older and younger W UMa binaries. This result, however, is consistent with the very brief lifetime of a contact stage, which was predicted by Guinan & Bradstreet (1988) as 0.1 < tcontact < 1 Gyr, and the kinematical ages of the sample as a whole which is 4.43 Gyr. The dispersions on the U − V diagram are produced in a time scale not only covering the contact stage but also covering the pre-contact stages of all. Obviously the contact stage for many W UMa stars is too short to be effective on the observed dispersions. Therefore, it is possible that a W UMa system with a longer pre-contact evolution may reach to a contact configuration at kinematically larger ages that the f value can be very small. But, on the other hand it is also possible for a W UMa system, with a much shorter precontact stage (small kinematical ages), to have larger value for the f . Therefore f value criterion fails to discriminate between kinematically young and old systems.
The present W UMa sample were said above to be homogeneous in a narrow range (0.22 < P < 1.13 days) of the short orbital periods. However, the correlations of orbital periods with the dispersions on the U − V diagram is well presented in Fig. 6 in a sense that the short period W UMa systems have larger dispersions. The sub groups according to the total masses (M = M1 + M2) display a similar correlation that less massive systems have larger dispersions than more massive systems.
All sub groups discussed above are summarized numerically in Table 3. The numerical values (velocity averages and dispersions) of the sub groups confirm eye inspection of the dispersions on U − V diagrams on the Fig. 4 and Fig.  6. Indeed the grouping according to spectral type, systems type (A or W), mass ratio, and f value in Fig. 4 do not show very much differences in the dispersions. But grouping according to orbital period and total mass (Fig. 6) is confirmed strongly in Table 3. Using the tables of Wielen (1982), a kinematical age was assigned to each hypothetical sub-group. The ages represent a mean kinematical age of all the stars in a group. The age to be meaningful depends on the meaningfulness of the group. The sub groups using orbital period and total mass criteria are indeed meaningful because the decrease of orbital period and total mass, which is established for CAB , appears to be a process continuing also in the contact stage. Because of a relatively very short contact stage, there is no guarantee about the sub groups of total mass and orbital period being homogeneous. One way of selecting out younger population W UMa binaries among the sub samples according to orbital period, is to pick out possible moving group members as done in CAB sample by Karataş et al. (2004).

Possible MG members among W UMa systems
Moving groups (MGs) are kinematically coherent groups of stars that share a common origin. Eggen (1994) defined a supercluster of stars gravitationally unbound in the solar neighborhood, but sharing the same kinematics while occupying the extended regions in the Galaxy. Therefore, a MG, unlike the well known open clusters covering a limited region, can be observed all over the sky. The kinematical criteria, which were originally defined by Eggen (1958aEggen ( , b, 1989Eggen ( , 1995, for determining the possible members of the bestdocumented MGs are summarized by Montes et al. (2001a, b). Evidence has been found that many young and active late-type binaries can be the members of some young moving groups (Jeffries 1995, Montes et al. 2001b, King et al. 2003. Indeed, possible moving group members determined by Eggen's kinematical criteria have been proved to be very useful for separating kinematically heterogeneous CAB sample into two sub samples representing younger and older populations ) better than the classical approach of pre determined sub groups with a dividing line of a chosen parameter.
The difficulty of separating kinematically young and old populations in the velocity space is obvious. The dispersions increase with age but there are always some stars naturally occupying the regions near the LSR. It is, therefore, not safe to pick stars randomly near the LSR and then to form a kinematically young group with them. Eggen's kinematical criteria, however, objectively select some stars which have space velocity vector parallel to the converging point of each pre-determined and well known MGs within an acceptable uncertainty. There are two criteria that one sets a range of the direction of the test star's proper motion and other puts limits on the test stars radial velocity vector. Fulfilling one of the criteria makes the test star a possible member. But, fulfilling both criteria does not guarantee membership since there is always a possibility that the same velocity space could be occupied by the MG members and the non-members. Further independent criteria implying a common origin and same age as the member stars are needed to confirm the true membership. Therefore, we should always remember that Eggen's criteria determines only the possible members of a MG. The parameters of the five bestdocumented MGs and the possible membership criteria to them have been summarized by Karataş et al. (2004) for the CAB binaries. Here we apply the same criteria to the stars in the present W UMa sample and 28 systems were found to satisfy at least one of the criteria for one of the five MGs which were listed in Table 4. The possible moving group members among the W UMa binaries in the present sample is marked in the latest columns of Table 2 with the names of MG associated.
After determining the possible moving groups, the whole sample has been divided into three sub groups. The first one contains the possible moving group members and named MG. The second group contains only five stars which are previously known to be the members of well known open clusters. The third one is called 'Field Contact Binaries' (FCB) which contains field W UMa systems free from the possible MG and the known open cluster members in the solar neighborhood. Fig. 7 compares the U − V diagram of the MG and the FCB. The detailed kinematics and implied kinematical ages of MG and FCB are included in Table 3.
The velocity dispersions of field contact binaries (FCB) imply a mean kinematical age of 5.47 Gyr. The mean kinematical age is found to be 500 Myr for the possible MG members. Although, this age appears to be consistent with the ages of MG in Table 4, it may not represent the true mean kinematical ages of all possible MG members. This is because, the ages in Table 3 are estimated from the dispersions with respect to the LSR. In reality, each MG has its own center of dispersion which is slightly different than the LSR. Therefore, we should keep in mind that members should be at the age of each MG listed in Table 4.  Table 3. Kinematical data and the predicted kinematical ages of the sub groups of W UMa.

Comparing physical parameters between FCB and MG
The kinematical criteria select out kinematically young W UMa systems without a dividing line according to any physical parameter of W UMa characteristics. However, this does not mean all kinematically young W UMa's are removed from the main sample when forming the group MG. There could be systems as young as the MG group in the FCB. Those are the systems which fail to satisfy kinematical criteria although they are young. Therefore young and old all sorts of W UMa system may exits in FCB. Thus, the 5.47 Gyr kinematical age represents an average age of all stars in FCB. On the other hand, One must remember that the MG group stars are not young because of their small dispersions on the velocity space. On the contrary, their dispersions are small because they are young. They are young primarily because they are possible members of young moving groups in Table 4. Nevertheless, the word "possible" implies a limited number of non-members may well exist in MG which we believe not changes the statistic of young W UMa phenomenon.
Comparing the MG group and field CAB's,  found some important clues indicating mass loss and orbital period decrease in the binary evolution. A similar study is intended here to study the contact stage of the binary evolution. The physical parameters of W UMa binaries are listed in Table 5. The columns are self explanatory to indicate order number, name, apparent brightness and color (B − V ), spectral type, binary type (A or W), orbital period and inclination, masses of components, mass ratio, and over-contact parameter f . The data was primarily collected from the same literature where the radial velocities were taken. Moreover, the orbital inclinations and f values are taken from Pribulla, Kreiner, & Tremko (2003) and Selam (2004).
The distribution according to spectral types are compared between the MG (younger) group and FCB (older) group in Fig. 8. It is interesting that both groups have a similar shape distribution. A slightly increased percentage of A type stars in MG group appears to be the only difference. Fig. 9 compares the orbital period distributions between MG and FCB. If one of the stars with an orbital period greater than 1 day in MG group is not counted, both groups cover nearly the same orbital period range (0.2 < P < 0.9 days). Both groups can be said to have a peak at P = 0.4 days. With 27 members the MG group has an average period < P >= 0.5258 days. With 97 members FCB group has an average period < P >= 0.4275 days. Comparing the shape of both histograms we can conclude that the relative number of longer period (P > 0.4 days) systems decreased and the relative number of shorter period systems (P < 0.4 days) increased in the older population sample (FCB).
These changes may appear as evidences of the period decrease in the contact binary evolution. Karataş et al. (2004) assumed the period histogram of possible MG members as the initial period distribution of field CAB. But, here, the situation is totally different. If the contact stage time scale is indeed short as estimated to be within the range 0.1 < tcontact < 1 Gyr by Guinan & Bradstreet (1988), MG contact binaries cannot be taken as an initial distribution of the FCB, because MG contact binaries will not be able to survive up to the mean kinematical age of FCB.
The mean kinematical age of FCB is 5.47 Gyr (Table  3). Karataş et al. (2004) assigned 3.86 Gyr age for the field CAB which are potential progenitors of field contact binaries (Demircan 1999). Therefore, if there is a continuous formation of CAB and evolution out of the CAB stage, some (or maybe most) of them become W UMa systems, and similarly, if the formation of W UMa systems and their evolution (coalescence) into a single star is a continuous process, and somehow if there is an equilibrium in the Galaxy, which could be investigated of course, the 1.61 Gyr age difference between field CAB and field FCB implies an upper limit for the timescale of the contact stage. Indeed, it is not much different than the estimate of 0.1 < tcontact < 1 Gyr by Guinan & Bradstreet (1988). Therefore, it is not possible to assume the MG group to be the initial stage of the FCB group. It is most likely that the MG contact systems are formed in the beginning of the main-sequence or during the pre-main-sequence contraction phase, either by a fission process (Roxburgh 1966) or most probably by fast spiraling in of two components in a common envelope. On the other hand, FCBs must be mostly formed from the detached progenitors.
The evidence of total mass and orbital period decrease appears to be better displayed in Table 6 where the field contact binaries are divided into four sub groups according to orbital period criterion. It is clearly displayed there that the average kinematical age increases as the orbital periods of the sub groups decrease. It is also clear that older sub groups have smaller total mass. As if, long period contact binaries in Table 6 lose mass and angular momentum, so their orbital period decrease within the time scale indicated in the Table. This scenario, however, is definitely misleading and cannot be true. This is because the age difference between the youngest and oldest sub groups in Table 6, is too long for a contact system to survive even if the empirical 1.61 Gyr time scale for the contact stage were taken into consideration.
According to the true scenario, the large dispersions (older ages) in Table 6 must have been produced not only during the contact stage, but also including the pre-contact stages before, which may be longer than the contact stage as indicated by Table 6. Thus, one should never expect, for a W UMa system in the youngest group in Table 6, to loose mass and angular momentum and join the shortest period (oldest) W UMa systems after t = 8.89 − 3.21 = 5.68 Gyr later. It is not yet clear, but it seems that when a detached system becomes a contact binary, the angular momentum loss becomes accelerated with the gravitational radiation as described by Guinan & Bradstreet (1988). If the total mass of the system does not decrease to fit in the decreasing Roche lobes, then, overcontact f parameter starts to increase. The pre-contact stage, which may differ one system to system, being much longer than the contact stage, spoils the correlation between the f parameter and the space velocity as described in Fig. 5.  between MG and FCB. It is the same with Fig. 11, which compares the mass ratio distribution between MG and the FCB groups. The mass ratio evolution during the contact stage cannot be deduced from Fig. 11 since MG group cannot be the initial distribution. On the other hand, all four histograms (Figs. 8,9,10,and 11) display an empirical evidence of contact binary evolution to indicate coalescence of W UMa systems into single stars. Otherwise, angular mo-mentum loss does not fit in the theory of binary evolution.
Then, it becomes difficult to explain why there are such differences between the MG and the FCB group W UMa stars.
A similar case also applies to the Table 6 data. We believe the age difference between MG contact binaries and the youngest FCB group in Table 6 is empirical evidence of coalescence into single stars. This is because the coalescence into a single star involves orbital period decrease as  well as angular momentum loss, most probably accelerated by gravitational radiation as described by Guinan & Bradstreet (1988) although the data in Table 6 is mostly affected by the long pre-contact stages. The derivation of the rates of orbital period decrease, mass and angular momentum loss from the present data of contact binaries requires a careful analysis and interpretation of Table 6 data. Due to limited space in this study derivation of those rates will be handled in a forthcoming study.

CONCLUSION
Kinematics of 129 W UMa binaries is studied. The sample is found to be heterogeneous in the velocity space that kinematically younger and older contact binaries exist in the present sample. Various sub groups are formed according to criteria involving the spectral types, binary type (A or W), mass ratio, and over-contact parameter f , orbital period and total mass. However, those criteria failed to produce kinematically homogeneous sub groups. Nevertheless, a correlation has been found to indicate shorter period and less massive systems show larger velocity dispersions than longer period more massive systems. The mean kinematical ages of all sub groups are estimated from the velocity dispersions using the tables of Wielen (1982) and listed in Table  3. The possible moving group members among the present W UMa stars are investigated according to the kinematical criteria originally defined by Eggen (1958aEggen ( , b, 1989Eggen ( , 1995 and 28 W UMa are found to be a possible member of five best documented MGs which are summarized in Table 4. The group of the field contact binaries (FCB) is formed by removing out the possible moving group members and the W UMa systems which are known to be the members of known open clusters from the main sample. The 5.47 Gyr mean kinematical age is estimated for the field contact systems (FCB). The age difference is found to be 1.61 Gyr between the 3.86 Gyr old CAB ) and the FCB. If there is a number equilibrium between the CAB and FCB established by the evolution, the upper limit of the lifetime of the contact stage can be estimated as 1.61 Gyr which is in close agreement with the estimation made by Guinan & Bradstreet (1988) as 0.1 < tcontact < 1 Gyr.
Since the contact stage appears to be very short in comparison with the mean kinematical age of FCB, the group containing possible MG stars cannot be used as an initial sub sample of FCB. Thus, the histograms (Figs. 8, 9, and 10) and ages of sub groups of FCB according to orbital ranges (Table 6) cannot be used directly to deduce evidence of period decrease and angular momentum loss during contact stage evolution. Nevertheless, since, those histograms and data in Table 6, cannot be explained without angular momentum loss and orbital period decrease in binary evolution, and since it is illogical to assume that angular momentum loss and orbital period decrease operate only for the pre-contact stages, the angular momentum loss and the orbital period decrease are evidently occuring as predicted by Guinan & Bradstreet (1988) even if one cannot deduce them directly from those histograms and Table 6.
We have found 27 systems to form the MG group. Existences of MG members is an exciting (perhaps the most exciting) finding of this study. This is because these W UMa systems do not have enough ages to be formed from detached binary progenitors by the mechanism involving angular momentum loss and orbital period decrease. In fact the age difference between the youngest FCB sub group (3.21 Gyr, in Table 6) and MG group (0.5 Gyr, in Table 3) is more than lifetime (1.61 Gyr) of the contact stage. Therefore, it could be concluded that the MG contact systems are formed in the beginning of the main-sequence or during the premain-sequence contraction phase, either by a fission process (Roxburgh 1966) or by fast spiraling the two components in a common envelope. As a result, it can be said that detached binary progenitors, presumably short period (P < 5 days) RS CVn binaries, are not the only source from which W UMa systems could be formed by the mechanism involving angular momentum loss and orbital period decrease. It is indeed a challenge to disprove true membership of MG stars in our list. This may not be enough, one also needs to prove their ages to be bigger than our estimate, that is, their ages must be proven to be big enough (bigger than the pre-main sequence contraction plus the contact stage life time) then one can claim the detached binary progenitors are the only source to form W UMa systems.