Formation and Evolution of W UMa Stars: Fallacies and Corrections
aa r X i v : . [ a s t r o - ph ] F e b Mon. Not. R. Astron. Soc. , 1– ?? (2007) Printed 31 October 2018 (MN L A TEX style file v2.2)
Formation and Evolution of W UMa Stars: Fallacies andCorrections
Z. Eker, , ⋆ O. Demircan , S. Bilir T ¨UB˙ITAK National Observatory, Akdeniz University Campus, 07058 Antalya, Turkey C¸ anakkale Onsekiz Mart University, Faculty of Sciences and Arts, Ulupınar Astrophysical Observatory, 17100 C¸ anakkale, Turkey Istanbul University, Science Faculty, Department of Astronomy and Space Sciences, 34119 Istanbul, Turkey
Accepted 2007 month day. Received year month day;
ABSTRACT
The period histograms of eclipsing binaries generated with ASAS data cannot only beinterpreted by orbital evolution. The eclipse probabilities, selection effects and spacedistributions in the solar neighborhood should be considered before any interpreta-tions are made. Depending upon physical dimensions (total mass and period) of theprogenitor stars and the efficiency of angular momentum loss (AML) mechanism, anewly formed W UMa type binary can be at any age up to several Gyr, and evolutionin the contact stage is controlled not only by angular momentum and mass loss butalso by mass transfer between the component stars. Thus, mean life of contact stagesshould be about 1.6 Gyr. A different time scale would cause inconsistencies.
Key words: stars: binaries: general, stars: activity, stars: evolution, stars: formation
Low-mass contact binaries, popularly known as W Ursa Ma-joris (W UMa) stars, are eclipsing binary stars with equallydeep eclipses. Observational data and theory of W UMa-type contact binaries (WCB) were revised extensively byMochnacki (1981); Vilhu (1981) and Rucinski (1982). Ac-cording to Rucinski (1986) the most promising mechanism toform WCB involves orbital angular momentum loss (AML)and the resulting orbital decay of detached but synchro-nized close binaries. AML by magnetic braking (Schatzman1959; Kraft 1967; Mestel 1968) became especially popularafter Skumanich’s (1972) study, which presented observa-tional evidence of decaying rotation rates for single stars.Magnetic braking and tidal locking were considered as mainroute forming WCB from the systems initially detachedbut comparable periods (Huang 1966; Okamoto & Sato1970; van’t Veer 1979; Vilhu & Rahunen 1980; Mestel 1984;Guinan & Bradstreet 1988; Maceroni & van’t Veer 1991;Stepien 1995; Demircan 1999). However, a small group ofvery young WCBs were found by Bilir et al. (2005). Suchvery young ( < ⋆ E-mail: [email protected]
Automated Survey (ASAS) data, Paczy´nski et al. (2006)have stated that “at this time the contact systems seem toappear out of nowhere” because the number of eclipsing de-tached systems appear insufficient to produce the observednumber of eclipsing contact systems. On the contrary, thesame period histograms of ASAS data, and the kinematicalages of W UMa sub groups, which were given by Bilir et al.(2005), have been interpreted by Li et al. (2007) that theyclaim after a pre-contact duration of 3.23 Gyr, WCBs mustbe formed from the detached progenitors with orbital pe-riods mostly less than 2.24 days and the duration of thecontact stage is 5.68 Gyr. However, Bilir et al. (2005) hasshown that both very young (age < c (cid:13) Eker et al.
The All Sky Automated Survey (ASAS) is a long-termproject, which lasted in three phases of operation dedi-cated to detecting and monitoring of bright stars ( V m )(Paczy´nski et al. 2006). Using a single instrument with anaperture of 7 cm, a focal length 20 cm, a standard V bandfilter and a 2K ×
2K CCD camera, in phase III among the50099 variable stars distinguished, 11076 eclipsing binarieswere identified and period histograms of 5384 contact (EC),2949 semi-detached (ESD) and 2743 detached eclipsing bi-naries (ED) were produced. Studying the period histogramsof EC, ESD and ED binaries with | b | > ◦ , Paczy´nski et al.(2006) have concluded that there are comparable numbersof contact and semi-detached systems but the relative num-ber of detached systems is inconsistently small as if obser-vational data does not support formation of W UMa starsfrom the detached systems of comparable orbital periods.Relying on the same data, Li et al. (2007) argue thatthe ASAS data supports the view of a formation from pro-genitors of orbital periods less than P = 2 .
24 days, via angu-lar momentum loss (AML) driven by magnetic stellar winds(MSW). The peak value of P = 2 .
24 days of the period dis-tribution of ED systems is now old and invalid. One of theirevidences was the estimated tidal locking limit of P = 2 . Being unaware of serious inconsistencies, Li et al. (2007) es-tablished a theory of W UMa formation just because theperiod distribution peak ( P = 2 .
24 days) of ASAS data ofED binaries were found with a value close to the old es-timate of the tidal locking limit of van’t Veer & Maceroni(1988). Similarly, just because a 3.23 Gyr decaying time fora typical ED to form a typical ESD binary by the ratesof Demircan et al. (2006) is close to the kinematical ageof the youngest sub-group (3.21 Gyr) of Bilir et al. (2005),Li et al. (2007) claimed that W UMa binaries must havebeen formed after a pre–contact stage of 3.23 Gyr maxi-mum. Moreover, just because the age difference between theyoungest and oldest groups in Bilir et al. (2005) is 5.68 Gyr,Li et al. (2007) adopted the 5.68 Gyr as the mean lifetime ofW UMa stars. Consequently, mean lifetime (5.68 Gyr) andtypical pre-contact duration (3.23 Gyr) require mean kine-matical ages of oldest W UMa stars to be 8.91 Gyr. Incon-sistency is clear because the kinematical data of Bilir et al. (2005), from which Li et al.’s (2007) theory was established,is known to produce 5.47 Gyr for the mean kinematical ageof the field W UMa stars. However, Li et al.’s (2007) theoryoverestimates mean kinematical ages as [8.91 (oldest) - 3.23(youngest)]/2 + 3.23 = 6.07 Gyr. Moreover, such a theoryappears to be established on a wrong conception that allstars in different age groups have similar ages which is nottrue. It is possible the oldest group may contain a W UMastar just formed at an age of 3.23 Gyr, while the youngestgroup may contain a W UMa star which is of about 9 Gyrof age. Finally, Li et al.’s (2007) theory fails to explain veryyoung (ages < P or M according to the mean kinematicalages of WCB sub-groups may provide a rate mathematicallybut would be meaningless physically. Note that, this is notthe case for CAB stars since there is no pre-CAB problem.It is still not known what would be the correct methodto deduce dynamical evolution for WCBs on a AM-totalmass diagram. The method of Li et al. (2007) would appear c (cid:13) , 1– ?? ormation and Evolution of W UMa Stars to be wrong because masses and periods of W UMa stars arenot arbitrary as in the case of the detached systems. Therecould be detached systems all having the same orbital periodbut their systemic masses may vary from half a solar massto tens of solar masses. This is not the case in WCBs sincemass contained in Roche lobes is limited; changing the massrequires the changing of the orbital period and then AMof the system will change accordingly. Consequently, usingkinematical ages to estimate dJ/dM will be useless to indi-cate true dynamical evolution since J (systemic AM) and M are not arbitrary and time dependence cancels when com-puting dJ/dM . More importantly, AM evolution of WCBsis not only due to AML through magnetic stellar winds, butmass transfer between the components also plays a dominantrole which is not easy to handle but still must be consideredin the evolution of WCBs.
1) It is possible to model the period histogram of binariesfrom the ASAS data theoretically. Such a model would con-tain mostly the eclipse probabilities and observational se-lection effects together with estimated true number densitydistribution of binaries with different masses and orbital pe-riods. Such a modeling would also be useful to estimate thetrue distribution which could be useful in studying the ori-gins of binaries.2) WCBs can be formed at any age depending upon thephysical conditions of their progenitors such as their periods,component masses and efficiency of the AM loss mechanism.Therefore, grouping them into various ages does not indi-cate the younger group is the progenitor of the older groupstars. If there is equilibrium in the population of WCBs,and if they are mostly formed from detached CAB systems,5.47 Gyr of kinematical age of the field WCBs (Bilir et al.2005), and 3.86 Gyr kinematical age of CAB systems indi-cates (Karata¸s et al. 2004) a mean life time of the contactstage is about 1.61 Gyr as in the pool problems. Otherwisea different lifetime would be inconsistent with existing kine-matical data.
Thanks are given to the referee Dr. Slavek Rucinski, whomade suggestions improved the overall quality of discussions.
REFERENCES
Bilir S., Karata¸s Y, Demircan O., Eker Z., 2005, MNRAS,357, 497Demircan O., 1999, Tr. J. Phys., 23, 425Demircan O., Eker Z., Karata¸s Y., Bilir S., 2006, MNRAS,366, 1511Eker Z., Demircan O., Bilir S., Karata¸s Y., 2006, MNRAS,373, 1483Eker Z., Demircan O., Bilir S., Karata¸s Y., 2007, in Demir-can O., Selam S.O, and Albayrak B., eds Solar and Stel-lar Physics Through Eclipses. Astronomical Society of thePacific, San Francisco, ASP Conference Series, Vol 370,p.151 Guinan E.F., Bradstreet D.H., 1988, in Dupree A.K., LagoM.T., eds Formation and Evolution of Low Mass Stars.Kluwer, Dordrecht, NATO Advanced Science Institutes(ASI) Series C, Vol 241, p. 345Huang S.S., 1966, ARA&A, 4, 35Karata¸s Y., Bilir S., Eker Z., Demircan O., 2004, MNRAS,349, 1069Kraft R.P., 1967, ApJ, 150, 551Li L., Zhang F., Han Z., Jiang D., 2007, ApJ, 662, 596Maceroni C., vant Veer F., 1991, A&A, 246, 91Mestel L., 1968, MNRAS, 138, 359Mestel L., 1984, in Baliunas S.L., Hartmann L., eds. Lec-ture Notes in Physics, Vol. 193, The Third CambridgeWorkshop Cool Stars, Stellar Systems, and the Sun.Springer-Verlag, Berlin, p. 49Mochnacki S.W., 1981, ApJ, 245, 650Okamoto I., Sato K., 1970, PASJ, 22, 317Paczy´nski B., Szczygiel D.M., Pilecki B., Pojma´nski G.,2006, MNRAS, 368, 1311Rucinski S.M., 1982, A&A, 112, 273Rucinski S.M., 1986, in Cottrell P.L., Hearnshaw J.B., eds,Proc. IAU Symp. 118, Instrumentation and Research Pro-grammes for Small Telescopes. Reidel, Dordrecht, p.159Rucinski S.M., 2006, MNRAS, 368, 1319Schatzman E., 1959, in Greenstein J. L., ed., Proc. IAUSymp. 10, p.129Skumanich A., 1972, ApJ, 171, 565Stepien K., 1995, MNRAS, 274, 1019van’t Veer F., 1979, A&A, 80, 287van’t Veer F., Maceroni C., 1988, A&A, 199, 183Vilhu O., Rahunen T., 1980, in Plavec M.J., Popper D.M.,Ulrich D.R., eds, Proc. IAU Symp. 88, Close Binary Stars.Reidel, Dordrecht, p. 491Vilhu O., 1981, Ap&SS, 78, 401 c (cid:13) , 1–, 1–