DOI QR코드

DOI QR Code

WZ Cephei: A Dynamically Active W UMa-Type Binary Star

Jeong, Jang-Hae;Kim, Chun-Hwey

  • Received : 2011.06.27
  • Accepted : 2011.06.30
  • Published : 2011.09.15

Abstract

An intensive analysis of 185 timings of WZ Cep, including our new three timings, was made to understand the dynamical picture of this active W UMa-type binary. It was found that the orbital period of the system has complexly varied in two cyclical components superposed on a secularly downward parabola over about 80y. The downward parabola, corresponding to a secular period decrease of $-9.{^d}97{\times}10^{-8}y^{-1}$, is most probably produced by the action of both angular momentum loss (AML) due to magnetic braking and mass-transfer from the massive primary component to the secondary. The period decrease rate of $-6.^{d}72{\times}10^{-8}y^{-1}$ due to AML contributes about 67% to the observed period decrease. The mass flow of about $5.16{\times}10^{-8}M_{\odot}y^{-1}$ from the primary to the secondary results the remaining 33% period decrease. Two cyclical components have an $11.^{y}8$ period with amplitude of $0.^{d}0054$ and a $41.^{y}3$ period with amplitude of $0.^{d}0178$. It is very interesting that there seems to be exactly in a commensurable 7:2 relation between their mean motions. As the possible causes, two rival interpretations (i.e., light-time effects (LTE) by additional bodies and the Applegate model) were considered. In the LTE interpretation, the minimum masses of $0.30M_{\odot}$ for the shorter period and $0.49M_{\odot}$ for the longer one were calculated. Their contributions to the total light were at most within 2%, if they were assumed to be main-sequence stars. If the LTE explanation is true for the WZ Cep system, the 7:2 relation found between their mean motions would be interpreted as a stable 7:2 orbit resonance produced by a long-term gravitational interaction between two tertiary bodies. In the Applegate model interpretation, the deduced model parameters indicate that the mechanism could work only in the primary star for both of the two period modulations, but could not in the secondary. However, we couldn't find any meaningful relation between the light variation and the period variability from the historical light curve data. At present, we prefer the interpretation of the mechanical perturbation from the third and fourth stars as the possible cause of two cycling period changes.

Keywords

W UMa-type sta;WZ Cep;period change;light-time effects;magnetic activities

References

  1. Applegate JH, A mechanism for orbital period modulation in close binaries, ApJ, 385, 621-629 (1992). http://dx.doi.org/10.1086/170967 https://doi.org/10.1086/170967
  2. Balázs J, WZ Cephei, Beob Zirk d A N, 19, 7 (1937).
  3. Baldwin ME, Samolyk G, Observed minima timings of eclipsing binaries, number 9 (American Association of Variable Star Observers, Cambridge, 2004).
  4. Baldwin ME, Samolyk G, Observed minima timings of eclipsing binaries, number 12 (American Association of Variable Star Observers, Cambridge, 2007).
  5. Bradstreet DH, Guinan EF, Stellar mergers and acquisitions: the formation and evolution of W Ursae Majoris binaries, ASPC, 56, 228-243 (1994).
  6. Demircan O, Dynamical evolution of the RS CVn-type binaries, TJPh, 23, 425-432 (1999).
  7. Detre L, Das system WZ Cephei, Budapest Mitt, 10, 3 (1940).
  8. Diethelm R, Timings of minima of eclipsing binaries, IBVS, 5920, 1 (2010).
  9. Diethelm R, Timings of minima of eclipsing binaries, IBVS, 5960, 1 (2011).
  10. Djurasevic G, An analysis of active close binaries (CB) based on photometric measurements. I. A model of active CB with spots on the components, Ap&SS, 196, 241-265 (1992a). http://dx.doi.org/10.1007/BF00692893 https://doi.org/10.1007/BF00692893
  11. Djurasevic G, An analysis of active close binaries (CB) based on photometric measurements. III. The inverse-problem method: an interpretation of CB light curves, Ap&SS, 197, 17-34 (1992b). http://dx.doi.org/10.1007/BF00645069 https://doi.org/10.1007/BF00645069
  12. Djurasevic G, Zakirov M, Hojaev A, Arzumanyants G, Analysis of the activity of the eclipsing binary WZ Cephei, A&AS, 131, 17-23 (1998). http://dx.doi.org/10.1051/aas:1998248 https://doi.org/10.1051/aas:1998248
  13. Eaton JA, SW Lacertae, W Urase Majoris, YY Eridani, and the prevalence of starspots in cool contact binaries, AcA, 36, 79-103 (1986).
  14. Flannery BP, A cyclic thermal instability in contact binary stars, ApJ, 205, 217-225 (1976). https://doi.org/10.1086/154266
  15. Harmanec P, Stellar masses and radii based on modern binary data, BAICz, 39, 329-345 (1988).
  16. Hoffmann M, Photoelectric observations of contact binary stars, VeBon, 96, 1-9 (1984).
  17. Irwin JB, The determination of a light-time orbit, ApJ, 116, 211-217 (1952). http://dx.doi.org/10.1086/145604 https://doi.org/10.1086/145604
  18. Irwin JB, Standard light-time curves, AJ, 64, 149-155 (1959). http://dx.doi.org/10.1086/107913 https://doi.org/10.1086/107913
  19. Kałużny J, Contact binaries with components in poor thermal contact. II. WZ Cephei, AcA, 36, 105-111 (1986).
  20. Kholopov PN, General catalogue of variable stars, 4th ed., vol. III, Constellations pavo-vulpecula (Nauka Publishing House, Moscow, 1987).
  21. Kim C-H, Lee C-U, Yoon Y-N, Park S-S, Kim D-H, et al., New CCD times of minima of eclipsing binary systems, IBVS, 5694, 1 (2006).
  22. Kim C-H, Nha I-S, Kreiner JM, A possible detection of a second light-time orbit for the massive, early-type eclipsing binary star AH Cephei, AJ, 129, 990-1000 (2005). http://dx.doi.org/10.1086/426747 https://doi.org/10.1086/426747
  23. Kley W, Peitz J, Bryden G, Evolution of planetary systems in resonance, A&A, 414, 735-747 (2004). http://dx.doi.org/10.1051/0004-6361:20031589 https://doi.org/10.1051/0004-6361:20031589
  24. Kreiner JM, Kim C-H, Nha I-S, An atlas of O-C diagrams of eclipsing binary stars (Wydawnictwo Naukowe Akademii Pedagogicznej, Krakow, 2001).
  25. Kwee KK, van Woerden H, A method for computing accurately the epoch of minimum of an eclipsing variable, BAN, 12, 327 (1956).
  26. Lee W-B, Kang Y-W, Oh K-D, CCD photometry of contact binary WZ Cephei, JASS, 25, 19-24 (2008). http://dx.doi.org/10.5140/JASS.2008.25.1.019 https://doi.org/10.5140/JASS.2008.25.1.019
  27. Lucy LB, W Ursae Majoris systems with marginal contact, ApJ, 205, 208-216 (1976). http://dx.doi.org/10.1086/154265 https://doi.org/10.1086/154265
  28. Maceroni C, van't Veer F, The galactic cluster NGC 188: W Ursae Majoris contact binaries as a clue to two separate bursts of star formation, A&A, 248, 430-434 (1991).
  29. Mullan DJ, On the possibility of magnetic starspots on the primary components of W Ursae Majoris type binaries, ApJ, 198, 563-573 (1975). http://dx.doi.org/10.1086/153635 https://doi.org/10.1086/153635
  30. Nagai K, Visual and CCD minima of eclipsing binaries during 2009, Var Star Bull, 50, 1-10 (2010).
  31. Parimucha S, Dubovsky P, Baluďansky D, Pribulla T, Ham-balekL, et al., Minima times of selected eclipsing binaries, IBVS, 5898, 1 (2009).
  32. ParimuchaS, Dubovsky P, Vanko M, Pribulla T, Kudzej I, et al., Minima times of selected eclipsing binaries, IBVS, 5980, 1 (2011).
  33. Peale SJ, Orbital resonances in the solar system, ARA&A, 14, 215-246 (1976). http://dx.doi.org/10.1146/annurev.aa.14.090176.001243 https://doi.org/10.1146/annurev.aa.14.090176.001243
  34. Press WH, Teukolsky SA, Vetterling WT, Flannery BP, Numerical recipes in C, 2nd ed. (Cambridge University Press, Cambridge, 1992), Chap.15.
  35. Robertson JA, Eggleton PP, The evolution of W Ursae Majoris systems, MNRAS, 179, 359-375 (1977). https://doi.org/10.1093/mnras/179.3.359
  36. Rucinski SM, Contact binaries: angular momentum loss in and out of contact, A&A, 112, 273-276 (1982).
  37. Samolyk G, Recent minima of 155 eclipsing binary stars, JAAVSO, 36, 171-185 (2008a).
  38. Samolyk G, Recent minima of 184 eclipsing binary stars, JAAVSO, 36, 186-206 (2008b).
  39. Samolyk G, Recent minima of 154 eclipsing binary stars, JAAVSO, 37, 44-51 (2009).
  40. Samolyk G, Recent minima of 185 eclipsing binary Stars, JAAVSO, 38, 1-10 (2010a).
  41. Samolyk G, Recent minima of 161 eclipsing binary stars, JAAVSO, 38, 85-92 (2010b).
  42. Schneller H, Sieben neue veranderliche, Astron Nachr, 233, 41-42 (1928). https://doi.org/10.1002/asna.19282330305
  43. Stepien K, Loss of angular momentum of cool close binaries and formation of contact systems, MNRAS, 274, 1019-1028 (1995).
  44. Stepien K, The low-mass limit for total mass of W UMa-type binaries, AcA, 56, 347-364 (2006).
  45. van't Veer F, The angular momentum controlled evolution of solar type contact binaries, A&A, 80, 287-295 (1979).
  46. Webbink RF, The evolution of low-mass close binary systems. I. The evolutionary fate of contact binaries, ApJ, 209, 829-845 (1976). http://dx.doi.org/10.1086/154781 https://doi.org/10.1086/154781
  47. Wilson RE, Devinney EJ, Realization of accurate close-binary light curves: application to MR Cygni, ApJ, 166, 605-619 (1971). http://dx.doi.org/10.1086/150986 https://doi.org/10.1086/150986
  48. Zhu LY, Qian SB, WZ Cephei: a close binary at the beginning of contact phase, AJ, 138, 2002-2006 (2009). http://dx.doi.org/10.1088/0004-6256/138/6/2002 https://doi.org/10.1088/0004-6256/138/6/2002

Cited by

  1. THE ALGOL SYSTEM SZ HERCULIS: PHYSICAL NATURE AND ORBITAL BEHAVIOR vol.143, pp.2, 2012, https://doi.org/10.1088/0004-6256/143/2/34
  2. Phenomenological Modeling of Newly Discovered Eclipsing Binary 2MASS J18024395 + 4003309 = VSX J180243.9+400331 vol.32, pp.2, 2015, https://doi.org/10.5140/JASS.2015.32.2.127
  3. The First Comprehensive Photometric Study of the Neglected Binary System V345 Cassiopeiae vol.30, pp.4, 2013, https://doi.org/10.5140/JASS.2013.30.4.213