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LY Aurigua: A mass-transferring O-type contact binary with a tertiary stellar companion
New Astronomy 26 (2014) 112–115
Contents lists available at ScienceDirect
New Astronomy journal homepage: www.elsevier.com/locate/newast
LY Aurigua: A mass-transferring O-type contact binary with a tertiary stellar companion Zhao Ergang a,b,⇑, Qian Shengbang a,b,c, Li Linjia a,b,c, He Jiajia a,b, Liu Liang a,b, Wang Jingjing a,b,c, Zhang Jia a,b,c a b c
Yunnan Observatories, Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming, China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, 650011 Kunming, China University of the Chinese Academy of Sciences, Beijing 100049, China
h i g h l i g h t s New CCD observation of contact binary LY Aur which has a period of near four days. The first O C analysis to the O-type binary LY Aur. Long-term period changes of LY Aur has been studied based on all Pe and CCD times of light minimum. The third body may play an important role in the evolution of early-type contact binary.
a r t i c l e
i n f o
Article history: Received 11 June 2013 Received in revised form 14 July 2013 Accepted 15 July 2013 Available online 20 July 2013 Communicated by E.P.J. van den Heuvel Keywords: Stars:binary:close Stars:binaries:eclipsing Stars:individual (LY AUR)
a b s t r a c t LY Aur is a contact massive close binary with a period of a little more than four days. The first O C analysis of this early-type binary presented in this paper suggests that the period of the system is increasing continuously at a rate of dP=dt ¼ þ7:2 107 days/year, while a cyclic oscillation with the period of 12.5 years is obvious. The long-term increasing can be explained by mass transfer from the less massive companion to the more one on the nuclear time-scale of less massive body, which suggests that the contact configuration will be broken and this binary will evolve into a semi-detached system. The periodic oscillation may be the consequence of the light-travel time effect of the third body, whose mass is no less than 3.4 M . It is expected that the third body may play an important role for the origin and evolution of the system by removing angular momentum from the central system, making the eclipsing pairs to have a low angular momentum, while initially it may have had a longer orbital period, with larger angular momentum. The original system may have evolved into the present contact configuration via a case A mass transfer. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction In general, the presence of a nearby companion impacts on the evolution of massive stars in binary systems, leading to the phenomena such as stellar mergers, X-ray binaries and gamma-ray bursts. Most massive stars are known to be members of binary systems, and a large fraction (3050%, e.g. Podsiadlowski et al., 1992) are in sufficiently close binaries that at some stage during their evolution they will interact. The structure of massive binary stars can be affected in three fundamentally different ways: by mass loss, mass accretion or common-envelope evolution. Studies of the physical characteristics of massive components of close ⇑ Corresponding author at: Yunnan Observatories, Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming, China. Tel.: +86 87163920788; fax: +86 87163920154. E-mail address: [email protected] (E.G. Zhao). 1384-1076/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.newast.2013.07.006
early-type binaries are needed for a detailed understanding of the stages of stellar evolution. LY Auriguae (HD 35921, HIP 25733) was suggested to be an irregular variable firstly, and then was proved to be an early-type eclipse binary by Mayer (1968) with the period of almost exactly four days. Due to the particular period, which is close to four integer days, it is impossible to collect a complete light curve within a few epochs from a ground-based observatory. Several people (e.g. Wood 1971a,b; Mayer and Horák, 1971; Hall and Heiser, 1972) made photometric observations and found both the components were O-type stars. The binary was classified as a detached system. With the spectroscopic data taken by Andersen et al. (1974), the star was considered to be a semi-detached system which has undergone Case A mass exchange. Four years later, Cester et al. (1978) analysed previous data and pointed out that LY Aur appeared to be a contact system. After this, during more than ten years, several authors argued about the configuration of the binary
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E.G. Zhao et al. / New Astronomy 26 (2014) 112–115
analysis of orbital period variations, the formation and evolutionary state of this binary are investigated.
Table 1 The Parameters of LY Aur. Parameter
Value
Unit
Period Separation R1 R2 M1 M2 Log (L1 =L ) Log (L2 =L )
4.002493 38.7 17.9 14.7 30.0 18.6 5.51 5.32
days R R R M M
and other problems. Based on the spectroscopic observations, Popper (1982) identified the contact configuration and determined the mass of the two components. But Li and Leung (1985) found that LY Aur was semi-detached binary with the cooler and less massive component filling its Roche lobe. On the other hand Drechsel et al. (1989) pointed out that the binary was in the configuration of marginal contact with a mass ratio of q ¼ 0.62, which is very close to Popper’s spectroscopic value. The parameters of the system obtained from these observations are listed in Table 1. LY Aur is one of the small group of early-type contact binaries. The spectral type O9.5III makes it important to study the physical characteristics of massive components. In this paper, based on the
2. New CCD photometric observations Due to the particular period close to four days, one always observes the same orbital phases, which complicates the observations. We obtained two times of light minimum of LY Aur (HJD 2454471.0581 (0:0005) and 2456268.1794 (0:0007)) in Jan. 5th 2008 and Dec. 12th 2012. During the first observation, more than 500 images were obtained with the PI1024 TKB CCD photometric system attached to the 1 m telescope at Yunnan Astronomical Observatory in China and the minimum is shown in the left-panel of Fig. 1. The integration time for each image was 6 s with R band which are close to that in the standard Johnson UBVRI system. The second observation, shown in the right-part of Fig. 1, was obtained with the Andor 20482048 CCD attached to the 60 cm telescope at the same place and with BVRI band close to the standard Johnson UBVRI system and N band which refers to no filter. The obtained images were corrected for bias and flat-field using the standard IRAF routines and were reduced with PHOT (measure magnitudes for a list of stars) of the aperture photometry package of IRAF.
Fig. 1. The two times of CCD light minimum of LY Aur obtained. Left: Jan 5th 2008 with V band. Right: Dec.12 2012 with BVRI bands and with no filter.
Table 2 Times of light minimum of LY Aur. JD.Hel 2400000+ 2439061.48000 2440858.58350 2441102.73810 2443820.43240 2446862.30400 2448293.20700 2448403.27910 2453046.17560 2453382.38260 2454471.05810 2454847.29200 2456268.17937
Error days
0.0016 0.001 0.006 0.0026 0.0009 0.0005 0.0004 0.0015 0.0009
Min.
E
(O-C)1 days
(O-C)2 days
Residual days
Ref.
I I I I I II I I I I I I
0 449 510 1189 1949 2306.5 2334 3494 3578 3850 3944 4299
0.0154 0.0006 0.0010 0.0034 0.0199 0.0082 0.0046 0.0002 0.0027 0.0053 0.0058 0.0035
+0.0075 0.00357 0.00553 +0.01064 0.007 +0.00556 +0.00912 +0.00842 +0.00516 0.00057 0.00225 0.00527
0.00103 0.00174 0.00108 0.00289 0.00035 0.002 0.00122 0.00021 0.00299 0.0009 0.00314 0.00137
Mayer (1968) Mayer and Horák (1971) Mayer (1980) Mayer (1980) BBASG (1987) Private Communication Private Communication Krajci (2005) Mayer et al. (2006) This paper Hubscher et al. (2010) This paper
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E.G. Zhao et al. / New Astronomy 26 (2014) 112–115
Min:I ¼ 2439061:4648ð0:0002Þ
3. Orbital period changes Linear ephemerides of LY Aur were obtained by several authors (e.g. Mayer, 1968; Wood 1971a,b; Mayer, 1980). All of the available photoelectric and CCD times of light minimum were collected and listed in the first column of Table 2. The ðO CÞ1 residuals of those data in Fig. 2 were computed with the ephemeris
MinI ¼ 2439061:4646 þ 4d :00249432 E:
ð1Þ
and are listed in Table 2. The corresponding ðO CÞ1 diagram is displayed in the upper panel of Fig. 2 where the big solid dots refer to photoelectric and CCD observations. As shown in Fig. 2, the general trend of the ðO CÞ1 curve shows an upward parabolic change, which indicating that the period is increasing continuously. After the long-term continuous increase was removed from the ðO CÞ1 curve, we found there is a cyclic oscillation in the residuals. Therefore, a cyclic term is added to a quadratic ephemeris to give a good fit to the observation (solid line in the up of Fig. 2). A weighted least-squares solution leads to the following quadratic ephemeris:
þ 4d :0024913ð0:0000017Þ E þ 3:92ð0:39Þ 109 E2 þ 0:0075ð0:0012Þsin½0: 316 E þ 41: 6ð8:3Þ :
ð2Þ
The quadratic term in the ephemeris suggests a continuous period increase at a rate of dP=dt ¼ þ7:2ð0:7Þ 107 days/year. The sinusoidal term in Eq. (2) reveals a periodic change with a period of P ¼ 12:5 years and an amplitude of A3 ¼ 0:0075ð0:0012Þ days, which is more easily seen in Fig. 3 where the ðO CÞ2 values calculated from the quadratic part of Eq. (2) were subtracted and the solid line in the figure represents the fit by the periodic term in Eq. (2). 4. Discussion and conclusion Based on the analysis of the O C curves, it appears that sinusoidal oscillations are discovered to be superimposed on secular period increases. In this section, mechanisms that may cause the period variation are discussed. 4.1. Mass transfer between the components The Photometric and spectroscopic observations by Drechsel et al. (1989) and Popper (1982) suggested that LY Aur is a marginal contact binary. The secular period increase at a rate of dP=dt ¼ þ7:2 107 days/year deduced from the O C analysis can be interpreted by mass transfer from the less massive component to the more massive one. That is in agreement with the conclusion of Cester et al. (1978) that the originally more massive star has lost mass to its companion which now is the primary one. By considering conservation of the mass and orbital angular momentum, a calculation with the following well known equation:
P_ _ 1 1 ; ¼ 3M P M2 M1
ð3Þ
gives that the mass transfer rate is about dM2 =dt ¼ 2:94 106 M =year. And the mass transfer time-scale is calculate to be s ¼ M 2 =M_ 2 ¼ 6:3 106 years. The nuclear time-scale of the secondary component star is Fig. 2. The O-C of LY Aur. The solid line in the upper panel refers a continuous period increase and a period oscillation. The residuals are shown in the lower panel.
sN ¼ 1011 M2 =L2 ;
ð4Þ
and the thermal time-scale of the secondary is
sth ¼ 2 107 M22 =L2 R2 ;
Fig. 3. The (O-C)2 residuals for LY Aur after the continuous increase was removed from the whole period change. The solid curve refers to a possible cyclic period oscillation.
ð5Þ
where M 2 ; R2 , and L2 are the mass, the radius, and the luminosity of the less massive component. With the parameters from the Table 1, we calculate that the nuclear and the thermal time-scales are sN ¼ 8:90 106 years, and sth ¼ 2:25 103 years, respectively. The time-scale of the orbital period change s ¼ 6:3 106 years is much longer than the thermal time-scale, but close to the nuclear times-scale of the secondary component of system. This suggests that the long-term period change can be interpreted by mass transfers on the nuclear time-scale of the less massive component. Four OB type contact binaries are listed in Table 3. Three of them (BH Cen, V382 Cyg, TU Mus) have a secular period increase which can be explained by the mass-transfer from less massive star to the more one similar to that of LY Aur. It indicates that these binaries have passed through a rapid phase of Case A mass transfer and are now in a slow phase of Case A mass transfer on the nuclear time-scale of the secondary. The contact configuration will be broken by the mass transfer from secondary to the primary, which supports the conclusions of Sybesma (1985,1986) that the early-type contact binaries go through a short-lived over-contact configuration
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E.G. Zhao et al. / New Astronomy 26 (2014) 112–115 Table 3 Some contact OB binaries. Name
Period (d)
BH Cen V701 Sco V382 Cyg TU Mus
0.7915814 0.76187371 1.8855 1.3873
SP. B3 + B3 B1–1.5 V O7.3 V + O7.7 V O7.5 V + O9.5 V
M1 (M ) 9.4 10.3 26.6 23.5
during the evolutionary phase of Case A mass transfer that is different from the situation of late-type contact binary stars. 4.2. The presence of the third component LY Aur consists of two early-type component stars that presumably contain a convective core and a radiative envelope. This suggests that the small-amplitude period oscillation can not be explained by the magnetic activity cycle mechanism, which is usually proposed to explain the cycle period change of solar-type binary stars (e.g. Applegate, 1992; Lanza et al., 1998). Therefore, the light-travel time effect via the presence of a third component is used to explain the periodic change of the orbital period (e.g. Borkovits and Hegedues, 1996; Chambliss, 1992). By assuming that the third body is moving in a circular orbit, the projected radius of 0 the orbit a012 sin i of the eclipsing pair rotating around the mass central of the triple system was computed with the equation, 0
a012 sin i ¼ A3 c
4p 2 GP 23
0 3
ða012 sin i Þ ;
ð7Þ
leads to a mass function of f ðmÞ ¼ 0:014 M . G and P3 in Eq. (7) are the gravitational constant and the period of the O C oscillation. Finally, the values of the masses and the orbital radii of the third com0 ponent for different values of i were estimated by the use of the following equation, 0 3
f ðmÞ ¼
7.9 10.3 18.0 15.3
dp/dt (days/year) 7
1.7(0.39)10 — 4.4(0.2) 107 4.0(0.5) 107
P3 (years) 44.6 41.2 47.7 47.73
while initially it may have had a longer orbital period. That is familiar to many other massive close binary stars shown in the Table 3, e.g., BH Cen, V701 Sco (Qian et al., 2006), V382 Cyg, TU Mus (Qian et al., 2007) and AI Cru (Zhao et al., 2010). To further confirm the period increase and periodic oscillation, more data are required. Acknowledgments This work is partly supported by Chinese Natural Science Foundation (Nos.11133007, 11103074 and 11203066). CCD photometric observations of LY Aur were obtained with the 1.0-m telescope and the 60-cm telescope at Yunnan Astronomical Observatory in China. The authors thank the referee for the useful comments and suggestions that helped to improve the original manuscript.
ð6Þ
where A3 is the amplitude of the O C oscillation and c is the light 0 speed. The result are a012 sin i ¼ 1:30. Then by using the parameters derived by previous observations, a computation with the following equation,
f ðmÞ ¼
M2 (M )
ðM3 sin i Þ
ðM1 þ M2 þ M3 Þ2
:
ð8Þ
From this one finds that the lowest mass of the third companion is 3:4 M and the separation between the binary and the third body is less than 22:3 AU. It is possible that the presence of the additional component of the binary has played an important role in the origin and evolution of the over-contact system by removing angular momentum from the central system. This may have caused the eclipsing pair appear to have low angular momentum now,
References Andersen, J., Batten, A.H., Hilditch, R.W., 1974. A&A 31, 1. Applegate, J.H., 1992. ApJ 385, 621. Borkovits, T., Hegedues, T., 1996. A&AS 120, 63. Cester, B., Fedel, B., Giuricin, G., Mardirossian, F., Mezzetti, M., 1978. A&A 62, 291. Chambliss, C.R., 1992. PASP 104, 663. Drechsel, H., Lorenz, R., Mayer, P., (1989). A&A 221, 49. Hall, D.S., Heiser, A.M., 1972. PASP 84, 33. Hubscher, J., Lehmann, P.B., Monninger, G., Steinbach, H.-M., Walter, F., 2010. IBVS 5918, 1. Krajci, T., 2005. IBVS 5592, 1. Lanza, A.F., Rodono, M., Rosner, R., 1998. MNRAS 296, 893. Li, Y.-F., Leung, K.-C., (1985). ApJ 298, 345. Mayer, P., 1968. PASP 80, 81. Mayer, P., 1980. IBVS 1724, 1. Mayer, P., Horák, T.B., 1971. BAICz 22, 327. Mayer, P., Wolf, M., Niarchos, P.G., Gazeas, K.D., Manimanis, V.N., Chochol, D., 2006. Ap&SS 304, 39. Podsiadlowski, P., Joss, P.C., Hsu, J.J.L., 1992. ApJ 391, 246. Popper, D.M., (1982). ApJ 262, 641. Qian, S.-B., Liu, L., Kreiner, J.M., 2006. NewA 12, 117. Qian, S.-B., Yuan, J.-Z., Liu, L., He, J.-J., Fernández Lajús, E., Kreiner, J.Z., 2007. MNRAS 380, 1599. Sybesma, C.H.B., 1985. A&A 142, 171. Sybesma, C.H.B., 1986. A&A 159, 108. Wood, F.B., 1971a. BAAS 3, 444. Wood, F.B., 1971b. IBVS 519, 1. Zhao, E.-G., Qian, S.-B., Fernández Lajús, E., von Essen, C., Zhu, L.-Y., 2010. RAA 10. 116th list of minima of eclipsing binaries. BBASG 1987;83:1.
Contents lists available at ScienceDirect
New Astronomy journal homepage: www.elsevier.com/locate/newast
LY Aurigua: A mass-transferring O-type contact binary with a tertiary stellar companion Zhao Ergang a,b,⇑, Qian Shengbang a,b,c, Li Linjia a,b,c, He Jiajia a,b, Liu Liang a,b, Wang Jingjing a,b,c, Zhang Jia a,b,c a b c
Yunnan Observatories, Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming, China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, 650011 Kunming, China University of the Chinese Academy of Sciences, Beijing 100049, China
h i g h l i g h t s New CCD observation of contact binary LY Aur which has a period of near four days. The first O C analysis to the O-type binary LY Aur. Long-term period changes of LY Aur has been studied based on all Pe and CCD times of light minimum. The third body may play an important role in the evolution of early-type contact binary.
a r t i c l e
i n f o
Article history: Received 11 June 2013 Received in revised form 14 July 2013 Accepted 15 July 2013 Available online 20 July 2013 Communicated by E.P.J. van den Heuvel Keywords: Stars:binary:close Stars:binaries:eclipsing Stars:individual (LY AUR)
a b s t r a c t LY Aur is a contact massive close binary with a period of a little more than four days. The first O C analysis of this early-type binary presented in this paper suggests that the period of the system is increasing continuously at a rate of dP=dt ¼ þ7:2 107 days/year, while a cyclic oscillation with the period of 12.5 years is obvious. The long-term increasing can be explained by mass transfer from the less massive companion to the more one on the nuclear time-scale of less massive body, which suggests that the contact configuration will be broken and this binary will evolve into a semi-detached system. The periodic oscillation may be the consequence of the light-travel time effect of the third body, whose mass is no less than 3.4 M . It is expected that the third body may play an important role for the origin and evolution of the system by removing angular momentum from the central system, making the eclipsing pairs to have a low angular momentum, while initially it may have had a longer orbital period, with larger angular momentum. The original system may have evolved into the present contact configuration via a case A mass transfer. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction In general, the presence of a nearby companion impacts on the evolution of massive stars in binary systems, leading to the phenomena such as stellar mergers, X-ray binaries and gamma-ray bursts. Most massive stars are known to be members of binary systems, and a large fraction (3050%, e.g. Podsiadlowski et al., 1992) are in sufficiently close binaries that at some stage during their evolution they will interact. The structure of massive binary stars can be affected in three fundamentally different ways: by mass loss, mass accretion or common-envelope evolution. Studies of the physical characteristics of massive components of close ⇑ Corresponding author at: Yunnan Observatories, Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming, China. Tel.: +86 87163920788; fax: +86 87163920154. E-mail address: [email protected] (E.G. Zhao). 1384-1076/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.newast.2013.07.006
early-type binaries are needed for a detailed understanding of the stages of stellar evolution. LY Auriguae (HD 35921, HIP 25733) was suggested to be an irregular variable firstly, and then was proved to be an early-type eclipse binary by Mayer (1968) with the period of almost exactly four days. Due to the particular period, which is close to four integer days, it is impossible to collect a complete light curve within a few epochs from a ground-based observatory. Several people (e.g. Wood 1971a,b; Mayer and Horák, 1971; Hall and Heiser, 1972) made photometric observations and found both the components were O-type stars. The binary was classified as a detached system. With the spectroscopic data taken by Andersen et al. (1974), the star was considered to be a semi-detached system which has undergone Case A mass exchange. Four years later, Cester et al. (1978) analysed previous data and pointed out that LY Aur appeared to be a contact system. After this, during more than ten years, several authors argued about the configuration of the binary
113
E.G. Zhao et al. / New Astronomy 26 (2014) 112–115
analysis of orbital period variations, the formation and evolutionary state of this binary are investigated.
Table 1 The Parameters of LY Aur. Parameter
Value
Unit
Period Separation R1 R2 M1 M2 Log (L1 =L ) Log (L2 =L )
4.002493 38.7 17.9 14.7 30.0 18.6 5.51 5.32
days R R R M M
and other problems. Based on the spectroscopic observations, Popper (1982) identified the contact configuration and determined the mass of the two components. But Li and Leung (1985) found that LY Aur was semi-detached binary with the cooler and less massive component filling its Roche lobe. On the other hand Drechsel et al. (1989) pointed out that the binary was in the configuration of marginal contact with a mass ratio of q ¼ 0.62, which is very close to Popper’s spectroscopic value. The parameters of the system obtained from these observations are listed in Table 1. LY Aur is one of the small group of early-type contact binaries. The spectral type O9.5III makes it important to study the physical characteristics of massive components. In this paper, based on the
2. New CCD photometric observations Due to the particular period close to four days, one always observes the same orbital phases, which complicates the observations. We obtained two times of light minimum of LY Aur (HJD 2454471.0581 (0:0005) and 2456268.1794 (0:0007)) in Jan. 5th 2008 and Dec. 12th 2012. During the first observation, more than 500 images were obtained with the PI1024 TKB CCD photometric system attached to the 1 m telescope at Yunnan Astronomical Observatory in China and the minimum is shown in the left-panel of Fig. 1. The integration time for each image was 6 s with R band which are close to that in the standard Johnson UBVRI system. The second observation, shown in the right-part of Fig. 1, was obtained with the Andor 20482048 CCD attached to the 60 cm telescope at the same place and with BVRI band close to the standard Johnson UBVRI system and N band which refers to no filter. The obtained images were corrected for bias and flat-field using the standard IRAF routines and were reduced with PHOT (measure magnitudes for a list of stars) of the aperture photometry package of IRAF.
Fig. 1. The two times of CCD light minimum of LY Aur obtained. Left: Jan 5th 2008 with V band. Right: Dec.12 2012 with BVRI bands and with no filter.
Table 2 Times of light minimum of LY Aur. JD.Hel 2400000+ 2439061.48000 2440858.58350 2441102.73810 2443820.43240 2446862.30400 2448293.20700 2448403.27910 2453046.17560 2453382.38260 2454471.05810 2454847.29200 2456268.17937
Error days
0.0016 0.001 0.006 0.0026 0.0009 0.0005 0.0004 0.0015 0.0009
Min.
E
(O-C)1 days
(O-C)2 days
Residual days
Ref.
I I I I I II I I I I I I
0 449 510 1189 1949 2306.5 2334 3494 3578 3850 3944 4299
0.0154 0.0006 0.0010 0.0034 0.0199 0.0082 0.0046 0.0002 0.0027 0.0053 0.0058 0.0035
+0.0075 0.00357 0.00553 +0.01064 0.007 +0.00556 +0.00912 +0.00842 +0.00516 0.00057 0.00225 0.00527
0.00103 0.00174 0.00108 0.00289 0.00035 0.002 0.00122 0.00021 0.00299 0.0009 0.00314 0.00137
Mayer (1968) Mayer and Horák (1971) Mayer (1980) Mayer (1980) BBASG (1987) Private Communication Private Communication Krajci (2005) Mayer et al. (2006) This paper Hubscher et al. (2010) This paper
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E.G. Zhao et al. / New Astronomy 26 (2014) 112–115
Min:I ¼ 2439061:4648ð0:0002Þ
3. Orbital period changes Linear ephemerides of LY Aur were obtained by several authors (e.g. Mayer, 1968; Wood 1971a,b; Mayer, 1980). All of the available photoelectric and CCD times of light minimum were collected and listed in the first column of Table 2. The ðO CÞ1 residuals of those data in Fig. 2 were computed with the ephemeris
MinI ¼ 2439061:4646 þ 4d :00249432 E:
ð1Þ
and are listed in Table 2. The corresponding ðO CÞ1 diagram is displayed in the upper panel of Fig. 2 where the big solid dots refer to photoelectric and CCD observations. As shown in Fig. 2, the general trend of the ðO CÞ1 curve shows an upward parabolic change, which indicating that the period is increasing continuously. After the long-term continuous increase was removed from the ðO CÞ1 curve, we found there is a cyclic oscillation in the residuals. Therefore, a cyclic term is added to a quadratic ephemeris to give a good fit to the observation (solid line in the up of Fig. 2). A weighted least-squares solution leads to the following quadratic ephemeris:
þ 4d :0024913ð0:0000017Þ E þ 3:92ð0:39Þ 109 E2 þ 0:0075ð0:0012Þsin½0: 316 E þ 41: 6ð8:3Þ :
ð2Þ
The quadratic term in the ephemeris suggests a continuous period increase at a rate of dP=dt ¼ þ7:2ð0:7Þ 107 days/year. The sinusoidal term in Eq. (2) reveals a periodic change with a period of P ¼ 12:5 years and an amplitude of A3 ¼ 0:0075ð0:0012Þ days, which is more easily seen in Fig. 3 where the ðO CÞ2 values calculated from the quadratic part of Eq. (2) were subtracted and the solid line in the figure represents the fit by the periodic term in Eq. (2). 4. Discussion and conclusion Based on the analysis of the O C curves, it appears that sinusoidal oscillations are discovered to be superimposed on secular period increases. In this section, mechanisms that may cause the period variation are discussed. 4.1. Mass transfer between the components The Photometric and spectroscopic observations by Drechsel et al. (1989) and Popper (1982) suggested that LY Aur is a marginal contact binary. The secular period increase at a rate of dP=dt ¼ þ7:2 107 days/year deduced from the O C analysis can be interpreted by mass transfer from the less massive component to the more massive one. That is in agreement with the conclusion of Cester et al. (1978) that the originally more massive star has lost mass to its companion which now is the primary one. By considering conservation of the mass and orbital angular momentum, a calculation with the following well known equation:
P_ _ 1 1 ; ¼ 3M P M2 M1
ð3Þ
gives that the mass transfer rate is about dM2 =dt ¼ 2:94 106 M =year. And the mass transfer time-scale is calculate to be s ¼ M 2 =M_ 2 ¼ 6:3 106 years. The nuclear time-scale of the secondary component star is Fig. 2. The O-C of LY Aur. The solid line in the upper panel refers a continuous period increase and a period oscillation. The residuals are shown in the lower panel.
sN ¼ 1011 M2 =L2 ;
ð4Þ
and the thermal time-scale of the secondary is
sth ¼ 2 107 M22 =L2 R2 ;
Fig. 3. The (O-C)2 residuals for LY Aur after the continuous increase was removed from the whole period change. The solid curve refers to a possible cyclic period oscillation.
ð5Þ
where M 2 ; R2 , and L2 are the mass, the radius, and the luminosity of the less massive component. With the parameters from the Table 1, we calculate that the nuclear and the thermal time-scales are sN ¼ 8:90 106 years, and sth ¼ 2:25 103 years, respectively. The time-scale of the orbital period change s ¼ 6:3 106 years is much longer than the thermal time-scale, but close to the nuclear times-scale of the secondary component of system. This suggests that the long-term period change can be interpreted by mass transfers on the nuclear time-scale of the less massive component. Four OB type contact binaries are listed in Table 3. Three of them (BH Cen, V382 Cyg, TU Mus) have a secular period increase which can be explained by the mass-transfer from less massive star to the more one similar to that of LY Aur. It indicates that these binaries have passed through a rapid phase of Case A mass transfer and are now in a slow phase of Case A mass transfer on the nuclear time-scale of the secondary. The contact configuration will be broken by the mass transfer from secondary to the primary, which supports the conclusions of Sybesma (1985,1986) that the early-type contact binaries go through a short-lived over-contact configuration
115
E.G. Zhao et al. / New Astronomy 26 (2014) 112–115 Table 3 Some contact OB binaries. Name
Period (d)
BH Cen V701 Sco V382 Cyg TU Mus
0.7915814 0.76187371 1.8855 1.3873
SP. B3 + B3 B1–1.5 V O7.3 V + O7.7 V O7.5 V + O9.5 V
M1 (M ) 9.4 10.3 26.6 23.5
during the evolutionary phase of Case A mass transfer that is different from the situation of late-type contact binary stars. 4.2. The presence of the third component LY Aur consists of two early-type component stars that presumably contain a convective core and a radiative envelope. This suggests that the small-amplitude period oscillation can not be explained by the magnetic activity cycle mechanism, which is usually proposed to explain the cycle period change of solar-type binary stars (e.g. Applegate, 1992; Lanza et al., 1998). Therefore, the light-travel time effect via the presence of a third component is used to explain the periodic change of the orbital period (e.g. Borkovits and Hegedues, 1996; Chambliss, 1992). By assuming that the third body is moving in a circular orbit, the projected radius of 0 the orbit a012 sin i of the eclipsing pair rotating around the mass central of the triple system was computed with the equation, 0
a012 sin i ¼ A3 c
4p 2 GP 23
0 3
ða012 sin i Þ ;
ð7Þ
leads to a mass function of f ðmÞ ¼ 0:014 M . G and P3 in Eq. (7) are the gravitational constant and the period of the O C oscillation. Finally, the values of the masses and the orbital radii of the third com0 ponent for different values of i were estimated by the use of the following equation, 0 3
f ðmÞ ¼
7.9 10.3 18.0 15.3
dp/dt (days/year) 7
1.7(0.39)10 — 4.4(0.2) 107 4.0(0.5) 107
P3 (years) 44.6 41.2 47.7 47.73
while initially it may have had a longer orbital period. That is familiar to many other massive close binary stars shown in the Table 3, e.g., BH Cen, V701 Sco (Qian et al., 2006), V382 Cyg, TU Mus (Qian et al., 2007) and AI Cru (Zhao et al., 2010). To further confirm the period increase and periodic oscillation, more data are required. Acknowledgments This work is partly supported by Chinese Natural Science Foundation (Nos.11133007, 11103074 and 11203066). CCD photometric observations of LY Aur were obtained with the 1.0-m telescope and the 60-cm telescope at Yunnan Astronomical Observatory in China. The authors thank the referee for the useful comments and suggestions that helped to improve the original manuscript.
ð6Þ
where A3 is the amplitude of the O C oscillation and c is the light 0 speed. The result are a012 sin i ¼ 1:30. Then by using the parameters derived by previous observations, a computation with the following equation,
f ðmÞ ¼
M2 (M )
ðM3 sin i Þ
ðM1 þ M2 þ M3 Þ2
:
ð8Þ
From this one finds that the lowest mass of the third companion is 3:4 M and the separation between the binary and the third body is less than 22:3 AU. It is possible that the presence of the additional component of the binary has played an important role in the origin and evolution of the over-contact system by removing angular momentum from the central system. This may have caused the eclipsing pair appear to have low angular momentum now,
References Andersen, J., Batten, A.H., Hilditch, R.W., 1974. A&A 31, 1. Applegate, J.H., 1992. ApJ 385, 621. Borkovits, T., Hegedues, T., 1996. A&AS 120, 63. Cester, B., Fedel, B., Giuricin, G., Mardirossian, F., Mezzetti, M., 1978. A&A 62, 291. Chambliss, C.R., 1992. PASP 104, 663. Drechsel, H., Lorenz, R., Mayer, P., (1989). A&A 221, 49. Hall, D.S., Heiser, A.M., 1972. PASP 84, 33. Hubscher, J., Lehmann, P.B., Monninger, G., Steinbach, H.-M., Walter, F., 2010. IBVS 5918, 1. Krajci, T., 2005. IBVS 5592, 1. Lanza, A.F., Rodono, M., Rosner, R., 1998. MNRAS 296, 893. Li, Y.-F., Leung, K.-C., (1985). ApJ 298, 345. Mayer, P., 1968. PASP 80, 81. Mayer, P., 1980. IBVS 1724, 1. Mayer, P., Horák, T.B., 1971. BAICz 22, 327. Mayer, P., Wolf, M., Niarchos, P.G., Gazeas, K.D., Manimanis, V.N., Chochol, D., 2006. Ap&SS 304, 39. Podsiadlowski, P., Joss, P.C., Hsu, J.J.L., 1992. ApJ 391, 246. Popper, D.M., (1982). ApJ 262, 641. Qian, S.-B., Liu, L., Kreiner, J.M., 2006. NewA 12, 117. Qian, S.-B., Yuan, J.-Z., Liu, L., He, J.-J., Fernández Lajús, E., Kreiner, J.Z., 2007. MNRAS 380, 1599. Sybesma, C.H.B., 1985. A&A 142, 171. Sybesma, C.H.B., 1986. A&A 159, 108. Wood, F.B., 1971a. BAAS 3, 444. Wood, F.B., 1971b. IBVS 519, 1. Zhao, E.-G., Qian, S.-B., Fernández Lajús, E., von Essen, C., Zhu, L.-Y., 2010. RAA 10. 116th list of minima of eclipsing binaries. BBASG 1987;83:1.