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First orbital period analysis of the Algol-type eclipsing binary RZ Aurigae
New Astronomy 15 (2010) 392–395
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First orbital period analysis of the Algol-type eclipsing binary RZ Aurigae Y.-G. Yang *, H.-F. Dai, X.-G. Yin School of Physics and Electric Information, Huaibei Coal Industry Teachers College, 235000 Huaibei, Anhui Province, China
a r t i c l e
i n f o
Article history: Received 17 September 2009 Received in revised form 8 November 2009 Accepted 17 November 2009 Available online 23 November 2009 Communicated by E.P.J. van den Heuvel Keywords: Binaries: eclipsing Binaries: close Individuals: RZ Aurigae—stars: multiple
a b s t r a c t A first analysis of the orbital period changes for the Algol-type eclipsing binary RZ Aur is presented, based on all available light minimum times. From the O C curve, it is discovered that the orbital period appears to show a cyclic variation, which may be possibly attributed to the light-time effect via the presence of the third body. Due to smaller differences between the residuals from Eqs. (2) and (3), those two equations may represent the orbital period changes of this binary. The periods and the semi-amplitudes of the cyclic oscillation are P3 ¼ 100:29ð1:57Þyr and A ¼ 0:0886ð0:0037Þd from Eq. (2), P 3 ¼ 94:61ð2:74Þyr and A ¼ 0:0792ð0:0026Þd from Eq. (3), respectively. The lowest mass of the assumed third body is 2:39ð0:06ÞM , which suggest that the unseen additional body may be a close binary. If it is true, RZ Aur may be a quadruple system. This kind of additional pair may remove angular momentum from the central system, which may play an important role for the formation and evolution of binary systems. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The Algol-type eclipsing binary RZ Aurigae (AN 29.1907,
aJ2000:0 ¼ 05h 49m 21:s 9 and dJ2000:0 ¼ þ31 420 1100 ) was discovered by Silbernagel (1907). Its magnitude varies from 11:m 9 to 14:m 0. The spectral type is of A0 þ F2 (Brancewicz and Dworak, 1980). Shapley (1913) first determined an orbital period of 3:d 11. Then Whitney (1959) revised its period to 3:d 010620 and found the period of this binary to be variable. Wood and Forbes (1963) and Kreiner (1971) subsequently derived the quadratic ephemeris with a continuous period increase. However, Rafert (1982) gave a periodic representation possible with a secular increase. Following Brancewicz and Dworak (1980), the absolute physical parameters of RZ Aur are M1 ¼ 3:0M and M2 ¼ 1:5M ; R1 ¼ 3:33R and R2 ¼ 3:37R , respectively. In this paper, new light minimum timings for RZ Aur are presented in Section 2. Section 3 is dedicated to studying its orbital period changes. Finally, the possible mechanism of period changes, e.g., light-time effect of the assumed third body, is discussed.
2. New light minimum timings The primary eclipse of RZ Aur was observed on January 1, 2009, using the 85-cm telescope at the Xinglong Station of National Astronomical Observatories of China (NAOC). This telescope was equipped with a standard Johnson–Cousin–Bessel multicolor CCD * Corresponding author. Fax: +86 561 3803256. E-mail address: [email protected] (Y.-G. Yang). 1384-1076/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2009.11.005
camera on the primary focus (Zhou et al., 2009). The PI1024 BFT camera has 1024 1024 square pixels, each subtending a projected angle on the sky of 0:00 96 and resulting in a field of view of 16:0 5 16:0 5. The reductions of observations were done using the IMRED and APPHOT packages in IRAF. Zero and flat-fielding corrections were applied to the images. Extinction corrections were small and were not made to the observations. The comparison star is HD 247910 ðaJ2000:0 ¼ 05h 49m 43:s 9; dJ2000:0 ¼ 31 450 28:00 7Þ. The coordinates of the check star are aJ2000:0 ¼ 05h 49m 27:s 41; dJ2000:0 ¼ 31 430 40:00 2), respectively. The integration times for VR measurements were 40 s and 30 s, respectively. The Heliocentric Julian Dates versus magnitude differences between the variable star and the comparison, are plotted in Fig. 1. Using the quadratic polynomial fitting method, the individual light minimum times with theirs errors are 2454833.1200 (±0.0003) for V band and 2454833.1189(±0.0002) for R band, respectively. 3. Orbital period changes for RZ Aurigae In order to investigate the period changes for RZ Aur, we collected all available light minimum times, including 2 plate, 4 photographic, 68 visual observations and 4 CCD measurements. Table 1 tabulates all available primary minimum times. Those compiled observations cover a long time interval of 101 years from 1908 to 2009, which should provide some new information about the orbital period changes of this binary. Using the linear ephemeris (Whitney, 1959),
Min:I ¼ HJD2422616:488 þ 3:010620 E
ð1Þ
393
Y.-G. Yang et al. / New Astronomy 15 (2010) 392–395 Table 1 (continued)
Fig. 1. The observed primary eclipse for RZ Aurigae in BV bands.
Table 1 All available light minimum times for the eclipsing binary RZ Aurigae. JD(Hel.) (1)
Epoch (2)
Method (3)
ðO CÞ (4)
ðO CÞ1 (5)
ðO CÞ2 (6)
Ref. (7)
2418028.362 2418052.458 2418061.475 2420533.156 2420545.192 2420599.402 2420840.233 2420888.402 2420903.464 2421168.386 2421255.693 2421460.430 2421469.451 2421496.559 2421544.715 2422372.625 2422610.476 2422616.492 2422646.578 2423164.428 2423429.338 2423435.383 2423468.484 2423495.594 2423763.521 2424094.667 2424528.203 2424585.427 2424591.446 2425654.178 2425699.335 2425943.165 2425979.327 2426024.473 2426027.478 2426030.509 2426295.435 2426325.525 2429342.17 2433301.19 2433307.240 2434833.626 2442447.516 2442450.531 2442775.692 2444636.271 2444663.370 2444669.388 2444958.419 2445259.472 2445298.618
1524.0 1516.0 1513.0 692.0 688.0 670.0 590.0 574.0 569.0 481.0 452.0 384.0 381.0 372.0 356.0 81.0 2.0 +0.0 +10.0 +182.0 +270.0 +272.0 +283.0 +292.0 +381.0 +491.0 +635.0 +654.0 +656.0 +1009.0 +1024.0 +1105.0 +1117.0 +1132.0 +1133.0 +1134.0 +1222.0 +1232.0 +2234.0 +3549.0 +3551.0 +4058.0 +6587.0 +6588.0 +6696.0 +7314.0 +7323.0 +7325.0 +7421.0 +7521.0 +7534.0
vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi p p pg pg vi vi vi vi vi vi vi vi vi
+0.0589 +0.0699 +0.0551 +0.0170 +0.0106 +0.0294 +0.0108 +0.0099 +0.0188 +0.0062 +0.0052 +0.0201 +0.0092 +0.0216 +0.0077 0.0028 +0.0092 +0.0040 0.0162 +0.0072 0.0174 +0.0064 0.0095 +0.0050 0.0132 0.0354 0.0287 0.0065 0.0087 0.0256 0.0279 0.0581 0.0235 0.0368 0.0425 0.0221 0.0306 0.0468 0.0431 +0.0116 +0.0404 +0.0420 +0.0741 +0.0784 +0.0925 +0.1083 +0.1117 +0.1085 +0.1200 +0.1110 +0.1189
0.0035 +0.0079 0.0068 0.0057 0.0119 +0.0077 0.0075 0.0077 +0.0014 0.0075 0.0073 +0.0103 0.0005 +0.0123 0.0010 0.0013 +0.0134 +0.0082 0.0116 +0.0172 0.0049 +0.0190 +0.0034 +0.0181 +0.0023 0.0171 0.0073 +0.0153 +0.0131 +0.0019 0.0002 0.0296 +0.0052 0.0080 0.0137 +0.0067 0.0011 0.0172 0.0180 +0.0018 +0.0305 +0.0132 0.0312 0.0269 0.0140 +0.0005 +0.0039 +0.0007 +0.0128 +0.0046 +0.0127
0.0074 +0.0040 0.0106 0.0076 0.0138 +0.0059 0.0090 0.0091 +0.0000 0.0086 0.0083 +0.0097 0.0011 +0.0117 0.0015 0.0008 +0.0141 +0.0090 0.0108 +0.0185 0.0034 +0.0205 +0.0049 +0.0197 +0.0040 0.0153 0.0054 +0.0172 +0.0151 +0.0036 +0.0014 0.0280 +0.0066 0.0065 0.0122 +0.0082 +0.0002 0.0159 0.0201 0.0028 +0.0259 +0.0093 0.0287 0.0244 0.0114 +0.0024 +0.0059 +0.0027 +0.0146 +0.0063 +0.0143
(1) (2) (2) (2) (2) (3) (3) (2) (2) (2) (3) (2) (2) (2) (2) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (4) (4) (5) (6) (7) (7) (8) (9) (10) (10) (11) (12) (13)
JD(Hel.) (1)
Epoch (2)
Method (3)
ðO CÞ (4)
ðO CÞ1 (5)
ðO CÞ2 (6)
Ref. (7)
2446406.505 2446412.540 2447195.298 2447207.338 2447496.362 2447529.466 2447824.499 2447854.600 2448131.549 2448619.282 2448628.331 2448956.491 2448971.532 2448983.570 2448986.603 2449778.380 2450046.343 2450898.340 2451163.287 2451533.5610 2451816.5360 2452310.2590 2452635.4150 2452644.4500 2453755.3392 2453764.3694 2454833.1195
+7902.0 +7904.0 +8164.0 +8168.0 +8264.0 +8275.0 +8373.0 +8383.0 +8475.0 +8637.0 +8640.0 +8749.0 +8754.0 +8758.0 +8759.0 +9022.0 +9111.0 +9394.0 +9482.0 +9605.0 +9699.0 +9863.0 +9971.0 +9974.0 +10343.0 +10346.0 +10701.0
vi vi vi vi vi vi pg vi vi vi vi vi vi vi pg vi vi vi vi vi vi CCD vi vi CCD CCD CCD
+0.0978 +0.1115 +0.1083 +0.1058 +0.1103 +0.0975 +0.0897 +0.0845 +0.0565 +0.0691 +0.0862 +0.0886 +0.0765 +0.0720 +0.0944 +0.0784 +0.0962 +0.0877 +0.1002 +0.0679 +0.0446 +0.0259 +0.0350 +0.0381 +0.0085 +0.0069 0.0131
0.0032 +0.0105 +0.0128 +0.0104 +0.0173 +0.0048 0.0004 0.0053 0.0306 0.0128 +0.0044 +0.0105 0.0014 0.0058 +0.0167 +0.0106 +0.0319 +0.0356 +0.0521 +0.0255 +0.0066 0.0042 +0.0102 +0.0135 +0.0024 +0.0010 0.0011
0.0024 +0.0113 +0.0130 +0.0106 +0.0173 +0.0048 0.0006 0.0055 0.0310 0.0135 +0.0037 +0.0097 0.0022 0.0066 +0.0158 +0.0095 +0.0308 +0.0344 +0.0509 +0.0244 +0.0056 0.0051 +0.0094 +0.0126 +0.0018 +0.0003 0.0020
(14) (15) (16) (17) (18) (17) (19) (20) (21) (22) (23) (24) (25) (24) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (36) (37)
References: (1) Zinner (1932); (2) Nijland (1920); (3) Nijland (1931); (4) Kukarkin (1956); (5) Kaho (1950); (6) Whitney (1959); (7) Locher (1975); (8) Locher (1976); (9) Locher (1981a); (10) Locher (1981b); (11) Locher (1982a); (12) Locher (1982b); (13) Locher (1983); (14) Borovicka (1986); (15) Locher (1986); (16) Locher (1988); (17) Manek (1992); (18) Locher (1989); (19) Hübscher et al., 1989; (20) Locher (1990a); (21) Locher (1990b); (22) Locher (1992a); (23) Locher (1992b); (24) Zejda (1995); (25) Locher (1992c); (26) Hübscher et al., 1994; (27) Locher (1995); (28) Locher (1996); (29) Locher (1998); (30) Locher (1999); (31) Locher (2000); (32) Locher (2001); (33) Diethelm (2002); (34) Diethelm (2003); (35) Koralewski (2003); (36) Hübscher et al. (2006); (37) Present work.
we calculated the ðO CÞ values for those light minimum times, listed in the fourth column of Table 1. Based on those data, an O C curve is plotted in the upper panel of Fig. 2. In the calculating process, weight 10 was assigned to CCD observations, while weight 1 to other data. Although the plate, photographic and visual minima times with relatively less accuracy were observed before 2002, the general trend of the O C curve apparently exhibits a continuous oscillatory variation. A weighted nonlinear least-squares fitting method yields the following equation,
O C ¼ þ0:0642ð0:0031Þ 5:87ð0:69Þ 106 E þ 0:0866ð0:0037Þ sin½5:16ð0:08Þ 104 E þ 4:0531ð0:0400Þ
ð2Þ
The weighted sum of the squares of residuals from Eq. (2) is Ri ðO CÞ2i ¼ 0:0168 days2 . The corresponding residuals ðO CÞ1 are also listed in the fifth column of Table 1, and displayed in the lower panel of Fig. 2. The solid and dotted lines were plotted by all contribution and the linear part of Eq. (2). Using the relation P3 ¼ 2pP=x with x ¼ 5:16ð0:08Þ 104 , the period of this variation can be determined to be P3 ¼ 100:29ð1:57Þyr, where P is the orbital period of RZ Aur in years. For RZ Aur, this kind of quasi-sinusoidal variation may be produced by a light-time orbit due to the presence of a third body. Therefore, the O C curve was alternatively fitted by a linear equation plus light-time effect (Irwin, 1952). The Levenberg–Marquardt technique (Press et al., 1992) was applied to solve for several fitted parameters. Using a weighted nonlinear fitting method, such an equation may be obtained as follows,
394
Y.-G. Yang et al. / New Astronomy 15 (2010) 392–395 Table 2 Parameters of the assumed third body for RZ Aur. Parameters
Eq. (2)
Eq. (3)
A(d) P 3 ðyrÞ e0 x0 ðarcÞ T p ðHJDÞ
0.0886(±0.0037) 100.29(±1.57) – – –
0.0792(±0.0026) 94.61(±2.74) 0.1027(±0.0227) 3.7067(±0.2223) 2435769.4(±900.1)
a12 sin i0 ðAUÞ f ðmÞðM Þ 0 M3 ðM Þði ¼ 90 Þ M3 ðM Þði0 ¼ 70 Þ M3 ðM Þði0 ¼ 50 Þ M3 ðM Þði0 ¼ 30 Þ a12 ðAUÞði0 ¼ 90 Þ 0 a12 ðAUÞði ¼ 70 Þ a12 ðAUÞði0 ¼ 50 Þ a12 ðAUÞði0 ¼ 30 Þ
14.9968(±0.6361) 0.3353(±0.0531) 2.56(±0.09) 2.78(±0.09) 3.68(±0.12) 7.14(±0.21) 26.42(±1.99) 25.88(±1.94) 23.93(±1.77) 18.93(±1.35)
13.7139(±0.4561) 0.2882(±0.0284) 2.39(±0.06) 2.59(±0.07) 3.43(±0.09) 6.55(±0.15) 25.8(±1.54) 25.3(±1.50) 23.5(±1.37) 18.8(±1.06)
Fig. 2. The ðO CÞ curve (upper panel) and the corresponding residuals ðO CÞ1 after subtraction of Eq. (2) (low panel) for the eclipsing binary RZ Aur. The open circles refer to the plate, visual or photographic observations, while the filled circles represent the CCD ones, respectively. The solid and dotted lines were constructed based on Eq. (2) using the entire equation and only the linear part, respectively.
O C ¼ þ0:0523ð0:0065Þ 3:47ð1:28Þ 106 E þ s
ð3Þ
and 0
s¼
a12 sin i c
1 e02 þ e0 sin x0 1 þ e0 cos m0
ð4Þ 0
The semi-amplitude of the light-time effect is A ¼ a12 sin i =c, where a12 is the semi-axis of the eclipsing-pair orbit around the common center of mass with the third body and c is the velocity of light. 0 In Eq. (4), the third body orbital parameters m0 ; e0 ; x0 and i are true anomaly, eccentricity, longitude of the periastron and inclination, respectively. Those fitted parameters of Eq. (4) are listed in Table 2, where T p is the time of periastron passage for the third body. The calculated residuals ðO CÞ2 from Eq. (3) are listed in the sixth column of Table 1, and shown in the lower panel of Fig. 3. The solid and dotted lines in the upper panel were constructed based on Eq. (3) using the entire equation and only the linear part, respectively. The weighted sum of the squares of residuals from Eq. (3) is Ri ðO CÞ2i ¼ 0:0163 days2 , which is a bit smaller that value from Eq. (2). The orbital period of the third body is P3 ¼ 94:61ð2:74Þyr.
Fig. 3. The ðO CÞ curve (upper panel) and the corresponding residuals ðO CÞ2 after subtraction of Eq. (3) (low panel) for the eclipsing binary RZ Aur. The solid and dotted lines were constructed based on Eq. (3) using the entire equation and only the linear part, respectively. Other symbols are the same as Fig. 2.
body, the mass function can be calculated by the following equation,
ðM 3 sin i Þ3 0
4p2
ða12 sin i Þ3 0
4. Discussions
f ðM 3 Þ ¼
From the O C curve of RZ Aur, there may exist a cyclic oscillation. Due to smaller differences between the residuals from Eqs. (2) and (3), those two equations may represent the orbital period changes of this binary. The periods of the cyclic variation are P3 ¼ 100:29ð1:57Þyr from Eq. (2) and P3 ¼ 94:61ð2:74Þyr from Eq. (3), respectively. Therefore, the complete period of this cyclic variation was just covered the observing minima times from 1908 to 2009. For a close binary, the cyclic variation may be generally attributed to either the light-time effect via the presence of the third body (Irwin, 1952) or the cyclic magnetic activities of one or two components (Applegate, 1992). Lanza (2006) pointed out that Applegate’s mechanism is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary star. The spectral type of RZ Aur is of A0 þ F2. Therefore, this cyclic variation may result from the light-time effect due to the assumed third body. This kind of light-time orbit may occur in many other Algols, such as V342 Aql and BZ Cas (Erdem et al., 2007), ZZ Cas (Liao and Qian, 2009), AH Cep (Kim et al., 2005), TX Her (Ak et al., 2004), DK Cep and UZ Sge (Zasche et al., 2008). For the third
where M 3 ; i and P3 are the mass, inclination and period of the third body. According the fitted parameters of Eqs. (2) and (4), we obtained the values of the mass function. For some several different 0 values of i , the masses and the orbital radii of the third body can be estimated, which are listed in Table 2. From this table, the lowest masses of the third component are 2:56ð0:09ÞM from Eq. (2) and 2:39ð0:06ÞM from Eq. (3), respectively. Therefore, the mass for the third component of RZ Aur is quite large. Knowing that the stars in this system are of type A0 and F2 and must be close to the main sequence, the mass of RZ Aur is estimated to be about 3M þ 1:5M (Cox, 2000). A third star with more than 2:39M is therefore expected to be more luminous than the two components of the close binary, and one would expect that its light and spectrum would be observable, if the third star is a single star. It is, however, possible, that it is itself a close binary of two stars of 1:2M , which in that case would have a much lower luminosity, and probably would not be visible next to the A0 þ F2 pair. If the existence of additional close binary is true, RZ Aur may be a unsolved quadruple system. This will further confirm the hypothesis that most close binary stars exist in multiple
ðM1 þ M 2 þ M 3 Þ 0
2
¼
GP 23
ð5Þ
Y.-G. Yang et al. / New Astronomy 15 (2010) 392–395
systems (D’Angelo et al., 2006; Pribulla and Rucinski, 2006; Rucinski et al., 2007). This kind of additional component may remove angular momentum from the central system via Kozai oscillation (Kozai, 1962) or a combination of Kozai cycle and tidal friction (e.g., Fabrychy and Tremaine, 2007), which may play an important role for the formation and evolution of binary. 5. Summary Based on the previous analyses, the following conclusions can be drawn: (1) The O C curve shows that there exists a cyclic variation in the orbital period of RZ Aur. Due to smaller differences between the residuals from Eqs. (2) and (3), those two equations may represent the orbital period changes of this binary. The observed light minimum times cover the complete period of the cyclic variation. (2) Due to the spectral type of A0 þ F2 for RZ Aur, the cyclic variation may result from the light-time effect via the presence of the third body. The lowest mass of the third companion is 2:39ð0:06ÞM , suggesting that the third pair may be another unseen close binary. Therefore, RZ Aur may be a quadruple system. Additionally, it is necessary to observe this binary RZ Aur by the photometry and spectroscopy, in order to obtain the absolute parameters and to identify the nature of period changes in our future work. Acknowledgements The authors would like to express our gratitude to an anonymous referee for his/her helpful comments and suggestions, which help to improve the original manuscript. The author acknowledge Professor J.M. Kreiner for sending his collected light minimum times of RZ Aur. This work is supported partly by the Joint Fund of Astronomy of the National Natural Science Foundation of China (NSFC) and the Chinese Academy of Sciences (CAS) (Grant No. 10778707), the Special Foundation of President and West Light Foundation of the Chinese Academy of Sciences, and Yunnan Natural Science Foundation (No. 2008CD157). References Ak, T., Albayrak, B., Selam, S.O., Tanriverdi, T., 2004. New Astron. 9, 265. Applegate, J.H., 1992. ApJ 385, 621.
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First orbital period analysis of the Algol-type eclipsing binary RZ Aurigae Y.-G. Yang *, H.-F. Dai, X.-G. Yin School of Physics and Electric Information, Huaibei Coal Industry Teachers College, 235000 Huaibei, Anhui Province, China
a r t i c l e
i n f o
Article history: Received 17 September 2009 Received in revised form 8 November 2009 Accepted 17 November 2009 Available online 23 November 2009 Communicated by E.P.J. van den Heuvel Keywords: Binaries: eclipsing Binaries: close Individuals: RZ Aurigae—stars: multiple
a b s t r a c t A first analysis of the orbital period changes for the Algol-type eclipsing binary RZ Aur is presented, based on all available light minimum times. From the O C curve, it is discovered that the orbital period appears to show a cyclic variation, which may be possibly attributed to the light-time effect via the presence of the third body. Due to smaller differences between the residuals from Eqs. (2) and (3), those two equations may represent the orbital period changes of this binary. The periods and the semi-amplitudes of the cyclic oscillation are P3 ¼ 100:29ð1:57Þyr and A ¼ 0:0886ð0:0037Þd from Eq. (2), P 3 ¼ 94:61ð2:74Þyr and A ¼ 0:0792ð0:0026Þd from Eq. (3), respectively. The lowest mass of the assumed third body is 2:39ð0:06ÞM , which suggest that the unseen additional body may be a close binary. If it is true, RZ Aur may be a quadruple system. This kind of additional pair may remove angular momentum from the central system, which may play an important role for the formation and evolution of binary systems. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The Algol-type eclipsing binary RZ Aurigae (AN 29.1907,
aJ2000:0 ¼ 05h 49m 21:s 9 and dJ2000:0 ¼ þ31 420 1100 ) was discovered by Silbernagel (1907). Its magnitude varies from 11:m 9 to 14:m 0. The spectral type is of A0 þ F2 (Brancewicz and Dworak, 1980). Shapley (1913) first determined an orbital period of 3:d 11. Then Whitney (1959) revised its period to 3:d 010620 and found the period of this binary to be variable. Wood and Forbes (1963) and Kreiner (1971) subsequently derived the quadratic ephemeris with a continuous period increase. However, Rafert (1982) gave a periodic representation possible with a secular increase. Following Brancewicz and Dworak (1980), the absolute physical parameters of RZ Aur are M1 ¼ 3:0M and M2 ¼ 1:5M ; R1 ¼ 3:33R and R2 ¼ 3:37R , respectively. In this paper, new light minimum timings for RZ Aur are presented in Section 2. Section 3 is dedicated to studying its orbital period changes. Finally, the possible mechanism of period changes, e.g., light-time effect of the assumed third body, is discussed.
2. New light minimum timings The primary eclipse of RZ Aur was observed on January 1, 2009, using the 85-cm telescope at the Xinglong Station of National Astronomical Observatories of China (NAOC). This telescope was equipped with a standard Johnson–Cousin–Bessel multicolor CCD * Corresponding author. Fax: +86 561 3803256. E-mail address: [email protected] (Y.-G. Yang). 1384-1076/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2009.11.005
camera on the primary focus (Zhou et al., 2009). The PI1024 BFT camera has 1024 1024 square pixels, each subtending a projected angle on the sky of 0:00 96 and resulting in a field of view of 16:0 5 16:0 5. The reductions of observations were done using the IMRED and APPHOT packages in IRAF. Zero and flat-fielding corrections were applied to the images. Extinction corrections were small and were not made to the observations. The comparison star is HD 247910 ðaJ2000:0 ¼ 05h 49m 43:s 9; dJ2000:0 ¼ 31 450 28:00 7Þ. The coordinates of the check star are aJ2000:0 ¼ 05h 49m 27:s 41; dJ2000:0 ¼ 31 430 40:00 2), respectively. The integration times for VR measurements were 40 s and 30 s, respectively. The Heliocentric Julian Dates versus magnitude differences between the variable star and the comparison, are plotted in Fig. 1. Using the quadratic polynomial fitting method, the individual light minimum times with theirs errors are 2454833.1200 (±0.0003) for V band and 2454833.1189(±0.0002) for R band, respectively. 3. Orbital period changes for RZ Aurigae In order to investigate the period changes for RZ Aur, we collected all available light minimum times, including 2 plate, 4 photographic, 68 visual observations and 4 CCD measurements. Table 1 tabulates all available primary minimum times. Those compiled observations cover a long time interval of 101 years from 1908 to 2009, which should provide some new information about the orbital period changes of this binary. Using the linear ephemeris (Whitney, 1959),
Min:I ¼ HJD2422616:488 þ 3:010620 E
ð1Þ
393
Y.-G. Yang et al. / New Astronomy 15 (2010) 392–395 Table 1 (continued)
Fig. 1. The observed primary eclipse for RZ Aurigae in BV bands.
Table 1 All available light minimum times for the eclipsing binary RZ Aurigae. JD(Hel.) (1)
Epoch (2)
Method (3)
ðO CÞ (4)
ðO CÞ1 (5)
ðO CÞ2 (6)
Ref. (7)
2418028.362 2418052.458 2418061.475 2420533.156 2420545.192 2420599.402 2420840.233 2420888.402 2420903.464 2421168.386 2421255.693 2421460.430 2421469.451 2421496.559 2421544.715 2422372.625 2422610.476 2422616.492 2422646.578 2423164.428 2423429.338 2423435.383 2423468.484 2423495.594 2423763.521 2424094.667 2424528.203 2424585.427 2424591.446 2425654.178 2425699.335 2425943.165 2425979.327 2426024.473 2426027.478 2426030.509 2426295.435 2426325.525 2429342.17 2433301.19 2433307.240 2434833.626 2442447.516 2442450.531 2442775.692 2444636.271 2444663.370 2444669.388 2444958.419 2445259.472 2445298.618
1524.0 1516.0 1513.0 692.0 688.0 670.0 590.0 574.0 569.0 481.0 452.0 384.0 381.0 372.0 356.0 81.0 2.0 +0.0 +10.0 +182.0 +270.0 +272.0 +283.0 +292.0 +381.0 +491.0 +635.0 +654.0 +656.0 +1009.0 +1024.0 +1105.0 +1117.0 +1132.0 +1133.0 +1134.0 +1222.0 +1232.0 +2234.0 +3549.0 +3551.0 +4058.0 +6587.0 +6588.0 +6696.0 +7314.0 +7323.0 +7325.0 +7421.0 +7521.0 +7534.0
vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi p p pg pg vi vi vi vi vi vi vi vi vi
+0.0589 +0.0699 +0.0551 +0.0170 +0.0106 +0.0294 +0.0108 +0.0099 +0.0188 +0.0062 +0.0052 +0.0201 +0.0092 +0.0216 +0.0077 0.0028 +0.0092 +0.0040 0.0162 +0.0072 0.0174 +0.0064 0.0095 +0.0050 0.0132 0.0354 0.0287 0.0065 0.0087 0.0256 0.0279 0.0581 0.0235 0.0368 0.0425 0.0221 0.0306 0.0468 0.0431 +0.0116 +0.0404 +0.0420 +0.0741 +0.0784 +0.0925 +0.1083 +0.1117 +0.1085 +0.1200 +0.1110 +0.1189
0.0035 +0.0079 0.0068 0.0057 0.0119 +0.0077 0.0075 0.0077 +0.0014 0.0075 0.0073 +0.0103 0.0005 +0.0123 0.0010 0.0013 +0.0134 +0.0082 0.0116 +0.0172 0.0049 +0.0190 +0.0034 +0.0181 +0.0023 0.0171 0.0073 +0.0153 +0.0131 +0.0019 0.0002 0.0296 +0.0052 0.0080 0.0137 +0.0067 0.0011 0.0172 0.0180 +0.0018 +0.0305 +0.0132 0.0312 0.0269 0.0140 +0.0005 +0.0039 +0.0007 +0.0128 +0.0046 +0.0127
0.0074 +0.0040 0.0106 0.0076 0.0138 +0.0059 0.0090 0.0091 +0.0000 0.0086 0.0083 +0.0097 0.0011 +0.0117 0.0015 0.0008 +0.0141 +0.0090 0.0108 +0.0185 0.0034 +0.0205 +0.0049 +0.0197 +0.0040 0.0153 0.0054 +0.0172 +0.0151 +0.0036 +0.0014 0.0280 +0.0066 0.0065 0.0122 +0.0082 +0.0002 0.0159 0.0201 0.0028 +0.0259 +0.0093 0.0287 0.0244 0.0114 +0.0024 +0.0059 +0.0027 +0.0146 +0.0063 +0.0143
(1) (2) (2) (2) (2) (3) (3) (2) (2) (2) (3) (2) (2) (2) (2) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (3) (4) (4) (5) (6) (7) (7) (8) (9) (10) (10) (11) (12) (13)
JD(Hel.) (1)
Epoch (2)
Method (3)
ðO CÞ (4)
ðO CÞ1 (5)
ðO CÞ2 (6)
Ref. (7)
2446406.505 2446412.540 2447195.298 2447207.338 2447496.362 2447529.466 2447824.499 2447854.600 2448131.549 2448619.282 2448628.331 2448956.491 2448971.532 2448983.570 2448986.603 2449778.380 2450046.343 2450898.340 2451163.287 2451533.5610 2451816.5360 2452310.2590 2452635.4150 2452644.4500 2453755.3392 2453764.3694 2454833.1195
+7902.0 +7904.0 +8164.0 +8168.0 +8264.0 +8275.0 +8373.0 +8383.0 +8475.0 +8637.0 +8640.0 +8749.0 +8754.0 +8758.0 +8759.0 +9022.0 +9111.0 +9394.0 +9482.0 +9605.0 +9699.0 +9863.0 +9971.0 +9974.0 +10343.0 +10346.0 +10701.0
vi vi vi vi vi vi pg vi vi vi vi vi vi vi pg vi vi vi vi vi vi CCD vi vi CCD CCD CCD
+0.0978 +0.1115 +0.1083 +0.1058 +0.1103 +0.0975 +0.0897 +0.0845 +0.0565 +0.0691 +0.0862 +0.0886 +0.0765 +0.0720 +0.0944 +0.0784 +0.0962 +0.0877 +0.1002 +0.0679 +0.0446 +0.0259 +0.0350 +0.0381 +0.0085 +0.0069 0.0131
0.0032 +0.0105 +0.0128 +0.0104 +0.0173 +0.0048 0.0004 0.0053 0.0306 0.0128 +0.0044 +0.0105 0.0014 0.0058 +0.0167 +0.0106 +0.0319 +0.0356 +0.0521 +0.0255 +0.0066 0.0042 +0.0102 +0.0135 +0.0024 +0.0010 0.0011
0.0024 +0.0113 +0.0130 +0.0106 +0.0173 +0.0048 0.0006 0.0055 0.0310 0.0135 +0.0037 +0.0097 0.0022 0.0066 +0.0158 +0.0095 +0.0308 +0.0344 +0.0509 +0.0244 +0.0056 0.0051 +0.0094 +0.0126 +0.0018 +0.0003 0.0020
(14) (15) (16) (17) (18) (17) (19) (20) (21) (22) (23) (24) (25) (24) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (36) (37)
References: (1) Zinner (1932); (2) Nijland (1920); (3) Nijland (1931); (4) Kukarkin (1956); (5) Kaho (1950); (6) Whitney (1959); (7) Locher (1975); (8) Locher (1976); (9) Locher (1981a); (10) Locher (1981b); (11) Locher (1982a); (12) Locher (1982b); (13) Locher (1983); (14) Borovicka (1986); (15) Locher (1986); (16) Locher (1988); (17) Manek (1992); (18) Locher (1989); (19) Hübscher et al., 1989; (20) Locher (1990a); (21) Locher (1990b); (22) Locher (1992a); (23) Locher (1992b); (24) Zejda (1995); (25) Locher (1992c); (26) Hübscher et al., 1994; (27) Locher (1995); (28) Locher (1996); (29) Locher (1998); (30) Locher (1999); (31) Locher (2000); (32) Locher (2001); (33) Diethelm (2002); (34) Diethelm (2003); (35) Koralewski (2003); (36) Hübscher et al. (2006); (37) Present work.
we calculated the ðO CÞ values for those light minimum times, listed in the fourth column of Table 1. Based on those data, an O C curve is plotted in the upper panel of Fig. 2. In the calculating process, weight 10 was assigned to CCD observations, while weight 1 to other data. Although the plate, photographic and visual minima times with relatively less accuracy were observed before 2002, the general trend of the O C curve apparently exhibits a continuous oscillatory variation. A weighted nonlinear least-squares fitting method yields the following equation,
O C ¼ þ0:0642ð0:0031Þ 5:87ð0:69Þ 106 E þ 0:0866ð0:0037Þ sin½5:16ð0:08Þ 104 E þ 4:0531ð0:0400Þ
ð2Þ
The weighted sum of the squares of residuals from Eq. (2) is Ri ðO CÞ2i ¼ 0:0168 days2 . The corresponding residuals ðO CÞ1 are also listed in the fifth column of Table 1, and displayed in the lower panel of Fig. 2. The solid and dotted lines were plotted by all contribution and the linear part of Eq. (2). Using the relation P3 ¼ 2pP=x with x ¼ 5:16ð0:08Þ 104 , the period of this variation can be determined to be P3 ¼ 100:29ð1:57Þyr, where P is the orbital period of RZ Aur in years. For RZ Aur, this kind of quasi-sinusoidal variation may be produced by a light-time orbit due to the presence of a third body. Therefore, the O C curve was alternatively fitted by a linear equation plus light-time effect (Irwin, 1952). The Levenberg–Marquardt technique (Press et al., 1992) was applied to solve for several fitted parameters. Using a weighted nonlinear fitting method, such an equation may be obtained as follows,
394
Y.-G. Yang et al. / New Astronomy 15 (2010) 392–395 Table 2 Parameters of the assumed third body for RZ Aur. Parameters
Eq. (2)
Eq. (3)
A(d) P 3 ðyrÞ e0 x0 ðarcÞ T p ðHJDÞ
0.0886(±0.0037) 100.29(±1.57) – – –
0.0792(±0.0026) 94.61(±2.74) 0.1027(±0.0227) 3.7067(±0.2223) 2435769.4(±900.1)
a12 sin i0 ðAUÞ f ðmÞðM Þ 0 M3 ðM Þði ¼ 90 Þ M3 ðM Þði0 ¼ 70 Þ M3 ðM Þði0 ¼ 50 Þ M3 ðM Þði0 ¼ 30 Þ a12 ðAUÞði0 ¼ 90 Þ 0 a12 ðAUÞði ¼ 70 Þ a12 ðAUÞði0 ¼ 50 Þ a12 ðAUÞði0 ¼ 30 Þ
14.9968(±0.6361) 0.3353(±0.0531) 2.56(±0.09) 2.78(±0.09) 3.68(±0.12) 7.14(±0.21) 26.42(±1.99) 25.88(±1.94) 23.93(±1.77) 18.93(±1.35)
13.7139(±0.4561) 0.2882(±0.0284) 2.39(±0.06) 2.59(±0.07) 3.43(±0.09) 6.55(±0.15) 25.8(±1.54) 25.3(±1.50) 23.5(±1.37) 18.8(±1.06)
Fig. 2. The ðO CÞ curve (upper panel) and the corresponding residuals ðO CÞ1 after subtraction of Eq. (2) (low panel) for the eclipsing binary RZ Aur. The open circles refer to the plate, visual or photographic observations, while the filled circles represent the CCD ones, respectively. The solid and dotted lines were constructed based on Eq. (2) using the entire equation and only the linear part, respectively.
O C ¼ þ0:0523ð0:0065Þ 3:47ð1:28Þ 106 E þ s
ð3Þ
and 0
s¼
a12 sin i c
1 e02 þ e0 sin x0 1 þ e0 cos m0
ð4Þ 0
The semi-amplitude of the light-time effect is A ¼ a12 sin i =c, where a12 is the semi-axis of the eclipsing-pair orbit around the common center of mass with the third body and c is the velocity of light. 0 In Eq. (4), the third body orbital parameters m0 ; e0 ; x0 and i are true anomaly, eccentricity, longitude of the periastron and inclination, respectively. Those fitted parameters of Eq. (4) are listed in Table 2, where T p is the time of periastron passage for the third body. The calculated residuals ðO CÞ2 from Eq. (3) are listed in the sixth column of Table 1, and shown in the lower panel of Fig. 3. The solid and dotted lines in the upper panel were constructed based on Eq. (3) using the entire equation and only the linear part, respectively. The weighted sum of the squares of residuals from Eq. (3) is Ri ðO CÞ2i ¼ 0:0163 days2 , which is a bit smaller that value from Eq. (2). The orbital period of the third body is P3 ¼ 94:61ð2:74Þyr.
Fig. 3. The ðO CÞ curve (upper panel) and the corresponding residuals ðO CÞ2 after subtraction of Eq. (3) (low panel) for the eclipsing binary RZ Aur. The solid and dotted lines were constructed based on Eq. (3) using the entire equation and only the linear part, respectively. Other symbols are the same as Fig. 2.
body, the mass function can be calculated by the following equation,
ðM 3 sin i Þ3 0
4p2
ða12 sin i Þ3 0
4. Discussions
f ðM 3 Þ ¼
From the O C curve of RZ Aur, there may exist a cyclic oscillation. Due to smaller differences between the residuals from Eqs. (2) and (3), those two equations may represent the orbital period changes of this binary. The periods of the cyclic variation are P3 ¼ 100:29ð1:57Þyr from Eq. (2) and P3 ¼ 94:61ð2:74Þyr from Eq. (3), respectively. Therefore, the complete period of this cyclic variation was just covered the observing minima times from 1908 to 2009. For a close binary, the cyclic variation may be generally attributed to either the light-time effect via the presence of the third body (Irwin, 1952) or the cyclic magnetic activities of one or two components (Applegate, 1992). Lanza (2006) pointed out that Applegate’s mechanism is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary star. The spectral type of RZ Aur is of A0 þ F2. Therefore, this cyclic variation may result from the light-time effect due to the assumed third body. This kind of light-time orbit may occur in many other Algols, such as V342 Aql and BZ Cas (Erdem et al., 2007), ZZ Cas (Liao and Qian, 2009), AH Cep (Kim et al., 2005), TX Her (Ak et al., 2004), DK Cep and UZ Sge (Zasche et al., 2008). For the third
where M 3 ; i and P3 are the mass, inclination and period of the third body. According the fitted parameters of Eqs. (2) and (4), we obtained the values of the mass function. For some several different 0 values of i , the masses and the orbital radii of the third body can be estimated, which are listed in Table 2. From this table, the lowest masses of the third component are 2:56ð0:09ÞM from Eq. (2) and 2:39ð0:06ÞM from Eq. (3), respectively. Therefore, the mass for the third component of RZ Aur is quite large. Knowing that the stars in this system are of type A0 and F2 and must be close to the main sequence, the mass of RZ Aur is estimated to be about 3M þ 1:5M (Cox, 2000). A third star with more than 2:39M is therefore expected to be more luminous than the two components of the close binary, and one would expect that its light and spectrum would be observable, if the third star is a single star. It is, however, possible, that it is itself a close binary of two stars of 1:2M , which in that case would have a much lower luminosity, and probably would not be visible next to the A0 þ F2 pair. If the existence of additional close binary is true, RZ Aur may be a unsolved quadruple system. This will further confirm the hypothesis that most close binary stars exist in multiple
ðM1 þ M 2 þ M 3 Þ 0
2
¼
GP 23
ð5Þ
Y.-G. Yang et al. / New Astronomy 15 (2010) 392–395
systems (D’Angelo et al., 2006; Pribulla and Rucinski, 2006; Rucinski et al., 2007). This kind of additional component may remove angular momentum from the central system via Kozai oscillation (Kozai, 1962) or a combination of Kozai cycle and tidal friction (e.g., Fabrychy and Tremaine, 2007), which may play an important role for the formation and evolution of binary. 5. Summary Based on the previous analyses, the following conclusions can be drawn: (1) The O C curve shows that there exists a cyclic variation in the orbital period of RZ Aur. Due to smaller differences between the residuals from Eqs. (2) and (3), those two equations may represent the orbital period changes of this binary. The observed light minimum times cover the complete period of the cyclic variation. (2) Due to the spectral type of A0 þ F2 for RZ Aur, the cyclic variation may result from the light-time effect via the presence of the third body. The lowest mass of the third companion is 2:39ð0:06ÞM , suggesting that the third pair may be another unseen close binary. Therefore, RZ Aur may be a quadruple system. Additionally, it is necessary to observe this binary RZ Aur by the photometry and spectroscopy, in order to obtain the absolute parameters and to identify the nature of period changes in our future work. Acknowledgements The authors would like to express our gratitude to an anonymous referee for his/her helpful comments and suggestions, which help to improve the original manuscript. The author acknowledge Professor J.M. Kreiner for sending his collected light minimum times of RZ Aur. This work is supported partly by the Joint Fund of Astronomy of the National Natural Science Foundation of China (NSFC) and the Chinese Academy of Sciences (CAS) (Grant No. 10778707), the Special Foundation of President and West Light Foundation of the Chinese Academy of Sciences, and Yunnan Natural Science Foundation (No. 2008CD157). References Ak, T., Albayrak, B., Selam, S.O., Tanriverdi, T., 2004. New Astron. 9, 265. Applegate, J.H., 1992. ApJ 385, 621.
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