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Magnetic Stars, 2011, pp. 431 ­ 434

The Triple Star AR Aurigae
z Mikul´ asek Z.1,2 , Zinovsky J.3 , Zejda M.1 , Zverko J.3 , Hubrig S.4 , Krti a J.1 , ´ ck 5 , Gazeas K.6 , Zola S.7, 8 , Ogloza W.7 , Albayrak B.9 , Chrastina M.1 , Dub ovsky P. A. ´ Gr´ T.2 , Jan´ J.1 , Kudzej I.5 af ik
1 2 3 4 5 6 7 8 9

Dept. of Theoretical Physics and Astrophysics, Masaryk University, Brno, Czech Republic Observatory and Planetarium of J. Palisa, VSB -- Technical University, Ostrava, Czech Republic Astronomical Institute, Slovak Academy of Sciences, Tatransk´ Lomnica, Slovak Republic a Astrophysical Institute Potsdam, Germany Vihorlat Astronomical Observatory Humenn´ Slovak Republic e, Dept. of Astrophysics, Astronomy and Mechanics, Faculty of Physics, University of Athens, Greece Cracow Pedagogical University, Krak´ Poland ow, Astronomical Observatory, Jagiellonian University, Krak´ Poland ow, Dept. of Astronomy and Space Sciences, Ankara University, Turkey

Abstract. New period of the third body in the system of the eclipsing HgMn binary star AR Aur was derived based on new photoelectric and CCD observations.

1

Intro duction

AR Aur (HD 34364, HR 1728) is a double­lined spectroscopic well­detached eclipsing binary with orbital period of 4d 13. The system is very young with a primary located on the ZAMS, while its . secondary component is evolving towards it. The primary and secondary eclipses are very similar and nearly total since the orbit inclination is i = 88.5 and radii of components are roughly equal; the orbits are nearly circular (see Nordstr¨ & Johansen, 1994). The spectral type of the primary is om B9.5 V with apparent HgMn­type peculiarity. Recently, Hubrig et al. (2006) found strong variations in spectral line profiles of several overabundant chemical elements (Pt, Hg, Sr, Y, Zr, He and Nd) and interpreted it as the consequence of their uneven distribution on the surface of the primary. To investigate the system comprehensively we need a precise knowledge of the photometric phasing of the eclipsing binary. This is complicated by a third body in the system (see Chochol et al., 1988; Albayrak et al., 2003) inducing a well pronounced light­time effect (hereinafter LiTE). The aim of this study is to describe the LiTE ephemeris of AR Aur in a simple form, and to test our method of determination of times of eclipses. The method will be described in detail in a forthcoming paper.

2

Observations

First photoelectrically detected minima of AR Aur were published by Huffer & Eggen (1947). Eight new photoelectric minima (including two based on the observations by Johansen (1970) were published by O'Connel (1979), who found that the period of AR Aur has undoubtedly changed. To explain these changes Zverko et al. (1981) and Chochol et al. (1988) acquired 11 new epochs of minima and explained the observed changes by a light time effect due to a third body in the system. Nordstr¨ & Johansen (1994) and Albayrak et al. (2003) on the basis of their new photoelectric om


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0.01 0.008 0.006 0.004 [d]
lin

0.002 0

O-C

-0.002 -0.004 -0.006 -0.008 -0.01 1940 1950 1960 1970 1980 1990 2000 2010

Figure 1: O­C diagram of AR Aur. Full line: our solution (Table 1), dashed line: Albayrak et al. (2003), dotted line -- uncertainty of the solution. Circles -- minima times computed by our method, squares -- minima times adopted from literature.

minima determinations published new periods of the third body and new physical characteristics of the system. Up to now almost all studies dealing with changes of periods in eclipsing binaries have been based on the analysis of times of minima determined by different methods. Thus, the results of such analyses were influenced by uneven treatment of individual photometric measurements and, namely, by the unreliability of the indicated accuracies of the minima times determined. To avoid this inconvenience, we use preferentially original observational data in our method, and only in the case that some are definitely lost, we utilize the published times of minima. We collected altogether 18 009 individual measurements of the AR Aur system starting with the first photoelectrically observed minima acquired by Huffer & Stebbins in the year 1935 (Huffer & Eggen, 1947). The present analysis is based on 17 482 mostly our own individual photometric measurements comprising 55 minima and 39 times of minima (both primary and secondary ones) adopted from Kreiner et al. (2001) and Paschke & Br´ (2009). All these data were processed simultaneously at assuming that both the shapes and amplitudes of the light curves are constant. This assumption considerably cuts the number of free parameters and enables to derive reliable values of minima times as well as their uncertainties. The efficiency of this approach (Mikul´ et al., 2006) is substantiated by the fact that the asek scatter of the published times of minima is more than 2.5 times larger than the scatter of the values obtained by our method.


THE TRIPLE STAR AR AURIGAE

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0.01 0.008 0.006 0.004 O-Clin [d] 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 -0.2 0 0.2 0.4 0.6 orbital phase3 0.8 1 1.2

Figure 2: Phase diagram of the third body effect in AR Aur, P = 23.79 yr. Same symbols are used as in Fig. 1.

3

Light­Time Effect in AR Aur

The LiTE ephemeris is described: = M0 + P â K + (t, A, , , T , P3 ), (1)

where is HJD of primary (K is an integer)/secondary (K is an integer + 0.5) light minimum of the eclipsing binary, P is its orbital period in days and is the time shift, caused by orbital motion of the eclipsing binary with respect to the gravity center of the triple system. This problem has been solved by Irwin (1959) and Mayer (1990): (1 - 2 ) sin( + ) + sin , 1 + cos

=O-C=A

(2)

where A = 0.005776 â a12 sin i [d/AU], a12 sin i is the pro jection of the semima jor­ma jor axis of the orbit of the eclipsing binary around the centre of gravity of the system, its eccentricity, is the argument of perihelion, and is the true anomaly. According to the second Kepler's law and the implicit Kepler's equation: tan E = M + sin E , = 2 1+ E tan , 1- 2 2 (t - T ) M= . P3 (3) (4)

where


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Table 1: Comparison of parameters of the triple system Parameter M0 P T P3 A a12 sin i f (m3 ) Albayrak et al. 2 452 596.4927(21) 4d 134 665 7(10) . 0.20 ± 0.04 33.0 ± 2.0 2 448 090 ± 45 23.68 ± 0.17 yr 0.008 4(2)dl 1.47(4) AU 0.005 7(4) M this paper 2 448 858.75467(8) 4d 134 665 70(5) . 0.320 ± 0.016 35.6 ± 2.7 2 448 193 ± 60 23.79 ± 0.09 yr 0.008 24(7)dl 1.427(12) AU 0.005 05(14) M

E and M are eccentric and mean anomalies, t is the instant HJD time, T is the perihelion passage date, and P3 is the orbital period of the third body in days. The implicit Kepler equation (4) can be well solved by a simple iterative procedure. Hence, for the complete expression of we need - seven parameters defining the column vector = (1 ; 2 ; . . . ; 7 ), especially the orbital period of the eclipsing binary P , the basic minimum M0 , the orbital period of the third body P3 , T the perihelion passage date, eccentricity , the argument of perihelion , and the pro jected semi­ma jor axis A in light days (dl ). Applying a non­linear weighted LSM procedure we arrived at the system parameters, which are compared to those by Albayrak et al. (2003) in Table 1.

4

Acknowledgements

This work is supported by grants: VEGA 2/0074/09, GACR 205/08/0003, MUNI/A/0968/ 2009, and the APVV pro ject SK­CZ­0032­09.

References
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