absolute properties of the eccentric eclipsing binary star ... - IOPscience

The Astronomical Journal, 141:195 (10pp), 2011 June  C 2011.

doi:10.1088/0004-6256/141/6/195

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

ABSOLUTE PROPERTIES OF THE ECCENTRIC ECLIPSING BINARY STAR FT ORIONIS Jeffrey A. Sabby1,5,6 , Claud H. Sandberg Lacy2,6,7 , Cafer Ibanoglu3 , and Antonio Claret4 1

Physics Department, Southern Illinois University Edwardsville, Edwardsville, IL 62025, USA; [email protected] 2 Physics Department, University of Arkansas, Fayetteville, AR 72701, USA; [email protected] 3 Astronomy and Space Sciences Department, Science Faculty, Ege University, 35100 Boronova, Izmir, Turkey; [email protected] 4 Instituto de Astrofisica de Andalucˆıa, CSIC, Apdo. Postal 3004, E-18080 Granada, Spain; [email protected] Received 2011 February 7; accepted 2011 March 22; published 2011 May 10

ABSTRACT Accurate absolute properties are determined for the first time for the 3.15 day period eccentric eclipsing binary star FT Ori based on new absolute photometry, five differential light curves, and a radial velocity curve. The stars appear to be normal for their spectral types, A0 + A2. The orbit is highly eccentric (e = 0.409) and shows apsidal motion with a period of 536 years. The absolute properties and the degree of central mass concentration of the stars are consistent with current theoretical models at an age of 190 Myr. Key words: binaries: eclipsing – binaries: spectroscopic – stars: fundamental parameters – stars: individual (FT Ori) Online-only material: machine-readable and VO tables

2. TIMES OF MINIMUM LIGHT AND EPHEMERIS CURVE SOLUTION

1. INTRODUCTION Eclipsing binary stars provide critical information that can be used to test our current theories of stellar evolution. By measuring accurately the changes in brightness over time (the light curve), times of minimum light (the ephemeris curve), and the pattern of changing radial velocities of the components (the radial velocity curve), orbital parameters may be determined including the masses, radii, and degree of central mass concentration. These observationally determined values may be compared with theoretical results from the current theory of stellar evolution to gauge the degree of completeness of the theory. That is the goal of this type of investigation. The detached main-sequence eclipsing binary star FT Ori (BD + 21◦ 1159, HD 42858, TYC 1326-910-1) is a relatively bright star (V = 9.26) with similar components (A0 + A2), but with a highly eccentric orbit currently oriented in such a way that spectral lines are clearly doubled for only a very narrow phase interval between secondary and primary eclipses (Lacy 1984). It was discovered as a variable star by Hoffmeister (1934). Cristaldi (1970) obtained a photoelectric light curve and determined the first photometric elements. Grønbech (1974) estimated the apsidal motion period as 520 ± 100 years, while Wolf & Sarounov´a (1995) estimated it as 481 ± 19 years. The many accurate times of minima that have been published since then have allowed for an improved estimate of the apsidal period (Section 2) and the internal structure constant (Section 6). New light curves (Section 3) and a radial velocity curve (Section 4) have allowed us to determine very accurate orbital elements (Section 5) and absolute properties of the stars, and these values are compared with theory in Section 6.

Published times of minimum light have been collected in Table 1 and analyzed by using the method of Lacy (1992b). This method allows one to accurately estimate many of the orbital parameters of the binary star by using an iterated least-squares fitting algorithm applied to the observed dates of minima, taking into account the published observational errors. The principal orbital parameters determined from fitting this so-called ephemeris curve are the eccentricity (e), anomalistic period (Pa ), longitude of periastron (ω), apsidal motion rate (ω), ˙ reference time of minimum light (To ), and apsidal motion period (U). Apsidal motion in this binary system is due to both a classical Newtonian interaction and the general relativistic effect, though the classical effect is the much stronger one in this case. Uncertainties in the dates of minima of a similar type (photographic, visual, photometric, or CCD) were adjusted by the fitting method in order to result in a reduced chi-square of unity, which is a necessary step for the accurate estimation of the fitted orbital parameter uncertainties. The orbital parameters so determined are given in Table 2, and the fit is displayed in Figure 1. No noticeable pattern is evident in the residuals to the fit, which is consistent with the assumption that the binary system does not appear to have any additional stellar components. 3. LIGHT CURVES In order to determine orbital parameters based on the variations in brightness as the component stars alternately eclipse each other, we have collected all available published and unpublished sources of photometry for FT Ori. These light curves were obtained by observers over the last 45 years, and are of high quality, produced by photoelectric photometers. Differential light curves are available from Cristaldi (1970), Ibanoglu (this paper, at Ege University), and Lacy (this paper, at Cerro Tololo Inter-American Observatory (CTIO)). The magnitude differences, like ΔB and ΔV, are all variable-star magnitude minus comparison-star magnitude.

5

Author to whom any correspondence should be addressed. Visiting Astronomer, Kitt Peak National Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation. 7 Visiting Astronomer, Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation. 6

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The Astronomical Journal, 141:195 (10pp), 2011 June

Sabby et al. Table 1 Published Times of Minimum Light for FT Ori

Year 1931.1 1932.1 1932.7 1938.2 1938.9 1940.0 1940.0 1940.0 1949.3 1958.1 1958.1 1959.2 1961.0 1961.1 1961.1 1961.1 1961.2 1961.2 1961.8 1962.0 1962.0 1962.1 1963.9 1964.0 1964.1 1964.2 1965.1 1966.0 1966.0 1966.2 1967.1 1969.1 1969.9 1970.8 1970.9 1971.0 1971.1 1971.2 1972.1 1972.1 1972.2 1972.7 1972.7 1973.0 1973.0 1973.0 1973.0 1973.1 1973.8 1973.9 1974.0 1974.0 1974.1 1974.1 1974.2 1974.3 1974.3 1975.1 1976.1 1976.3 1977.0 1977.1 1977.9 1978.7 1980.1 1980.1

HJD-2400000 26384.28 26743.43 26979.64 28983.33 29219.59 29619.70 29635.43 29638.62 33009.553 36232.412 36232.422 36629.368 37281.508 37319.308 37319.310 37319.314 37363.410 37363.411 37577.59 37659.556 37659.558 37697.32 38345.5340 38406.231 38431.3995 38453.4535 38783.4480 39120.5383 39139.4411 39184.349 39536.397 40274.3917 40554.782 40885.573 40926.532 40945.434 40982.459 41027.342 41348.6841 41363.6155 41405.388 41575.5135 41575.5136 41675.5043 41675.5043 41675.5048 41682.629 41717.286 41959.86478 41996.8441 42056.7019 42060.6778 42069.322 42095.334 42117.386 42158.339 42158.339 42451.3304 42829.385 42870.333 43128.673 43172.773 43459.460 43780.810 44259.652 44281.726

Error Estimate (days) 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.005 0.005 0.005 0.03 0.03 0.03 0.005 0.005 0.005 0.005 0.03 0.005 0.005 0.03 0.0003 0.03 0.0002 0.0003 0.0005 0.0005 0.0003 0.005 0.03 0.0010 0.005 0.005 0.005 0.005 0.03 0.005 0.0001 0.0004 0.005 0.0005 0.0003 0.0005 0.0005 0.0005 0.005 0.005 0.00005 0.0002 0.0005 0.0001 0.03 0.002 0.005 0.005 0.005 0.0010 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005

Cycle Number −7409 −7295 −7220 −6584 −6509 −6382 −6377 −6376 −5306 −4283 −4283 −4157 −3950 −3938 −3938 −3938 −3924 −3924 −3856 −3830 −3830 −3818 −3613 −3593 −3585 −3578 −3474 −3367 −3361 −3346 −3235 −3000 −2911 −2806 −2793 −2787 −2776 −2761 −2659 −2655 −2641 −2587 −2587 −2556 −2556 −2556 −2553 −2542 −2465 −2454 −2435 −2433 −2431 −2422 −2415 −2402 −2402 −2309 −2189 −2176 −2094 −2080 −1989 −1887 −1735 −1728

2

Typea 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 1 2 1 1 1 1 1 2 1 1 2 1 1 1 2 2 2 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1

Residual O − C (days) 0.03861 0.04277 −0.02741 0.00589 −0.01447 −0.00593 −0.02795 0.01164 0.00916 −0.00118 0.00882 0.00299 0.00776 0.00281 0.00481 0.00881 −0.00095 0.00005 −0.04898 0.00630 0.00830 −0.03465 −0.00478 0.03353 −0.00127 −0.00016 0.00438 0.00252 0.00296 −0.00050 0.00929 −0.00095 0.00249 −0.00001 0.00360 0.00311 0.04132 0.00033 0.00014 0.00054 −0.00343 −0.00033 −0.00023 0.00072 0.00072 0.00122 0.00107 0.00350 0.00032 0.00077 0.00117 0.00006 0.01971 0.00169 0.00078 −0.00161 −0.00161 0.00116 0.00590 −0.00151 0.00440 −0.00142 −0.00226 0.00530 −0.01598 0.00510

Methodb pg pg pg pg pg pg pg pg vis vis vis pg pg pg vis vis vis vis pg vis vis pg pe pg pe pe pe pe pe vis pg pe vis vis vis vis pg vis pe pe vis pe pe pe pe pe vis vis pe pe pe pe pg pe vis vis vis pe vis vis vis vis vis vis vis vis

Ref. 1 1 1 1 1 1 1 1 2 3 3 4 5 4 6 6 6 6 5 6 6 4 7 4 7 7 7 7 7 8 4 9 10 11 11 12 4 13 14 14 15 16 17 17 17 16 18 19 14 14 14 14 4 20 21 22 22 23 24 24 25 25 26 25 25 25

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Sabby et al. Table 1 (Continued)

Year 1981.0 1981.1 1982.2 1982.2 1983.2 1983.2 1985.0 1985.2 1985.2 1986.0 1987.1 1987.1 1987.1 1987.1 1987.1 1987.1 1987.1 1987.1 1987.1 1987.2 1987.9 1988.0 1988.0 1988.1 1988.2 1988.9 1988.9 1988.9 1989.2 1989.9 1990.0 1990.0 1990.1 1990.1 1990.1 1990.1 1991.0 1991.1 1991.1 1991.1 1991.1 1991.3 1992.0 1992.0 1992.1 1992.1 1992.2 1993.0 1993.1 1994.0 1995.0 1995.0 1995.0 1995.1 1995.1 1995.1 1995.2 1995.2 1996.0 1996.2 1996.2 1996.2 1997.1 1997.1 1997.1 1997.1

HJD-2400000 44590.4619 44631.4137 45028.367 45034.672 45406.418 45406.422 46058.562 46143.619 46143.620 46436.610 46814.662 46827.255 46827.256 46827.257 46827.260 46827.264 46827.265 46827.266 46827.269 46858.761 47132.84835 47151.748 47170.652 47205.314 47233.661 47482.5449 47482.5451 47507.74782 47605.4121 47840.80454 47898.396 47898.3999 47923.596 47939.356 47939.375 47945.655 48273.2988 48276.448 48279.592 48279.59924 48282.75125 48358.357 48606.3490 48632.444 48651.346 48651.348 48692.312 48984.379 49013.648 49347.596 49721.5833 49724.7338 49725.6427 49759.3856 49760.2966 49763.4476 49782.3502 49800.3458 50094.253 50138.3508 50138.3534 50138.359 50472.300 50475.443 50494.3442 50494.3446

Error Estimate (days) 0.0005 0.0010 0.0010 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.00024 0.005 0.005 0.01 0.005 0.0010 0.0010 0.00012 0.0010 0.00017 0.005 0.0002 0.005 0.005 0.005 0.005 0.0015 0.005 0.005 0.0002 0.00047 0.005 0.0010 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.0007 0.0003 0.0001 0.0006 0.0002 0.0001 0.0002 0.0008 0.005 0.0020 0.0020 0.005 0.005 0.005 0.0010 0.0010

Cycle Number −1630 −1617 −1491 −1489 −1371 −1371 −1164 −1137 −1137 −1044 −924 −920 −920 −920 −920 −920 −920 −920 −920 −910 −823 −817 −811 −800 −791 −712 −712 −704 −673 −599 −580 −580 −572 −567 −567 −565 −461 −460 −459 −459 −458 −434 −356 −347 −341 −341 −328 −236 −226 −120 −2 −1 0 10 11 12 18 23 117 131 131 131 237 238 244 244

3

Typea 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1

Residual O − C (days) 0.00018 −0.00343 −0.00264 0.00152 −0.00167 0.00233 0.00597 0.00170 0.00270 0.00387 0.00575 −0.00292 −0.00192 −0.00092 0.00208 0.00608 0.00708 0.00808 0.01108 −0.00110 −0.00010 −0.00295 −0.00146 0.00594 −0.00082 0.00006 0.00026 −0.00036 0.00095 −0.00221 −0.00404 −0.00014 −0.00738 0.00053 0.01953 −0.00131 −0.00102 −0.00224 −0.00865 −0.00141 0.00018 −0.00411 0.00020 −0.00352 −0.00404 −0.00204 0.00652 −0.01513 −0.00018 0.00342 0.00102 0.00114 −0.00015 −0.00119 −0.00086 −0.00028 −0.00019 0.00412 0.01111 0.00304 0.00564 0.01124 0.00780 0.00038 −0.00093 −0.00053

Methodb pe pe pe vis vis vis vis vis vis vis vis vis vis vis vis vis vis vis vis vis pe vis vis pe vis pe pe pe pe pe vis pe vis vis vis vis pe vis vis pe pe vis pe vis vis vis vis vis vis vis pe pe pe pe pe pe pe pe vis pe pe vis vis vis pe pe

Ref. 27 28 29 25 30 30 25 25 25 25 25 31 32 31 31 31 31 31 31 25 33 25 25 34 25 35 35 33 36 37 38 39 25 40 41 25 42 38 25 37 37 43 44 45 45 45 46 47 25 25 48 48 48 49 49 49 49 49 50 35 35 50 51 51 52 52

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Sabby et al. Table 1 (Continued)

Year 1997.1 1997.2 1997.8 1997.8 1998.0 1998.1 1998.1 1999.0 1999.2 2000.0 2000.1 2000.2 2000.2 2000.2 2000.2 2001.2 2002.1 2002.2 2003.1 2003.1 2003.2 2003.2 2003.2 2003.8 2005.0 2005.0 2005.9 2005.9 2005.9 2006.1 2006.1 2006.1 2006.9 2007.0 2007.0 2007.0 2008.0 2008.0 2008.1 2008.1 2008.2 2008.8 2009.0 2009.9

HJD-2400000 50494.353 50516.3938 50726.5519 50749.5217 50828.296 50849.4177 50850.3423 51165.392 51268.414 51562.333 51580.3032 51602.3560 51602.369 51625.343 51625.343 51987.646 52296.3852 52337.3406 52692.3848 52693.3383 52715.390 52715.391 52715.3913 52939.0726 53354.9266 53385.4662 53682.57045 53685.7214 53701.4728 53760.3602 53764.468 53764.4813 54073.2216 54085.8242 54097.4483 54104.7267 54457.5738 54460.7240 54494.3950 54494.3957 54523.7326 54755.8755 54829.3235 55153.8167

Error Estimate (days) 0.005 0.005 0.0015 0.005 0.005 0.0008 0.0002 0.005 0.005 0.005 0.0008 0.0004 0.005 0.005 0.005 0.005 0.0004 0.0004 0.0019 0.0003 0.005 0.005 0.0001 0.0004 0.0001 0.0017 0.0001 0.0002 0.0009 0.0011 0.005 0.0005 0.0010 0.0002 0.0005 0.0001 0.0001 0.0001 0.0030 0.0007 0.0001 0.0001 0.0004 0.0001

Cycle Number 244 251 317 325 350 356 357 457 489 583 588 595 595 603 603 718 816 829 941 942 949 949 949 1020 1152 1161 1256 1257 1262 1280 1282 1282 1380 1384 1387 1390 1502 1503 1513 1513 1523 1596 1620 1723

Typea 1 1 2 1 1 2 1 1 2 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1

Residual O − C (days) 0.00787 −0.00427 −0.00002 −0.00741 0.00641 0.00119 −0.00023 0.00751 −0.00218 −0.00437 0.00012 0.00031 0.01331 −0.00276 −0.00276 0.00195 −0.00001 −0.00007 0.00063 0.00016 −0.00108 −0.00008 0.00022 0.00168 0.00020 0.00073 0.00032 0.00085 0.00014 0.00088 −0.01307 0.00023 −0.00069 0.00023 −0.00038 0.00021 0.00018 −0.00004 0.00007 0.00077 0.00015 0.00016 0.00022 0.00006

Methodb vis vis pe vis vis pe pe vis vis vis pe pe vis vis vis vis pe pe pe pe vis vis pe pe pe pe pe pe pe pe vis pe pe pe pe pe pe pe pe pe pe pe pe pe

Ref. 51 53 54 53 55 56 57 55 55 58 59 60 58 58 61 62 63 64 63 63 65 66 63 67 62 68 69 62 70 70 71 70 72 62 73 62 74 75 76 77 75 78 79 80

Notes. a 1, primary eclipse; 2, secondary eclipse. b Methods: pg, photographic; vis, visual; pe, photoelectric/CCD. References. (1) Hoffmeister 1947; (2) Ashbrook 1952; (3) Braune & Quester 1962; (4) Haussler 1991; (5) Huth 1963; (6) Dueball & Lehmann 1965; (7) Cristaldi 1970; (8) Braune et al. 1970; (9) Pohl & Kizilirmak 1970; (10) Baldwin 1974; (11) Diethelm & Locher 1970; (12) Diethelm & Locher 1971a; (13) Diethelm & Locher 1971b; (14) Grønbech 1974; (15) Locher 1972; (16) and (17) Kizilirmak & Pohl 1974; (18) Baldwin 1976a; (19) Baldwin 1976b; (20) Pohl & Kizilirmak 1975; (21) Locher 1974a; (22) Locher 1974b; (23) Pohl & Kizilirmak 1976; (24) Locher 1976; (25) Baldwin & Samolyk 1996; (26) Locher 1977; (27) Pohl et al. 1982; (28) Fernandes 1980; (29) Diethelm 1982; (30) Braune et al. 1983; (31) Mikulasek et al. 1992; (32) Braune & Hubscher 1987; (33) Caton et al. 1989; (34) Hubscher & Lichtenknecker 1988; (35) Hegedus et al. 1996; (36) Wunder et al. 1992; (37) Caton & Burns 1993; (38) Mikulasek 1994; (39) Ogloza 1995; (40) Hubscher et al. 1990; (41) Paschke 1990; (42) Hanzl 1994; (43) Diethelm 1991; (44) Diethelm 1992; (45) Hubscher et al. 1992; (46) Paschke & Diethelm 1992; (47) Hubscher et al. 1993; (48) Lacy et al. 1995; (49) Wolf & Sarounov´a 1995; (50) Hubscher & Agerer 1996; (51) Hubscher et al. 1997; (52) Biro et al. 1998; (53) Mikulasek 1996; (54) Diethelm 1998a; (55) Hubscher et al. 1999; (56) Diethelm 1998b; (57) Agerer et al. 1999; (58) Hubscher et al. 2001; (59) Diethelm 2000; (60) Agerer & Hubscher 2002; (61) Hubscher et al. 2000; (62) Baldwin & Samolyk 2007; (63) Agerer & Hubscher 2003; (64) Diethelm 2002; (65) Hubscher 2005; (66) Hubscher et al. 2003; (67) Sobotka 2007; (68) Hubscher et al. 2005; (69) Brat et al. 2007; (69) Hubscher et al. 2006a; (71) Hubscher et al. 2006b; (72) Nagai 2007; (73) Diethelm 2007; (74) Liakos & Niarchos 2009; (75) Bialozynski 2008; (76) Hubscher et al. 2009; (77) Hubscher et al. 2008; (78) Dvorak 2009; (79) Hubscher et al. 2010; (80) Samolyk 2010.

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The Astronomical Journal, 141:195 (10pp), 2011 June

Sabby et al. Table 5 Absolute UBV Photometry of FT Ori and Comparison Stars Star FT Ori Std. error N + 21◦ 1172 Std. error N + 22◦ 1250 Std. error N

V 9.259 0.004 3 9.043 0.005 3 9.250 0.006 3

B−V 0.096 0.002 3 0.197 0.003 3 0.211 0.003 3

U−B 0.070 0.008 3 −0.669 0.007 3 0.229 0.005 3

Table 6 Differential B-band Photometry of FT Ori from Ege University Observatory Orbital Phase 0.99720 0.00010 0.00160

Figure 1. Ephemeris curve data from the times of minimum light and the fitted curve for FT Ori. Data from dates of primary eclipse (the deeper eclipse) are plotted as open circles, and data from secondary eclipse are plotted as solid dots. The error bars are shown for each point, but in many cases, especially the more recent observations, the error bars are smaller than the points. The interval shown spans about 80 years of observations. The full cycle length is 536 years.

Table 7 Differential V-band Photometry of FT Ori from Ege University Observatory

Fitted Values 0.4102 ± 0.0012 3.1504438 ± 0.0000005 37.0 ± 0.3 0.00184 ± 0.00002 49725.64285 ± 0.00009 89.5 (fixed) 536 ± 7

Orbital Phase 0.99720 0.00010 0.00160

0.72917 0.73051 0.73181

ΔB (mag)

HJD-2400000

0.366 0.322 0.306

49343.59119 49343.59540 49343.59949

Table 4 Differential V-band Photometry of FT Ori from CTIO

0.72930 0.73063 0.73193

ΔV (mag)

HJD-2400000

0.491 0.444 0.444

49343.59158 49343.59579 49343.59988

HJD-2400000 41575.49260 41575.50180 41575.50650

accuracy of the 223 pairs of differential observations was about 0.007 mag in B and V. ΔB is the B-band magnitude difference between the variable star and the comparison star. In order to accurately determine the luminosity and surface temperatures of the stars, absolute photometry is also needed, including the apparent magnitude and color indices. Absolute UBV photometry determined by utilizing the methods of Lacy (1992a) is listed in Table 5. Photomultipliers of the ITT FW130 type with S-20 photocathodes were used with a UBV filter set. An entrance diaphragm of 20 arcsec diameter was used in good seeing conditions. The differential observations consisted of sets of 10 s integrations in B and V of the variable star, sky, comparison star, and check star. Ibanoglu’s differential photometry in B and V was obtained at Ege University Observatory in Turkey during 1972. A 1P21 photomultiplier and a chart recorder were used. The comparison star was BD + 21 1168 (B0). The set consists of 189 pairs of observations with an accuracy of about 0.011 mag. The ephemeris is HJD Min I = 3.1504148 n + 2,441,348.68416 based on the work of Grønbech (1974). The data are contained in Tables 6 and 7. Cristaldi’s (1970) light curve was obtained with a nonstandard filter (effective wavelength of 5150 Å, blue–green (BG)). He did not publish the original light curve data, but did publish normal points instead. The poor phase resolution of this type of light curve limits the discrimination of the model fits near the narrow bottoms of the eclipses. The ephemeris HJD Min I = 3.15040 n + 2,433,009.553 based on the work

(This table is available in its entirety in machine-readable and Virtual Observatory (VO) forms in the online journal. A portion is shown here for guidance regarding its form and content.)

Orbital Phase

ΔV (mag) 0.315 0.414 0.476

(This table is available in its entirety in machine-readable and Virtual Observatory (VO) forms in the online journal. A portion is shown here for guidance regarding its form and content.)

Table 3 Differential B-band Photometry of FT Ori from CTIO Orbital Phase

HJD-2400000 41575.49260 41575.50180 41575.50650

(This table is available in its entirety in machine-readable and Virtual Observatory (VO) forms in the online journal. A portion is shown here for guidance regarding its form and content.)

Table 2 Orbital Parameters Fitted to the Dates of Minimum Light Parameters e Pa (days) ω (deg) ω˙ (deg day−1 ) To (HJD-2400000) i (deg) U (years)

ΔB (mag) 0.060 0.193 0.247

(This table is available in its entirety in machine-readable and Virtual Observatory (VO) forms in the online journal. A portion is shown here for guidance regarding its form and content.)

The CTIO data are contained in Tables 3 and 4. These data were obtained from the CTIO 0.6 m Lowell telescope during the Southern Hemisphere summers of 1993–1995. The comparison star was BD + 21◦ 1172 (B0) and the check star was BD + 22◦ 1250 (A2). The instantaneous ephemeris HJD Min I = 3.1504189 n + 2,449,725.6427, which is based on the ephemeris curve solution, was used to compute phases. The 5

The Astronomical Journal, 141:195 (10pp), 2011 June

Sabby et al.

Figure 2. Light curves for FT Ori observed in the blue–green by Cristaldi (1970, top curve), in B by Ibanoglu (middle curve), and in B by Lacy at CTIO (bottom curve). The curves are offset vertically for convenience. The solid curves are the fitted models. Note that the secondary eclipse is shifted by different amounts at different observing epochs due to the apsidal motion in this system.

Figure 4. Secondary eclipse of FT Ori as observed by Lacy at CTIO. The eclipse appears to be total. Table 8 Fitted Parameters for the Light Curves of Lacy Parameter Js rp + rs k up us i (deg) e ω (deg) yp = ys q rp rs Ls /Lp Lp Ls σ (mmag) N

B 0.672 ± 0.002 0.2427 ± 0.0008 0.866 ± 0.002 0.55 ± 0.04 0.60 ± 0.04 89.7 ± 0.3 0.4087 ± 0.0007 36.4 ± 0.2 1.0 (fixed) 0.818 (fixed) 0.1301 ± 0.0009 0.1126 ± 0.0009 0.493 ± 0.021 0.667 ± 0.009 0.329 ± 0.009 7.22738 223

V 0.735 ± 0.003 0.2434 ± 0.0009 0.869 ± 0.007 0.47 ± 0.04 0.52 ± 0.04 89.7 ± 0.3 0.4081 ± 0.0011 36.3 ± 0.2 1.0 (fixed) 0.818 (fixed) 0.1301 ± 0.0010 0.1133 ± 0.0010 0.546 ± 0.020 0.644 ± 0.008 0.352 ± 0.008 7.62158 223

Combined Values 0.2430 ± 0.0008 0.867 ± 0.002 89.7 ± 0.3 0.4085 ± 0.0007 36.4 ± 0.2 0.1301 ± 0.0009 0.1129 ± 0.0008

Figure 3. Primary eclipse of FT Ori as observed by Lacy at CTIO. The eclipse appears to be annular.

4. RADIAL VELOCITIES In order to determine the absolute sizes of the orbits and the masses of the stars, it is necessary to measure their orbital velocities from the Doppler shifts in their spectra. Spectra of FT Ori were obtained by J.A.S. in 1999–2001 with the coud´e spectrometer and the 1 m coud´e-feed telescope at Kitt Peak National Observatory (KPNO). The spectra were obtained with the F3KB CCD and camera 5 and have a resolving power of about 15,000 at a central wavelength of 4500 Å, covering about 300 Å of spectrum in the blue region. The exposure times were typically 30 minutes, resulting in a signal-to-noise ratio in the spectra of about 50. The spectra were flat-fielded by using a quartz lamp in the spectrometer, then wavelength-calibrated by using an attached hollow-cathode Th-A emission tube. Spectra of the radial velocity standard stars 68 Tau (RV = + 39.0 km s−1 ) and HR 8404 (RV = + 0.2 km s−1 ) obtained with the same equipment during the observing series were used with the IRAF task fxcor to determine radial velocities by the cross-correlation technique. In this region of the spectrum, the 4481 Å Mg ii lines of both binary star components are by far the strongest absorption lines visible. The resultant radial velocities based on

of Cristaldi (1970) was used. The accuracy of the 129 normal points is about 0.007 mag. The light curves have been fitted by using the NDE model (Nelson & Davis 1972; Popper & Etzel 1981; Etzel 1981) with the jktebop program of Southworth & Maxted (2004). This model is adequate for uncomplicated and well-detached binaries such as FT Ori. It determines the values of the orbital parameters, such as the relative sizes and brightnesses of the stars, such that the fitted light curve minimizes the squares of the residuals of the observations. The results of the fitting are given in Tables 8–10 and shown in Figures 2–4. One can see from Figure 4 that at the epoch of Lacy the secondary eclipse was total. The principal parameters that determine the fit are the central surface brightness of the secondary Js (the central surface brightness of the primary is unity), the sum of radii rp + rs (the semimajor axis is the unit of length), the ratio of radii (k), the limb-darkening parameters of the primary and secondary (up and us ), the orbital inclination (i), the orbital eccentricity (e) and orientation (ω), the gravity brightening coefficients (y), the normalized luminosities (L), and the mass ratio (q). 6

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Table 9 Fitted Parameters for the Light Curves of Ibanoglu Parameter Js rp + rs k up us i (deg) e ω (deg) yp = ys q rp rs Ls /Lp Lp Ls σ (mmag) N

B 0.676 ± 0.008 0.2420 ± 0.0015 0.869 ± 0.007 0.55 ± 0.08 0.60 ± 0.08 89.9 ± 0.6 0.4042 ± 0.0013 19.3 ± 0.6 1.0 (fixed) 0.818 (fixed) 0.1295 ± 0.0015 0.1125 ± 0.0016 0.511 ± 0.036 0.659 ± 0.015 0.337 ± 0.015 10.84542 189

V 0.736 ± 0.007 0.2435 ± 0.0014 0.871 ± 0.007 0.55 ± 0.08 0.60 ± 0.08 89.0 ± 0.3 0.4010 ± 0.0007 17.7 ± 0.4 1.0 (fixed) 0.818 (fixed) 0.1302 ± 0.0014 0.1134 ± 0.0016 0.558 ± 0.036 0.639 ± 0.014 0.357 ± 0.014 10.83154 189

Combined Values 0.2428 ± 0.0010 0.870 ± 0.005 89.4 ± 0.5 0.4025 ± 0.0016 18.5 ± 0.8 0.1299 ± 0.0011 0.1130 ± 0.0012

Figure 5. Radial velocity curve of FT Ori. Open circles are primary star observations and filled circles are secondary star observations. The two slightly different fitted curves for each component correspond to the instantaneous orbits at the dates of the first and the last observation. The two curves differ very slightly due to apsidal motion that occurred during the relatively short period of spectroscopic observation (about two years).

Table 10 Fitted Parameters for the Light Curve of Cristaldi Parameter Js rp + rs k up us i (deg) e ω (deg) yp = ys q rp rs Ls /Lp Lp Ls σ (mmag) N

BG 0.725 ± 0.004 0.2384 ± 0.0008 0.909 ± 0.084 0.36 ± 0.06 0.41 ± 0.06 88.4 ± 0.6 0.4087 ± 0.0013 15.4 ± 0.9 1.0 (fixed) 0.818 (fixed) 0.1249 ± 0.0008 0.1135 ± 0.0009 0.600 ± 0.021 0.623 ± 0.008 0.374 ± 0.008 6.98260 129

synchronous value at periastron, 68 ± 1 km s−1 . Both stars have the same age, but these facts seem to imply that the secondary component is old enough to have become locked into this type of rotational synchronism by tidal gravitational forces, but the primary component, having more mass and initial rotational inertia, is not yet old enough to have been synchronized. The implication is that this binary system must be relatively young. The orbital velocities and masses of the stars are determined from the plot of radial velocity and orbital phase—the radial velocity curve. A radial velocity curve for FT Ori was fitted to the data by using the iterated least-squares fitting method of Daniels (1966) in order to determine a number of orbital parameters. Because some of the parameters used in the fit are much more accurately determined by other techniques, such as the eccentricity and the apsidal motion rate determined by the ephemeris curve solution, these well-determined values have been fixed at those values during the radial velocity fit. The fitted and fixed parameters are listed in Table 12, and the solution is displayed in Figure 5. The parameters common to both orbits (γ , ω, and T) are identical within the uncertainties, as would be expected. The standard errors of the radial velocities, about 3.8 km s−1 , are reasonable considering the relatively large rotational velocities of the components, and the fact that they are due to measurements of only a single spectral line. The strengths of spectral lines contain information about the temperatures and chemical compositions of the stellar surfaces. Equivalent widths (line strengths) of the binary’s 4481 Å Mg ii components were measured in the spectra. The ratio of these line strengths, 0.617 ± 0.007, would be expected to be close to the luminosity ratio in the blue if both stars had the same spectral types (temperatures) and intrinsic line strength (chemical compositions; Petrie 1950). The average luminosity ratio from the two blue light curve fits is 0.50 ± 0.02, though the BG luminosity ratio of Cristaldi (1970) gives 0.60 ± 0.02. The significant difference between the line strength ratio and the luminosity ratio values might be due to Am-type metallicity effects in one or both stars that make the intrinsic line strengths in the spectra different than would be expected.

the Doppler shifts of these lines (relative to the standard stars’ lines) are listed in Table 11. An important clue to the evolution of the binary star system is the rotational state of the stars. Are they synchronized with the orbital motion by tidal dissipation, or is the system still too young for that to have occurred? Rotational velocities may be measured from the widths of the absorption lines in the spectra. Line widths of the binary star components’ 4481 Å Mg ii lines were measured on 23 unblended spectra and compared to artificially widened spectra of 68 Tau and HR 8404, which have very small observed values of projected rotational velocities v sin i (4 km s−1 and 11 km s−1 , respectively; Fekel 2003). By matching the observed line widths of the FT Ori components’ lines with the artificially rotationally widened standard star lines, we then determined the values of rotational velocities of each binary star component. The results for FT Ori are v sin i values of 95 ± 2 km s−1 for the primary (hotter, larger) star and 71 ± 2 km s−1 for the secondary star. For the FT Ori binary stars, the observed rotational velocity of the primary component is significantly faster than the synchronous value at periastron, 78 ± 1 km s−1 , but the corresponding value for the secondary component is not significantly different from the 7

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HJD-2400000 51243.7653 51243.7945 51246.7642 51246.7968 51247.7139 51451.8863 51454.8780 51454.9109 51454.9439 51549.6196 51550.7866 51552.6087 51552.6415 51552.6742 51552.7072 51791.9335 51791.9650 51794.9249 51794.9567 51794.9963 51908.6144 51908.6614 51908.6943 51911.7250 51911.7665 51911.8045 51911.8480

Primary RV (km s−1 ) 156.5 158.2 127.3 +134.6 −59.5 +128.8 +153.8 +159.7 +150.1 +101.4 −56.6 +157.4 +150.9 +139.3 +128.5 +155.8 +158.4 +118.2 +134.7 +139.9 +157.9 +150.2 +130.6 +156.7 +156.2 +148.9 +129.1

Primary O − C (km s−1 ) −0.6 −0.9 −2.8 −2.7 −1.4 −1.3 −5.3 +1.0 −5.4 +3.9 +2.2 +2.4 +2.3 +0.2 +1.8 −0.7 −0.2 −10.1 −0.5 −3.4 +5.0 +8.9 +1.0 −1.2 +3.6 +5.4 +0.8

Secondary RV (km s−1 ) −167.1 −172.2 −131.7 −141.3 +91.9 −142.8 −170.0 −167.8 −165.7 −104.0 +99.2 −168.5 −152.4 −142.4 −137.1 −167.2 −170.9 −131.1 −139.8 −147.4 −164.1 −148.9 −136.0 −168.6 −166.6 −157.4 −139.2

Table 12 Spectroscopic Orbit of FT Ori Parameter γ (km s−1 ) k (km s−1 ) e ω (deg) T (HJD)-2400000 P (days) ω˙ (deg day−1 ) σ (km s−1 )

Primary 9.8 ± 1.9 113.1 ± 1.3

Secondary O − C (km s−1 ) +1.7 −1.0 +4.1 +3.2 −2.5 −7.1 +1.2 +2.9 +1.1 −8.1 +3.9 −2.3 +5.9 +4.3 −5.5 +0.9 −0.3 +2.4 +2.2 +4.4 −0.4 +0.6 −0.8 +1.1 −3.3 −5.2 −5.7

Table 13 Absolute Properties of FT Ori Secondary

Property

11.8 ± 1.7 138.3 ± 1.2

Mass (solar units) Radius (solar units) log g (cm s−2 ) log k2 Teff (K) log L (solar units) Mv EB−V (mag) AV (mag) d (pc)

0.409 fixed 36.5 ± 3.1 at T 35.4 ± 2.4 49725.458 ± 0.013 fixed 49725.453 ± 0.010 3.1504189 fixed 0.00184 fixed 3.8 3.9

Primary

Secondary

2.182 ± 0.022 1.783 1.860 ± 0.013 1.616 4.237 ± 0.006 4.272 −2.45 ± 0.02 9600 ± 400 8600 1.486 ± 0.023 1.179 1.15 ± 0.04 1.81 0.09 ± 0.04 0.29 ± 0.13 421 ± 20

± 0.020 ± 0.013 ± 0.007 ± 300 ± 0.025 ± 0.04

5. ABSOLUTE PROPERTIES gravitational potentials are not spherically symmetric. This slight asymmetry causes slow orbital precession due to a purely Newtonian interaction. The well-known general relativistic effect also contributes to this apsidal motion. As stars age, their masses become more centrally concentrated (their moment-ofinertia factors become smaller). The rate of apsidal motion in such a system then measures the internal structure of the stars. The mean internal structure constant, which measures the degree of central mass concentration, is based on the observed apsidal motion period corrected for relativistic effects by using Equation (4) of Claret & Willems (2002).

The fitted orbital parameters resulting from the analyses of the ephemeris curves, light curves, and radial velocity curves (above) may be combined to yield absolute properties of the component stars. The results are shown in Table 13. Here, the distorting effects of interstellar dust—reddening (EB−V ) and absorption (AV ) of the transmitted light—have been estimated from the absolute photometry of Table 5 by using the Q-method of Johnson & Morgan (1953). This method utilizes the fact that the amounts of reddening in different color indices are related by fixed ratios. Because the spectral types of the stars are near A0, the resulting error estimates for the interstellar reddening and temperatures, based on the B − V calibration of Popper (1980), are somewhat larger than for other spectral types. This wellknown problem is basically due to the fact that the interstellar reddening vector is parallel to the main sequence at A0 in a color–color plot. Because stars are not point masses, and because binary stars are distorted by the tidal forces between the components, their

6. DISCUSSION The observational results derived above may be compared to modern theory, such as that of the Granada group (Claret 2004; Claret & Gim´enez 2010), which predicts all of the physical and orbital parameters as a function of time. The comparisons in the logg versus Teff and radius versus mass diagrams are shown in 8

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Figure 8. Components of FT Ori (solid points with error bars) in the radius–mass plane. Open circles show other well-determined eclipsing binary star components (Torres et al. 2010). The curve is the zero-age main sequence of the Granada models (Claret & Gim´enez 2010).

Figure 6. Observations (points with error bars) and an isochrone for models with a log age (in years) of 8.28. The models have a chemical composition of X = 0.70, Z = 0.02, overshooting parameter of α ov = 0.20, and mixing-length parameter α ML = 1.68.

Figure 9. Components of FT Ori in the absolute magnitude–mass plane relative to other well-determined eclipsing binary star components (Torres et al. 2010).

Figure 7. Comparison of the models and observations in the radius vs. mass plane (same models as in Figure 6).

very close to it, however, though true circular synchronization cannot occur until later when the orbit is circularized.

Figures 6 and 7, where the curves are theoretical isochrone fits for a log age (in years) of 8.28. The parameters of the models (such as chemical composition and age) were adjusted to fit the observed data best, and they are very close to solar chemical composition values. The internal structure constant measures the degree of central mass concentration in a star. The theoretical value of the mean internal structure constant logk2 is −2.42 ± 0.08, which was corrected for the effects of rotation (Claret 1999), and is consistent with the observed value in Table 13, −2.45 ± 0.02. The rotational state of the system has been calculated from the models by using the formalism of Hut (1981). According to this formalism, orbital circularization due to tidal effects should occur at a critical time of log t = 8.95 (yr), so the fact that the orbit is still very eccentric is consistent with the younger fitted log age of 8.28 (yr), based on the observed absolute properties. According to the tidal theory, synchronization of the primary should occur at log t = 8.92 (yr), and synchronization of the secondary at 8.94 (yr). Rotation of the primary is clearly supersynchronous now, so this is consistent with the theory. The secondary component seems to be synchronous at periastron or

7. CONCLUSIONS The absolute properties of FT Ori determined in this paper are accurate enough to place it in the category of the best determined in the sense of Torres et al. (2010), being accurate at the 1% level in its absolute properties. Modern theory predicts accurately the observed properties of the system at an age of about 190 Myr. The positions of the components relative to those of other well-determined eclipsing binary star components are shown in Figures 8 and 9. They appear to be typical of relatively littleevolved main-sequence stars. This good agreement between stellar theory and observations of eclipsing binaries is the usual outcome of these types of studies, but it is worth pointing out that in a few systems, such as V1061 Cyg (Torres et al. 2006), accurate observations show that some stars definitely do not obey the current standard theory of stellar evolution. Special thanks go to Daryl Willmarth for his help at KPNO with the spectroscopic observations, and to the staff at CTIO for their help with the photometric observations there. 9

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REFERENCES

Hubscher, J., Agerer, F., Busch, H., Goldhahn, H., Hassforther, B., & Lange, T. 2000, BAV-Mitt., 131, 1 Hubscher, J., Agerer, F., Busch, H., Goldhahn, H., Hassforther, B., & Lange, T. 2001, BAV-Mitt., 143, 1 Hubscher, J., Agerer, F., Hassforther, B., Lange, T., & Paschke, A. 2003, BAVMitt., 157, 1 Hubscher, J., Agerer, F., Hassforther, B., & Wunder, E. 1997, BAV-Mitt., 101, 1 Hubscher, J., Agerer, F., & Wunder, E. 1992, BAV-Mitt., 60, 1 Hubscher, J., Agerer, F., & Wunder, E. 1993, BAV-Mitt., 62, 1 Hubscher, J., Lehmann, P., Monninger, G., Steinbach, H.-M., & Walter, F. 2010, IBVS, 5918 Hubscher, J., & Lichtenknecker, D. 1988, BAV-Mitt., 50, 1 Hubscher, J., Lichtenknecker, D., & Wunder, D. 1990, BAV-Mitt., 56, 1 Hubscher, J., Paschke, A., Vohla, F., & Walter, F. 2006a, BAV-Mitt., 179, 1 Hubscher, J., Paschke, A., & Walter, F. 2005, IBVS, 5657 Hubscher, J., Paschke, A., & Walter, F. 2006b, IBVS, 5731 Hubscher, J., Steinbach, H.-M., & Walter, F. 2008, IBVS, 5830 Hubscher, J., Steinbach, H.-M., & Walter, F. 2009, IBVS, 5874 Hut, P. 1981, A&A, 99, 126 Huth, H. 1963, Mitt. Verand. Sterne (Sonneberg), 2, 126 Johnson, H. L., & Morgan, W. W. 1953, ApJ, 117, 313 Kizilirmak, A., & Pohl, E. 1974, IBVS, 937 Lacy, C. H. S. 1984, IBVS, 2489 Lacy, C. H. S. 1992a, AJ, 104, 801 Lacy, C. H. S. 1992b, AJ, 104, 2213 Lacy, C. H. S., et al. 1995, IBVS, 4194 Liakos, A., & Niarchos, P. 2009, IBVS, 5897 Locher, K. 1972, BBSAG Bull., 2, 1 Locher, K. 1974a, BBSAG Bull., 14, 1 Locher, K. 1974b, BBSAG Bull., 15, 1 Locher, K. 1976, BBSAG Bull., 26, 1 Locher, K. 1977, BBSAG Bull., 35, 1 Mikulasek, Z. 1994, Contr. N. Copernicus Obs. Planet. Brno, 31, 1 Mikulasek, Z. 1996, Contr. N. Copernicus Obs. Planet. Brno, 32, 1 Mikulasek, Z., Silhan, J., & Zejda, M. 1992, Contr. N. Copernicus Obs. Planet. Brno, 30, 1 Nagai, K. 2007, Var. Star Bull. (Japan), 45, 1 Nelson, B., & Davis, W. D. 1972, ApJ, 174, 617 Ogloza, W. 1995, IBVS, 4263 Paschke, A. 1990, BBSAG Bull., 94, 1 Paschke, H., & Diethlem, R. 1992, BBSAG Bull., 101, 1 Petrie, R. M. 1950, Publ. Dom. Astrophys. Obs. Victoria BC, 8, 319 Pohl, E., Evren, S., Tumer, O., & Sezer, C. 1982, IBVS, 2189 Pohl, E., & Kizilirmak, A. 1970, IBVS, 456 Pohl, E., & Kizilirmak, A. 1975, IBVS, 1053 Pohl, E., & Kizilirmak, A. 1976, IBVS, 1163 Popper, D. M. 1980, ARA&A, 18, 115 Popper, D. M., & Etzel, P. B. 1981, AJ, 86, 102 Samolyk, G. 2010, J. Am. Assoc. Var. Star Obs., 38, 183 Sobotka, P. 2007, IBVS, 5809 Southworth, J., & Maxted, P. F. L. 2004, MNRAS, 351, 1277 Torres, G., Andersen, J., & Gim´enez, A. 2010, A&AR, 18, 67 Torres, G., Lacy, C. H., Marschall, L. A., Sheets, H. A., & Mader, J. A. 2006, ApJ, 640, 1018 Wolf, M., & Sarounov´a, L. 1995, A&AS, 114, 143 Wunder, E., Wieck, M., Kilinc, B., Gulmen, O., Tunca, Z., & Evren, S. 1992, IBVS, 3760

Agerer, F., Dahm, M., & Huebscher, J. 1999, IBVS, 4712 Agerer, F., & Hubscher, J. 2002, IBVS, 5296 Agerer, F., & Hubscher, J. 2003, IBVS, 5484 Ashbrook, J. 1952, AJ, 57, 63 Baldwin, M. 1974, J. Am. Assoc. Var. Star Obs., 3, 60 Baldwin, M. 1976a, J. Am. Assoc. Var. Star Obs., 5, 37 Baldwin, M. 1976b, J. Am. Assoc. Var. Star Obs., 5, 88 Baldwin, M., & Samolyk, G. 1996, AAVSO: Observed Minima Timings of Eclipsing Binaries, No. 3 (Cambridge, MA: AAVSO), 1 Baldwin, M., & Samolyk, G. 2007, AAVSO: Observed Minima Timings of Eclipsing Binaries, No. 12 (Cambridge, MA: AAVSO), 1 Bialozynski, J. 2008, J. Am. Assoc. Var. Star Obs., 36, 171 Biro, I. B., Borkovits, T., Hegedus, T., & Paragi, Z. 1998, IBVS, 4555 Brat, L., Zejda, M., & Svoboda, P. 2007, Open Eur. J. Var. Stars, 74, 1 Braune, W., & Hubscher, J. 1987, BAV-Mitt., 46, 1 Braune, W., Hubscher, J., & Mundrey, E. 1970, Astron. Nachr., 292, 185 Braune, W., Hubscher, J., & Mundry, E. 1983, BAV-Mitt., 36, 1 Braune, W., & Quester, W. 1962, Astron. Nachr., 286, 167 Caton, D. B., & Burns, W. C. 1993, IBVS, 3900 Caton, D. B., Hawkins, R. L., & Burns, W. C. 1989, IBVS, 3408 Claret, A. 1999, A&A, 350, 56 Claret, A. 2004, A&A, 424, 919 Claret, A., & Gim´enez, A. 2010, A&A, 519, A57 Claret, A., & Willems, B. 2002, A&A, 388, 518 Cristaldi, S. 1970, A&A, 5, 228 Daniels, W. E. 1966, University of Maryland, Physics and Astronomy Technical Report No. 579 Diethelm, R. 1982, BBSAG Bull., 59, 1 Diethelm, R. 1991, BBSAG Bull., 97, 1 Diethelm, R. 1992, BBSAG Bull., 99, 1 Diethelm, R. 1998a, BBSAG Bull., 116, 1 Diethelm, R. 1998b, BBSAG Bull., 117, 1 Diethelm, R. 2000, BBSAG Bull., 122, 1 Diethelm, R. 2002, BBSAG Bull., 127, 1 Diethelm, R. 2007, IBVS, 5781 Diethelm, R., & Locher, K. 1970, Orion, 122, 1 Diethelm, R., & Locher, K. 1971a, Orion, 123, 1 Diethelm, R., & Locher, K. 1971b, Orion, 124, 1 Dueball, J., & Lehmann, P. B. 1965, Astron. Nachr., 288, 167 Dvorak, S. W. 2009, IBVS, 5870 Etzel, P. B. 1981, in Photometric and Spectroscopic Binary Systems, ed. E. B. Carling & Z. Kopal (NATO ASI Ser. C., Vol. 69; Knudsen: NATO), 111 Fekel, F. C. 2003, PASP, 115, 807 Fernandes, M. 1980, BAV-Mitt., 32 Grønbech, B. 1974, A&A, 37, 435 Hanzl, D. 1994, IBVS, 4097 Haussler, K. 1991, Beobachtungs-Zirkular der Bruno H. Burgel Sternwarte Hartha, 97, 1 Hegedus, T., Biro, I. B., Borkovits, T., & Paragi, Z. 1996, IBVS, 4340 Hoffmeister, C. 1934, Astron. Nachr., 253, 195 Hoffmeister, C. 1947, Verof. Stern. Sonneberg, 1, 114 Hubscher, J. 2005, BAV-Mitt., 171, 1 Hubscher, J., & Agerer, F. 1996, BAV-Mitt., 93, 1 Hubscher, J., Agerer, F., Busch, H., Goldhahn, H., Hassforther, B., & Dahm, M. 1999, BAV-Mitt., 122, 1

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