COMMISSION 27 OF THE I. A. U. INFORMATION BULLETIN ON VARIABLE STARS Number 1900 Konkoly Observatory Budapest 1980 December 29 HU ISSN 0374-0676 DETERMINATIONS OF SIX TIMES OF MINIMA, AND A NEW EPHEMERIS FOR BS Dra During a recent investigation of the photometric orbit of BS Dra by Popper and Etzel^1, it became necessary to redetermine the ephemeris of the system. The B, V observations used in the determinations of the six additional times of minima given here were described by Popper and Dumont.^2 These determinations were then combined with all previous ones known at the time to derive the new ephemerides given below. The determinations of the times of minima made use of the symmetry of the eclipses to determine the temporal mean of the ascending and descending branches in a manner very similar to the method of Hertzsprung.^3 Observations on the steeper portions of the curve were reflected onto the opposite branch by linear interpolation to give a time of minimum for each observation. The mean of all these gave the time of minimum determination, along with an estimate of the uncertainty. This method was automated by computer programming to allow flexibility. It was found to be a superior method compared to polynomial fitting of the observations within the minima. Such a method, using third-order polynomials" was proposed by Breinhorst et al.^4 for use with asymmetric light curves. Whereas the results of the simple temporal averaging were fairly insensitive to the selection of observations for a given eclipse, the polynomial fitting was sensitive both to the distribution of the observations and to the order of the polynomial. Polynomial orders of two to five were used in the tests. Similar problems with polynomial fitting, and other such methods, were reported by Van Diest^16 in connection with asymmetric minima. Table I lists the results of the determinations for six observed minima. Table I Mean B & V Determinations of Times of Minima for BS Dra From the Observations of Popper and Dumont^2 Date Minima No.0bs. HJD (obs) U.T. P/S V/B +2400000 s.e. 13 Jul 72 P 35/31 41511.8842+-.0006 18.Tul 72 S 16/16 41516.9311+-.0007 14 Aug 72 S 42/41 41543.8428+-.0005 19 Aug 72 P 12/15 41548.8891+-.0005 1 Jun 73 P 52/52 41834.8302+-.0004 22 Oct 73 S 15/17 41977.8009+-.0006 A search of the literature available at the time when the investigation by Popper and Etzel was commencing yielded 36 other determinations of times of minima. These, along with the determinations from Table I, are given in Table II. Also given are the epoch and O-C (computed from the adopted ephemeris), the weight and type of determination, and the reference(s). Unit weights were generally assigned to photoelectric (pe) determinations in one filter, double weights to the average of two-color photoelectric determinations, weights of 0.2 to visual estimates (vis), and 0.1 to photographic values (pg). Some photographic determinations were rejected due to their obviously poor quality, but the remaining ones did improve the period derived from using the photoelectric observations alone. Table II Ephemeris Solution for BS Dra -- All Determinations Assuming J.D.min 2,441,461.4245+ 3.3640103E HJD (obs) +2400000 Epoch 0- C wt. Method ref. 26444.467 -4464.0 -.016 0.1 pg 5 26942.369 -4316.0 .013 0.1 pg 5 26942.390 -4316.0 .034 0.0 pg 5 26942.408 -4316.0 .052 0.0 pg 5 27216.522 -4234.5 -.001 0.1 pg 5 27312.396 -4206.0 -.001 0.1 pg 5 28020.522 -3995.5 .001 0.1 pg 5 28782.422 -3769.0 -.048 0.0 pg 5 28809.373 -3761.0 -.009 0.1 pg 5 29911.460 -3671.5 -.001 0.1 pg 5 29438.467 -3574.0 .015 0.1 pg 5 36420.422 -1498.5 -.033 0.0 pg 5 36452.368 -1489.0 -.045 0.0 pg 5 41392.452 - 20.5 -.010 0.2 vis 6 41461.4252 0.0 .0007 2.0 pe 7,8 41471.5163 3.0 -.0003 1.0 pe 7,8 41471.5166 3.0 .0000 1.0 pe 7,8 41488.3335 8.0 .0031 1.0 pe 7,8 41488.3345 8.0 .0021 1.0 pe 7,8 Table II (Continued) HJD (obs) +2400000 Epoch 0- C wt. Method ref. 41493.3817 9.5 -.0009 1.0 pe 7,8 41493.3838 9.5 .0012 1.0 pe 7,8 41498.4290 11.0 .0004 1.0 pe 9 41508.5199 14.0 -.0008 1.0 pe 9 41511.8842 15.0 -.0005 2.0 pe This study 41516.9311 16.5 .0004 2.0 pe This study 41543.8428 24.5 .0000 2.0 pe This study 41548.8891 26.0 .0003 2.0 pe This study 41594.3040 39.5 .0011 1.0 pe 7 41631.3123 50.5 .0052 1.0 pe 9 41772.5934 92.5 -.0021 1.0 pe 9 41794.4600 99.0 -.0016 1.0 pe 9 41826.4196 108.5 .0000 1.0 pe 7,8 41834.8302 111.0 .0005 2.0 pe This study 41977.8009 153.5 .0008 2.0 pe This study 42302.4277 250.0 .0006 1.0 pe 8,10 42302.4280 250.0 .0009 1.0 pe 8,10 42371.3907 270.5 .0014 1.0 pe 10 42435.312 289.5 .006 0.2 vis 11 42529.491 317.5 -.007 0.2 vis 12 42958.405 445.0 .004 0.2 vis 13 42990.368 454.5 .001 0.2 vis 14 43059.321 475.0 -.008 0.2 vis 15 It was initially assumed that the separations of the minima were exactly 0.5p from individual preliminary ephemeris solutions on the primary and secondary eclipses. The subsequent analysis by Popper and Etzel showed e cos omega to be less than 0.0001 and there is also no significant difference in the average weighted O-C for the two minima. The adopted ephemeris and standard errors for the 42 determinations in Table II are: J.D. = 2,441,461.4245 + 3.3640103 E, min +-.0004 +-.0000006 with the standard error of one minimum of normalized unit weight being 0.0025 days, which is a slightly shorter period than found by Ibanoglu et al.^8 A solution setting all photoelectric determinations equal to unit weight, regardless of the number of colors used for a single quoted value, gave the same solution. A test solution using only the 23 photoelectric determinations yielded the ephemeris J.D. = 2,441,461.4244 + 3.3640144 E, min +-.0004 +-.0000038 with a standard error of 0.0014 days, which is essentially identical to that found by Ibanoglu et al. The difference between the two values of the period illustrates the value of including earlier low-weight photographic determinations for improving the period. It is noteworthy to point out the usefulness of visual de-terminations even in this mechanized era of astronomy. This work was supported under NSF Grant AST77-22672 Popper/Plavec. PAUL B. ETZEL Department of Astronomy University of California Los Angeles, CA 90024 U.S.A. References: 1) Popper, D.M. and Etzel, P.B.: Photometric Orbits of Seven Detached Eclipsing Binaries, Astron. J.(in press,1981), also UCLA Astronomical Papers, Reprint Vol.18, No.35,1980. [BIBCODE 1981AJ.....86..102P ] 2) Popper, D.M. and Dumont, P.J.: Astron. J., 82, 216, 1977. [BIBCODE 1977AJ.....82..216P ] 3) Hertzsprung; E.: B.A.N., 4, 178, 1928. [BIBCODE 1928BAN.....4..178H ] 4) Breinhorst, R.A., Pfleiderer, J., Reinhardt, M. and Karimie, M.T.: Astron. Astrophys., 22, 239, 1973. [BIBCODE 1973A&A....22..239B ] 5) Strohmeier, W., Knigge, R. and Ott, H.: Bamberg Verof.,5, no.14,5. 6) Diethelm, R.: B.B.S.A.G. Bul. no. 2, 1972. 7) Kizilirmak, A. and Pohl, E.: I.B.V.S., no. 937,1974. 8) Ibanoglu, C., Bozkurt, S., Gudur, N. and Gulmen,O.: I.B.V.S., no. 1100, 1976. 9) Chis, D., Pop, V. and Todoran, I.: I.B.V.S., no. 1079,1976. 10) Pohl, E. and Kizilirmak, A.: I.B.V.S., no. 1053,1975. 11) Locher, K.: B.B.S.A.G. Bul. no.20,1975. 12) Diethelm, R.: B.B.S.A.G. Bul. no.22,1975. 13) Germann, R.: B.B.S.A.G. Bul. no.28,1976. 14) Germann, R.: B.B.S.A.G. Bul. no.29,1976. 15) Germann, R.: B.B.S.A.G. Bul. no.30,1976. 16) Van Diest, H.: Astron. Astrophys.,42,465,1975. [BIBCODE 1975A&A....42..465V ]