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Astron. Astrophys. 346, 87-90 (1999)

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2. Observations and reductions

Our analysis of the light variations of BD+61o2213 is based on the following sets of photoelectric observations:

  1. 50 differential observations in the DAO photometric system relative to HD 208440 = NGC 7160*3, secured by Hill et al. (1976) at Mt. Kobau in 1972 and 1973. The DAO [55], [44] and [35] magnitudes were transformed into the standard UBV system of accurate magnitudes derived by Harmanec et al. (1994) with the help of transformation formulæ derived by us earlier - cf. Hill et al. (1997).

  2. 5 differential UBV observations relative to HD 208440, secured at Hvar between 1973 and 1982 and published by Harmanec et al. (1997). These observations were carefully transformed to the standard system with the help of the reduction program HEC22, based on non-linear transformation formulae. Details of the reductions were described by Harmanec et al. (1994) and the reduction software itself was published and fully documented by Harmanec & Horn (1998).

  3. 107 accurate all-sky [FORMULA] observations secured from 1989 to 1993 during the Hipparcos satellite mission and published by Perryman et al. (1997). They were transformed into the standard V magnitude of the Johnson system following Harmanec (1998). The mean values of colour indices of BD+61o2213 derived by Harmanec et al. (1994) and quoted above were used in the transformation formula.

  4. 8 UBV differential observations relative to HD 208440, secured at San Pedro Mártir in 1998 and reduced to the standard system again with the help of HEC22 rel. 13.1 program.

  5. 22 differential UBV observations relative to HD 208440, secured at Hvar and also reduced with HEC22 rel.13.1.

To derive final UBV values for analyses, the following mean Hvar all-sky UBV values of the comparison HD 208440, derived by Harmanec et al. (1994)

V = 7[FORMULA]935, [FORMULA] = +0[FORMULA]074, [FORMULA] = -0.729

were added to the standard magnitude differences BD+61o2213 - HD 208440 for all differentially obtained observations. In most cases, all-sky or differential (again relative to HD 208440) observations of the check star HD 208218 = NGC 7160*1 were also obtained. The journal of all data sets is in Table 1 where also mean or seasonal mean UBV values of the variable are listed. We note that the rms errors of the mean values of BD+61o2213 exceed those of the check star HD 208218. While it is true that HD 208218 is much brighter than BD+61o2213 and can, therefore, suffer from a somewhat smaller observational scatter, it is necesarry to realize that both stars were reduced in most cases relative to HD 208440 the brightness of which is closer to BD+61o2213 than to HD 208218. The mean values of Table 1 seem, therefore, indicate variability of BD+61o2213 .


Table 1. Journal of differential photoelectric observations of BD+61o2213 relative to HD 208440 = NGC7160*3. All quoted errors of the V magnitude are the mean rms errors per 1 observation of unit weight.
Column "Station" Running numbers of observing stations follow the numbering system used in the Ond ejov data archives, cf. Harmanec & Horn (1998): 1... Hvar 0.65-m reflector, EMI6256B tube; 3... Skalnaté Pleso 0.60-m reflector, EMI6256B tube; 13... Mt. Kobau 0.41-m reflector, a four-channel photometer; 30... San Pedro Mártir 0.84-m reflector, the "cuenta-pulsos" photometer with an RCA 31034 tube; 61... Hipparcos satellite photometry.
Column "Remarks" A... DAO [55], [44] and [35] photometry transformed into the standard UBV system following Hill et al. (1997); B... Hipparcos [FORMULA] photometry transformed into Johnson V following Harmanec (1998).

It is fair to warn the readers that our comparison star, HD 208440, is also suspected of variability and was listed as NSV 25788 by Kazarovets et al. (1998) on the basis of a report by Rufener (1989) who once observed it as faint as 8[FORMULA]12. However, none of the photometric data sets at our disposal, including the Hipparcos observations, shows evidence of similar light decreases of HD 208440. Also Ardeberg & Sarg (1974) give V = 7[FORMULA]95 for HD 208440 on the basis of 3 observations obtained in summer 1968.

To investigate the variability of BD+61o2213 further and to map the possible time scales of the variations, we inspected various sample plots of the V observations of BD+61o2213 and its comparisons vs. time. As an illustrative example, two longest series of the Hipparcos observations are plotted in Fig. 1. One can see that the data scatter is increasing with the decreasing magnitude of the object as expected. However, there is no convincing evidence of real rapid (shorter than about 0[FORMULA]3) light variations of BD+61o2213 . On the other hand, a real light variation of BD+61o2213 between the two series of observations is clearly observed. This is also confirmed by our San Pedro Mártir observations which show that the brightness of BD+61o2213 changed for 0[FORMULA]05 between two consecutive nights. On the other hand, the mean values of Table 1 show a rather good secular stability.

[FIGURE] Fig. 1. Time plots of Hipparcos all-sky photometry of BD+61o2213 and its comparisons HD 208440 and HD 208218, transformed to the standard Johnson V magnitude, for two longest series of observations secured within one day. One can see real light variation of BD+61o2213 between the two series of observations

We therefore subjected all V observations to a period search over the range of periods from 0[FORMULA]5 to 1000[FORMULA]0 using the PDM (phase dispersion minimalization) period search technique - see Stellingwerf (1978). The resulting PDM periodogram is shown in Fig. 2. A period of 1[FORMULA]2028269 and its one-day alias were clearly detected as the best ones, without too much aliasing problems. A non-linear least-squares fit of the data carried out with the help of program Period98 (version 1.0.6) by Sperl (1998) led to an improved ephemeris [FORMULA] = HJD 2446299.237(12) + 1[FORMULA]2028251(13) [FORMULA] E.

[FIGURE] Fig. 2. The PDM periodogram of all 195 V observations of BD+61o2213 secured between 1972 and 1998 which shows that the variations have a periodic component near 1[FORMULA]2

Only this period and its first harmonics were sufficient to a good description of the variations observed, all higher harmonics having (formal) amplitudes of the fit below 0[FORMULA]003. The rms of the fit per one observation was 0[FORMULA]020, i.e. slightly higher than what would be expected for the data noise only, and addition of higher harmonics did not decrease this value significantly. The light curve corresponding to the least-squares fit is shown in Fig. 3.

[FIGURE] Fig. 3. All V observations of BD+61o2213 and its check star HD 208218 are plotted vs. phase of the 1[FORMULA]2028251 period. A double-wave variation, reminiscent of an ellipsoidal or eclipsing variable, is clearly seen. Data from different observatories are show by different symbols as follows: +... Hvar; x... Skalnaté Pleso; circle... Mt. Kobau, triangle... San Pedro Mártir; diamond... Hipparcos

In Fig. 4 we also plot five available radial velocities of BD+61o2213 from the papers by Hayford (1932), Liu et al. (1989) and Liu et al. (1991) for the ephemeris given above. It is seen that there is a good mutual correspondence between the phases of expected conjunctions of the putative binary system and the phases of the light minima. This finding firmly confirms earlier tentative reports that the star is a binary. As demonstrated by, e.g., Harmanec (1981), most of the known B binaries have orbital periods between 1 and 3 days. The observed value of the orbital period of BD+61o2213 falls inside that range.

[FIGURE] Fig. 4. Available radial velocities of BD+61o2213 plotted vs. phase of photometric period and epoch. It is seen that the star is indeed a large-amplitude spectroscopic binary

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© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999