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Astron. Astrophys. 346, 134-138 (1999)

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4. Mid-term variation

In the case of HR 1960, it is possible to perform a very interesting variability analysis because we benefit from a series of advantages, allowing a careful check of our results:

  • The density of the measurements of HR 1960 in Geneva photometry was especially high between 6 851 and 7 684 (in HJD - 2 440 000), due to the monitoring of SN 1987A.

  • During the same period, another comparison star was also intensively measured, HR 1744.

  • Between 7 891 and 9 052, HR 1960 was measured by Hipparcos. As noted in Sect. 2, 101 of these measurements have been used.

Fig. 2 shows the period analysis of these various data, according to the Discrete Fourier Transform (DFT) method by Deeming (1975), which can be used for unequally-spaced data. It appears that:

  • The DFT of the 567 Geneva photometric data (see Sect. 2) of HR 1960 clearly shows a peak at frequency [FORMULA]0.0023 d-1 (continuous line).

  • The DFT of the 101 Hipparcos data (see Sect. 2) also presents its highest peak at the same frequency (dashed line). Secondary peaks can also be noted at frequencies [FORMULA]0.0060 and [FORMULA]0.0075 d-1. We have not taken into account these secondary frequencies in the following analysis because the complexity of the resulting calculated light curve would then look completely unrealistic.

  • The DFT of the Geneva photometric data of HR 1744 (dashed-pointed line) does not show any significant peak.

[FIGURE] Fig. 2. Discrete Fourier Transform of the V magnitude measurements of HR 1960 and HR 1744. The type of line refers to: continuous line for the Geneva data of HR 1960 in the range 6 851-7 684 in HJD-2 440 000, dashed line for the Hipparcos data (range 7 891-9 052), dashed-pointed line for the Geneva data of HR 1744 in the range 6 851-7 684.

Thus, the conclusion is that a mid-term periodic photometric variation was observed in HR 1960 , at least present in the range 6 851-9 052 in HJD-2 440 000, i.e. between February 1987 and March 1993. The light curve in the V magnitude is shown in Fig. 3. The best period has been calculated by minimizing the standard deviation around the fitted curve:


The values of the parameters are given in Table 1. Then, the characteristics of the variability of HR 1960 are a period of 395 d and an extremely small semi-amplitude of 3 millimags inVand 2 millimags in [FORMULA] . It was possible to reveal such a variability thanks to our photometric measurements which were accurate and obtained with an equipment having been maintained very stable during many years.

[FIGURE] Fig. 3. The mid-term (P = 395.480 d) light and colour curves of HR 1960, for the data in the range 6 851-9 052 in HJD-2 440 000. Data from Geneva photometry are identified by filled squares and Hipparcos V magnitudes by crosses. The fitted curve according to Eq. 1 and the moving average (step of 0.01, interval of 0.10) are indicated. The very small semi-amplitude, i.e. respectively only about 3, 2 and 4 millimags in V, [FORMULA] and [FORMULA], is especially noteworthy.


Table 1. Parameters of light and colour curves of HR 1960 (see Fig. 3) according to Eq. 1. The origin of time is [FORMULA] = 6 785. The mean values are respectively [FORMULA] = 6.2750 [FORMULA]0.0002, -1.0242 [FORMULA] 0.0002 and 1.3627 [FORMULA] 0.0002 for V, [FORMULA] and [FORMULA] curves, and the residual standard deviations around the fitted curves are respectively 0.0043, 0.0046 and 0.0053

Any tentative to obtain a more complete description of the light curve, for example by including secondary frequencies, would result in an overinterpretation of the data. Let us recall that the detected semi-amplitude is only about two thirds of the precision of one measurement!

The photometric data are not uniformly distributed in phase. Fig. 3 shows in particular:

  • A high concentration of points in the phase interval 0.17-0.20, which is due to the active monitoring of SN 1987A during the first weeks after the discovery; consequently, a large number of measurements of the comparison stars HR 1960 and HR 1744 were also obtained.

  • A smaller density of points between the phases [FORMULA]0.35 and [FORMULA]0.65, due to the fact that: i) The difficulties of the measurements of these stars from La Silla are more important between June and September, due to the air mass values; therefore, the number of the high quality photometric data is variable within a 1 year periodicity. ii) The period of the variability of HR 1960 is nearly one year (1.08 y). iii) The monitoring from La Silla was intense during only about 2.3 cycles (2.5 y).

An important characteristic of the mid-term variability is the fact that the V light curve and the [FORMULA] colour curve are anti-correlated (see Fig. 3), in the sense that the star is found to be redder when brighter in the Paschen continuum . Note that the same property has been observed in the case of another periodic Be star, HR 2968, as shown by Carrier et al. (1999). This is probably a crucial point for the model proposed for these two stars (see Sect. 5). Indeed, they have very similar periods, respectively 371 and 395 d for HR 2968 and HR 1960, as well as the same kind of light to colour variability.

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© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999