## 4. Mid-term variationIn 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 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 0.0060 and 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.
Thus, the conclusion is that The values of the parameters are given in Table 1. Then, the
characteristics of the variability of HR 1960 are
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 0.35 and 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
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