Astron. Astrophys. 346, 134-138 (1999)
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
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.
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
. 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.
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, and , 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 = 6 785. The mean values are respectively = 6.2750 0.0002, -1.0242 0.0002 and 1.3627 0.0002 for V, and 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
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
0.65, 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
An important characteristic of the mid-term variability is the fact
that the V light curve and the
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
© European Southern Observatory (ESO) 1999
Online publication: May 6, 1999