## 3. Results## 3.1. Frequency analysisAnalysis of frequencies of our data was carried out using the
Discrete Fourier Transform method, as described in López de
Coca et al. (1984). The When the Fourier analysis is applied to 20 CVn, the
periodograms showed a principal peak at
=8.2168 cd
Frequency analysis was also carried out on the different data sets available from earlier authors, especially on the three best ones, i.e. to the 1969 B and V data of Shaw (1976) and the 1980 V data of Peña & González-Bedolla (1981). In all the cases we find similar results to those found with our data, that is, when the main frequency is prewhitened the resulting periodograms do not show any trace of another peak. Nevertheless, in these cases, the noise level is much higher than in our data. Therefore, we conclude that there are no remaining periodicities in the light variation of 20 CVn. In our case, the standard deviations, as determined by residuals
from the solution, were of 0.
## 3.2. O-C analysisAssuming 20 CVn as a monoperiodic pulsator, the classical O-C
method can be used. Twelve times of light maxima were obtained from
the new data by using the method described in Rodríguez et al.
(1990), where each light maximum was derived as an average over the
three With the aim of using the largest number of maxima as possible to
determine the ephemeris of 20 CVn, we made use of the radial
velocity data available from the bibliography to calculate the
corresponding maxima and to transform to light maxima. For this
purpose, we calculate the phase shift between the instants of maximum
in radial velocity and light using the spectroscopic data from Mathias
& Aerts (1996) and our own photometric data. Note, that these two
sets of observations were collected at the same epoch. In this way, we
obtain that light maximum occurs after that corresponding to radial
velocity by 0. Consequently, forty times of maxima (from 1969 to 1997), listed in
the second column on Table 2, were used to determine the
ephemeris of the pulsation of 20 CVn by means of the classical
O-C method. At first, we applied this method to the maxima obtained in
the epoch 1980-1983. T
This result means that the pulsation period of 20 CVn is
decreasing at a rate of dP/dt=-11.6(
0.4)10 ## 3.3. Amplitude variationsLong term amplitude variations seem to be common in low amplitude
Sct stars. This is different to that
suspected in the high amplitude ones. For any of the known high
amplitude Sct stars, long term amplitude
variability had not been established at the time. In this sense, we
have analysed the different data sets available for 20 CVn from
the bibliography. Unfortunately, only the two early data sets from
Shaw (1976) in BV and Peña & González-Bedolla (1981)
in V are reliable for this subject. Table 3 lists the amplitudes
from these data sets together to the one obtained from our data. In
all the cases, these amplitude determinations were carried out making
the Fourier fitting with only one term for the frequency
8.2168 cd
## 3.4. PhotometryFig. 3 shows the light and colour index variations of
20 CVn along the pulsational cycle assuming the quadratic
ephemeris derived in Sect. 3.2. As can be seen, the curves in V and
b-y are phased. However, the maximum in the c
In order to discuss the pulsational characteristics of this star it
is useful to know its physical parameters. The following
Strömgren values of V=4. With these corrections and using the relation by Crawford (1975b)
for luminosity, Code et al. (1976) for bolometric correction and the
grids by Lester et al. (1986) with [Me/H]=0.0 for temperature and
gravity we obtain the following values of M The values found for T Moreover, using the relation by Petersen & Jorgensen (1972), a
value of Q=0. ## 3.5. Pulsation mode identificationDue to only one frequency being found in the light curve of
20 CVn, methods based on period ratios or frequency differences
are excluded in order to identify the pulsation mode of this star.
However, the methods based on the phase shifts and amplitude ratios
between the observed light and colour variations, in Table 4 lists the phase shifts, in degrees, and amplitude
ratios between the different bands and colour indices, as resulting
from Table 1. We can see that the phase shifts of both
The question now arises when interpreting the high resolution
spectroscopy results of Mathias & Aerts (1996). They find that
20 CVn is a multiperiodic variable pulsating in a nonradial mode
with l=3 or 2. Their data seem to be of very high quality but, we feel
they collected a too small amount of data to get a definitive
conclusion. In fact, they have observations of only one pulsational
cycle. Nevertheless, nonradial pulsation in 20 CVn was also
suspected by Smith (1982) and Yang & Walker (1986). In the former
case, Smith (1982) used the classical method which consists of a
comparison between the observed spectrum and a theoretically computed
one on a trial-and-error basis. This author found that on profile
fitting alone the radial pulsation solution can not be ruled out for
the primary mode of 20 CVn. Then, his nonradial suggestion is
based in two other points: 1) multiperiodic behaviour and
2) low value of 2K/ m However, taking into account the spectroscopic results of Smith (1982) and Mathias & Aerts (1996) it might be that the spectroscopic and photometric behaviour of this star is different. In this sense, and in order to accurately identify the mode(s) and to decide on the mono/multiperiodic behaviour of 20 CVn, it would be very interesting to perform a long campaign to observe this star collecting simultaneously high resolution spectroscopy and multicolor photometry. © European Southern Observatory (ESO) 1998 Online publication: February 4, 1998 |