## 3. Period searchBecause the photometric sets provide the largest part of the observational data and usually are more accurate than the spectroscopic data from the point of view of the dispersion, they were given a higher priority in the period analysis. The light curves of CU Vir have slightly different amplitudes and shapes in different spectral bands. Therefore we first normalized all data by their amplitudes to obtain homogeneous data sets. The same procedure was done with the spectroscopic observations. We then divided our data into two groups: U+u+ (Si II 6347) and B+b+ (Si II 4128-31, 4201). The intensity variations of the Si II 6347 line is closer in shape to the U+u and possibly the y light curves while those of Si II 4128-31 have a similar shape to the B+b light curve. Three different approaches were used for period analysis, discussed below. ## 3.1. Constant periodFirst we searched for a constant period over the whole range of the photometric data using Stellingwerf's (1978) method. The best period is 0520702810.00000016 and it is defined mainly by the recent more extensive photometric data sets. Fig. 2a represents a plot of all data with the constant period (left panel). The right panel shows a plot of the deviations from the mean curve. The rms is 0.168. One may easily see that a few data sets do not fit at all with this period. Note, the the error in the period determinations is mainly defined by the entire time interval of the data used, therefore it is smallest for the constant period because the time interval is the largest, more than 40 years.
## 3.2. Linearily changing periodThe search for the linearily changing period was done using the method by Cuypers (1986) realized in Pelt's (1992) package. The best fit to all our data was achieved with the following ephemeris: where =2435178.92 and S=. This corresponds to P_ days per cycle. A plot of all photometric data with this period is shown in Fig. 2b. Again, the right panel of Fig. 2b shows deviations of the points from the mean curve with the rms being 0.127. The linearily changing period shows practically the same scatter in the final plot for the photometry as does a solution with 2 different periods for all but the # 5 data set, which is definitely shifted by about 0.2 of the period. This shift cannot be explained by any incorrectness of the reduction or normalization procedure because Winzer's data were always included in any period search by previous investigators, and showed a very good phase agreement with all photometric and spectroscopic variations reported before 1985. Moreover, when we plot the equivalent width data with the linearily changing period (Fig. 3a) we obtain noticible phase shifts between the different data sets.
## 3.3. Two periods solutionFirst we constructed an O-C diagram with the ephemeris, The period was estimated by Pyper (1994) as the one that best fit
the photometric data from 1955-1984. Then we measured the phases of
the maxima for each data set; they are plotted in Fig. 4a and b. The
phases of the maxima and minima were found by a sinusoidal fit to the
observational points. It is seen that our data can be fit by two
straight lines that intersect near epoch JD=2446000 (1985). Period
analyses perfomed separately for two groups of data before and after
2446000 by Stellingwerf's (1978) method resulted in two different
periods: 052067780.00000020
(JD2446000) and
0520703080.00000019
(JD2446000). The O-C diagram obtained with two
periods is shown in Fig. 4c,d for maxima and minima and for different
spectral bands. The U+u and B+b light curves give slightly different
phases of minimum, therefore we averaged them and finally obtained the
following ephemeris which fit all photometric and spectroscopic
observations for 40 years (more than 29000 rotations) of the
observations:
Those who would like to use the maximum as a starting phase can use the following moment JD(B light max)=2435178.9025. Combined B+b light curves obtained with the above two periods for all photometric observations are plotted on Fig. 2c (left panel). The deviations from the mean curve are shown in the left panel of Fig. 2c. The rms is 0.114. According to the Fisher test the rms-values in all three approaches for the period search are different with 99.3% confidence level. Combined Si II intensity variations are plotted on Fig. 3b ( 4128-31, 4201). Note that we slightly shifted the equivalent widths from different spectroscopic sets by constant values. These shifts may arise from different treatments of the continuum as well as from different registration (CCD, Reticon, photographic plates), and have no influence on the period search procedure. Fig. 5 displays combined curves of the effective magnetic field variations (a); He I 4026 (b); and He I 4471 (c) line intensity variations. Here we did not need any vertical shifts to combine the spectroscopic data. Fig. 6 represents the hydrogen line equivalent width variations (a); variations of the -index (b), and radial velocity variations (c).
## 3.4. Does a period change still continue?Continuing observations with the FCAPT are being made in order to see whether the period of CU Vir continues to change or has stabilized. A period search of the P10 data (data sets #15, 16, 18) using the Scargle (1982) algorithm, yielded a slightly shorter period of 05206987. O-C diagrams of the P10 and FCAPT data using this period are plotted in Fig. 7. Investigators of eclipsing binary light curves (e.g., Cherewick & Young 1975) have found that a continually varying period results in an ephemeris where is the rate of change of the period
( d cyc
© European Southern Observatory (ESO) 1998 Online publication: October 22, 1998 |