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Astron. Astrophys. 326, 218-220 (1997)

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3. Period analysis

The used sampling pattern of the phaseresolved observation was adjusted for the period of ([FORMULA]) h derived by Schmidt & Norsworthy (1991 ) for KPD 0253+5052. Thus six circular polarization spectra were always taken at the same phase points within each 4.1 h period. The starting time of "phase 1" was arbitrarily chosen. About 1.5 periods could be observed every night. In Fig. 1 spectra for the clockwise and counterclockwise rotating E-vectors from different nights for "phase 6" according to the 4.1 h period are shown. Phase deviations within the 4 nights of our observing run can be noticed, which correspond to a temporal phase shift and imply a slightly different period for KPD 0253+5052 . The period estimation of Schmidt & Norsworthy (1991 ) is based on data of one night only. But if all their data are folded with the period of 4.1 h it can be seen (Fig. 2) that the measurements obtained during their other observing runs are not consistent with this period, either.

[FIGURE] Fig. 1. Spectra for the clockwise and counterclockwise rotating E-vectors (solid, dotted) from different nights for "phase 6" according to the 4.1 h period. A phase shift between these spectra can easily be noticed. The two spectra of the 4th night were taken with half the exposure time used in the nights before. But the exposure and start times were chosen such that together they completely cover "phase 6".
[FIGURE] Fig. 2. White light polarimetric data (Schmidt & Norsworthy 1991 ) of KPD 0253+5052 folded with a period of 4.1 h (top) and 3.79 h (bottom). [FORMULA] symbols are observations which were not used by Schmidt & Norsworthy in their period determination.

In order to improve the period estimation we simulated broad band circular polarization measurements for H [FORMULA] (4500-5060 Å) and H [FORMULA] (4170-4480 Å) from our spectropolarimetric data. Data of all four nights were used, despite the bad signal-to-noise of the fourth night, due to a shorter exposure time. In a first approach, the temporal behavior of the mean circular polarization measured for H [FORMULA] and H [FORMULA], respectively, was analyzed by fitting a linear trend plus a sinusodial oscillation to the data. Furthermore we also analyzed the time series of one distinct H [FORMULA] Zeeman component (4840 Å), which can be fairly seen in all spectra.

The mean circular polarimetric H [FORMULA] time series can be well modelled by a sinusoidal oscillation with a period of ([FORMULA]) h which is significantly lower than the former period estimation of Schmidt & Norsworthy (1991 ). Fig. 3 shows the used range of trial periods and the corresponding [FORMULA] -values for the H [FORMULA] line. The strong fluctuations are due to the large observational gaps. The minimum value of the [FORMULA] envelope yields the [FORMULA] -value of 34.3 (51 d.o.f). The corresponding H [FORMULA] time series yields a best period of ([FORMULA]) h with a [FORMULA] -value of 65.8 (51 d.o.f.). If the data are folded with the newly derived period of 3.79 h (Fig. 4) no phase shifts occur during the observations. From the H [FORMULA] Zeeman component a period of ([FORMULA]) h is derived, in good agreement with period values from the circular polarization. The corresponding large [FORMULA] -value of this period estimation of 110.1 might be due to phase dependent diminishing of this Zeeman component and a possible confusion with other nearby Zeeman components.

[FIGURE] Fig. 3. [FORMULA] values of the sinusoidal fits for different trial periods of the mean circular polarization of the H [FORMULA] line. The solid and dashed lines are the 99%, 90%, and 68% confidence levels (top to bottom), respectively.
[FIGURE] Fig. 4. White light polarimetric data (Schmidt & Norsworthy 1991 , top) and simulated broadband polarimetric data (this observation) at the positions of the H [FORMULA] and H [FORMULA] lines (middle and bottom, respectively) of KPD 0253+5052 folded with a period of 3.79 h . Phase 0 corresponds to the epoch given by Schmidt & Norsworthy.

As it can be seen in Fig. 4 there is a phase shift between the folded mean circular polarization data of H [FORMULA] and H [FORMULA] of about 0.4. The negative polarization maximum of H [FORMULA] nearly coincides with the minimum of the H [FORMULA] pulse profile. The reason might be that the blue side of the H [FORMULA] line is already influenced by the [FORMULA] components of H [FORMULA], whereas the [FORMULA] components of H [FORMULA] do not interfere with H [FORMULA] in the magnetic field strength range considered here.

A mean circular polarization for the whole covered spectral range was also determined. It shows a sinusoidal oscillation around a mean value of about -0.5%, slightly more negative than the data of Schmidt & Norsworthy, but in phase with the older data. The deviation in the mean values of the two observations could be caused by the different wavelengths ranges.

A period search using common techniques such as epoch folding or Fourier analysis is strongly biased due to the large observational gaps, and cannot be used to get individual period estimates, therefore. But besides many aliases caused by harmonics due to the exposure time of 41 min for an individual spectrum a peak was found at a period of 3.8 h in the [FORMULA] -distribution of the epoch folding.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998
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