Astron. Astrophys. 332, 526-540 (1998)

2. Observations

RE 0751+14 was observed at the Special Astrophysical Observatory (Nizhnij Arkhyz, Russia) from February 1993 to March 1996 (see the journal of observations in Table 2). Spectroscopic observations were performed in 1993, 1994 using the SP-124 spectrograph at the Nasmyth secondary focus of the 6 meter Bolshoi Azimutal Telescope, BTA, (Ioannisiani et al. 1982). The spectrograph was equipped with a 1200 lines/mm grating giving a dispersion of 50 Å/mm. A television scanner with two lines of 1024 channels recorded the sky and object spectra simultaneously in a photon-counting mode (Somova et al. 1982; Drabek et al. 1986; Afanasiev et al. 1991).

In March 1996 observations were carried out in a spectropolarimetric mode. In this mode the achromatic analyzer of circular polarization (Najdenov & Panchuk 1996) was installed in front of the slit of the spectrograph and two spectra were recorded in the circular polarizations simultaneously. The sky was observed between the exposures. A 2-arcsecond aperture (in spectral mode) and slit (in spectropolarimetric mode) were used. The spectra in the wavelength passband  Å in the range 3900-5200 Å with a dispersion of 1 Å/channel were obtained with a temporal resolution of 32 ms. The spectra were recorded continuously (1200-5400 s), and between the exposures a He-Ne-Ar lamp was measured for the wavelength calibration. General characteristics and the journal of our obsrvations are presented in Table 1 and Table 2.

Table 1. Parameters of observations

Table 2. Journal of the observations of RE 0751+14

2.1. Data reduction

The data reduction was performed with the help of a special algorithm. The mathematical justification of the algorithm is given in appendix to the paper. We present here only a short description of this method. As a result of every exposure, a file with the coordinates (2x1024 channels) and the time of registration (resolution 32 ms) for every photoelectron was written on a hard disk in the computer.

The possibility of extracting of spectra integrated during the time from 32 ms to the time of exposure (3000-5000 s) from original information (coordinates, 2x1024 channels, and the time of arrival) about photoelectrons with an accuracy limited by the time resolution (32 ms) is the basic idea of our method of data reduction. The range of the investigated periods from 300 s to 2000 s was chosen. This choice makes it possible to analyze the oscillations near the spin period (834 s) and its harmonic and the double period. The resolution along the period was 5 s in the range from 300 s to 600 s, 10 s in the range 600-1200 s and 50 s in the range 1200-2000 s.

For every period
(300 s, 305 s, ..., 600 s, 610 s, ..., 1200 s, 1250 s, ..., 2000 s)
the spectra with the time of acquisition
(30 s, 30.5 s, ..., 60 s, 61 s, ...,120 s, 125 s, ..., 200 s)
were extracted from the original spectral data (the file with the parameters of photoelectrons) and folded in ten bins. Every bin contains two spectra (object and sky or two objects in the polarimetric mode of observations). The number of photons in one bin is equal approximately to the total number of photons in the exposure divided by ten. For every bin, after the substraction of the sky spectrum (which was strongly smoothed), the continuous spectrum was calculated as a 3d-4th power polynomial and every spectrum was divided by the continuous spectrum. The normalized bin will be

where is the number of a bin,
is the spectrum accumulated in one bin,
is the corresponding continuous spectrum,
is the spectrum in one bin in relative units,
is the wavelength corresponding to the channels.
Further we assume but not underline a discrete character of . This conversion to relative units suppresses the broad-band spectral variability (guiding effects, variability of the object itself and spectral window). Then we calculated the power, amplitude and phase of the oscillations in relative units (the level of continuous spectrum is equal to 1) for every channel (wavelength). The Fourier coefficients corresponding to the period of interest were determined as

The power of the spectral oscillations is equal to

where is a complex amplitude of the pulsation.

This method is similar to the method of synchronous detection widely used in astronomical observations. The algorithm was realized in the last version of the special programming language SIPRAN (Somov 1986). The integral spectrum was calculated by simple integration of the photoelectrons. The wavelength calibration (Kopylov et al. 1986) was made with the help of the He-Ne-Ar lamp. The result of data reduction is the dependence of the power of oscillations on the period (periodogram) and on the wavelength (spectrum), but we will name it a power spectrum for simpicity. In the case of spectropolarimetry as an additional information about circular polarization of the oscillations, the second power spectrum was calculated.

The method was checked by a computer simulation and by observations of standard stars (sun-like star, spectral standard stars without emission lines) and several astrophysical objects such as three intermediate polars and one polar.

To distinguish the difference between our method of observations and data reduction and classical methods we use the word "dynamic" for our case.

© European Southern Observatory (ESO) 1998

Online publication: March 23, 1998
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