I. Determination of the orbital parameters and of the frequencies

We present the analysis of 445 high signal-to-noise spectra of the Si III triplet at 4553 Å, 4568 Å, 4575 Å of the lineprofile variable star ε Persei. The data were gathered during 14 consecutive nights and fully cover the orbital cycle of the binary. The orbital parameters that we derive from our data for the close binary are in full agreement with those found in 1995 by Tarasov et al. Our data does not offer a conclusive test of the presence of the 4156-d period. With the CLEAN-method, we identify 5 periods in the intensity variations across the line profiles, after the latter are corrected for the binary motion: 5.300, 5.890, 6.250, 6.875, and 10.585 c d−1. The results of our frequency analysis are consistent with previous ones based on the CLEAN algorithm. In terms of sinusoidal variations with constant phase, we thus find that the line-profile variations have a multiperiodic pattern. The Hipparcos photometry reveals yet another candidate frequency of 5.23280 c d−1. It is not clear yet if this frequency is connected to those found in the spectra. With the PDM-method, we find some indications leading to the “super” period Psuper ≡ 1. d11878, as introduced by Harmanec (1999). On the other hand, many other periods between 1 and 3 days are equally likely than Psuper. Some of the frequencies found using CLEAN are integer submultiples of Psuper. We do not have a sufficient amount of data to estimate the importance of tidal effects for the line-profile variability near periastron for ε Persei.