Astron. Astrophys. 324, 109-120 (1997)

6. Open questions and conclusions

Though it has been extensively observed, the magnetic cataclysmic binary BY Cam is far from been well understood. The debate about the periods has been reactivated by the study of the UV emission lines by Zucker et al. (1995). They demonstrate the presence of the so-called orbital period in the radial velocity measurements of these lines and are led to assume a formation of the UV lines far from the white dwarf, in the orbital plane. We have shown above that, because of their broad widths, the bulk of these lines cannot be produced either in the horizontal stream or in the heated hemisphere. The most natural contribution to the UV lines is the accreting column out of the orbital plane, as it has been previously proposed for several polars, based on the fact that their orbital variations are in phase with the broad optical components (Mukai et al. 1986, de Martino 1995). We show below that the temporal behaviour of the UV lines is indeed consistent with this origin. The scattering of the periods found in BY Cam (Fig. 8) can be explained by a scenario, in which, in the orbital frame, the position of the rotational axis is moving slowly with the beat period of about fourteen days. The accretion column is thus formed along different field lines according to the beat phase. Schematically, the accreted material is slowly dragged by the magnetic field during the relative motion of the white dwarf, up to a certain extent when the accretion is no more possible along these lines. Accretion has then to occur at the opposite pole, causing the jump observed in Fig. 9. To compute this effect, we have calculated the position, on the white dwarf surface, of the footprints of the field lines which intercept the orbital plane at the capture radius. This is done for a fixed given co-latitude angle of the dipole magnetic field and for different values of the longitudinal angle which measure the different phases inside the beat cycle. When the capture region is close to the white dwarf, the accretion spot is significantly distinct from the magnetic pole and for different capture regions, its location on the white dwarf surface varies. We find that the co-latitude of the footprint, with respect to the rotational axis, is weakly variable with the beat phase, while its longitude , defined in the orbital plane with respect to the line joining the centres of the two stars, may strongly vary along the beat cycle. This implies a lag of the impact spot with respect to the magnetic pole and the resulting phase drift would be interpreted as an apparent period longer than the true spin period. If furthermore, one assumes that the accretion occurs in the opposite hemisphere as soon as the threading point is situated at an angular distance from the magnetic axis larger than , then at one time, the computed longitude abruptly goes down to low values and increases again in the cycle. We find that the sudden change of the longitude value, due to the switching of the accretion, occurs before the longitude reaches the standard value of 180 usually expected if one assumes that the accretion occurs at the magnetic pole itself. In this varying geometry, we have fully computed the phasing of the radial velocity curve produced by material falling down the magnetic lines just above the white dwarf surface. The amplitude of the shift is determined as soon as and the beat period are fixed. The curve plotted in Fig. 9b) is computed for values of and a beat period of 14 days, and fits the data reasonably well. The RV phase slowly varies with the beat period as observed, distorting the period determination. The sudden change in the phasing when the pole switches, also well reproduces the magnitude of the phase jump () observed in the UV O-C measurements. It appears twice during a beat cycle. A beat value can be evaluated from the point distribution as days. A pole-switching behaviour has been also suggested from photometric data by Silber (1995, Fig. 3). However large phase uncertainties are introduced, in this case, by the fact that the shapes of the light curves are variable and strongly depart from a sinusoidal curve. Strictly speaking, one does not expect to observe the same shape of the beat modulation for lines formed close to the white dwarf and for lines emitted at other positions along the accretion column. The emitting region is also moving, depending on the line production mechanism, and may introduce additional drifts. The present knowledge of the detailed emission line processes at work in these systems is not yet sufficient to allow a better evaluation of this effect. An interesting consequence of this phase-drift model is the fact that any period determination is biased depending on the length of the observation. Measurements extended on more than a beat period will reveal the orbital period, while data obtained in a few days will show either a shorter period than the orbital one or will not allow any period determination if situated close to the jump. Thus a large spread of period values may result as it is indeed observed in Fig. 8. The considerations above also apply to the broad line components usually thought to be formed in the accretion column. Interestingly, the radial velocities of the broad component measured by Sauter (quoted in Zucker et al. 1995) also show variations at the orbital period ( frequency), while they have been found to be modulated with the short spin period ( frequency) by SBIOR, based on a set of data spread over six nights only. We predict that the O-C measurements by Sauter would mimic the same behaviour as for the NV line. In addition our reanalysis of Piirola data has shown that a long period is also present in the polarization flux (see Sect. 5.3), together with an indication of the (2 ) combination period. These periods are indeed expected for a cyclotron emission produced at the basis of the accretion column (Wynn & King, 1992). By combining the two periods of 3.3308h and 3.3749h found in Piirola polarization data, a short (2 ) period of 3.2878h is derived independently, quite consistent with values determined by Silber (1995) and Mason et al. (1995a, b) from photometric data. From the same two values, a long beat period () of 10.621 3 days is also derived. This value is not strictly consistent with the range of values (13-16 days) determined from the UV data, and with the similar 14 day period suggested by Mason et al. (1995a) and Silber (1995).

In conclusion, we have shown that the period determinations are biased depending on the temporal extension of the set of data. The phase-drift model described above explains the inability to determine a unique adequate value for the periods, when the white dwarf is not exactly synchronized. This simple picture has to be modified if one takes into account more physical complex configurations such as a multipole geometry (Mason et al. 1995), a decentered dipole, field line distortions at the threading region (Hameury, King & Lasota 1986) or possible inhomogeneous blobs in the infalling material. Moreover it is most probable that accretion would occur on both sides for intermediate configurations. The orbital period value is still inaccurate. It can, in principle, be unambigously established from the study of the absorption lines associated with the companion atmosphere. A search for the Na lines was tentatively done but without success, implying that either the companion is very faint or that it is of an earlier spectral type than had been expected (Zucker et al. 1995). Finally, the discussion of the UV line formation suffers from the absence of a -velocity value determination, which combined with the RV amplitude should allow to constrain the emitting region in the accretion column. This can be solved with the Hubble Space Telescope and a higher spectral resolution than provided by the IUE satellite.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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