4 Discussion

We have made a number of simplifications and assumptions in our light curve model that need some further attention.

(1) We have assumed that the accretion stream emission does not vary over the orbit, and have treated its contribution as a free parameter to fit the observed flux level. The computation of realistic accretion stream spectra is a problem of great complexity (e.g. Ferrario & Wehrse 1999), and certainly beyond the scope of our paper. However, a short inspection of the general spectral features of accretion stream emission lends support to our assumption.

The optical high state spectrum of AMHer is characterized by strong Balmer and Helium emission lines and by a strong Balmer jump in emission (e.g. Schachter et al. 1991). The origin of such a spectrum is clearly a plasma in which the optical depth in the continuum is below unity (optically thin in the continuum), and the optical depth in the lines is much larger than in the continuum, i.e. $\gg$1 (optically thick in the lines). The details of the spectrum depend on the temperature, the density, and the extension of the plasma region, but the general characteristics are (a) significant continuum emission in the near-ultraviolet part of the Balmer continuum, (b) a strong contribution in the B band, which covers the higher lines of the Balmer series, Ca K+H in emission, as well as the Balmer jump, and (c) a weak contribution in the V band, which covers practically only the weak continuum between ${\rm H\alpha}$ and ${\rm H\beta}$. As already stated in Sect. 3.3, Gänsicke et al. (1995) detected strong near-ultraviolet continuum emission with a weak phase-dependence, and identified the accretion stream as the source of this emission. In AMHer, with $B\approx14$MG, cyclotron emission cannot contribute significantly at such short wavelengths, the secondary star can be excluded, and the white dwarf contribution was already modelled in the analysis of Gänsicke et al. (1995). We feel, therefore, it is safe to identify the observed near-ultraviolet continuum flux with the accretion stream feature (a) defined above.

We find in our present analysis that the accretion stream contributes more in B than in V. In fact, the stream emission dominates the practically flat B band light curve. This result appears entirely plausible, as our above considerations show that the stream is indeed expected to be brigher in B than in V. We note that weak photometric modulation at blue wavelengths is a hallmark of AMHer during the high state (e.g. Olson 1977). A more sophisticated approach would need simultaneous phase-resolved spectroscopy, so that the stream contribution in the B and V bands could be quantitatively estimated e.g. from the orbital variation of the emission line fluxes. Hence, in summary, the observed weak phase dependence of the near-ultraviolet stream emission and the fact that the stream is expected to be brighter in B than in V strongly supports our assumption of a phase-independent stream contribution. This in turn implies, as shown in Sect. 3.6, that cyclotron emission is the dominant phase-dependent contribution to the observed V band high state light curve.

(2) We ignore the geometric occultation of the accretion column by the body of the white dwarf. For $i+\beta=105^{\circ}$ structures extending less than than $\sim$0.035  $R_{\rm wd}$ above the white dwarf surface will be totally eclipsed at $\mbox{$\phi_{\rm orb}$ }\approx0.5$. However, for the low magnetic field and the rather low mass flow density, the shock is expected to stand $\sim$0.1  $R_{\rm wd}$ above the white dwarf surface (Fischer & Beuermann 2001). The X-ray data of AMHer clearly show that at least part of the accretion region is eclipsed at $\mbox{$\phi_{\rm orb}$ }\approx0.5$ (i.e. when $\vartheta$ reaches its maximum) by the white dwarf (e.g. Hearn & Richardson 1977). In contrast to this, significant polarized emission is still detected during this phase, indicating either that the cyclotron emission arises at a greater height above the white dwarf surface than the X-rays (Bailey et al. 1984), or that additional cyclotron emission comes from the opposite magnetic pole (Wickramasinghe et al. 1991). An indication that an eclipse of the accretion column by the white dwarf might be relevant comes from the UBVRI polarimetry of Piirola et al. (1985): the secondary minimum at $\mbox{$\phi_{\rm orb}$ }\approx0.6$has practically the same shape in V, R, and I. This is unexpected, as the cyclotron beaming decreases towards the lower cyclotron harmonics (i.e. longer wavelengths). In fact, R and I band light curves calculated with our model give reasonable magnitudes, but do not show a strong secondary minimum.

(3) We have neglected that the accretion column has a finite lateral extent, which will cause a variation of the magnetic field strength and, more importantly, of its orientation within the cyclotron emitting region. The expected result of such variation is a smoothing of $\vartheta(\mbox{$\phi_{\rm orb}$ })$, and, consequently, of the cyclotron light curve. In addition, a significant lateral extent of the cyclotron emitting region would counteract to some extent the self-eclipse just described above.

(4) We deliberately restrict our model to a single cyclotron region near the main (upper) pole. The X-ray emission of AMHer is known to switch between (at least, see below) two different patterns. In the normal mode, hard and soft X-rays are emitted in phase from the upper pole. During the reversed mode, the soft X-ray emission originates predominantly at the lower pole, while the hard X-rays are still emitted from the upper pole (Heise et al. 1985). Despite this apparently drastic change in the accretion pattern, the optical light curve of AMHer does not change between normal and reversed mode (Mazeh et al. 1986). These observations strongly suggest that only the high mass flow densities may switch back and forth between the poles, while the upper pole is fed during both states by low mass flow densities - associated with the emission of hard X-ray and cyclotron emission. This interpretation supports our one-pole cyclotron emission model.

An ultimate puzzle, though, remains: while our optical data from 1998, August 20/22 presented here are completely typical of AMHer in either the normal mode or the reversed mode, they were obtained only about a week after our BeppoSAX observations (1998, August 12) which showed the system in an hitherto unknown state with significant hard X-ray emission during $\mbox{$\phi_{\rm orb}$ }\simeq0.5$ (Matt et al. 2000). RXTE and EUVE observations obtained on 1998, August 4 confirmed the atypical X-ray light curve (Christian 2000). We are left with the possibility that AMHer returned into one of the previously known - normal or reversed - modes by the time of our optical campaign. Considering that also the optical high state light curve of AMHer noticeably changed on a (to our knowledge) single occasion (Szkody 1978), it appears that AMHer occasionally drops into short-lived "atypical'' behaviour. A multiwavelength campaign covering one of these "atypical'' states could reveal whether they are related to the switching between the normal and the reversed accretion mode.

Acknowledgements

We thank Klaus Beuermann for many discussions on this topic and the referee Steve Howell for a number of helpful comments. This research was supported by the DLR under grant 50OR99036.