Accretion funnels in AM herculis systems - I. Model characteristics

We present calculations of the thermal structure of accretion funnels heate d by hard X-ray emission from the accretion shock, soft X-ray reprocessed r adiation from the white dwarf surface and magnetic heating in the matter-fi eld interaction region close to the orbital plane. The calculations determi ne self-consistently the thermal structure of the funnel, allowing for radi ative transfer, electron scattering and the trapping of radiation within th e funnel, and represent a substantial improvement on previous purely kinema tical models. We show that, while models that allow only for X-ray heating can explain the observed intensities of the Balmer lines, they cannot, at t he same time, explain the intensities of the He I and He II lines in the op tical spectra. These lines appear to be formed mainly in the magnetically h eated transition region near the orbital plane, with this region playing a role similar to the hotspot in accretion discs. We show that, with the incl usion of this region, models can be constructed that are in close agreement with the optical line and continuum emission observed in AM Herculis syste ms: that is, they exhibit a flat or inverted Balmer decrement, He I lines, a strong He II lambda 4686 line and complex emission-line profiles which va ry dramatically in velocity and shape over the orbital period of the white dwarf. We also show that the continuum emission from the accretion funnel p rovides an important source of unpolarized background radiation, which redu ces the degree of polarization of the cyclotron radiation from the accretio n shocks, and produces the polarization standstills that are a well-known c haracteristic of these systems.