--------------------------------------------------------------------- PREDNASAJUCI / LECTURER : Ivan L. Andronov Odessa National Maritime University NAZOV / TITLE : Space Laboratory to Study Accretion in Magnetic Cataclysmic Variables: The Case of Exotic Newly-Discovered Polar OTJ 071126+440405 ABSTRAKT / ABSTRACT : Self-consistent mathematical model of the exotic object OTJ 071126+440405= CSS 081231:071126+440405 is discussed. The system was discovered as a polar at the New year night 31.12.2008/01.01.2009 by D.Denisenko (VSNET Circ), and we have initiated an international campaign of photometric and polarimetric observations of this object (totally ~80 runs in Ukraine, Korea, Slovakia, Finland, USA). This work is a part of the "Inter-Longitude Astronomy" (ILA) project on monitoring of variable stars of different classes (Andronov et al., 2003). Results of this campaign will be published separately (Andronov et al., 2009). Here we present the geometrical and physical model of the system. In an addition to the usual assumption that cataclysmic variables contain a Roche-lobe filling red dwarf and an accreting white dwarf, we propose an interpretation of three types of the brightness minima, as the eclipses by the red dwarf, white dwarf and the accretion column itself (self-eclipse). In the low luminosity state, when the accretion rate is suggested to vanish, a "quiescence" is observed at the light curve, i.e. the optical flux comes from the illuminated secondary star and the non-accreting side of the white dwarf. When the accretion column becomes visible, the light curve exhibits a `hump" interrupted by the main eclipse by the red dwarf. In the "intermediate" luminosity state, the brightness increases at all phases, however, the main hump shifts to smaller phases and an additional minimum (self-eclipse) is observed. In this state, the emitting accreting region becomes larger, and is not significantly eclipsed by the white dwarf. The phase difference between the preliminary and main eclipses is smaller than in the high luminosity state, what is interpreted by the dependence of the position of the thread point, where magnetic field of the white dwarf captures the (initially ballistic) accretion stream. At the high state, the thread point approaches the cross-section of the ballistic stream with the magnetic axis, whereas at the intermediate state, the thread point may lie from 70% to 100% of the distance between the white dwarf and the inner Lagrangian point. As the ballistic trajectory nearly coincides with the magnetic field lines near the inner Lagrangian point, this argues for an "energetically optimal" orientation of the magnetic axis. As the system is of ~20 mag at minimum, no spectral observations were made to determine parameters of the red dwarf. From the statistical relationship, the mass of the red dwarf is estimated to be ~0.165 solar masses, for the white dwarf (from eclipse duration) - from 0.5 to 1.76 solar masses. As the system resembles ER UMa in some characteristics, the lower value may be assumed. The inclination of the system and other physical parameters are estimated. The object is an excellent laboratory to study multiple physical processes in the magnetic systems.