Modeling the Remarkable Multiwavelength Light Curves of EF Eridanus: The Detection of Its Irradiated Brown Dwarf-like Secondary Star

We present optical and infrared phase-resolved photometry of the magnetic cataclysmic variable EF Eri during a low state. The BVRIJ light curves are very similar in appearance; all exhibit a dip of a few tenths of a magnitude near binary orbital phase 0.5. In contrast, however, the H- and K-band light curves show very large modulations, with maxima at orbital phase 0.5. We show that these modulations are not due to ellipsoidal variations but to the reflection/heating of one face of the very cool secondary star by the white dwarf primary. We find that the dips in the BVRIJ light curves are best modeled by a single hot spot on the white dwarf primary that is self-eclipsed once per orbit. By using an orbital inclination of i=45°, we find the colatitude of the hot spot is 35°+/-10°, its temperature is 12,000 K, and its radius is 29°+/-15°. To explain the larger minimum seen in the J-band light curve requires that ~20% of the observed flux be supplied by an additional source of luminosity, which we believe is residual cyclotron emission. To model the observed amplitudes in the H- and K-band light curves requires a very cool irradiated brown dwarf-like secondary star with temperature T_eff~900 K (for i=45°). The irradiated side of this secondary star, however, has T_eff<~1600 K. We present a new K-band spectrum of EF Eri that is consistent with this result. To properly model the light curve of EF Eri will require the incorporation of brown dwarf atmospheres into the Wilson-Divinney program, as well as better estimates for the irradiated limb-darkening coefficients and albedos of such objects. Finally, we present a three-dimensional hydrodynamic model for EF Eri that demonstrates that the accretion stream from the secondary star is almost fully controlled by the magnetic field of the white dwarf primary. This model predicts that the narrow dips observed in the high-state infrared light curves of EF Eri, which nominally should lead the binary in orbital phase, can occur very close to phase 0.0, as required by our light-curve modeling.