Properties of the close binary and circumbinary torus of the Red Rectangle

New diffraction-limited speckle images of the Red Rectangle in the wavelength range 2.1-3.3 mum with angular resolutions of 44-68 mas (Tuthill et al. 2002) and previous speckle images at 0.7-2.2 mum (Osterbart et al. 1997; Men'shchikov et al. 1998) revealed well-resolved bright bipolar outflow lobes and long X-shaped spikes originating deep inside the outflow cavities. This set of high-resolution images stimulated us to reanalyze all infrared observations of the Red Rectangle using our two-dimensional radiative transfer code. The high-resolution images imply a geometrically and optically thick torus-like density distribution with bipolar conical cavities and are inconsistent with the flat disk geometry frequently used to visualize bipolar nebulae. The new detailed modeling, together with estimates of the interstellar extinction in the direction of the Red Rectangle enabled us to more accurately determine one of the key parameters, the distance D approximate to 710 pc with model uncertainties of 70 pc, which is twice as far as the commonly used estimate of 330 pc. The central binary is surrounded by a compact, massive (M approximate to 1.2 M-.), very dense dusty torus with hydrogen densities reaching n(H) approximate to2.5 x 10(12) cm(-3) (dust-to-gas mass ratio rho(d)/rho approximate to 0.01). The model implies that most of the dust mass in the dense torus is in very large particles and, on scales of more than an arcsecond, the polar outflow regions are denser than the surrounding medium. The bright component of the spectroscopic binary HD44179 is a post-AGB star with mass M-star approximate to 0.57 M-star, luminosity L-lozenge approximate to 6000 L-., and effective temperature T 7750 K. Based on the orbital elements of the binary, we identify its invisible component with a helium white dwarf with M-WD approximate to 0.35 M-., L-WD similar to 100 L-., and T-WD similar to 6 x 10(4) K. The hot white dwarf ionizes the low-density bipolar outflow cavities inside the dense torus, producing a small HII region observed at radio wavelengths. We propose an evolutionary scenario for the formation of the Red Rectangle nebula, in which the binary initially had 2.3 and 1.9 M-. components at a separation of similar to130 R-.. The nebula was formed in the ejection of a common envelope after Roche lobe overflow by the present post-AGB star.