3 Description of the images

Figure 2: Multi wavelength observations of the central part of the $\eta$ Car nebula. The double ring structure is traced at all four wavelengths. The "+'' indicates the central source.

Figure 3: Temperature map as derived from the 7.9, 11.9, 12.9 and 20 $\mu$m observations (see text). The central point source, indicated by the "+'', has a derived temperature of 600 K.

The mid-IR image presented in Fig. 1 shows the familiar homunculus with an overall shape which is similar to that reported by previous authors (e.g. Morse et al. 1998; Smith et al. 1998; Mor99; PL00). At the core of the homunculus we find a central point-like source which dominates the emission from the nebula at short wavelengths. This point source very likely coincides with the central star or binary. Mor99 show that the 2-8 $\mu$m wavelength range of the ISO spectrum of $\eta$ Car is well represented by a power law, with a steeply rising spectrum towards longer wavelengths. It is therefore reasonable to assume that the central point source is responsible for the power law component. At 20 $\mu$m the central point source no longer dominates the emission, which shows that there is not a large amount of cold dust at this location. If the continuum in the 2-8 $\mu$m region is due to thermal emission from dust, the power law nature of the spectrum points to a flat temperature gradient in the hottest dust (nearest to the central object), which is typically seen in optically thick disks. We stress that imaging at the sub-arcsecond scale is required to determine the true geometry of the innermost regions of the $\eta$ Car nebula. Optical speckle imaging polarimetry supports the presence of a disk (Falcke et al. 1996).

The N band and Q band images give a detailed view of the innermost few arcsec of the homunculus, where in the optical images the waist is situated. Previous studies revealed the presence of emission blobs of different intensity roughly 1.5 arcsec northeast and southwest of the central point source. These emission blobs have been interpreted as evidence for an equatorial torus (Pol99; Mor99). This torus has been held responsible for the strongly bipolar geometry of the homunculus (Mor99). From the ISO spectrum a temperature of the matter in the torus of 110 to 130 K was derived, and a dust mass of about 0.15 $M_{\odot}$.

Our new images show for the first time the detailed geometry of the material emitting at these wavelengths down to very low brightness levels. The images show that the mid-IR emission is not due to limb-brightening of a torodial dust distribution seen edge-on (in Mor99 assumed to be co-spatial with the distribution of the massive cold material). Rather, the blobs reported by previous studies turn out to be two arcs of emission. A careful inspection of the 11.9 $\mu$m image shows that the arc southwest of the central star is a closed ring. We will refer to these two structures as "the two rings'' in what follows, because both arcs have the same size and inclination. The southwest ring passes through the central point source, so this point source cannot be at the centre of the rings. The northeast structure has an irregular surface intensity with a strong intensity maximum in the north. The axis connecting both rings is not aligned with the projection of the long axis of the homunculus on the sky (see below). We note that one of the two rings can be recognised in the 20 $\mu$m images published by Pol99; Mor99 and PL00. However, the factor of two better spatial resolution at 10 $\mu$m compared to 20 $\mu$m together with the high sensitivity allows for a much clearer view of these structures.

The temperature map shows that the two rings have roughly similar temperatures of 280-380 K. These temperatures agree well with the values derived by previous studies (Smith et al. 1998; Pol99; PL00). If we assume that there is no large difference in the foreground extinction towards both rings, this shows that the dust in the two rings is heated similarly. The question arises what the location of the 110-130 K massive dust component, inferred from the ISO observations is. Since this spectral component peaks at 30 $\mu$m and no flux jumps due to SWS aperture transitions are seen, it must fit within the SWS band 3A beam. The low temperature implies a different physical component from that in the lobes or rings, such as a torus, as previously suggested by Mor99. Davidson & Smith (2000) have shown that this cold component should have a minumum projected area of 37 arcsec² in order to reproduce the required flux levels. An inclined torus of that size (which would not show limb-brightening) fits easily within the SWS beam.

We have constructed a geometrical model for the mid-IR emission of the equatorial regions (sketched in Fig. 4). The model assumes the presence of two circular rings. We varied the position angle on the sky as well as the inclination angle until a good match with the observations was obtained. The result is shown in Fig. 4. We find that the rings have a diameter of 1.8 arcsec and a de-projected distance between the two rings of 3 arcsec. The structure is rotated by 117 or 297 degrees in the plane of the sky with respect to north-south (depending on which of the two rings is in front). The inclination between the major axis of the homunculus and of the axis connecting the centres of the two rings is either 37 or 58 degrees, using an inclination of the axis of the homunculus to the plane of the sky of 40 degrees. The error on these angles is about 10 to 15 degrees, mostly determined by the wide range of values given in the literature for the inclination of the homunculus (e.g. Hillier & Allen 1992). Note that the region in our model where the projection of both rings overlap on the sky coincides with an intensity maximum in the observed images, again supporting our two ring model.