4 Doppler tomography

The orbital variation of the emission lines profiles detected by us indicates a non-uniform structure of the accretion disk. The distribution of the disk's emission can be explored by computing a Doppler map, using the method of Doppler tomography. Doppler tomography is an indirect imaging technique which can be used to determine the velocity-space distribution of the emission in close binary systems. A tomogram is constructed from the line profiles obtained at a variety of orbital phases. In other words, the Doppler map accumulates information about all profiles of the emission line in different phases of an orbital period. An accretion disk producing usually double-peaked emission lines should appear on the tomogram as a ring with an inner radius of $V_{\rm in} \sim 600{-}800$ kms^-1, plus additional emission that can be seen extending outward from the ring to a velocity of over $V_{\rm out} \sim 1200$ kms^-1 or more corresponding to the rest of the disk. This is because the outer edge of the disk becomes the inner edge in velocity coordinates, while the inner disk is represented by the outermost parts of the image. But we can also obtain single-peaked lines from the accretion disk. This can happen for many reasons, for example insufficient spectral resolution, a small inclination angle of the binary system, some line-broadening mechanisms. In this case the distribution of the emission on tomograms will not be ring-shaped but circular. Full technical details of the method are given by Marsh & Horne (1988) and Marsh (2001). Examples of the application of Doppler tomography to real data are given by Marsh (2001).

The Maximum Entropy Doppler maps of the H$\beta$, H$\gamma$, HeI $\lambda$4471 and HeII $\lambda$4686 emission were computed using the code developed by Spruit (1998). The resulting tomograms are displayed as a gray-scale image in Figs. 9 and 10. These figures also show trailed spectra in phase space and their corresponding reconstructed counterparts. A help in interpreting Doppler maps are additional inserted plots which mark the positions of the white dwarf, the center of mass of the binary and the Roche lobe of the secondary star. These markers are necessary to us only for facilitation of the interpretation of the tomograms, therefore the calculations of their positions can be done using our preliminary system parameters obtained in Sect. 3.6. Here we have used q=0.22, $M_{1}=0.46~M_{\odot}$ and $i=65^{\circ}$.

Figure 9: Doppler tomograms for the H$\beta$ (left) and H$\gamma$(right) emission lines of FS Aur. These maps display a roughly symmetric and very nonuniform distribution of the emission centered near to the white dwarf. In addition to the symmetrically distributed emission, at least two additional emission sources can be seen. The first, brighter enhanced emission component is centered roughly on ( $V_x \approx -100$ kms-1, $V_y \approx -260$ kms-1) (the corresponding phase of the intersection of the line-of-sight with this bright region is about 0.6). The second source is located opposite the first one and occupies an extensive area at phases about 0.85-1.15. In addition, the tomogram of H$\gamma$ shows an emission ring with a radius of about 225 kms-1, which is centered on ( $V_x \approx 0$ kms-1, $V_y \approx -20$ kms-1). In the center of this ring there is a compact bright spot.

The Balmer Doppler maps display a roughly symmetric and very nonuniform distribution of the emission centered near the white dwarf. So, on the H$\beta$ tomogram, in addition to the symmetrically distributed emission, at least two additional emission sources can be seen. The first, brighter enhanced emission component is centered roughly on ( $V_x \approx -100$ kms^-1, $V_y \approx -260$ kms^-1). The second occupies an area extending from azimuths about $300^{\circ}$ to $60^{\circ}$ (the corresponding phase of the intersection of the line-of-sight with this bright region is about 0.85-1.15). The first spot is well visible also on the Doppler maps of H$\gamma$ and HeI $\lambda$4471: in the case of HeI it is a primary radiating source. In addition, the tomograms of H$\gamma$ and HeII $\lambda$4686 show an emission ring with radius of about 225 kms^-1, which is centered on ( $V_x \approx 0$ kms^-1, $V_y \approx -20$ kms^-1). In the center of this ring there is a compact spot, which especially in HeII is a bright radiating source.

The interpretation of the spot structure detected in the accretion disk is ambiguous. Neither the first nor the second bright region can contribute to the emission from the bright spot on the outer edge of the accretion disk, as both areas of additional emission lie far from the region of interaction between the stream and the disk's particles. The brighter spot can be interpreted as due to an enhanced emission region located opposite to the bright spot expected by the standard model. Earlier Mennickent (1994) has shown that the bright spot region seems "to migrate" towards the back of the disk in systems with low mass ratios. This "reversed bright spot" phenomenon can be explained by a gas stream which passes above the disk and hits its back, or alternatively, by the disk thickening in resonating locations. We will analyze the nature of the detected structure of the accretion disk in the following section.

Figure 10: Doppler tomograms for the HeI $\lambda$4471 (left) and HeII $\lambda$4686 (right) emission lines of FS Aur. The main emission source in HeI $\lambda$4471 is the first bright spot visible in H$\beta$(Fig. 9). The tomogram of HeII shows an emission ring with a radius of about 225 kms-1, which is centered at ( $V_x \approx 0$ kms-1, $V_y \approx -20$ kms-1). In the center of this ring there is a compact bright spot.