Future Work

Future Work

The Doppler tomogram of KU Cygni, presented in the previous section, revealed the presence of an symmetric accretion disk, as well as the location of the stream-disk impact region. The tomogram utilized a limited, but reasonably adequate, number of spectroscopic observations of finite spectral resolution. The spectra of KU Cyg were not initially obtained for tomographic analysis, but rather for use in spectroscopic orbital analysis. Therefore, equally-spaced phase sampling of the system was not important at the time. The majority of the spectra obtained by Olson et al. (1995) were obtained near primary eclipse, which eventually, were excluded in the creation of the Doppler maps. For some orbital phase intervals, only one spectrum of KU Cyg was obtained (e.g., phase intervals 0.30-0.39 and 0.60-0.69). Future spectroscopic observations of KU Cyg should be equally-spaced in orbital phase and obtained for all phases outside of disk eclipse. Disk eclipse observations should also be obtained to adequately measure the extent of the disk. Equally-spaced observations will reduce the streaks apparent in the Doppler tomograms of KU Cygni. The chosen dimensions and velocity extent of the tomograms, presented in this thesis, depended on the wavelength dispersion of the spectroscopic data. The dimensions of the image are constrained by the Fourier-filtering techniques; on the other hand, the velocity extent of the map depends on the wavelength (hence, velocity) dispersion of the data. To avoid interpolation between data points, the velocity extent of the Doppler map complements the velocity dispersion of the data points for the chosen image dimensions. In order to create higher-resolution Doppler tomograms, spectra with better wavelength resolution are required. With higher-resolution data, the back-projection technique can resolve smaller velocity bins in the tomograms, which will not be undersampled for larger dimensions or oversampled for smaller dimensions.

Presently, KU Cygni is only the second long-period Algol-type binary to be analyzed by Doppler tomography. Comparison of this Doppler tomogram to others for long-period systems would be useful in understanding any possible stream-disk interaction and accretion-disk structures. For example, RZ Ophi ($P=262$d) and DN Ori ($P=12.97$d) are expected to contain stable, Keplerian accretion disks. Determination of the accretion-disk radius from eclipse timings should be compared to the possible emission regions in their Doppler tomograms. The relative intensity of any enhanced region, possibly resulting from the stream-disk impact region, can be used to constrain the stream velocity as it impacts the edge of the disk.

Different methods of inversion, other than back projection, can be used to construct Doppler tomograms from spectral information. Marsh & Horne (1988) introduced the application of Doppler tomography to map emitting regions in binary systems. They applied maximum entropy methods (MEM) to construct the Doppler images from the trailed spectrogram information. In this non-linear inversion technique, a template Doppler map is created and projected along various angles to create spectral profiles. These calculated profiles are compared to the observed spectra by using $\chi^2$ satistics to estimate the ``goodness'' of fit (Marsh & Horne 1988). With MEM, spectroscopic observations are not required to be equally spaced in orbital phase because the method attempts to find the most uniform Doppler image that best recreates the observed spectral profiles. Unlike the linear-inversion method of back projection, MEM utilizes complex, iterative algorithms that require large amounts of computing time. Most of the Doppler tomograms created for Algol-type systems have incorporated the back-projection techniques and not MEM. In any case, a Doppler map of KU Cygni, created with the MEM technique, could be constructed to test different velocity field assumptions, other than Keplerian ones.

Hydrodynamic modeling of the mass-transfer process and creation of an accretion disk in Algol-type binaries can be used to compare theoretical accretion structures to observed structures imaged in Doppler tomograms. Because the Doppler tomogram cannot be transformed directly to a spatial map without knowledge of the velocity field, hydrodynamical models, which are based in Cartesian space, can be projected into velocity space and compared to Doppler tomograms. Hydrodynamic simulations determine the conditions of the gas throughout the entire binary system, as a function of time and position. Many different parameters, such as temperature, density, velocity, cooling rates, mass-transfer rate, and numerous other conditions, are calculated simultaneously for the stream as it exits at the L1 point (Blondin, Richards & Malinowski 1995). Interaction of the stream with the gainer star and any accretion structures are of interest here. The spatial origin of enhanced emission can be located within the system and then compared to velocity images of the tomograms. Recently, these simulations in H$\alpha$ have been accomplished for $\beta$ Per (or Algol) by Blondin et al. (1995) and Richards & Ratliff (1998) and for TT Hya by Richards & Ratliff (1998). $\beta$ Per has a short-period ($P=2.87$d) and it displays evidence of transient accretion structures. Here, the mass-transfer stream impacts the surface of the primary star. Richards and Ratliff (1988) assumed that the mass-transfer stream obliquely impacts the primary star in TT Hya, as determined from their assumed values of r=0.092 and q=0.269. Van Hamme & Wilson (1993) calculated the parameters r=0.088 and q=0.226 for TT Hya that place this binary below the $\omega_{min}$ curve in Fig. 4.4; therefore, the mass-transfer stream loops around the primary star to form a stable accretion disk. Analysis of these two systems reveal structures, which coincide with the structures apparent in their Doppler tomograms. The best simulations of the mass-transfer process would be three-dimensional hydrodynamic models, which would require large amounts of computing time. With Doppler tomography, only two-dimensional images can be re-constructed from spectral information because of the observational configuration of the system, which is nearly ``edge-on''.

For many different types of eclipsing binary systems, Doppler tomography introduces another avenue of research that can probe the structure of accretion disks, the mass-transfer stream, and chromospheric activity. Creation of Doppler tomograms, using other emission-line features from different spectral regions, could map different emitting regions of differing temperatures. Comparison of these regions can reveal temperature differences surrounding the stellar components. Although first applied astronomically to cataclysmic variable systems, Doppler tomography has revealed and reinforced observational evidence for accretion disks in Algol-type binaries.