Algol-Type Binary Systems

Algol-Type Binary Systems

Algol-type binaries represent a unique class of semi-detached systems that contain a main-sequence star and a less massive, Roche-lobe-filling subgiant star. Most Algol binaries are characterized by their early A or B spectral type main-sequence primary star and late G or K spectral type subgiant. (Note that many stars, classified as Algol-like from their light curves alone, are not true Algols, if the above semi-detached configuration is used). According to stellar evolutionary theories, the stellar mass dictates the rate of stellar evolution from stellar birth to stellar death. The more massive stars fuse their core hydrogen more quickly, because of a higher core temperature; therefore, the evolution of these massive stars occurs on a shorter timescale. On the other hand, less massive stars ``burn'' hydrogen at a slower rate, allowing more time to pass before their fuel is depleted. In the case of the prototype binary, Algol, the less massive component is the more evolved star. How can the less massive star be the more evolved component when theories suggest that the more massive star should have evolved first? The Algol Paradox remained a mystery until astronomers realized that individual stellar evolution can affect the evolution of the other component in binaries with small orbital separation.

J. A. Crawford (1955) explained the apparent Algol Paradox in terms of evolutionary dependency on the Roche model, as applied to stellar surfaces. In Algol's past history, the subgiant component had been the more massive star; it did evolve off the main sequence before its less massive, main-sequence partner. The outer envelope of this more massive star expanded and filled its Roche lobe. Gaseous matter streamed through the inner Lagrangian (L1) point and moved towards the less massive star. This mechanism of mass transfer is termed Roche lobe overflow. Mirek Plavec (1983) coined the term loser and gainer to describe the mass-losing and mass-gaining components, respectively, in interacting binary systems. As the loser (subgiant) continued to expand as it evolved, the mass transfer process reduced its mass. The Roche lobe of the loser shrinks in size to adjust for the mass change. This size adjustment of the Roche lobe perpetuates mass transfer through the L1 point. A stage of rapid mass transfer occurs in the early history of the Algol-type star, which soon reverses the mass ratio of the system. Thus, the loser (subgiant) quickly becomes the less massive component. Mass transfer continues through the L1 point towards the gainer (main-sequence star), but at a much slower rate. We observe most Algols in this slow stage of mass transfer. Support for this hypothesis came from many spectroscopic observations that pointed towards the presence of gaseous material within many binaries, which distorted their radial velocity curves. For example, A. B. Wyse (1934) was the first person to report observations of spectral features that revealed the existence of this material within a close binary systems. Wyse detected Balmer emission lines in the spectra of RW Tau, an Algol-type binary, during the total eclipse of the primary (gainer) star by the secondary (loser) star. The observed double-lobed emission features of H$\beta$, H$\gamma$, and H$\delta$ revealed radial velocity displacements of 350 km/sec longward and shortward of the central absorption feature. A. H. Joy (1942) confirmed the presence of these emission lines, and noted their variability. Joy observed that during second contact, when the secondary star starts to totally eclipse the primary star, only the longward emission feature is seen. At third contact, when the secondary star just ends the total eclipse, only the shortward emission line is observed. (First and fourth contact times refer to beginning and ending times of total eclipse, respectively). No emission lines are seen at mid-eclipse. Joy (1942) explained the existence of the emission lines as having ``originate(d) in an extended gaseous region surrounding the equatorial region of the primary B9 star''. As the secondary star eclipses the primary, it also eclipses the gaseous ring surrounding the primary star. If the rotation of the disk moves in same sense as the orbital revolution of the components, then the approaching edge of the ring will be eclipsed first. Therefore, the shortward emission feature will not be observed at the start of totality. Similarly, at the end of totality, the receding edge of the ring is eclipsed by the secondary star. Hence, the longward emission feature will not be observed. In the case of RW Tau, the secondary star completely eclipses the gaseous ring during mid-eclipse.

According to Kuiper (1941), mass transfer can occur through the L1 point between the two stars in a binary system, if the Roche geometry is assumed. The mass that spirals towards the primary star contains a large amount of angular momentum. If the stream should eventually settle on the surface of the primary star, the excess energy must be dissipated. An accretion annulus or disk forms around the primary star, so that angular momentum may be shed through numerous processes. Current theories suggest that excess angular momentum may be shed through viscous forces within the disk, transporting angular momentum outward (Shakura & Sunyaez 1973). Eventually, matter will travel from the outer edge of the disk to the inner edge of the disk and deposit itself onto the surface of the gainer. Wyse and Joy reported the first crucial evidence for the existence of a disk around a binary system component. Otto Struve (1949, 1948) first suggested that gaseous rings formed around primary star from accreted gas of the secondary star. Without the geometry of an eclipsing system, the nature of the accretion disk could not be well studied.

Radial velocity curves provide pertinent information on the velocity of the gases around the primary star. The emission and absorption line profiles reveal a great deal about the nature of the gaseous disk. Some properties that can be obtained from spectral line profiles are the opacity of the gas, the scale height of the disk, the temperature of the gas, and the velocity field of the disk. In some systems, the mass-transfer stream impacts the outer edge of the disk, which can be observed as a ``hot spot'' in the spectra of the system. For an ``edge-on'' system, the observer collects information on the disk from different orientations within the orbital plane (that is, different orbital phases), as the system rotates around the center of mass. Thus, eclipsing binary systems of the Algol-type offer a unique perspective that can be utilized to study gas dynamics, mass-transfer mechanics, and the structure of line-forming regions.

In general, spectroscopic observations record wavelength and intensity information of the emitting and absorbing regions of the stellar photospheres, as well as contributions from any intervening gaseous regions in the line of sight to the stellar components. If adequate phase coverage is achieved spectroscopically, the entire set of one-dimensional spectra can be transformed into a two-dimensional velocity image, or Doppler tomogram, by using the mathematical technique of back projection (Marsh & Horne 1988). The medical field utilizes back-projection techniques to create CAT and MRI scans.

This thesis analyzes spectroscopic observations of the long-period Algol-type binary KU Cygni, and utilizes the H$\alpha$ emission lines to construct a velocity map of the emitting regions within the accretion disk. Since KU Cygni is a long-period Algol binary, the orbital separation between the components is large enough to contain a permanent accretion disk. Previous spectroscopic and photometric studies, summarized in Chapter II, revealed the existence of this accretion disk. Chapter III presents spectroscopic observations of KU Cygni obtained during the 1989-1991 and 1993 observing seasons. A preliminary analysis of the spectral features as a function of orbital phase is presented.

The following chapters of this thesis will analyze KU Cygni in a different manner from the previous studies presented in Chapter II. Chapter IV details the calculations required in the restricted three-body problem, construction of the Roche-lobe surfaces for KU Cygni, and mass-transfer stream calculations. The intensity distribution of disk emission regions will be mapped in velocity space, as a diagnostic tool, to analyze the interaction, if any, between the outer edge of the disk and the gas stream. The Doppler tomogram does not display a spatial image of the emitting regions of the gas. On the other hand, the tomogram displays the intensity of emitting regions of a certain velocity within the disk. Chapter V introduces the mathematical techniques used in the Fourier-filtered back-projection technique, which is used to create the Doppler tomogram of KU Cygni. The existence or non-existence of enhanced emission region can be probed by this Doppler mapping technique. Trajectory calculations of the mass-transfer stream, using restricted three-body calculations and Keplerian velocities, will be positioned on the Doppler tomogram to compare enhanced emission regions to theoretical calculations. In Chapter VI the Doppler tomogram of KU Cygni will be interpreted in order to understand the velocity position of the emitting regions, as well as nature of interactions between the mass-transfer stream and the outer edge of the disk.