(Adapted from Richards, M. 2000, The Journal to Algol, Mercury, Vol. 29, No. 4, p. 34.)
Algol-type binaries contain a faint orange-red F - K giant or subgiant star, called the secondary, and a luminous blue B - A main sequence companion, called the primary. When you view Algol binaries through a telescope, all you can see is a single dot of light. However, these systems actually contain pairs of stars and some, like Algol, contain a third star orbiting the inner pair. Since we cannot separate the pair of stars even with the largest telescopes, we say that the Algols are unresolved binaries. There is hope that the twin Keck Telescopes on Mauna Kea in Hawaii or NASA's upcoming Space Interferometry Mission might be able to produce a picture of an Algol binary showing two distinct stars, but we are still a long way from obtaining direct pictures of these binaries that are as beautiful as those of nebulae or galaxies. Instead, we are obliged to use theoretical computer models, and other techniques like tomography, to produce images of the gas flows in these binaries.
Scale model of an Algol-type binary system showing the predicted path of the gas stream, the range of spectral types, the luminosity classes, and the lines of sight for different orbital phases (angles divided by 360 degrees). Primary eclipse occurs at phase 0.0 and secondary eclipse occurs at phase 0.5. Illustration courtesy of M. Richards.
The Algols have been studied actively for more than two centuries since 1783, when the Englishman John Goodricke explained that the light variations in beta Persei were probably due to one star eclipsing another star. For thousands of years prior to that, ancient astronomers had noticed the dramatic decrease in light, by 1.2 magnitudes within a mere five hours, that gave rise to the name of this famous binary: Al-Ghul, the eye of Medusa, the Demon Star. The eclipses are dramatic because the primary contributes about ninety percent to the light of the binary in the visible band, and most of this light is blocked during the eclipse of the primary. The eclipse of the secondary produces a very small diminution in the light from the binary. Outside of the eclipses, the spectrum of an Algol binary shows absorption lines from the primary, while the spectrum of the fainter secondary star can be detected only during primary eclipse.
The light curves of Algol (beta Per) at wavelengths from the ultraviolet (1920 Angs.) to the infrared (12000 Angs.). Illustration courtesy of M. Richards.
The triple system of beta Persei is only 29 parsecs, or about 100 light years, from the Sun. Algol contains the brightest and closest eclipsing binary in our sky, and this binary is the prototype of the class of Algol-type binaries. Its close proximity to the Sun has made it one of the most studied objects, in all wavelength regions from gamma rays to radio. However, the same is not true of other members of the class. Only a few hundred Algols are known; most of these are visible from the northern hemisphere, their distances are uncertain, and only a small fraction of them are near the Sun. Quite often, the spectral type of the faint, late-type, secondary star is not well-known.
Most Algols undergo eclipses because of the chance alignment of their orbital planes with our line of sight. In fact, it is the detection of eclipses that leads to the discovery of these binaries. However, we have already identified six new Algol binaries, including CX Draconis, which do not undergo eclipses but have spectra that resemble the other Algols. These non-eclipsing Algols were originally classified as Be stars, or single B stars with hydrogen emission lines in their spectra. Other members of the class of Be stars may soon be reclassified as non-eclipsing Algols.
The Algols are also classified as spectroscopic binaries, since we can discern the presence of two stars from the cyclic Doppler shifts, in the wavelengths of the spectral lines. These wavelength shifts occur as each star moves in its orbit about the center of mass of the binary. Under these circumstances, as one star moves toward us, the other star will be moving away. Moreover, when one star is approaching us, its spectral lines are shifted away from their rest wavelengths toward shorter wavelengths (or blueshifted); and the lines will be shifted to longer wavelengths (or redshifted) when the star is moving away from us. In the majority of these binaries, the stars are also tidally locked to each other, much as the Moon in the Earth-Moon system, so that the sides of the stars facing each other do not change.
From a theoretical point of view, Algol-type binaries are close, interacting binaries. These are binary star systems in which the two stars are so close that each star can influence the evolution of its companion. This was first discovered in the case of beta Persei, after astronomers realized that the more massive primary star in the binary was a main sequence star, and hence was less evolved than its less massive companion. This situation was termed the Algol Paradox because it contradicted what is known about stellar evolution; namely, that a more massive star should evolve faster than a less massive star. The paradox was resolved when astronomers realized that the secondary star in beta Persei was originally the more massive star of the pair, but had previously transferred a lot of material to its companion.
An artist's concept of a close Algol-type binary. The relative size of the Sun is illustrated by the small circle to the upper right of the figure. Illustration courtesy of M. Richards.
In Algol-type binaries, one of the stars has evolved and expanded to fill a droplet-shaped potential surface, called the Roche lobe, within which material is gravitationally bound to the star (see Figure 1). The Roche surface is, therefore, the surface along which the gravitational potential is common between the stars. Once a star fills its Roche lobe, gas moves into the Roche lobe of the companion star and is pulled in toward that star. This process of mass transfer is referred to as Roche lobe overflow. Binaries in this stage of mass transfer are called semi-detached binaries, because only one of the stars is actually in contact with its Roche surface. The subsequent flow of gas between the stars is called the gas stream or mass transfer stream. During Roche lobe overflow, mass transfer feeds gas particles in the stream from the inner Lagrangian point (L1), where the two Roche lobes touch. This gas stream free-falls onto the companion star, much like rocks dropped from a building. However, the path of the gas stream becomes curved because it feels the orbital motion of the binary (or the Coriolis force) as it falls.
Over the years, astronomers have become very interested in the products of Roche lobe overflow because they can help us to understand how mass transfer works in a binary system. These products are collectively termed circumstellar material and consist of any gas within the binary that is not physically part of a star, namely, the gas stream and any gas that surrounds the mass gaining star. It seems that the type of circumstellar gas produced by Roche lobe overflow depends on the size of the mass gaining star compared to the distance between the stars (or the binary separation). In compact binaries, the mass gaining star is a white dwarf, neutron star or black hole, that is generally faint and small relative to the size of the entire binary system. In such compact systems, the gas stream has enough room to form a fairly stable accretion disk around the central star. Since the disk is brighter than the stars, its spectrum typically displays distinctive double-peaked emission lines with blueshifted and redshifted components. Here again, the blueshifted emission arises from the part of the disk that is moving toward us, while the redshifted component is from the part of the disk that is moving away from us. Such disks are found in the dwarf novae, low mass x-ray binaries, and some novae-like cataclysmic variables.
The Algol-type binaries present an even more interesting situation because they are in the stage of Roche-lobe overflow during which mass transfer occurs very slowly. The evolutionary stages of close binaries in Table 1 shows that the Algols are also in the early stages of mass transfer compared to the compact binaries. So the Algols provide us with an opportunity to study the mass transfer process (e.g., the gas stream) under calm conditions, instead of the final products of mass transfer (e.g., the accretion disk) as in the compact binaries.
The Algols can be divided into two main groups which seem to display different types of circumstellar gas depending on the orbital period of the binary. The long-period Algols have orbital periods greater than about 6 days. In these binaries, the mass gaining star is small relative to the distance between the stars, so there is enough room for the gas stream to form an accretion disk around the mass gainer. The spectrum of a long-period Algol shows strong double-peaked emission lines that look similar to those seen in the spectra of compact binaries. Examples of long-period Algols include TT Hydrae, AU Monocerotis, and RZ Ophiuchi.
The situation is quite different in the shorter period Algol binaries because the mass gainer is large relative to the binary separation. Examples include beta Persei, RW Tauri, U Sagittae, and delta Librae. In the short-period Algols, the gas stream does not have enough room to form a classical accretion disk, so it strikes the stellar surface directly. The circumstellar material in this latter group of Algols is usually much fainter than the stars, which makes it difficult to detect. In fact, the spectra of some short-period Algols contain either weak or no emission lines at all, depending on orbital period.
In order to extract the contribution of the circumstellar material to the light from one of these systems, we have to remove the stellar contribution from the observed spectrum. When this extraction procedure is completed, we are left with a difference spectrum that shows evidence of double-peaked emission. Subsequent analysis of this difference spectrum suggests that the circumstellar material in the short-period Algols is in the form of a variable structure, called a transient accretion disk or an accretion annulus, that at least partially surrounds the mass gaining star.
The change in the appearance of Halpha, the strongest hydrogen line in the visible region, with orbital period, P (left panel): RZ Oph (P = 262 days), AU Mon (P = 11.1 days), TT Hya (P = 6.9 days), SW Cyg (P = 4.5 days), and U Sge (P = 3.4 days). Difference spectra for TT Hya, SW Cyg, and U Sge are also shown in the right panel. Images courtesy of M. Richards and G. Albright.
We can find evidence of different types of circumstellar material through intense examination and study of the observed spectra. However, there is always the temptation to produce a model of the gas distribution that is based on some favored or popular theory. I, myself, spent two years studying some difference spectra of beta Persei, but I could not convince myself that I had produced an unbiased model. So, I set out to find different ways to produce images from the observations that were reasonably free of my personal biases. This search led me to the technique of Doppler tomography, which is a version of tomography that was outlined in 1917 by a mathematician named Johann Radon. The technique was first used by radio astronomers, and is now used within the medical profession and by astronomers.
The technique of tomography is routinely used in the field of medicine to produce or reconstruct three-dimensional (or 3D) images of parts of the human body from two-dimensional (or 2D) pictures or ``slices.'' Examples include Computed Axial Tomography, or CAT scans; Positron Emission Tomography, or PET scans; Nuclear Magnetic Resonance, or NMR images; and traditional x-ray pictures. In these techniques, the patient is stationary while the instruments move about her.
In the simplest form of tomography, a 3D image is reconstructed by adding up the 2D slices. In astronomy, this same technique uses the one-dimensional information provided by the Doppler shifts of the emission lines in the spectrum to generate 2D velocity images of the circumstellar material in the orbital plane of an eclipsing binary. In this case, the ``slices'' are the emission-line spectra of the binary seen at different positions in the orbit of the binary from one eclipse to the next. Whereas the patient is stationary and the detector circles in medical tomography, in Doppler tomography, the detector is essentially fixed here on Earth while the stellar patient turns. Since the Doppler shifts give us information about the motions of the gas, we can easily convert these wavelength shifts into velocity shifts. The latter shifts are then used within the tomography program to produce an image of the circumstellar gas in dimensions of velocity, rather than the usual spatial/linear or Cartesian dimensions. This image can be converted to spatial dimensions only if we know exactly how the speed of the flow depends on its location in the binary.
The quality of a reconstructed image improves if we take more pictures during each orbital cycle. In medicine, it would be harmful to the patient if too many scans are taken, but in astronomy we have the opportunity to take as many pictures as we wish. Our main problem is that we cannot collect optical spectra while the Sun is up, so it can take as long as three weeks to obtain enough spectra around the orbit of a binary that has an orbital period of about three days. I have found that fairly good Doppler tomograms can be obtained from spectra collected at regular time intervals over a week.
The systematic collection of spectra required to produce a good tomogram could not have been accomplished without the availability of an observing facility, like the 0.9m Coude Feed Telescope at Kitt Peak National Observatory, which allocates multi-night observing shifts to observe stars. The observed hydrogen-line spectra were all converted to difference spectra before the Doppler tomograms were generated. Most of these tomograms were made from the Halpha line, which, at a wavelength of 6563 Angs., is the strongest hydrogen line in the visible region. The tomograms were scaled individually to emphasize the strongest features in each system. The rest of the work required the use of fast computers because tomography is a CPU-intensive routine in which hundreds of spectra often were processed to produce each image.
Some Doppler images of the circumstellar hydrogen gas in Algol-type binaries are shown here. These images are in the velocity coordinates V_x and V_y which correspond to the spatial coordinates x and y. We can draw reference lines to help us make the mental conversion to spatial dimensions by using the spatial models shown on the left side of the Figure. First, the stars are shown as circles within their tear-drop-shaped Roche lobes; they keep their shapes in the Doppler map. We can also draw the gravitational free-fall path of the gas stream because we know how gravity behaves in both spatial and velocity dimensions; this is the solid trajectory that is marked by small circles. These small circles are marked at intervals of a tenth of the distance between the L_1 point and the place where the gas stream path comes closest to the center of the mass gainer. In the spatial map of each binary, the place where the gas stream (shown in red) strikes the stellar surface (shown in blue) is where the two contours cross. The location of this impact site is shown by the asterisk in the Doppler maps. The center of mass of the binary is shown by the plus sign in both spatial and velocity pictures. Finally, if a stable accretion disk has formed in the binary, it should be located in the spatial map between the surface of the blue star and the Roche surface of that star. This Roche surface is marked by the dashed blue contour in the spatial map. In the Doppler map, this accretion disk would be found between the large solid and dashed circles which are marked in red, in keeping with the corresponding spatial map. These large red circles in the Doppler maps represent the speeds at the surface of the star (marked by solid outer circle) and at the edge of the Roche lobe of the mass gainer (marked by dashed inner circle). Any stable accretion disk should spin faster on the inside than on the outside. This is what we call Keplerian motion, and is similar to how the planets move in our Solar System; for example, the innermost planet (Mercury) revolves around the Sun fastest and the outermost planet (Pluto) revolves slowest.
Spatial models (left frames) and Halpha Doppler tomograms (right frames) of the Algol-type binaries beta Per, U CrB, SW Cyg, and TT Hya, in order of increasing orbital period, P (in days). The path of the gas stream is the curved line along which small circles are marked at intervals of a tenth of the distance from the inner Lagrangian point (L1) to the distance of closest approach to the mass gainer. In the tomograms, the strongest sources of emission are shown in purple or red, while the weakest signal is green. Any emission found between the large solid and dashed circles resembles an accretion disk, while any emission along the predicted path of the gas stream suggests actual gas stream flows along that path. The markings on the Doppler tomograms are explained in detail in the text. Images courtesy of M. Richards.
The tomogram of U Coronae Borealis (U CrB) generated from spectra collected in 1994 shows a distinct flow of gas along the predicted gravitational free-fall path. This represents the first convincing image of the gas stream for the entire class of interacting binaries. The tomograms of U CrB, obtained from data collected at different times, illustrate that the structure of circumstellar gas can change dramatically from an accretion disk to a gas stream distribution, sometimes overnight. Similar results are known for U Sagittae (U Sge).
Systems with orbital periods greater than 4.6 days display emission in the tomogram within the locus of a classical accretion disk, with little evidence of any emission from a gas stream. However, the rings seen in SW Cygni (SW Syg) and TT Hydrae (TT Hya) have different properties. The red ring of emission in SW Cyg represents an accretion structure that may touch the surface of the primary star, while the ring in TT Hya seems be separated from the star. These results suggest that the disks found in the long-period Algols, like TT Hya, are similar to those found in the cataclysmic variables. Tomograms of other systems, like beta Persei, are not as easy to interpret, but they seem to include hydrogen emission from the chromosphere of the cool secondary star, which is similar to the Sun.
We can also create theoretical models of these close binaries from the known
properties of the stars and simple assumptions about the properties of the gas
stream. These hydrodynamic calculations, are computer simulations of the
density, pressure, and velocity of the circumstellar gas which allow us to make
movies of the gas flowing in the binary. It is almost like being there, except
that these models are based on theory and not the observations. However, we can
compare the results from the theoretical models with the observations, until our
movies truly represent the information buried within the spectra. A movie of a
two-dimensional simulation of Algol can be seen here in both Cartesian (spatial) and
Hydrodynamic simulation of gas flows in Algol (beta Per). Figure courtesy of M. Ratliff and M. Richards.
With the help of observational and computer models, we can complete the journey within our minds. We can close our eyes and imagine that we are in a spaceship getting closer and closer to Algol. Soon, the single point of light becomes double as we see two stars in motion. One of the stars, the primary, is blue and much brighter than its companion. The other star, the secondary, is orange-red and looks more like a pear or a water droplet; it is cool and much like our Sun. The other, primary, star is blue and much brighter than its companion. Moving closer still, we begin to see spots, flares, and prominences on the secondary star. Soon we can see a flow of gas moving from the narrow part of the secondary toward the primary. We find ourselves within the gas stream; first moving slowly then getting faster and faster until we reach a speed of about 500 km/s. That's more than a million miles per hour! Suddenly, we hit the surface of the star, much like a stream of water from a garden hose striking hard against a wall. The gas is heated by the impact as we bounce off the surface and are catapulted around the star like excited children on a roller-coaster ride at the fair.
The journey has only just begun...
February 28, 2002