THE BAA OBSERVERS’ WORKSHOPS Cambridge Winchester York 2003 February 15 2003 April 26 2003 September 6 A fascinating insight into observing and analysing the orbital dance of distant binary stars. Observing eclipsing Workshop No. 2: variables: a beginner’s guide Winchester 2003 April 26 by Tony Markham The General Catalogue of Variable Stars It is not orbit of Mercury. (GCVS)1 lists many different classes of clear when Figure 1 shows the primary eclipse of variable star. Some of these are well known the bright- Algol, in which the brighter star is eclipsed and contain many members; others are more ness varia- by the fainter star. This light curve com- obscure and contain only a few examples. tions of Algol bines observations of several eclipses from However, it is also possible to split variable were first 1999 made by members of the Society for stars into just two basic categories: the recog-nised. Popular Astronomy Variable Star Section intrinsic variables − stars like Mira Offic-ially (SPA VSS). The vertical axis shows the variables, Cepheid variables, novae and the credit goes to Geminiano Montanari in magnitude (i.e. the brightness) and the supernovae − in which the stars themselves 1667, but it is likely that the variations were horizontal axis shows the phase − the phase are varying in brightness, and the extrinsic known earlier to Arab astronomers and is the fraction of the orbit that has been variables, in which the individual stars possibly also to the Chinese. However, completed. themselves do not actually vary, and early reports merely noted that Algol As we move from left to right in the light prominent among these are the eclipsing sometimes faded, and it was not until 1782 curve, the brightness of Algol fades as the variables. that it was realised that these fades were brighter star is progressively covered and not occurring randomly. In that year, the then rises again as it emerges from eclipse. English astronomer John Goodricke This is all over in about 10 hours, and for recognised that the fades occurred at regular the remaining 2d 11h of the orbit we see no intervals, and he found this interval to be significant brightness changes. Types of eclipsing approximately 2 days and 21 hours. variable Not only did Goodricke recognise this pattern, he also put forward the correct Beta Lyrae type explanation. Goodricke suggested that Algol Algol type is not merely a single star whose brightness Not all eclipsing variables behave like Algol. is varying. Instead, there must also be a Only two years after recognising the The most famous eclipsing variable is darker object which is in orbit around it. pattern in the variations of Algol, Goodricke probably Algol (Beta Persei). For most of The orbital plane must be edge on as seen discovered another eclipsing binary − β the time, Algol is the second brightest star in from the Earth so that every 2d 21h, the Lyrae − in which the period of variation is the constellation of Perseus − only Alpha darker object will obscure most of the light approximately 13 days. Persei is brighter. However, sometimes it from the bright star. Goodricke had no way Figure 2 shows the variations of β Lyrae becomes much fainter. of knowing what the ‘darker object’ was, over a whole 13-day orbital cycle. This light but we now know curve combines all observations made that it is another during 1998 by members of the SPA VSS. star. Indeed, it is not There is some scatter, as is usually the case actually ‘dark’ − it is when combining the visual estimates of comparable in several different observers, but the main brightness with our features of the light curve can be seen. Sun, but is much We can see the primary eclipse, near less luminous than phase 0.25, in which the brighter star is the brighter star in eclipsed by the fainter star. We can also see the Algol system. a secondary eclipse, near phase 0.75, in The two stars are which the fainter star is eclipsed by the approximately 6 brighter star. In the case of Algol, the million miles apart secondary eclipse is so shallow that we and so, on the scale cannot easily detect it visually. The most of our solar system, important difference is that whereas in the their orbits would case of Algol, there is a long interval Figure 1. The eclipse of Algol in 1999, using GCVS elements. easily fit inside the between eclipses when there is no signifi- J. Br. Astron. Assoc. 114, 4, 2004 215 Markham: Observing eclipsing variables Figure 2. Light curve of β Lyrae over a 13-day orbital period in Figure 3. Light curve of W UMa in 1996–1999, from observations 1998. by the author. cant change in brightness, this is not the Most significantly, because the two stars eclipsed. However, once the brighter star is case for β Lyrae − the brightness is changing are in contact with each other, there is no totally eclipsed, the fading stops and the all the time. gap between eclipses − as soon as the magnitude of the system remains constant Like Algol, the β Lyrae system consists primary eclipse ends, the secondary eclipse for about two hours while the brighter star of two stars of unequal brightness which starts immediately; as soon as the second- is hidden. Finally the brighter star starts to periodically eclipse each other. The orbital ary eclipse ends, the primary eclipse starts, emerge from eclipse and the brightness period is longer because the stars are further and so on. Hence you never need to look up increases again. − over 20 million miles − apart. predicted times of eclipses for a W UMa In the case of RZ Cas, we only see a However, whereas in systems like Algol, type variable, as it will always be in eclipse. partial eclipse. The magnitude drops as the two stars are more or less spherical, in more and more of the brighter star is the case of β Lyrae, the two stars have eclipsed and the system is faintest when the distorted each other gravitationally and partial eclipse reaches its maximum extent. become more egg-shaped. When we see Immediately after this, however, the such egg-shaped objects side on (as is the Partial and total brightness starts to increase again and case midway between eclipses) we are eclipses consequently the eclipse is not flat- seeing light from a bigger surface area than bottomed. In summary, partial eclipses are when we see them end on (just before and As has been described, after the eclipses). Seeing a bigger surface there are three main area means that we see more light from the types of eclipsing stars. Thus, even after the eclipse ends we β variables, whose see Lyrae still continuing to brighten, and differently shaped it becomes brightest midway between light curves provide eclipses. information about the stars which make up these systems. We can W Ursae Majoris type also extract further information by looking Although Algol type and β Lyrae type at the shapes of the eclipsing binaries are the most well known, primary eclipses. they probably are not the most common Figure 4 shows the type of eclipsing binary. The most common primary eclipse of the type are probably the W Ursae Majoris Algol type variable type eclipsing variables. RZ Cassiopeiae. Figure 3 combines observations of Figure 5 shows the Figure 4. A primary eclipse of RZ Cassiopeiae in 1993. Note the eclipses of the variable W Ursae Majoris, primary eclipse of U sharp V-shape of the light curve. made by the author over a number of years. Cephei, another Algol These systems consist of two stars more or type variable. As can less in contact with each other. Typically, be seen , the shapes of the two stars are comparable in brightness the two light curves with our Sun and so less luminous than the are different. The light stars in Algol or β Lyrae, and so not visible curve of RZ Cas is over such large distances in the galaxy. fairly ‘V’-shaped Indeed the brightest examples are only whereas that of U Cep about 8th magnitude. is more flat-bottomed. In most cases, the two stars are similar to The light curve of each other and consequently the primary U Cep is flat- and secondary eclipses tend to be of similar bottomed because we depth − differing by only about 0.1 mag in are seeing a total the case of W Ursae Majoris itself. For the eclipse. The initial same reason, they have short orbital fade occurs as more periods, in the case of W UMa, about 8 and more of the hours. brighter star is Figure 5. The U-shaped eclipse of U Cephei in 1996 (GCVS elements). 216 J. Br. Astron. Assoc. 114, 4, 2004 Markham: Observing eclipsing variables ‘V’-shaped whereas total eclipses are flat- add 2.4930475 days bottomed. often enough, you will eventually reach the current year and find out when eclipses are due in the coming Comparing months. However, we can observations with also run this process predictions in reverse and, for an observation made at a given date and time, The light curves shown so far have had the calculate the predicted magnitude shown on the vertical axis and phase − i.e. the the phase on the horizontal axis. We now fraction of the orbit need to consider where these phase values that should have been are coming from. After all, when you make completed. This is a Figure 6. Eclipse of U Cep in 1999 (GCVS elements).