Eclipsing Binaries & VSS
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- Last Updated on Saturday, 30 March 2013 10:29
- Written by Tom Richards
Binary stars play a very significant role in astrophysics: the only way you can directly obtain the mass and size of a star is if you can observe it orbiting with another star - then Kepler's laws of orbital motion and Newton's laws of gravitation can be applied. When they eclipse, occult or transit one another, we can often derive the ratio of luminosities and radii of the two stars, the ratio of the radii to the orbital radius, and information about the orbital inclination and eccentricity - just from the light curve that shows the eclipses, such as the one below. Add radial velocity data from spectroscopy and you pin down the absolute values of masses, and stellar and orbital radii.
Nature provides us with a rich zoo of eclipsing binaries, which are not easy to classify. You can classify them empirically by the shape of their light curves - though there are no neat boxes in which to put the different light curves. You can classify them astrophysically by the relation of the two stars to each other: all the way from two completely distinct spherical stars orbiting each other around their common centre of gravity, to a pair so close they touch and even share an atmosphere. For more on classification see the official GCVS classification guide.
The "Phase plot" above shows the light curve of RR Centauri. (The vertical axis is brightness, not magnitude, relative to its maximum brightness. The horizontal axis is its phase over a full orbit, with the primary minimum taken as phase 0.) There is much to be learned from phase plots like this. Particularly in the Southern Hemisphere, catalogue data on eclipsing binaries can be decades old, with little or no new data since discovery - so new data can give rich pickings.
It is possible to analyse these light curves using software, to determine the shapes and relative distances of the two stars. Here's a model of RR Cen derived from the above light curve (images credit: R.E. Wilson). The open circle is the Sun to the same scale. Note these two stars are actually in contact with each other. It's not hard to relate the nine positions shown to particular phases in the above phase plot, and explain things like why only one minimum has a flat bottom.
The basic data an observer needs to obtain on an eclipsing binary is a time series of time and magnitude data. Time needs to be expressed as Heliocentric Julian Date to avoid light-time effects from the orbiting Earth.
An important goal of eclipsing binary studies is to find times of minimum - the midpoint of the eclipses. The phase plot of RR Cen above shows one minimum on the left (partial eclipse of the larger star) and on the right a total eclipse of the smaller star. A widely used program for finding times of minimum, which also produces phase plots from your files of HJD - mag observational data, is Tonny Vanmunster's PERANSO - available fromwww.peranso.com. Others can be found on the AAVSO website www.aavso.org. A typical research project on an eclipser, such as VSS's Equatorial Eclipsing Binaries Project, will gather weeks or months of time series data on a star, then analyse it in PERANSO to find not only times of minima but the star's light elements. Light elements consist of the HJD of one observed time of minimum or epoch, usually written E0, and the orbital period P in days. Then any future eclipse HJDmin can be predicted using the equation HJDmin = E0 + P x E, where E is the number of epochs (times of minimum) elapsed since E0. For
RR Cen this is 2452500.523 + 0.6056922 x E (from the Krakow database http://www.as.up.krakow.pl/o-c/ - see below).
Frequently one finds that over years or decades the predicted time of minimum diverges from the observed time. This departure is plotted in an (O-C) diagram, (for Observed minus Calculated). Here it is for RR Cen, from the Krakow database.
This covers over 60 years of data, and shows observed epochs getting steadily later than predicted. From the shape of these diagrams much can be learned about mass transfer from one star to the other, or mass loss from the system.
The Eclipsing Binary work of VSS is aiming to fill in a lot of gaps in our knowledge of southern and equatorial eclipsing binaries. While observers with any type of equipment can contribute to Eclipsing Binary work, CCD-equipped telescopes are particularly valuable, as you can obtain a precise and lengthy time-series of data over a night that might capture in detail an entire eclipse, or indeed the full orbit of the binary. DSLR cameras are rapidly becoming the instruments of choice for bright eclipsing stars. VSS eclipsing binary work needs observers with any of the above equipment setups, and it also needs armchair analysts. If eclipsers interest you, please contact me and I'll give you a heap of work to do! At present there are two projects: QZ Carinae (leader: Stan Walker) and Equatorial Eclipsers (leader: myself).
The World Wide Web has many useful resources on eclipsing binaries. A particularly important one is the Krakow (Mount Suhora Observatory) Database of linear elements for eclipsing binaries, a statistics of minima database to which you can add your results, and an atlas of O-C diagrams. See http://www.as.up.krakow.pl/ephem/. Another is the Czech Astronomical Society's "O-C Gateway" with tables of times-of-minimum data for eclipsing binaries from which O-C diagrams can be displayed. Again, you can add your own data. Seehttp://var.astro.cz/ocgate/.
VSS work on Eclipsing Binaries is very much aided by the generous assistance of Dr Bob Nelson of Canada. Bob is an internationally recognised expert on eclipsers, which he has studied over a long career. His website,http://members.shaw.ca/bob.nelson/, has many useful programs for downloading, such as Minima (finds times of minimum using 6 methods), Period Search (finds periods based on portions of light curves), EB_Min (tells you what stars will have observable minima from your location on a given night) and WDwint (a Windows front-end to the Wilson-Devinney star modelling package, which is included).
The WD program with Bob's front-end is a standard tool used by eclipsing binary researchers. Once you have a phase plot for an eclipser you can use WD to find out a whole range of geometrical and astrophysical information about the two stars, as described at the beginning of this article. Warning - it's a test-and-compare iterative process which can take a long time to get good results. Also, radial-velocity data from spectroscopy is often needed. Then you can also use BinaryMaker 3 (www.binarymaker.com) to derive pictorial models of the rotating star system, like the one for RR Cen above.
Bob has also written a must-read three-part article on observing eclipsers, for the VSS Newsletters (2009 May, August and November issues).
Plainly there is a very great deal the amateur astronomer can do with eclipsing binaries. Join a VSS eclipsing binary project and contribute to our knowledge of this important area of astrophysics.
