Coordinator: Tom Richards

“Everybody knows” that wide, visually separated binaries provide an indispensable first step to astrophysics as well as the distance scale ladder. All we need to know is their distance by parallax methods, their orbital period P, and the apparent size of the orbit. True orbit follows, then their masses. Magnitudes at that distance give true luminosities which with their colour gives temperatures, thence their size. There’s no other way of making this first interstellar step.

But many binaries are too close to separate optically offer other crucial astrophysical insights, including stellar evolution. This is because many of them are close enough to each other to interact in various ways (the close binaries) and, if their orbital planes are close to our line of sight, we can obtain revealing eclipse phenomena. These eclipsers are the object of our studies.

About half the stars in our galaxy were born and die as binary pairs. Sometimes they are very close pairs, orbiting within a very few diameters of each other. At some stage in their lives together, there will almost certainly be a physical interaction between them. Stellar evolution tells us stars on the main sequence of the H-R diagram swell slowly though their lifetime there, and the more massive stars evolve faster. If the two stars are very close indeed (typically an orbital period of at most two days), the more massive one (call it Star 1) may swell enough until its atmosphere reaches the inner Lagrange point L1 on the line of centres of the two stars, where the opposing gravitational attractions cancel out. That point is always nearer the less massive star, which has a weaker gravitational field. (Stars typically double in diameter during their main-sequence life.) Then its atmosphere will leak through that point, dumping onto the smaller less massive star 2. This leakage through L1 is called Roche Lobe Overflow (RLOF) – see Figure 1 – and will continue until Star 1 loses so much mass it contracts away from L1. This case of RLOF, caused by swelling on the main sequence, is called RLOF Case A.

Figure 1. Roche Lobe Overflow. The dotted figure 8 (3D hourglass in reality) is the inner Roche lobe, a surface of constant gravitational potential containing the inner Lagrangian point L1 where the gravitational pull of both stars equalizes.

Case B is similar: here the two stars are further apart with periods up to 100 days and normal main sequence swelling won’t reach to L1. But as Star 1 nears the end of its core hydrogen burning, it swells and swells up to 50 diameters, and if left alone would move to the Asymptotic Giant Branch of the H-R diagram or become a giant. But it’s not left alone, for at some point it may swell enough to reach L1, and we have RLOF Case B.

For really widely separated stars with even longer periods, even red-giant size isn’t sufficient to make contact. It may be necessary to wait until Star 1 contracts out of its giant phase then swells even more to reach supergiant size, and make RLOF Case C. The three cases are shown in Figure 2.

Figure 2. The size evolution of a star of 5 times the mass of the Sun in a binary system with a secondary half its mass, showing the phases where RLOF cases A B and C can occur, depending on orbital period P (and hence separation). (From Paczynski, 1971)

RLOF can sometimes happen extremely quickly. The donor may not be able to contract away fast enough from the ever-approaching L1 as it loses mass; so positive feedback happens and there’s a dump of much of Star 1’s mass onto Star 2, perhaps in the course of only 1000 years. Fast or not, the result can be that Star 2 ends up the more massive while Star 1, now much less massive can continue a cooler slower life on the main sequence often as a red dwarf, while Star 2, now more massive, does the opposite. So now it’s its turn to evolve faster, swell to L1, and dump mass back onto Star 1.

This sort of dance between the stars can become very complex and depends on stellar masses and mass-ratios and their rates of change. You can even get the less massive star – an evolved sub-giant – transferring mass in a stream down to the more massive one on the main sequence. The eclipsing binary Algol is an example of this paradox: why is the less massive star more evolved? Part of the answer is that what’s now the less massive – currently the donor star – was more massive, evolved off the main sequence to red giant, a Case B mass transfer started from it, and is still continuing since L1 gets ever closer to it as it loses mass and Star 1 gains mass.

Case C – supergiant plus main-sequence pair – can lead to cataclysmic variables. The supergiant’s envelope encloses the other star, braking the system until the period is only hours long and the orbits are far smaller. The common envelope is blown away by stellar winds and the supergiant is reduced to its core, often a white dwarf, receiving a gas stream from the low-mass main sequence star. This situation can lead to thermonuclear explosions of the accreted gas on the white-dwarf surface (novae) or in a “hot-spot” where the stream encounters transferred gas orbiting the white dwarf. OY Carinae is an example of an eclipser like this.

Figure 3. A negative face-on and edge-on model of OY Car. The donor star is on the left. The hot spot is where the stream meets the circumstellar disc.

What can eclipses tell us?

Period and period change

This is where the study of eclipsing binaries comes in. Eclipses allow the very precise determination of orbital period; and if observed over years and decades a change in period can be detected. This can be used to calculate the rate of mass transfer, and also mass loss from the system entirely. The investigation of period change is by an O-C diagram (Observed minus Calculated). Start with the known period P of the binary, and a well-timed minimum, often called the Zero Epoch E0 – together these are called the system’s Light Elements or Linear Ephemeris (LE). Then observe an eclipse much later, find its time of minimum O, and calculate from the LE when it should have happened, C. The difference, O-C, is a sensitive measure of period change especially if the time interval is many years. Plotting O-C values against orbital cycle numbers can yield most revealing trends, as in Figure 4. The VSS Southern Eclipsing Binaries group collects all the times of minima its observers measure, and their O-C values, for publication annually in a refereed journal, e.g. (Richards et al, 2017).

Figure 4. O-C diagram for WW Cyg. The upward parabola indicates a steadily increasing period. (credit: O-C Gateway)

Whether the orbital period of an eclipser is long or short, eclipses happen suddenly, usually lasting a few hours at most, and their depths are less than a magnitude – often very much less. This explains why they were not popular targets in the days of visual observing and even photoelectric photometry. But with CCDs in relatively inexpensive astronomical cameras, or DLSRs on a driven mount, it is possible to take hundreds of images a night automatically and obtain beautiful light curves – even of entire orbits. Eclipsing binary research in amateur hands is now a very hot topic. Plenty of targets can be found at all magnitudes, and the professionals with expensive equipment and much competition for telescope time rarely get granted the necessary all-night stand. Amateur work is vital.

Light curve shapes

Light curves, not just eclipse minima, are important. By compiling a light curve for a whole orbit – perhaps over several nights – you can tell from the shape a very great deal about the binary system. What matters here are the phased light curves, formed by folding raw light curves on the system’s orbital period. Examples are in Figure 5, which for clarity show an entire orbital period twice.

Most observed light curve shapes fall roughly into three classes, as in Figure 5. The EW or W UMa binaries (bottom of Figure 5) have very short periods, usually less than 1 day. Typically, these stars are joined at L1, forming an hourglass shape. With a common atmosphere their temperatures are almost the same, so their two eclipses – front and back – have about equal depth and the overall light curve shape is smoothly curved. These are typically Case A contacts. Another rough class, the EBs or Beta Lyraes (middle of Figure 5) have stars so close but without touching, that they are drawn by tidal forces into prolate ellipsoids pointing towards each other. Their light curves are similar to EWs, but since the stars can be of different temperatures the two eclipses can have very different depths. They might even not eclipse – the changing projected shapes of the ellipsoids as they orbit create the light variation. Periods are usually less than 1 day but can be rather longer. The final rough class is the EAs or Algols (top of Figure 5). Here the stars are usually sufficiently far apart to be about spherical. These have flat light curves outside of the eclipses, or nearly so, unlike the other two classes. Periods rarely less than 1 day, and no upper limit.

There can be intermediate light curve shapes that are hard to classify; and also, the shapes are not a definitive guide to the astrophysics. Beta-Lyrae types – no contact – could have an EW type light curve if the two stars are very similar. And eclipsing cataclysmic variables like OY Car are another story altogether. Plainly the relation between light curve morphology and astrophysical features is not very close. Starting with light curve shape and attempting to derive the astrophysical parameters is part of the challenge of this research. To do the job properly requires specialized light curve analysis software (see below) and preferably orbital radial velocity data acquired spectroscopically. Nevertheless, a thoughtful study of light curve shapes can reveal a surprising amount about the binary system. See my series of VSS Newsletter articles “The Stellar Detective” (Richards 2016a, b, 2017a, b).

A primary astrophysical classification of close binaries is in terms of the type of physical contact between the stars, if any. A detached pair have no physical contact at all. These are often EAs or EBs in terms of eclipse light curve shapes. A semi-detached pair have one star depositing mass (atmosphere) onto the other, as with Algol many EAs and cataclysmics. These are case B or C contacts. A contact or over-contact pair have a common atmospheric envelope as with most EW light curve shapes.

Figure 5. The three main types of light-curve shape. EA: flat or nearly so out of eclipse, EB and EW curved everywhere, EW both eclipses of similar depth. Each diagram shows a complete phased light curve twice, for clarity.

Do it with software

There is plenty of software – some free – to handle most aspects of analysis of eclipsers.

The first software job is to carry out the photometry on your night’s images to create a light curve. The next software job is to measure the times of minima in your light curves. Then a third type of software will assist you in exploring your light curves to find out what configuration the binary has in order to deliver such a light curve. At this level of computer work you are effectively deriving the astrophysical properties of your binary – which is a publishable result.

The Southern Eclipsing Binaries group of VSS carries out all these types of research, and more. Teamwork is the watchword so we’re always looking out for people to join our work. You need a driven telescope with an astronomical CCD camera or a DSLR camera on a driven mount, and software to run it all for you while you sleep. That’s all really.

If you are interested, contact me using the link above, and we’ll give you access to our subweb which explains in detail what to do, and we’ll get you going.

Resources and Reading

In my opinion the best introductory book on variable stars is by John Percy (2007). The chapter on eclipsing binaries is very good indeed, but beware of typos particularly in the maths.

For a thorough overview of the field of close binaries see (Hilditch 2001). Another comprehensive introduction to the study of eclipsers with emphasis on modelling is by Kallrath & Milone (2009). The collection edited by Sterken & Jaschek (1996) is an invaluable introduction to the study of light curves, with a good chapter on eclipsers.

On the Web, the AAVSO’s Variable Star Index is an excellent portal to multiple resources on any particular variable. The Czech Astronomical Society’s O-C Gateway provides minima data on eclipsers – add your own. CALEB is an online atlas of light curves and astrophysical models for hundreds of eclipsers. The VSS website has a subweb for the Southern Eclipsing Binaries group, with thorough guides on how to observe and analyze eclipsers, and many resources.

As to software, MaxIm and AstroArt are widely used to control the camera imaging and carry out photometry on the results. AIP4Win is a popular photometry tool. MPO Canopus does photometry and light curve analysis and period finding. PERANSO has a comprehensive suite of algorithms for period analysis. Minima25 carries out minima estimation by several methods. BinaryMaker 3 is popular for astrophysical modelling, The Wilson-Devinney program is more sophisticated (Wilson 1994) – a good interface to it is WDwint.

Is this research for you?

• Eclipsing binaries offer widely varied fields of study.
• The southern sky is full of them at all magnitudes, many scarcely studied.
• For most of them, equipment is a tracking DSLR or telescope of any size with CCD camera, and computer-controlled image acquisition that can run unattended all night.
• Read the Southern Eclipsing Binaries pages for detailed research procedures.

References

Hilditch, R.W., 2001. Introduction to close binary stars. Cambridge, CUP.

Kallrath, J. & E.F. Milone, 2009. Eclipsing Binary Stars: Modeling and Analysis. Dordrecht, Springer.

Paczynski, B. (1971). “Evolutionary Processes in Close Binary Systems” Annual Review of Astronomy and Astrophysics. 9: 183-208. 1971ARA&A…9..183P

Percy, John R., 2007. Understanding Variable Stars. Cambridge, Cambridge University Press.

Richards, Tom, 2016a. “The Stellar Detective”. VSS Newsletter, 2016-3, 24-27. Link

Richards, Tom, 2016b. “The Stellar Detective II”. VSS Newsletter, 2016-4, 21-27. Link

Richards, Tom, 2017a. “The Stellar Detective III”. VSS Newsletter, 2017-1, 24-25. Link

Richards, Tom, 2017b. “The Stellar Detective IV”. VSS Newsletter, 2017-2, 11-14. Link

Richards, Tom; Blackford, Mark; Bohlsen, Terry; Butterworth, Neil; Lowther, Simon; Jenkins, Robert; Powles, Jonathan, 2017. Southern Eclipsing Binary Minima and Light Elements in 2016. OEJV 182. [2017OEJV..182….1R]()http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2017OEJV..182....1R&db_key=AST&link_type=ABSTRACT&high=59a635945e25371

Sterken, C. & C. Jaschek (eds). 1996. Light Curves of Variable Stars, a pictorial atlas. Cambridge, CUP.

Wilson, Robert E., 1994. Understanding Binary Stars via Light Curves. IAPPP Communications, 55. [1994IAPPP..55….1W]()http://adsabs.harvard.edu/abs/1994IAPPP..55....1W