Eclipsing Binary Stars: Future Work

Astrophysics of Variable Stars ASP Conference Series, Vol. 349, 2006 C. Sterken & C. Aerts Eclipsing Binary Stars: Future Work Dirk Terrell Dept. of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite 400, Boulder, CO 80302 USA Abstract. The analysis of eclipsing binary stars has reached an impressive level of sophistication in recent years but many interesting problems in the structure and evolution of binary stars remain unresolved. Future approaches to solving these problems will involve both acquiring and analyzing new kinds of observables an looking at existing data in new ways. In this preview article I discuss the extension of analysis models to new kinds of observables and datasets of unprecedented size to solve both old problems and new ones that have arisen in recent years. 1. Introduction To most astronomers, binary stars are probably of interest only for their ability to provide fundamental data on stars such as masses and radii. To that crowd, all of the interesting work on binaries has been done and those of us in the field are merely cleaning up a few details here and there to extract an additional few percent in the accuracy of derived stellar parameters. Surely there must be more interesting subjects for research? Of course, there are myriad reasons why people find things interesting or not. At my Institute I am surrounded by people with an interest, for example, in the soil of Mars who aren t terribly interested when I start talking about binaries. I m the same way after hearing a tenth talk on elemental abundances in Martian soil since I lost my interest in dirt at about five years of age. The analysis of eclipsing binary star data is a relatively mature field (viz. Wilson, these proceedings) but there is still much to be done. Perhaps the biggest issue facing us is how to deal with the huge numbers of eclipsing binary light curves that will be observed by projects such as the Large Synoptic Survey Telescope and the Gaia mission. These new datasets will present a formidable analysis challenge but the result will be answers to long-standing questions about binary stars. The Ph.D. Conference in Pecs was a fascinating gathering of people interested in variable stars and I was particularly pleased to see so many young astronomers focusing their boundless energy and cleverness on problems in the field. New datasets and instrumentation arriving in the next decade will provide new ways of probing variable stars of all types, making this an exciting time to be doing research on stars. 91

92 Terrell 2. Additional Observables The goal of all the work we do in observing and modeling binaries is to understand their various intrinsic properties. What are the masses, radii and luminosities of the components? What is the age of the binary? What is the internal structure of each star? If large-scale mass transfer between the components has occurred, what did the original binary look like? Answering such questions often leads to further questions such as Was this binary originally a triple system? as in the case of OW Gem (Eggleton (2002); Terrell et al. (2003a)). By far, the bulk of data gathered on eclipsing binaries to date has consisted of photometry and spectroscopy. With the advent of inexpensive charge-coupled device (CCD) cameras in the last decade, it is rather easy to gather large datasets of high-precision data in multiple filters. An example of current capabilities is the dataset of Genet et al. (2005) on V523 Cas where they obtained 27 complete light curves totaling over 20,000 individual observations during one observing season. One of the goals of their observing program is to understand the timescales involved in the long-known variability of the light curves of some W UMa binaries. These kinds of datasets will enable us to look at binaries in new ways. Spectroscopy, because of its requirement for larger telescopes, has not seen the same level of growth in datasets but impressive increases in capabilities have occurred in the last decade. New spectrographs, designed to find the m s 1 variations in stellar radial velocities driven by planets, have been used to measure high-precision radial velocities of binaries (e.g., Terrell et al. 2003b, 2005). Multifiber spectrographs have enabled efficient searches of clusters for spectroscopic binaries (e.g., Meibom & Mathieu 2005). One very impressive improvement in obtaining radial velocity data on close binaries has been the broadening function approach developed by Rucinski (2002) and applied to dozens of short-period eclipsing binaries (Rucinski et al. 2005, and references therein). Simultaneous solutions of light curves and radial velocity curves (Wilson 1979) are now commonly performed. It is obvious that a simultaneous solution of multiple types of observations, assuming the model is capable of accurately predicting the observables, will lead to a more accurate solution for the binary parameters than independent analyses of the various datasets. Separate analyses lead to problems such as multiple values for a common parameter (e.g., the orbital eccentricity from light and velocity curve datasets), whereas a simultaneous solution incorporates the information from all datasets and results in a logically consistent value that properly accounts for parameter correlations. Having multiple kinds of observables results in more accurate estimates of parameters if they are analyzed properly. And different kinds of observables can also yield different parameters. For example, the semi-major axis of the orbit (a), which sets the physical scale of the system, is a parameter in radial velocity curve solutions but it has no effect on the light curves. However, because of its perfect correlation with the orbital inclination (i), radial velocities can only yield a value for a sin i. So, in this example, the simultaneous solution enables us to get the most out of the data because the light curves break the a i correlation. New observables are, therefore, desirable. Progress, however, requires work on both the instrument side and the modeling side. Observers are loathe to make observations if there is no way to analyze them. Modelers are loathe to build

Eclipsing Binaries: Future Work 93 capabilities into analysis codes if there are no observations to analyze. R.E. Wilson, Walter Van Hamme and I have plans to add additional observables to the Wilson-Devinney (WD) program (Wilson & Devinney 1971) over the next few years. Some of these modifications have already been made in unreleased versions of the program but require extensive testing before they can be released publicly. New observables that we hope to add to the public version of WD are X-ray pulses, polarization curves and spectral energy distributions. 2.1. X-ray Pulses Although a small subset of close binaries, high-mass X-ray binaries are very important objects because they allow us to determine fundamental properties of neutron stars. In some of these systems, the X-rays arrive in pulses and the times of arrival of those pulses (t p ) can be very accurately measured. The pulse arrival times contain information on the orbital and rotational motions of the neutron star. An additional piece of information is also frequently available in the duration (or semi-duration) of the X-ray eclipse, when the neutron star is eclipsed by the supergiant companion. WD has long had the ability to apply the X-ray eclipse semi-duration constraint via the use of WD s mode -1 (viz. Leung & Wilson 1977, for a description of the various WD modes). By extending WD to analyze X-ray pulses, we can improve WD s usefulness for analyzing X-ray binaries by enabling simultaneous light, radial velocity and X-ray curve solutions. Wilson & Terrell (1994, 1998) developed a rigorously unified model for light/velocity/pulse curve analysis and implemented it in an unreleased version of WD. A key point in their approach is the use of pulse arrival time rather than pulse delay as the independent variable in the solution. The arrival time (heliocentric Julian day) of a pulse is given by t = t ref + S(n n ref )P p + t t ref, where t ref is the arrival time of a reference pulse. The n n ref term is the number of pulses before or after the reference pulse and P p is the intrinsic pulse period. The terms t and t ref represent the light time delays for a given pulse and the reference pulse, respectively. The use of arrival time rather than pulse delay results in a cleaner and more straightforward analysis since it is a directly observed quantity while pulse delay is not. Pulse delay is the difference of the pulse arrival time and an expected arrival time in the absence of the orbital light time effect. The latter obviously depends on the various orbital parameters of the neutron star but those are quantities that we are trying to determine in the first place. We need the orbital parameters to compute delays so that we can fit the delays to get the orbital parameters. Thus, using pulse delays results in a messy situation that is better avoided altogether by using arrival times. Wilson & Terrell (1998) give the details necessary to model pulse arrival times including the analytical derivatives involved in fitting pulse arrival times. They applied the program to existing radial velocity and pulse data for the GP Velorum/Vela X-1 system and discussed the practical problems involved in an analysis of this type. Future work on the system might include the addition of the light curves to the solution. Wilson & Terrell (1994) attempted to include light

94 Terrell curve data in the solution but concluded that the supergiant component exhibited dynamical tides and these tides caused the amplitudes of the light curves to be much larger than expected from the equilibrium (but phase variable) tides computed in their model. The orbit of the system is eccentric and this is probably a major driver of the tides. The GP Velorum/Vela X-1 system thus makes a good system for testing models of non-equilibrium tides. 2.2. Polarization Curves Interest in the topic of polarized light in binaries goes back to the work of Chandrasekhar (1946) who predicted that the polarization of light due to Thomson scattering would be most easily observed during the primary minimum of an eclipsing binary with an early-type component. The promise of this so-called limb polarization effect has been tempered by the fact that the amplitude of the effect is very small in most circumstances (of order 0.01% in Algol, for example). The observational detection of this effect has not been unambiguously made. Kemp et al. (1983) claimed to have detected the limb polarization in Algol and Wilson & Liou (1993) showed that the variations in the Stokes quantities during primary eclipse in the Kemp et al. data were reasonably well matched by the predictions of their model based on the WD program but the predicted variations are not much larger than the scatter of the data. Widespread acceptance of the claim of detecting the limb polarization effect will require better data than currently exist. Polarized light in close binaries can also arise from scattering due to circumstellar material. Algols are, therefore, good targets for polarization observations. The main attraction of Algol itself is the fact that it is so bright and photons are always at a premium when looking for such small amplitude effects. However, other, fainter Algols would make better targets because they have larger amounts of circumstellar material and hence larger polarization amplitudes. But these fainter targets require much larger telescopes, making it difficult to get enough telescope time to observe the episodic nature of the circumstellar flows. Terrell (1994) combined the Wilson-Liou code with a hydrodynamical flow program and showed that polarization observations of binaries would make very powerful probes of the location and physical properties of circumstellar material. Polarization observations of binaries are not at all rare but useful ones are. Polarization arising from circumstellar material is governed by the episodic nature of the gas flows. Isolated, individual polarization measurements (the vast majority of the existing datasets) are, therefore, not of much use when trying to discern such things as the distribution of the material within the binary to test hydrodynamical models. What we need are datasets with large numbers of observations spread over individual orbital cycles. Such datasets will be difficult to obtain for many binaries because of the aforementioned need for larger telescopes but simulations demonstrate that they will provide very powerful tests of our models of circumstellar flows. 2.3. Spectral Energy Distributions When developing models to fit observations, one has to recognize and deal with the limitations of the available computing power. Often this means that the model must be simplified as in the early light curve work of Russell. In the case

Eclipsing Binaries: Future Work 95 of spectra of eclipsing binaries, they are often used to measure radial velocities which are then used in analysis programs like WD. In the spirit of modeling observations as directly as possible, it is natural to entertain the idea of computing spectra for binaries for direct comparison to observed ones but it is a computationally demanding task. Computation of a synthetic binary is a straightforward process in principle. One needs values of effective temperature, surface gravity and chemical composition for the visible surface elements of the binary components. We also need to know the Doppler shifts arising from the orbital and rotational motion for each surface element. Values for these quantities are already computed by light curve programs such as WD so the natural approach is to add stellar atmosphere routines to an existing light curve program. Line profiles must account for the main broadening mechanisms, such as thermal Doppler broadening and damping (from the stellar atmosphere model) and broadening due to rotation and orbital motion (from the binary model). Previous work has been done on binary spectrum synthesis. Linnell & Hubeny (1994) developed a program to compute synthetic spectra of binaries and applied it to spectra of the well-detached binary EE Peg and the near-contact system SX Aur. Their program was extended to include synthetic photometry capability (i.e., light curves based on actual filter bandpasses rather than monochromatic light curves at effective wavelengths of filters) and applied to MR Cyg (Linnell et al. 1998) which led to the conclusion that the system was semi-detached. Orosz & Hauschildt (2000) and Shahbaz (2003) built spectrum synthesis programs based on the NextGen atmospheres code for low mass stars. One advantage of the spectrum synthesis approach is that it renders unnecessary the use of an approximation law for the stellar limb darkening because it computes local intensities from atmosphere models. The appeal of spectrum synthesis is obvious and continued growth in computing power should enable us to apply it to many more binaries than has been possible previously. Plans are in place to give WD a spectrum synthesis capability and we hope to do so soon, subject, of course, to the necessary support of funding agencies. 3. Modeling and Software Improvements The WD program has served us well over the last three decades but there are still many useful features that could be added to improve both the astrophysical capabilities of the program and the efficiency with which analyses can be done. Wilson (2005) discusses several items that are in the queue for WD development, some of which I will only briefly mention here. The reader is encouraged to consult Wilson (2005) for further elucidation of these topics. 3.1. Direct Solutions for Eclipsing Binary Distances Eclipsing, spectroscopic binaries can be used to measure very accurate distances. Contrary to some papers that use the term incorrectly, eclipsing binaries are not, in general, standard candles, wherein membership in some class of distancecalibrated objects allows for the estimation of luminosity. Instead, eclipsing binaries can be used as distance indicators because the solution of their light and velocity curves yields a measured luminosity. Note that W UMa binaries

96 Terrell can be used as standard candles via their period-color-luminosity relation as described by Rucinski & Duerbeck (1997). The traditional approach to computing the distance to an eclipsing binary is to take the luminosity (or absolute magnitude) of the binary from the light-velocity solution and compute the distance modulus given the apparent magnitude of the binary. But there is no reason why the distance can t be a parameter in the solution from the start. This approach requires that observed and computed light curves be on an absolute scale rather than the more traditional relative scale (e.g., all light curves normalized to unity at maximum) but this is not difficult to achieve. One must also have a quantitative estimate of the interstellar extinction or, if the data permit, it too could be a parameter in the solution. Wilson (2005) discusses the details of computing distances directly within a light curve analysis program. 3.2. Multiple-Origin Unified Curve Ephemerides An extensive collection of the times of minimum of eclipsing binaries has been gathered. Time of minimum observing programs are popular with amateur astronomers because the necessary observing time is much smaller than programs involving complete light curves since coverage is only needed at the minima and filtered observations are not crucial. Analysis of the photometric data, usually based on assumptions about symmetry of the eclipses, yields a time of minimum. With minima spread over a sufficient time period, ephemeris parameters can be reliably determined from the analysis of the O C values. Phenomena such as mass transfer between the binary components and light time effects due to tertiary companions can be studied via these timing diagrams. The ephemeris parameters, including the zero-point reference (HJD 0 ), period (P) and period time derivative ( P), affect the locations of all points in light/velocity/etc. curves so it makes sense that using entire sets of observables should help better determine the ephemeris parameters. One big improvement that results from using entire curves is the elimination of any assumptions about the shape of the minima. Because we are fitting a realistic model to the minima, gone is the need to assume that the ascending and descending branches of eclipses are symmetrical about the minimum. Another advantage of this approach is in the estimation of the error estimates of the ephemeris parameters since these are determined simultaneously with the other binary parameters, allowing for the proper influences of parameter correlations. Wilson (2005) introduced the idea of Multiple-Origin Unified Curve Ephemerides (MOUCE), although WD had been modified some years earlier to allow for the inclusion of HJD 0, P and P as solution parameters. This capability was made available in the 1998 version of the program and several authors have applied the method to individual binaries (e.g., Chochol & Wilson 2001; Terrell et al. 2003b, 2005). Additional parameters for MOUCE solutions are the apsidal motion rate (already available in WD) and the parameters associated with lighttime effects due to the influence of a tertiary companion (soon available in WD). Wilson (2005) describes an implementation of MOUCE that includes period change events so that P need not be constant. Given the large database of times of minima, MOUCE should also allow for their inclusion in analyses and this is a simple thing to do since WD computes

Eclipsing Binaries: Future Work 97 times of conjunction. Thus it will soon be possible to do simultaneous analyses of light curves, radial velocity curves and times of minimum to accurately determine ephemeris parameters with realistic error estimates. 3.3. Software Improvements WD was developed over thirty years ago when the concept of the graphical user interface (GUI) did not even exist. In order to keep the program portable across computing platforms, it is written standard Fortran and uses simple text files for input and output. Analysis of results such as plotting fits to data requires the use of external programs. Now that cross-platform GUI technologies are available, efforts to create a more efficient work environment around WD have appeared. Over the years I developed GUI environments for WD that ran on the Windows and OS/2 operating systems. Recently, I have been working on a GUI written in Java that can run on any operating system that has a Java interpreter. A much more powerful environment is PHOEBE, developed by Andrej Prša and described in Prša & Zwitter (2005). PHOEBE is much more than a GUI on top of WD. It is a complete environment for performing analyses of eclipsing binary data that happens to include a GUI. It consists of three components: a library of functions, the scripter and the GUI. The heart of PHOEBE is the library of functions that compute various astrophysical quantities needed for binary stars. The scripter makes it easy to perform various tasks involved in eclipsing binary data analysis such as computing a light curve given a set of binary parameters or fitting observations using different optimization schemes. This modularized approach enables users to create an analysis environment that fits their needs. One could, for example, create a new GUI for PHOEBE that has capabilities not included in the distributed version. PHOEBE was developed to make data analysis more efficient and this will become more and more important as the number of quality datasets for eclipsing binaries increases. In the next decade datasets of astounding size and accuracy will arrive and these will require much more efficient analysis techniques than we currently use. Munari et al. (2001) estimate that Gaia will observe approximately 4 10 5 eclipsing binaries brighter than V = 15 and that 10 5 of those will be double-lined. Traditional analysis techniques will obviously be insufficient to deal with this volume of data so automated analyses will be crucial. Preliminary work along these lines has been done (e.g., Wilson & Wyithe 2003) but this will prove to be a vigorous area of research over the next few years. 4. Planets in Binaries One very exciting new area of research is the detection and analysis of extrasolar planets in binary systems. In the past decade nearly 200 extrasolar planets have been discovered and a few of them are in binaries. These planets in binaries are all of the type where they orbit one star of the binary while the other star orbits farther away. There is no reason to believe, however, that planets could not exist in orbits around a close binary. Searches for planetary transits in eclipsing binaries could prove fruitful since the eclipsing nature of the binary means, in most instances, that the orbital

98 Terrell plane of the binary is close to edge-on, increasing the probability that potential circumbinary planets would transit the stars. The first search for terrestrial-size planets around a star (binary or otherwise) was performed by Doyle et al. (2000) who observed the low-mass eclipsing binary CM Dra. Now that large numbers of gas giant planets have been discovered around other stars, the race is on to discover Earth-like extrasolar planets that might potentially be habitable. Almost all of the theoretical work on habitability has been done in the context of single star solar systems like our own. But close binaries might also prove to be interesting subjects for habitability studies. My colleagues David Kaufmann and Mark Bullock and I have begun work on a set of codes to look at climate development on terrestrial planets in binaries. Full treatments of the dynamics, stellar evolution and climatology will be done. We follow the evolution of the stars, including any mass transfer and mass loss from the system, and integrate the motion of the planets. The stellar evolution code gives the properties of the stars (e.g., surface temperatures and luminosities) which are then input into WD to predict the spectrum of radiation at the top of the planetary atmospheres. A climate code then predicts how the planetary atmosphere responds to this changing radiation field. Four questions arise when considering the possible existence of habitable planets in binaries: (1) Can planets form in binary star systems? (2) Can these planets remain in stable orbits for long (i.e., gigayear) periods of time? (3) Can the stellar components remain stable for sufficiently long periods of time? (4) Can habitable planets develop in binary star systems? The first question appears to have been affirmatively answered both observationally and theoretically. Giant planets have been detected in binary systems (Butler et al. 1997; Cochran et al. 1997) and circumstellar and circumbinary disks are frequently observed in pre-main-sequence binaries (e.g., Rodriguez et al. 1998; McCabe et al. 2003). Theoretical studies of terrestrial planet accretion during binary formation (e.g., Quintana et al. 2002; Barbieri et al. 2002; Marzari & Scholl 2000) indicate that planet formation should occur but the question of terrestrial planet formation in close binaries, which is naturally more complex than that in single star systems, is the subject of active research. The second question has been studied in some detail (Holman & Wiegert 1999, and references therein) and although important questions still exist, simulations indicate that the required dynamical stability can be achieved. One of the goals of our work is to explore the stability question more thoroughly and more realistically than has previously been done by including the effects of the evolution of the binary. The answer to the third question depends greatly on the nature of the particular binary system. Detached binaries with solar-type components and the very common W UMa binaries are just two examples of binaries where the evolution of the stars proceeds on a gigayear timescale with interesting (but not catastrophic) stages occurring on shorter timescales that could affect habitability. Given the high frequency of binary stars and the fact that pre-main-sequence binaries very often have circumstellar and circumbinary disks capable of forming planets, we think it is important to explore the interesting question of the climatic evolution of planets in binary systems. The issue of habitability is more complex in binaries than in single star systems because the spectral energy distribution reaching a planets atmosphere and its evolution with time depend on two

Eclipsing Binaries: Future Work 99 stars that may be evolving at different rates and whose evolutionary timescales may be radically altered by the presence of the other star. This complexity must be dealt with via detailed calculations of stellar structure and evolution, planetary dynamics and planetary atmospheres of the kind we are currently undertaking. We hope to use these simulations to find the kinds of binary systems that are most favorable to habitability. The results should enable us to choose optimal targets for projects designed to detect Earth-like planets. Given the large numbers of binary systems, they must be included in extrasolar planet surveys if we are truly to understand the frequency and properties of these planets. 5. Conclusion The next decade will see the arrival of eclipsing binary datasets unprecedented in size and accuracy. These datasets will enable us to probe binary stars in new ways and provide answers to questions that have puzzled us for decades. New analysis techniques and codes will have to be developed to fully extract the information in these datasets. The prospect of having an overabundance of high-quality data will make for an exciting period to be involved in research on eclipsing binary stars. The topic of extrasolar planets in binary star systems is also sure to receive a lot of attention from both observers and theorists. Who knows, even Mars researchers might suddenly become interested in binary stars when we discover habitable planets orbiting them and I might have a resurgence in my interest in dirt. References Barbieri, M., Marzari, F., & Scholl, H. 2002, A&A, 396, 219 Butler, R. P., Marcy, G. W., Williams, E., Hauser, H., & Shirts, P. 1997, ApJ, 474, L115 Chandrasekhar, S. 1946, ApJ, 103, 351 Chochol, D., & Wilson, R. E. 2001, MNRAS, 326, 437 Cochran, W. D., Hatzes, A. P., Butler, R. P., & Marcy, G. W. 1997, ApJ, 483, 457 Doyle, L. R., et al. 2000, ApJ, 535, 338 Eggleton, P. P. 2002, Exotic Stars as Challenges to Evolution, C. A. Tout and W. Van Hamme (ASP Conf. Ser. 279) (San Francisco: ASP), pp. 37-45 Genet, R. M., Smith, T. C., Terrell, D. & Doyle, L.(2005), Proceedings of the 24th Annual Conference of the Society for Astronomical Science, pp. 45 54, http://www.socastrosci.org/files/sas_proceedings_2005.pdf Holman, M. J., & Wiegert, P. A. 1999, AJ, 117, 621 Kemp, J. C., Henson, G. D., Barbour, M. S., Kraus, D. J., & Collins, G. W. 1983, ApJ, 273, L85 Leung, K.-C., & Wilson, R. E. 1977, ApJ, 211, 853 Linnell, A. P., Etzel, P. B., Hubeny, I., & Olson, E. C. 1998, ApJ, 494, 773 Linnell, A. P., & Hubeny, I. 1994, ApJ, 434, 738 Marzari, F., & Scholl, H. 2000, ApJ, 543, 328 McCabe, C., Duchêne, G., & Ghez, A. M. 2003, ApJ, 588, L113 Meibom, S. & Mathieu, R. D. 2005, ApJ, 620, 970 Munari, U., et al. 2001, A&A, 378, 477 Orosz, J. A., & Hauschildt, P. H. 2000, A&A, 364, 265 Prša, A., & Zwitter, T. 2005, ApJ, 628, 426

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