High resolution is essential for spectral analysis, whereas low resolution may be quite sufficient for spectral classification. To be useful in binary star modeling, radial velocities as displayed in Fig. 2.5 must have a high level of precision and accuracy. Red shifts for distant galaxies are very large, for example, and there may be a paucity of (identified) lines in the visible region, so precisions of tens and even hundreds of km/s may not be considered too low. In binary star or pulsating variable star work, the radial velocity precision must be much higher to yield fundamental stellar data, such as the radii of pulsating stars or the masses of eclipsing system components. At present writing, typical radial velocity uncertainties are of order 1 km/s. Some very high precision has been achieved by specialized techniques, however; the use of absorption cells to ensure stability in conjunction with high-resolution spectrographs on large telescopes [see, e.g., Campbell et al. (1988), who used a hydrogen fluoride absorption cell] provided a means to detect very low-mass companions to nearby stars. The best that has been achieved to 1995 was ~10m/s; in 1998 it was ~ 4m/s (Kuerster et al. 1994). This improvement has been the main reason for the burst of discoveries of planetary systems of other stars beginning in 1995. See Butler et al. (1996) for a summary of these radial velocity improvements, and the likely prospects of further improvement in the near future, perhaps to 1 m/s.
Spectra can be measured directly or cross-correlated against a reference spectrum. The process of cross-correlation involves a method of systematic digital comparison between two spectra, in order to obtain the difference between the two radial velocities. Simkin (1974) first applied the technique to astronomy (in her case, to galaxy spectra). Typically, the Fourier transform of the linearized and rectified
50.025.0-g O.O--25.0-50.0-75.0 ■)——--1--[-1-1-1—---1--1 --1-1-
Fig. 2.5 Radial velocity curve of AIPhoenicis. This figure [Fig. 3 of Milone et al. (1992), adapted from Andersen et al. (1988)] of the long-period totally eclipsing system shows the observed and computed radial velocity curves
spectrum of the program star along with the conjugate transform of the reference spectrum is calculated, and the product of the transforms is evaluated. The cross-correlation function (CCF) can be described as the Fourier transform of this product. The reference spectrum may be that of a standard star with well-established radial velocity, a spectrum of the program star itself (at a specified phase), or a synthetic spectrum. Especially useful software programs, REDUCE and VCROSS, were developed to reduce and analyze stellar spectra by Hill et al. (1982) and Hill (1982). Wilson et al. (1993), working with this software, used for the 5 Scuti star EH Librae a reference spectrum of the same star obtained at a phase where the expansion was close to zero. This work achieved relative velocity precisions of a few hundreds of meters per second. The velocity difference was obtained from the spectral shift which produced the peak of the resulting CCF. When the program star is an EB, the CCF typically has two peaks, as in Fig. 2.6. Additional complications may be present, as we note below and in Sect. 2.2.3, but cross-correlations have measured radial velocities in many cases that were considered unpromising only a decade earlier, at least to the level of uncertainty of ~10km/s. Beginning in the 1980s [cf. McLean (1981)], cross-correlation techniques have proven crucial to our understanding of contact and other short-period interacting systems. A somewhat different method, involving a spectral "broadening function" (BF) and a modified singular value decomposition technique (SVD), has been used in recent years to obtain radial velocities by Rucinski (2002) and references therein. The broadening function basically transforms a narrow-lined standard star spectrum into a rotation-ally broadened one, more suitable for comparison with a short-period EB. The templates are standard star spectra and the method works best if they are of the same spectral types as the component stars of the binary. In fact, three-component systems
83438. <), * 0.236 36232. 0.286 36135, = 0.098 66244, $ - 0.261
Comp HD 151417 Comp. HD 103G9& Comp. HD154417 Comp. H0102STO
83438. <), * 0.236 36232. 0.286 36135, = 0.098 66244, $ - 0.261
Comp HD 151417 Comp. HD 103G9& Comp. HD154417 Comp. H0102STO
■400 0 4-100 -400 0 +400 -400 0 4-400 -400 0 4-400
RADIAL VELOCITIES IN km/sec
Fig. 2.6 Cross-correlation functions for RW Comae Berenices. This figure is Fig. 1 in Milone et al. (1984, p. 110)
■400 0 4-100 -400 0 +400 -400 0 4-400 -400 0 4-400
RADIAL VELOCITIES IN km/sec
Fig. 2.6 Cross-correlation functions for RW Comae Berenices. This figure is Fig. 1 in Milone et al. (1984, p. 110)
can be handled as well. The coefficients of the polynomial that defines a particular BF are determined by least squares, with Rucinski's (1992, 1999) SVD treatment. Higher RV precision is achieved by Rucinski in the cases where both BF and CCF methods are tried.
Whatever detection method is used, standards need to be intercompared because different techniques may have systematic differences. The IAU "Reports" lists the status of standard stars and indicates those suspected of variability. An up-to-date list can be found in the Astronomical Almanac for the current year. For bright stars, high-resolution techniques have yielded very small errors of measurement such that planets are being sought and detected with increasing confidence. However, the very high precision obtained for this purpose is unlikely to be achieved soon for short-period interacting EBs because of their rotational broadening and line blending.
Suppose we are observing from space so that atmospheric extinction problems are absent. If we can accomplish the necessary standardizations of effective passbands, the combination of spectroscopy and photometry can provide a rich bounty for light curve analysis. A large number of narrow passbands can greatly improve the radiative modeling of stars, because the wavelength-dependent parameters are adjustable for each passband and together provide strong leverage for the determination of the temperatures and for any thermal perturbations projected onto the disk surfaces. In addition, the weight of the nonwavelength-dependent parameters is increased by virtue of the large number of light curves. Suppose now that we attempt to do similar observations from Earth. As for broad- or intermediate-band photometry, the spec-trophotometric narrow-band photometry can be carried out relative to comparison stars, but corrections must be applied for differential extinction, and practically, it is very hard to do the comparison star observations.
The photometric precision requisite for high-quality narrow-band light curves is possible only if the photon flux is high enough. For a precision of 1% (neglecting other noise sources), we require a signal-to-noise ratio
of 100 so that the mean count n needs to be n « 10, 000. (2.2.6)
If the resolution element is of order 1 nm, only bright stars can be observed with intermediate-sized telescopes for reasonable length (t < 30 min) exposure times, because the signal-to-noise ratio, S/N a jr. In practice, some compromise between size of telescope and spectral resolution must be made. Schlosser et al.
(1991, pp. 206-207) demonstrate the effects of increasing the observing time on the S/N of spectrophotometry data.
Phase-dependent spectrophotometry has been carried out by Etzel (1988, 1990), who demonstrates its value for determining flux distributions and therefore color temperatures of components in totally eclipsing systems.
A promising technique to disentangle the separate spectral distributions of the component stars from the composite spectrum of an EB is discussed by Simon & Sturm (1994). The method of spectra disentangling (Hadrava, 1995) combines simultaneously the splitting of the spectra observed at different orbital phases into spectra of individual components of the spectroscopic binary, the measurement of radial velocities at each phase and the solution of orbital elements. The first part of this problem for known radial velocities may be solved, e.g., by the method of tomography separation. The second part is the aim of the cross-correlation method, for which template spectra of the components known are needed to find their shifts in the observed spectra. Finally, the third part involves the solution of the radialvelocity curves. The direct fitting of observed spectra by the best component spectra and the orbital parameters (or individual radial velocities) is thus a more reliable and less laborious procedure. The method could be generalized to get still more information from the line-profile variations.
KOREL is a code developed by Hadrava (2004) for spectra disentangling using Fourier transforms. It allows application of the method of "relative line photometry," i.e., to find the variations of line strengths. From the beginning in 1997 KOREL takes into account up to five components in a hierarchical structure of a multi-ple7 stellar system. One of them (e.g., the widest one) can be identified with the telluric lines, which can be separated from the observed spectra in this way and can yield a check (or correction) of the proper wavelength scales of individual exposures. Several regions around important spectral lines can be solved simultaneously. The numerical method of the solution is based on the fact that the modes of Fourier transforms of component spectra are multiplicative factors at the complex exponentials corresponding to Doppler shifts in the Fourier transformed space of frequency logarithms. They can thus be calculated by the least-squares method, whereas the orbital parameters (or radial velocities) can be fitted, e.g., by the Simplex method. The quadratures could enable to expose individual spectra for a rare case of visual binaries with elongation about an arcsec (but these would have long periods and small radial velocity amplitude and an interferom-etry would provide better light ratio). But the individual spectra could be obtained during eclipses, what Simon & Sturm (1994) used to prove that their methods works well.
The technique is said to work on artificial spectra down to a signal-to-noise ratio of 10. An important requirement to identify which part of the continuum originates from each star to be able to scale properly equivalent widths of the lines in the
7 Another code, spsyn by Barden and Huenemoerder dating back to Barden (1985), also supports the analysis of triple systems and is based on Fast Fourier Transforms.
decomposed spectra is that the light ratio in the range of the spectra must be known with high precision - either from light curve analysis or from the spectra themselves if the separate features of the spectra can be discerned (at quadratures,8 say) and the components are not too dissimilar in temperature and luminosity. The pure determination of orbital parameters is reliable without this condition as the light ratio can be estimated from fitting the decomposed spectra by model spectra. The requirement that the light ratio does not vary with phase tends to limit the technique to widely separated eclipsing (or noneclipsing) binaries, although the authors indicate that the limitations of the constant light ratio assumption is overcome by the variable line strength factors implemented in KOREL of 1997. A more difficult but not impossible task is to overcome the requirement that there be no variation of line-profile shape. To disentangle any variability requires the model, for instance, of Cepheid pulsations, to be fitted with some free parameters. Light-ratio variability is disentangled by the line-strength factors, variations of shape need more sophisticated models.
Lines in stellar spectra are images of the input slit on the output plane of the spec-trograph. However, even after allowance for the finite width of the input slit and instrumental diffraction, it is seen that spectral lines are broadened by a number of mechanisms originating in the star itself. The most basic of these mechanisms is the natural broadening that arises because the atoms' energy levels have probability distributions. According to the Heisenberg Uncertainty Principle, the product of uncertainties in position and in momentum and the product of uncertainties in time and in energy are of the order of Planck's constant, h:
Ax Ap > h, At A E > h, h = 6.62608 ■ 10-34 Js. (2.2.7)
Because the energy of a photon is equal to the difference between two energy levels of the radiating or absorbing atom, the frequency or wavelength of the photon will be affected accordingly. In particular, an atom absorbs from the continuum radiation at a wavelength which may be slightly different from the most probable one. The combination of all such absorptions produces an absorption profile.
A second source is collisional broadening. This broadening is due to perturbations of the energy level of the atom because of either of two effects. First, the passage of an atom in the vicinity of an atom undergoing an absorption or emission of a photon changes both the kinetic energy of the disturbing atom and the energy of the photon. This is known as collisional damping. A second effect is due to the
8 The quadratures could enable to expose individual spectra for a rare case of visual binaries with elongation about an arcsec (but these would have long periods and small radial velocity amplitude and an interferometry would provide better light ratio). But the individual spectra could be obtained during eclipses, what Simon & Sturm (1994) used to prove that their methods works well.
effects of the electromagnetic fields of nearby charged particles. This mechanism is known as Stark broadening; in most stars, the first effect is the more important except in the lines of hydrogen and of some helium lines. The denser the stellar atmosphere, the stronger these perturbations and the broader the spectral lines. This effect is important in the strong lines and is relatively strong in dwarf stars, which are more compact, than in giants and supergiants, which are much less dense. If the number of absorbers is small, the broadening is mainly due to thermal Doppler broadening (discussed next). As the number of absorbers increases, the line core saturates and the "damping wings," due to a combination of natural and collisional damping, begin to dominate. The curve of growth9 of spectral lines can be deduced from high-resolution spectra, and the abundances found.
A third major broadening source is thermal Doppler broadening. In the high-temperature environment of stars, the line-of-sight motions will be Doppler shifted relative to both the radiation upwelling from below and to the observer. The result is again a displacement of the absorption from line center for many photons, and a finite width. Because the motions of the atoms depend on the temperature of the stellar atmosphere, Doppler broadening depends on the temperatures of the regions in which the absorptions occur. This is the dominant source of line broadening for weak lines in the spectra of slowly rotating stars.
A discrete splitting of the energy levels of certain species of atoms occurs in the presence of magnetic fields. This is called Zeeman splitting. The number of components and their relative strengths differ from line to line; the lines are also polarized (see Sect. 2.3) in this process. Basically the splitting is proportional to the magnetic field strength, and inversely proportional to the mass of the atom. The typical pattern is a triplet, but each component of the triplet may itself be split into multiple components. The outside members of the triplet (or triplet groups) are called the a-component(s) and the inside ones, the n-component(s). The longitudinal effect is seen if the a -components are circularly polarized (in opposite directions, with left-handed circular polarization producing the higher frequency component) and the n-component absent; this occurs when the line-forming region is viewed along the direction of the magnetic field. The transverse effect is seen if the a -components are linearly polarized perpendicular, and the n -component linearly polarized parallel, to the direction of the magnetic field. When there are many noncoherent local magnetic fields associated with the line-producing region, a blend of these effects can be expected, blurring the Zeeman components and causing a net broadening of the line.
Mass motions on stellar surfaces (micro- and macro-turbulence, large-scale circulations, and stellar rotation, for example) contribute to line broadening through Doppler shifts. The effect of star rotation on spectral lineprofiles of EBs (Mukherjee et al. 1996) can be observed during eclipses in the form of the Rossiter effect, where
9 The term curve of growth refers to a graph of line strength versus the effective number of absorbing atoms [cf. Aller (1963)].
one of the two observed sets of radial velocities varies with the masking of the velocity contributions of the eclipsed part of a star (see Fig. 3.28). In binary systems of very short period, rotational broadening can degrade radial velocity accuracy and even prevent measurement, especially for stars near spectral types A and earlier. In such stars, the spectrum is dominated by very broad hydrogen and helium lines, but even the weak lines of other elements are spread out into a characteristic dish-shaped profile. "Blending" of lines compounds the problem. It is all the more remarkable, therefore, that over-contact systems containing stars of early spectral types (i.e., high-temperature stars) have been analyzed at all, let alone with good precision. With cross-correlation and related techniques being used regularly, the situation is expected to improve even more.
Cetera desunt (The remaining (parts) are lacking)
Polarization of the light of a binary component was predicted by Chandrasekhar (1946a, b). While searching for a confirmation of the prediction, Hall (1949a,b, 1950) and Hiltner (1949a,b) discovered the polarization of starlight due to scattering by interstellar dust. Additional sources of polarization in interacting binaries are
• light of one component scattered at the surface of the other;
• starlight scattered by a circumstellar disk, stream, or other locus of concentrated gas;
• thermal bremsstrahlung in the stellar environment (electron scattering in gas flows or in coronae); or,
• nonthermal bremsstrahlung (from flares);
• electron scattering in high-temperature atmospheres; and
• magnetic surface fields.
Observationally, the light observed through different rotations of a polarizing analyzer is measured at certain angles and corrected for instrumental polarization. The basic parameters are the following:
1. The fractional polarization,
Fmax Fmin where F refers to the observed flux or power through the polarizing filter (or polarizing analyzer), whereas the subscripts indicate maximum or minimum transmission of the flux at particular angular settings of the analyzer, 90° apart. 2. The position angle of maximum transmission, 0.
The polarization can also be given in terms of the weighted means of the Stokes quantities,10 Q and U. Concisely expressed,
Much astrophysical information about the nature of scattering disks and electron scattering envelopes around stars can be obtained in this way [see Wilson (1993)].
Although there are many polarimetric publications on EBs, most have been in the form of surveys rather than time-wise variation. Surveys can be very useful in identifying candidate stars, but tell us little about specific polarimetric behavior. Of course, polarimetry requires much brighter stars (or larger telescopes) than does photometry, and also much more sophisticated instrumentation. Still, polarimetric curves have been published for interesting close binaries but they typically have serious shortcomings. For example, the observational difficulties mentioned above result in rather small numbers of data points being collected. Attempts to compensate for this problem lead to folding of polarimetric curves on the orbital period, yet most polarimetric phenomena are not strictly periodic so that phased polarimetry has very limited usefulness.
Pioneering work in astronomical polarimetry was carried out by James Kemp (1927-1988), who was the first to discover circular polarization in the continuum of a white dwarf, GJ 742 (Kemp et al. 1970), and the first (Kemp et al. 1983) to discover the limb polarization in an EB (Algol, in fact) that was predicted by Chandrasekhar (1946a, b).
In recent years, much progress has been made in this field. Work by J. Land-street and his group in Canada and by J-F. Donati and his associates in France has been carried to a high level of precision through instruments such as ESPaDOnS (Echelle SpectroPolarimetric Device for the Observation of Stars) in use at the Canada-France-Hawaii telescope. The device is designed to measure polarization in spectral lines and permits the sky spectrum to be measured simultaneously. The exposures cover nearly the entire range 370-1050 nm, at resolutions of 68,000 and 80,000, depending on observing mode. With this instrument, stars as faint as 14th magnitude have been studied. The instrument must still take four exposures to produce the four Stokes quantities. However, there is another concern. In addition to the extensive observing time, painstaking care must be taken to keep the target object centered in the observing aperture, because systematic drift to one edge of the aperture can introduce continuum polarization; moreover, determination of the amount of polarization requires measurement of the difference in intensity between two beams emerging from the Wollaston prism, and these beams are transmitted by fiber optics to the spectrograph, and guiding errors may effect the two beams
10 Usually referred to as the "Stokes parameters." R. E. Wilson has pointed out that these quantities are measured directly. They are better called "Stokes quantities" to avoid confusion with parameters derived from light curve analysis.
differently. It has been estimated that instrumental scatter due to these effects can amount to 1 percent. When S/N requirements are 500 or more to achieve the goal of exploring polarization of weak sources as a function of phase, to permit magnetic field mapping, this level of uncertainty can be a concern. On the modeling side, polarimetric curves have had to be "rectified" to treat unwanted effects, as in the old light curve analysis days. Such analyses required removal of those effects from the observations, rather than expansion of the theory to reproduce them, as in normal scientific practice. Another shortcoming has been the use of artificial fitting functions (such as Fourier series) rather than direct representation in terms of a definite model. Finally, the majority of polarimetry papers have contained no published observations but only graphical presentations, so data have not been available in suitable form for improved analysis. Hopefully, practices will improve in the future.
Another reason for lack of adequate polarimetry studies may have been that until recently there have been few modeling programs which made use of polarization data. This is no longer the case, and hopefully, investigators will pay this important field more attention. Closer collaboration between model developers and observers of polarimetric data would also improve the situation. Observers should strive for good coverage not only in phase but also in time (see Sect. 2.6, item 5).
Embarras des richesses (Embarrassment of riches)
George E. Hale (1908) discovered magnetic fields in sunspots. Despite failures to detect a general solar field, he foresaw the possibility of detecting magnetic fields in other stars, a feat which was accomplished in 1946. A catalogue of stars showing large Zeeman effects (implying the existence of magnetic fields as high as 5000 GauB) was published by H. W. Babcock (1958). The technique (Babcock, 1962) involves separating the Zeeman components with the help of a polarization analyzer; the Zeeman splitting is different for the perpendicular and parallel components of the magnetic field. High-precision spectrophotometry and thus large telescopes are required. The stars with strong magnetic fields were mostly of early type (the "magnetic variables" are typically anomalous A-type stars), although large magnetic fields have been found in F-type stars also. In solar and cooler stars polarization is not easily measured, because the circular components of opposite polarity tend to cancel when localized dipolar fields add together. Marcy (1984) succeeded in measuring magnetic fields in 19 of 29 G and K stars examined through a technique which involved linear polarization components. He also found evidence for magnetic fields in bright RS CVn-type stars. To be fully useful for light curve modeling, the technique must be coupled to a mapping process. This has already been performed for polarization variations connected to radial velocity fields, as we note in the next section.
The comprehensive analysis of the eclipsing magnetic binary E1114+182 by Biermann et al. (1985) shows what data might be available in magnetic binaries. This binary is the first eclipsing AM Herculis binary system and the shortest eclipsing cataclysmic variable known. Einstein X-ray, optical photometry and spectropho-tometry, linear polarimetry, and radio emission data enter the analysis and provide tight information on the physical and geometrical status of this binary system.
2.5 Doppler Profile Mapping
De proprio motu (of its own motion)
Armin Deutsch (1958), William Wehlau (1967), and, more recently, John Rice (1996) and references therein, and other observers have applied line profile analysis to locate dark regions on single, rotating stars with strong magnetic fields. Goncharsky et al. (1982, 1983) used Doppler profile measuring techniques to analyze Ap stars, and Vogt et al. (1987) and Strassmeier (1994) used it to map cool spot regions on RS CVn-type binaries. The idea is that a spotted region will cause a depression in the continuum flux of the star from that region. If the region can be associated with a particular velocity field, and thus with a wavelength shift in the profile, analysis of the line profile for dips (absorptions due to dark spots) or bumps (emission due to bright spots) can then help to locate the longitude with respect to the central meridian of the spotted region. The method prefers fast rotating stars because it requires11 v sin i > 20km/s [see, for instance, Strassmeier (1997, Sect. 5.3)] in order to be effective, a condition that does not usually hold in stars of spectral types F, G, and K (Gray 1988, Chap. 7, p. 21). However, Strassmeier & Rice (1998) succeeded even in analyzing EK Draconis with v sin i > 17.5 km/s. Gray (1988, Chap. 7, p. 23) suggests an additional method of determining the longitude placement of "star patches" using profile asymmetries. Stellar tomography is a term that has been used to describe the use of high-resolution spectral profiles to explore the velocities of components of Algol and other binary star systems that have cir-cumstellar material. One of the most successful of the codes of which we are aware is SHELLSPEC, developed by Jan Budaj and Mercedes Richards.The simultaneous use of WD-type codes with this type of software tool may prove invaluable for future investigations. In fact Miller et al. (2007) seems to do just this. Details about SHELLSPEC may be found at the url http://www.astro.sk/ budaj/shellspec.html.
2.6 Advice to Observers
Docendo discimus (We learn by teaching)
This section contains suggestions to observers of EBs to help improve the database and its subsequent analysis.
1. Mid-range to long-period binaries (P > 5d, but especially P > 50d) need observations of all kinds. The P > 50d systems with giant or bizarre components may have interesting light curves even if they do not eclipse. The longer period binaries are nearly unexplored territory. They are perfectly suitable for APTs, (robotic) automatic photometric telescopes [cf. Milone et al. (1995) or Strassmeier et al. (1997)].
2. Infrared light curves have been neglected relative to optical light curves. Infrared light curves are especially needed for binaries with large temperature differences between the two components. Observations over at least one full cycle are critically important, especially if an optical light curve can be observed simultaneously. The main problem in the infrared has been the lack of a single set of standard passbands to which observations that are made from any observing site could be transformed. This is because the original Johnson JHKLMNQ passbands were not designed to fit cleanly within the Earth's atmospheric windows. Subsequent observers dealt with the problem by redesigning passbands suitable for their own observing sites. These, too, were not optimum for sites with different water vapor content. Consequently, there have been several generations of such passbands produced, and transformations between infrared passbands of different generations are particularly prone to systematic errors. The difficulty is that atmospheric water vapor absorption produces curvature in the extinction curve between 0 and 1 air- (actually water vapor) mass, an effect named after Forbes (1842), and this curvature may differ from hour to hour as well as night to night, let alone from season to season. Even differential light curves may be affected by systematic as well as random noise depending on the distance of comparison from target stars and the data sampling frequency. Beginning in the late 1980s (Milone 1989), a new approach was undertaken by IAU Commission 25. An infrared working group (IRWG) was set up to design a new of passbands that are optimally placed in the atmospheric windows. The result by Young et al. (1994) is a new set of infrared passbands (iZ, iJ, iH, iK, iL, iL', iM, iN, in, iQ) are transformable to a higher precision than are all previous passbands. The near infrared set (iZ, iJ, iH, iK) have been field tested and found useful for any site at which photometry can be carried out, with superior S/N and greater insensitivity to water vapor than nearly all previous infrared passbands (Milone & Young 2005). With such passbands, precise light curves may be achievable, and with that precision, more precise and accurate parameters made be determined.
3. Some "observational" papers that do not list any observations are being published. Advances in interpretation are such that 5 or 10 years after publication, the observations may remain the only worthwhile part of a paper. Graphs of observations and phased observations (without the absolute time information) are no substitute for actual data. Nor are promises of availability a substitute for published numbers. CD ROMs, data archives (such as the CDS in Strasbourg), and World Wide Web pages now make it easy to publish most kinds of observations. We should consider the likely long-term permanency of the repository to be selected. The commissions 27 (Variable Stars) and 42 (Close Binary Systems)
of the International Astronomical Union (IAU) might also support the archiving of variable-star data (Sterken & Jaschek, 1997, p. 2).
4. Certain binaries with active mass flow need to be followed continuously over at least several orbits. Such objects are suitable targets for APTs.
5. Concerning polarimetry, it is very important to observe over several consecutive orbits and to document the absolute time instead of only phases. Although light curves are nearly periodic, polarization curves mainly reveal transient events. They usually show only a jumble if folded in phase space. Whereas most light curves are published and nonpublication is (or should be) the exception, it is the other way around for polarization curves - usually they are not published and soon lost.
6. X-ray binaries constitute a new candidate class for precise light curve analysis. These objects provide X-ray duration constraints and arrival times of X-ray pulses. Here again, it is very important to publish actual observations, including absolute time information. As is shown in Sect. 7.3.1, X-ray binaries can provide excellent data for simultaneous fitting (see Sect. 22.214.171.124) of multiband light curves, optically determined radial velocities, and pulse arrival times -potentially a remarkable bounty of separate kinds of information.
7. Spectrophotometry provides an even greater potential bounty, and, in principle, thousands of light curves. Important requirements are that the spectra must be free of scattered light effects and similar comparison star spectra must be available (both conditions are rarely met). Consequently, precise spectrophotometry is rare. Such data need to be carefully processed so that the resulting light curves have the requisite precision. Data may be binned in order to improve precision, at the expense of spectral resolution, but the advantages of many multiwavelength light curves still obtain - the chief of which are the radiative properties of the components.
Many surveys have been conducted and those that have high resampling rates have produced variable star discoveries. One such survey known to us is that being conducted with the Baker-Nunn Patrol Camera (BNPC) of the University of Calgary's Rothney Astrophysical Observatory. This f/1 instrument as currently configured has a 4096 x 4096 chip in an FLI CCD camera as its detector and yields more than 19 square degrees of the sky on a single exposure. M. Williams has used the instrument to detect more than 30 variable stars in the range 11-15 magnitude (in a passband approximately equivalent to Johnson's R) in a single sky field. Of these, 24 are eclipsing variables. A fitted Rj is shown in Fig. 2.7. The analysis was carried out with the WD package including both simplex and damped least-squares options. The fitted curve is for a semi-detached model.
Much wider surveys have been carried out in searches for gravitational lens-ing (OGLE for Optical Gravitational Lensing Experiment), which is monitoring the
Model bn07ai2 BNPC light curves: Johnson R relative flux versus PHASE 1.1
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