## Phenomenological Classification of Eclipsing Binary Light Curves

Examples of prototypical light curves are shown in Fig. 1.1. They correspond to the classical categories, discussed above, of Algol, ft Lyrae, and W UMa light curves, also known as EA, EB, and EW light curves, respectively. Fig. 1.1 (continued) Classes of light curves. (a) Shows a synthetic Algol-type light curve (V band). It has been produced using the parameter file algolv.bmd from the Binary Maker 2.0 examples collection (Bradstreet, 1993). (b) Shows a synthetic ft Lyrae-type light curve (V...

## Third Body Effects on Light and Radial Velocity Curves

EBs are sometimes members of multiple star system cf. Mayer (2005) and references therein . Among 728 multiple systems with 3-7 components contained in an extended 6 1999 edition of the Tokovinin (1997) catalogue of physical multiple stars, there are 83 eclipsing binaries. In the simplest case a third body orbits with the binary around the system barycenter. Observational evidence of third bodies comes from spectroscopy (disturbances of the radial velocity curve), or from analysis of times of...

## References

M., Torres, G., Latham, D. W., Sozzetti, A., Mandushev, G., Belmonte, J. A. , Charbonneau, D . , Deeg, H. J. , Dunham, E. W. , O'Donovan, F. T., & Stefanik, R. P. 2004, TrES-1 The Transiting Planet of a Bright K0 V Star, ApJ Letters 613, L153-L156 Basri, G. 2000, Observations of Brown Dwarfs, Annual Review of Astronomy and Astrophysics 38, 485-519 Benedict, G. F., McArthur, B. E., Forveille, T., Delfosse, X., Nelan, E., Butler, R. P., Spiesman, W., Marcy, G., Goldman,...

## Star Spots and Other Phenomena of Active Regions

As is observed on our own Sun (Fig. 3.22 ), stars can have spots. Stellar surface imaging by microlensing cf. Sasselov (1998a, b) shows directly that spots are present on other stars as well. A star spot is a region with higher or lower temperature than the surrounding photosphere, and thus it modifies the local flux. By way of physical analogy to the Sun, we should expect magnetic spots to result from convection in the outer envelope and differential rotation. Accompanying phenomena include...

## Morphological Classification of Eclipsing Binaries

The dynamic forces controlling the stellar mass distributions involve the effects of rotation, tides, and noncircular orbits. For an introductory-level discussion of all these effects, see Wilson (1974). Fortunately, tidal forces produce circular orbits and synchronous rotation in many interacting binaries. A detailed and excellent analysis of the tidal evolution in close binary systems is provided by Hut (1981). The orbital period of a synchronous rotator in a circular14 orbit is the same as...

## Hills Model

The program LIGHT2 Hill (1979), Hill & Rucinski (1993) is the result of mating Hill's previous modeling program called LIGHT, which combined the Roche model with Wood's (1971, 1972) GauB-Legendre quadrature scheme, and Rucin-ski's WUMA3 (see Sect. 6.3.5) model which was derived from Lucy (1968). It achieves an accurate representation of the system brightness while dealing with horizons and eclipses. The LIGHT2 program has the following characteristics blackbody semi-empirical hybrid of...

## Nightfall

NIGHTFALL by Wichmann (2002) is a freely available amateur code2 for modeling eclipsing binary stars. It supports a large range of binary star configurations, including over-contact (common envelope) systems, eccentric (noncircular) orbits, mutual irradiance of both stars (reflection effect), surface spots and asynchronous rotation (stars rotating slower or faster than the orbital period), and the possible existence of a third star in the system. It allows the user to produce animated views of...

## Gravity Brightening

Hydrostatic equilibrium is equivalent to constant density and pressure on equipo-tential surfaces. If we assume that density p, temperature 26 T, and pressure p are related to each other by an equation of state, e.g., the ideal gas law, 26 Note that this temperature is the local thermodynamic temperature which differs conceptually from the effective temperature defined as a function of bolometric flux. p RpT, R 8.31451 J mol-1K-1, (3.2.9) with the universal gas constant R, then on...

## Determining Individual Temperatures

One of the main difficulties of modeling EBs is the accurate determination of the individual temperatures. Frequent practice in the literature is to assume the temperature of one star, or better to obtain it from spectra or color indices in an a priori step as described on page 199, after which the other star's temperature follows by fitting the light curve model to the data. In this two-step approach, the accuracy of the estimated temperature depends either on the how well the individual...

## The Wilson Devinney Program Extensions and Applications

Since the Wilson-Devinney program is the most widely used of all the light curve modeling tools, it is appropriate to describe its features, capabilities, and continuing development in some detail. The WD program itself has seen continual improvements, and the current version briefly summarized in Chap. 6 with its powerful features provides the opportunity to extract a maximum of information from a variety of observational data. As a side-effect, publications on the WD model and on the WD...

## Light Curve Software with Graphical User Interface and Visualization

Ad unguem to a fingernail exactly nicely done In this chapter we summarize the approach and current contributions to this area by a number of authors. Here, however, direction rather than specific packages must be emphasized because this subfield is rapidly changing. Graphics and visual support1 include the plotting of light curves, graphing of the fit and residuals, providing projected views of the components, and sometimes the distribution of such physical quantities as surface brightness,...

## Star Planet Systems and Eclipsing Binary Models

In EB models or programs we need to characterize planets by those parameters usually used to describe stars. The fundamental parameters are mass, radius, and temperature. A star-planet or other low-luminosity object system, with transits and radial velocities for the star only, is analog to a single-lined spectroscopic and detached EB. The orbital period, P, can be obtained from either radial velocities or light curves of the system and is usually the most precisely determined quantity. The...

## Passband Luminosities Phoebe

Where the second column applies to main sequence stars V , sub-giants IV , giants III , and bright giants II , the third one I to supergiants. To make use of this scheme, CIs from other passbands, e.g., Johnson V and Cousins I, need to be trans formed into B - V in order to use Flower 1996 , e.g., by exploiting Caldwell et al. 1993 who provide different color index dependencies on B - V .As these calibrations only serve to obtain an initial value of TB t , there is no need to worry about...

## Phoebe

PHOEBE PHysics Of Eclipsing BinariEs by Prsa amp Zwitter 2005b is a modeling package for eclipsing binary stars, built on top of WD program Wilson amp Devinney 1971, Wilson 1979 . The introductory paper by Prsa amp Zwitter 2005b overviews most important scientific extensions incorporating observational spectra of eclipsing binaries into the solution-seeking process, extracting individual temperatures from observed color indices, main sequence constraining and proper treatment of the reddening ,...

## Info

This potential may be used without significant inconsistencies, if the timescale for nonradial oscillations is much smaller than the orbital period P. In the eccentric orbit case d depends on phase 0 instead of Q r q, d so we also use the notation Q r q,0 in the context of eccentric orbits to indicate that the potential and stellar surface depend on phase. We also need the gradient VQ, i.e., the partial derivatives r2 x2 y2 z2 r2 d - x 2 y2 z2 and for the secondary component in the same...

## The Eclipsing Binary Orbit Program EBOP

Etzel's 1981 Fortran program EBOP is based on the Nelson amp Davis 1972 spheroidal model called the NDE model. It is an efficient software for the analysis of detached binary systems with minimal shape distortion due to proximity effects. 4 It is not appropriate for modeling significantly deformed components. The NDE model and its assumptions are close to those in the rectification model by Russell amp Merrill 1952 . However, as EBOP computes light curves directly, it is much more flexible and...

## Dynamics and Orbits

Points of the stellar surface are considered to belong to an equipotential surface. The mathematics of such level surfaces is similar to that of the zero velocity curves in the restricted three-body problem cf. Szebehely 1967 , in which a particle of negligible mass is subject to gravitational forces of two massive orbiting bodies. Within that framework two cases are distinguished circular orbits and elliptic or eccentric8 orbits. We treat them separately because the circular and the eccentric...

## D

If the distance is measured in parsecs and the parallax is measured in arc-seconds, the constant is kn 1. To couple the parallax to the binary model it is more convenient to measure the distance in units of the semi-major axis a. First, we include the parallax both as an observable and also as an adjustable parameter. Second, instead of the normalized light or flux l 0 usually used in light curve analysis, the flux lD 0 in absolute physical dimensions energy time wavelength unit receiver area...

## Mathematical Nomenclature and Symbols Physical Units

What's in a name Shakespeare Romeo and Juliet, ii, 2 A few general rules are observed vectors are marked as bold characters, e.g., x, n, or r. The product a b of two vectors a, b e IRn is always understood as the scalar product aTb Xn 1 aibi. Matrices are indicated with sans serif font, e.g., A. The list below gives our mathematical symbols and operators. IRn the n-dimensional vector space of real column vectors with n components V gradient operator V Vx gt gt dr applied to a scalar-valued...

## Viq

Reasonably good matches with the observedprofiles of several Algol-type binaries. He also used the more extensive radiative transfer code of Ko amp Kallman 1994 which treats several atomic species, but further work must be done to improve the efficiency of the calculations. Terrell amp Wilson 1993 computed the disk matter distribution and motion. Figure 3.25 shows their result for SX Cassiopeiae disk images at 0.32, 1.11, 3.18, and 7.96 orbital revolutions. Based on these calculations, their...