The WilsonDevinney 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,...
StarPlanet 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 Nhy
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...
N Vjf
Aiv xk Axk Wvdv xk Axk 0, i 1, , n. 4.3.4 Taylor-series expansion up to first-order derivatives gives A xk AxTG W d xk AT xk Axk 0, or with the Hessian matrix G interpret this as an M n, n matrix at each data point indexed by v 5 Many photometric light curve data have been analyzed with the Wilson-Devinney program Wilson amp Devinney, 1971 who were the first to use the method of Differential Corrections with a physical light curve model. Gij dv x , G e M n, n, N . 4.3.5 Multiplication and...
Info Uon
This gives a measure independent of the number m of free parameters and the number of data points, n. Thus, the inverse problem of light curve analysis is reduced to the following problem Given a light curve model and a parameter vector x x , x2,xm T, we seek a solution in multidimensional parameter space minimizing the quadratic form RTR. Equivalently, as a measure for the quality of the fit, we minimize afit, which is normalized by the number of observed data points and free parameters. 3...
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...
References 1
Aitken, R. G. 1964, The Binary Stars, Dover Publications, Philadelphia, PA, 3rd edition Baade, W. 1944, The Resolution of Messier 32, NGC 205, and the Central Region of the Andromeda Nebula, ApJ 100, 137-146 Baldwin, J. E., Beckett, M. G., Boysen, R. C., Burns, D., Buscher, D. F., Cox, G. C., Haniff, C. A., Mackay, C. D., Nightingale, N. S., Rogers, J., Scheuer, P. A. G., Scott, T. R., Tuthill, P. G., Warner, P. J., Wilson, D. M. A., amp Wilson, R. W. 1996, The First Images from an Optical...
D 1
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...
Info Vpv
V 0 Vc 0 Vt 0 3.5.5 of the primary, with an analogous expression for the secondary. In absolute units we eventually get Vj 0 -ajosin 0 sini rnaAVij 0 y, j 1, 2. 3.5.6 Here a constant velocity, y , is added to account for the velocity of the center-of-mass of the binary system. More realistic modeling of the proximity effects and their influences on the radial velocity curves might consider the variation of line strength. To measure line strength the line equivalent width is used. On stars with...
Info Bhz
Fig. 4.5 Noise contributions in various regimes of star brightness. Adapted from Fig. 1 in Code and Liller 1962, p. 285 . For the brightest stars, seeing or scintillation dominates for fainter stars, shot noise is most important and for the faintest stars, fluctuations in the sky background contribute significantly to the noise. Notice the region where the shot noise due to the sky background Sky Limited becomes dominant over the shot noise from the star
X 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...