f (x ) = y « p3(x ) = ^^^ + v4y0 + 41 (42 y—1 + 42 y0)
The implementation of this method of interpolation should provide an option to compare the exact light curve with the interpolated one by inspecting the standard deviation and the maximum deviation, thus allowing some control over the error produced by interpolation. Since the standard error of a single observation of observed light curves, aobs, usually (if light is normalized to unity) is not smaller than 0.005, any error caused by interpolation, say, by a factor of 10 smaller than aobs, can be safely neglected. This level of accuracy is usually achieved with n = 50 or n = 100 subintervals. Since well-observed EB light curves cover a few hundred data points, say 300-400, the reduction in computational time is significant. The simple interpolation scheme presented above may be replaced by a more sophisticated cubic spline interpolation.
In order to choose appropriate surface grids, we should consider that the time needed to compute lcal(0) is proportional to the number n+ of integration points on the stellar surface. When constructing a grid of surface points or elements, we should have accuracy, symmetry, and the exploitation of symmetry by mirror imaging in mind. Symmetry properties, as discussed in Sect. 4.5.1, may reduce computation and memory. Let us assume that the x-y and x-z planes are symmetry planes for each component. Notice that there is a potential problem in carrying out the actual mirror imaging, in that equatorial and polar points will be duplicated upon reflection. Accordingly we can eliminate equatorial and polar points. We can do this by placing the first and last latitude curves at half-spaces from the pole, and near-equatorial curves at half-spaces above and below the equator. If we have N of latitude curves, they are located at polar angles
A similar argument holds for the distribution of longitude points on the latitude curves. In addition, it improves accuracy if the density of points is reasonably uniform over the entire surface. This goal is obtained, for instance, if the number Ni of longitude points on a latitude curve is proportional to the sine of the polar angle of that curve, i.e., as used in the Wilson-Devinney program, and the points are distributed uniformly on this curve. The proportionality factor 1.3 is an artifact of the integration accuracy requirements of the WD program. The total number of grid points on the stars thus depends on the number N of latitude curves on a hemisphere according to the following formula:
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