Q - q for component 1 and the transformation (6.3.3) for changing into the coordinate frame of component 2. Iterations are stopped if

E.31 PLANCKINT - Planck Intensity

This subroutine returns the Planck intensity of the disk center over the range of temperature 500 K < T < 500,300 K. This is the integral of the Planck function (or blackbody function) folded by the response function of a particular bandpass over the whole star.

E.32 READLC* - Reading Program Control Parameters

This subroutine reads all control parameters needed in WD95 in order to run the least-squares solvers or to produce graphics.

E.33 RING - The Interface Ring of an Over-Contact Binary

This subroutine is called by SURFAS and is related to the construction of the surface of over-contact binaries. It computes the area fraction of surface elements intersecting the ring (resp. the plane), separating the components of over-contact binaries. Finally, subroutine RING, computes a Fourier representation of the ring.

E.34 RanGau - Generation of Gaussian Random Numbers

Subroutine RanGau generates pseudo random numbers with Gaussian probability in the range [-to,

E.35 RanUni - Generation of Uniform Random Numbers

Subroutine RanUni generates pseudo random numbers with uniform probability in therange[-1, +1]. The input number Sn, from which both output numbers are generated, should be larger than the modulus 108 and smaller than twice the modulus. The returned number smod will be in that range and can be used as the input Sn+1 on the next call.

E.36 ROMQ - Distance Computation of Surface Points

This subroutine replaces the older subroutine ROMQSP, which was programmed in single precision.

E.37 ROMQSP - Distance Computation of Surface Points

For a single point (0, <) on the surface of a component, this subroutine computes the distance r to the center of that component

In addition, the following derivatives are computed:

dr dr dtt

dq dtt dr

ROMQSP provides a convenient means to generate tables of dimensions and useful derivatives for output of the main program. The subroutine was replaced with ROMQ in the 1998 and later versions.

E.38 SIMPLEX* - Simplex Algorithm

This subroutine contains the Simplex algorithm. It calls subroutine SSR to compute light curves for a parameter vector x suggested by the Simplex algorithm.

E.39 SinCos - Surface Grid Sine and Cosines

This subroutine computes and stores the sine and cosine values for all surface grid points. This save some computing time.

E.40 SQUARE - Building and Solving the Normal Equations

This subroutine builds the normal equation, inverts the left-hand side of the normal equations, and determines the parameter corrections. Furthermore, the correlation matrix and parameter standard deviations are computed. The inversion of the normal equations is performed by subroutine DMINV.

E.41 SPOT - Modeling Spots

This subroutine checks whether a surface point (0, <) lies within any of n specified spots and corrects the local temperature. If a surface point is in more than one spot, this subroutine adopts the product of the spot temperature factors. Note that WD uses North polar "latitudes," running from 0° at the "North" pole to 180° at the other. In addition, 0sc and <s refer to the coordinates on stars of a particular spot of radius ps. The angular distance 4s of the point (0, <) from the center of spot s follows from (3.4.3), and the spot-free local temperature T at (0, <) is modified by the temperature factor tf according to (3.4.5). The effects of star spots are treated as part of the aspect computations. The reason is that only a quarter of the surface points are stored, so as to save on memory needs. Note that spots break the up-down and right-left symmetry of the model star.

E.42 SSR* - Computation of Curves and Residuals

This subroutine receives the adjustable parameters from the Simplex algorithm, and the Levenberg-Marquardt algorithm picks up the all other input parameters from common blocks, prepares the total set of parameters and other data to the WD program, and invokes subroutine DC to compute all light and radial velocity curves for all observed phase values and residuals. SSR is used within the context of the Simplex algorithm and the Levenberg-Marquardt-type damped differential corrections algorithm. The standard deviation of the fit and errors of the parameters are returned to the calling subroutines.

E.43 SURFAS - Generating the Surfaces of the Components

This subroutine generates the spherical and rectangular coordinates of the surface elements of each component, computes the rectangular components of the surface potential gradient and other quantities which only depend on the surface elements. The grid spacing and the motivation for it has been described in Sect. 4.5.3.

E.44 VOLUME - Keeping Stellar Volume Constant

For eccentric orbits, this subroutine computes the phase-dependent Roche potential such that the volumes of the stars are kept constant.


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