Choosing a gradient estimator

Now the program knows which stars have been observed, and can show you a two-color diagram of the available standards. It displays a plot of the two nearest color indices for each band. For example, in the uvby system, plots of vs. are displayed for the u and v passbands, and plots of against for both b and y. The degree of correlation between the two displayed color indices is also printed. The goal is to select an appropriate estimator of the stellar spectral gradient across each passband.

You are now asked to choose whether to use the single default color index (which would be for u, and for v), or both colors displayed on the plot, as the basis for transformations. In general, if the plot shows a high degree of correlation, adding the second index adds little information, and may weaken the solution by allowing an additional degree of freedom to be adjusted. If the points cover an appreciable two-dimensional area, or follow a curved line rather than a straight one, you may gain substantial accuracy in transforming by using both indices as independent variables. When in doubt, ask the program for help.

Note that you make this choice separately for each passband. (It might make sense to use two colors in reducing b, but only one in reducing y, even though the same 2-color diagram is presented in each case.) Once you have set this choice, it will be followed throughout the remainder of the run.

Note that you will be given this choice only if there are enough standard stars to make it a reasonable course of action. With only a few standards, and too many adjustable parameters, there is the danger that the program may simply fit a function to a few points and ignore the rest.

In principle, these plots should employ the instrumental rather than the standard colors of the standard stars. Unfortunately, the choice of a gradient estimator must be made before extinction-corrected instrumental colors are available, so the standard colors must stand in for the instrumental ones. In practice, this should not be a problem, unless the instrumental system is a very poor match to the standard one. For example, if the B band of a UBV photometer includes too much ultraviolet, the instrumental B-V index may contain appreciable contamination from U that would not be seen in the standard 2-color plot.