Appendix E: Convergence of auto-folder solutions as the numbers of included Fourier modes increase

The actual number of modes used for the folding of any given rotation curve is determined by
the mode-choosing strategy of Sect. 7, and this strategy assumes that this
number has a maximum limit determined by Sect. 6.2.
However, we find that the folding solution over the whole set of rotation curves
(defined as the
distribution) can be considered converged for all practical
purposes when a maximum of only *five* Fourier modes are included.
The illustration of this fact is given in Fig. E1, which displays
the solutions for the four cases of the 1-mode solution, the 3-mode solution,
the 5-mode solution and the 10-mode solution.
It is quite clear that the solution converges extremely rapidly.

In practice, all the Mk II, III and IV auto-folder solutions shown in the earlier figures have been computed using just five Fourier modes.

Copyright The European Southern Observatory (ESO)