Appendix F: Miscellaneous comments

F.1. The damped Mk IV auto-folder

The basic Mk IV auto-folder gives excellent folds for most rotation curves, and all of the Mk IV solutions displayed have been generated using from basic model. However, for a very few individual rotation curves, it gives folds which are manifestly poor, and the problem always manifests itself in the form of allowing the estimated position of $O_{{\rm dyn}}$ to be greatly in error. It is found that replacing the standard function-to-be-minimized,

$$F(M) = \sum^M_{m=0} \left[ A(m) \right]^2$$

by

$$F(M) = \sum^M_{m=0} \left[ A(m) \right]^2 + 4 (\Delta O_{{\rm dyn}})^2,$$

where $\Delta O_{{\rm dyn}}$ is the calculated correction (measured in arcseconds) to the initial estimate for the position of $O_{{\rm dyn}}$, damps the overgrowth of $\Delta O_{{\rm dyn}}$ in the few pathological cases, but without having any marked effect on the well behaved majority.

F.2. Missing rotation curves

Although the PS sample contains 900 folded rotation curves, the corresponding data base used here to develop the auto-folder only contains data for 877 (unfolded) rotation curves. The discrepancy of 23 rotation curves has arisen because the corresponding galaxies were supplied with incomplete information in one of the source data-bases provided by MFB.

F.3. Failure to fold thirteen rotation curves

Of the 877 rotation curves, the auto-folder failed to fold thirteen. Investigation showed that this was because, after choosing only those velocities for which MFB's cross-correlation coefficient exceeded 0.4 (see Sect. 2.1 concerning data quality) eleven of the thirteen rotation curves concerned had no velocity measurements on one side of the rotation curve, whilst two had only one measurement.