2 The problem of folding

A typical unreduced rotation curve is shown in Fig. 1 and, in this figure, the origin of the angular coordinate axis denotes the measured optical centre, $O_{{\rm opt}}$ say, of the galaxy; apart from projection corrections (required because spiral galaxies are generally not seen edge-on), a successful folding of this rotation curve requires (a) an accurate estimate of the cosmological redshift, $V_{{\rm sys}}$say, that must be subtracted from the velocity measurements along the whole curve; (b) an accurate estimate of the dynamical centre, $O_{{\rm dyn}}$say, of the rotation curve.

Figure 1: Typical unfolded rotation curve

The MFB data-base for the unreduced curves provides approximations for $V_{{\rm sys}}$and $O_{{\rm dyn}}$ (this latter being identified with $O_{{\rm opt}}$) which are sufficiently good for the peculiar velocity studies which motivated MFB but not good enough for the dynamical studies which motivated PS. So, the problem resides entirely in the accuracy with which $V_{{\rm sys}}$ and $O_{{\rm dyn}}$ can be determined, and the major obstacle to obtaining this accuracy is simply the noisiness of rotation curve data - if the galaxies from which the data was drawn were perfectly rotationally symmetric, and if the measurements were exact, then it would be a trivial task to find the centre of asymmetry of any rotation curve.

   
2.1 Assessment of noise in MFB $H_\alpha$ velocity data

As a means of determining the level of noise in each velocity measurement, MFB provided a cross-correlation coefficient, $0 < \rho \leq 1$, derived by comparing the H$_\alpha$ line profile with an artificial template line profile (see MFB for details). In their analysis, PS found that selecting those velocities for which $\rho > 0.35$ gave a mean rms of less than about 10 km s^-1, whilst for $\rho \leq 0.35$ an rms of up to 20 km s^-1 was to be expected. For this reason, they restricted their data to values for which $\rho > 0.35$.

In our development, we have found that $\rho > 0.4$ is necessary for the accurate operation of the auto-folder being developed.