Up: On the automatic folding
Rotation curves are the primary source of information about spiral galaxy dynamics
and, as such, they are essential tools for any programme which seeks to determine
relationships between dynamics and mass distributions in spiral galaxies -
whether this is for dark matter studies, or for testing gravitational theories.
However, before they can be used in any dynamical context, they must be accurately
Prior to the PS contribution of 900 accurately folded optical rotation curves,
there was no large data base available and, so far as we are aware, even though a large amount
of unfolded data is available, no other large data base of folded rotation curves
has subsequently been made available.
The reason for this absence is most probably that rotation curve folding has
hitherto been a labour-intensive "by eye'' process - fine for small
volumes of data, but extremely time consuming for large volumes of data.
For this reason, we undertook to attempt the development of an automatic
In the event, it has turned out that a successful development has only
been possible because of the availability of the PS data-base of 900
rotation curves which has acted as an essential template against which
the performance of the auto-folder described here was judged in the various stages of
In addition to this, the development has required the recognition, and
use, of certain correlations (previously unsuspected, so far as we are aware)
which point directly to underlying physical processes, the study of
which may lead to a deeper understanding of spiral galaxies and their evolution.
The PS sample of folded optical rotation curves was analysed in Roscoe 1999A,
and gave rise to the following primary result: defining R to be the radial
displacement from the kinematic centre and V to be the rotational velocity
at radial displacement R, then, to a very high statistical precision,
rotation curves conform to the law
where M denotes absolute magnitude, S denotes surface brightness and
is a parameter, constant for any given galaxy, but which which
varies between galaxies.
The high statistical precision which accompanied this result implied, in its
the PS folding process was very reliable and that their sample of folded
rotation curves could be considered as a "model solution'' against
which the success, or otherwise, of any automatic folding algorithm could
be properly judged.
Consequently, in all that follows, the developing auto-folder is continually
tested by using it to fold the raw MFB data which formed the core of the PS sample,
and comparing the resulting solution with the PS solution over the same sample.
In Sect. 2 we describe the general problem of folding rotation curves
whilst, in Sect. 3, we describe precisely what quality of the PS model
solution is used to judge the automatic folding algorithm under development
and in Sect. 4 we briefly discuss a class of methods which
were considered, but proved to be insufficiently robust.
In the remaining sections we provide a sequential description of a robust
auto-folder development paying particular attention to the difficulties which
arose, and to the manner of their resolution.
Up: On the automatic folding
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