Why Does Hubble-type Correlate Poorly With Arm Pitch-angle of Spiral Galaxies?

Astronomy and Astrophysics – Astronomy

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Since Hubble himself classified spiral galaxies according to arm "sweep” and bulge size, one might naturally expect that the carefully measured angle-of-pitch of arms in spiral galaxies should correlate very well with Hubble Type, for example, at least with Sa, Sb and Sc types. In fact, ever since Kennicut measured arm-pitch in the 1980's to recent measurements by Seigar, little or no correlation has been found. We discuss two root causes: (1) misclassification of galaxies; and (2) the assumption that "average pitch" is a good correlation parameter. Although the first cause contributes significantly to errors since classification is qualitative, the second contributes fundamentally. A logarithmic spiral, having constant pitch, is typically used to describe galaxy shape. However, the pitch angle of galaxy arms is, in general, not constant, so an average pitch is calculated. This value depends strongly on start and end points for the average along an arm and is seen to vary by a factor 2-4 between authors. We show that even after correcting for the first cause, "average pitch” still shows little correlation with Hubble-type. We introduce a new formula, r(f) = Α / log[B tan(f /(2 N))], that describes the natural pitch variation of all spiral galaxies. A is a scale parameter while B and N determine the pitch. The formula can be recast in a form dependent only on a single "pitch-parameter". We compare the correlation of our pitch parameter to Hubble type with that of the traditional logarithmic spiral for 21 well-shaped galaxies. The pitch parameter of our formula, for the first time, produces an excellent correlation to Hubble Type. Representative examples of fitted galaxies are shown. We wish to thank Marc Seigar for comments.

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