Astron. Astrophys. 343, 788-800 (1999)

An analysis of 900 optical rotation curves: the universal rotation curve as a power-law and the development of a theory-independent dark-matter modeller

D.F. Roscoe

School of Mathematics, Sheffield University, Sheffield, S3 7RH, UK (e-mail: D.Roscoe@ac.shef.uk)

Received 26 June 1998 / Accepted 27 October 1998

Abstract

One of the largest rotation curve data bases of spiral galaxies currently available is that provided by Persic & Salucci, hereafter PS 1995, which has been derived by them from unreduced rotation curve data of 965 southern sky spirals obtained by Mathewson, Ford & Buchhorn, hereafter MFB 1992. Of the original sample of 965 galaxies, the observations on 900 were considered by PS 1995 to be good enough for rotation curve studies, and the present analysis concerns itself with these 900 rotation curves.

The analysis is performed within the context of the basic hypothesis that the phenomenology of rotation curves in the optical disc (that is, away from the dynamical effects of the bulge) can be systematically described in terms of a general power-law , valid for , where is an estimate of the transition radius between bulge-dominated and disc-dominated dynamics. The analysis begins by showing how this model provides an extremely good description of the generic behaviour of rotation curves in the optical disc and, furthermore, how it imposes very detailed correlations between the free parameters, A and , of the model.

These correlations are investigated, and shown to imply, via first and second-order models, a third-order model according to which the rotation velocity, V, at any radial displacement in the optical disc of any given spiral galaxy is given by , where , and are given as approximate functions of the galaxy's absolute magnitude and surface brightness whilst is an unidentified function of other galaxy parameters - of which the most significant ones will be the relative proportions of the disc, bulge and halo mass-components. It is this latter function which provides the opportunity for a dark-matter modelling process which is independent of any particular dynamical theory.

Furthermore, it is shown that the conclusion of PS 1986, that optical-disc dynamics contain no signature of the transition from disc-dominated dynamics to halo-dominated dynamics, is extremely strongly supported by this analysis.

Key words: galaxies: fundamental parameters galaxies: kinematics and dynamics galaxies: spiral cosmology: dark matter

Send offprint requests to: D.F. Roscoe

This article contains no SIMBAD objects.

Contents

• 1. Introduction
• 2. The data
• 3. A necessary condition for the power-law hypothesis
• 4. The minimization of bulge-dominated dynamics in rotation curve data
• 5. A basic correlation imposed by power-law rotation curves
• 6. The first-order 70% model
  • 6.1. The basic analysis
  • 6.2. Geometric implications
  • 6.3. The intersection frequency diagram
  • 6.4. A geometric illustration of rotation curve convergence
  • 6.5. A comparison of three estimates
• 7. The second-order 85% model
  • 7.1. The basic analysis
  • 7.2. The refined analysis
• 8. The third-order 90% model
  • 8.1. A secondary test of the model
  • 8.2. The brightest quartile
  • 8.3. The surface-brightness cut-off
• 9. A comparative test of the first, second and third-order models
• 10. Equivalence classes of rotation curves
• 11. The universal rotation curve
  • 11.1. The general situation
  • 11.2. A simple approximation
• 12. Theory-independent dark-matter models
• 13. Conclusions
• Appendix
  • A: the constancy of
  • B: data reduction
  • C: determination of fixed points,
• References

© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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