Galaxies are complex systems the evolution of which apparently results from the interplay of dynamics, star formation, chemical enrichment, and feedback from supernova explosions and supermassive black holes 1 . The hierarchical theory of galaxy formation holds that galaxies are assembled from smaller pieces, through numerous mergers of cold dark matter 2,3,4 . The properties of an individual galaxy should be controlled by six independent parameters including mass, angular-momentum, baryon-fraction, age and size, as well as by the accidents of its recent haphazard merger history. Here we report that a sample of galaxies that were first detected through their neutral hydrogen radio-frequency emission, and are thus free of optical selection effects 5 , shows five independent correlations among six independent observables, despite having a wide range of 2 properties. This implies that the structure of these galaxies must be controlled by a single parameter, although we cannot identify this parameter from our dataset.Such a degree of organisation appears to be at odds with hierarchical galaxy formation, a central tenet of the cold dark matter paradigm in cosmology 6 .About 300 sources, from part of the much larger blind 21-cm survey for neutral hydrogen made with the Parkes radio telescope 7,8,9 , overlap a region surveyed by the Sloan Digital Sky Survey (SDSS) in the optical spectral region 10 . Two hundred were unambiguously identified as individual galaxies, and are representative of the whole range of galaxies between giant spirals and extreme dwarfs, missing only the ~10% of largely neutral-gas-free galaxies found mainly in big clusters. -r)). For comparison, we can imagine galaxies being controlled by seven physical quantities, namely total mass, baryon fraction, age, specific angular momentum, specific heat energy (random motion), radius and concentration, only six of which can be independent, owing to the Virial theorem. We thus have as many independent observables as we do controlling physical parameters, making an examination of the correlation structure potentially very interesting. Each discovered correlation, if independent of the rest, will set a further constraint on galaxy physics. For instance, PCA has been used to show that elliptical galaxies lie on a 'fundamental plane' 21,22 , that is, in a two-dimensional space. Because such a correlation analysis relies on linear relations between variables, we use logarithmic quantities (the colour, being a magnitude, is also logarithmic)
23.Colour turns out to be more complex than the other observables, so we omit it at first then reintroduce it later. Figure 1 demonstrates the strong correlations that exist between the five other variables. This is emphasised in Fig. 2 where all are seen to be strongly correlated with the first principal component, PC1, and scattered with respect to the other principal components. A high degree of organisation is already evident. The eigenvalue of PC1 is 4.1, in comparison with a maximum possible of 5.0 (1 for each variabl...
