Scaling Relations of Spiral Galaxies: Theory vs Observation

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We use a simple model of disc-galaxy formation in the ΛCDM cosmology to simultaneously reproduce the slopes, zero-points, scatter and uncorrelated residuals in the observed velocity- luminosity (VL) and radius-luminosity (RL) relations. Observed I-band luminosities are con- verted to stellar masses using the IMF-dependent relation between stellar mass-to-light ratio, ϒ, and color. The model treats halo concentration, spin parameter, and disc mass fraction as inde- pendent log-normal random variables. Our main conclusion is that the VL and RL zero-points and the uncorrelated residuals can only be reproduced simultaneously if adiabatic contraction is avoided. One or the other could be fixed by appealing to unrealistic values for ϒ, halo concentra- tion c, and spin parameter λ, but not all together. The small VL scatter is naturally determined by the predicted scatter in c and in ϒ, quite independent of the large scatter in λ. However, the RL scatter, driven by the scatter in λ, can be as low as observed only if σ ln λ 0 25, about half the ¡ ¢ value predicted for CDM haloes. This may indicate that discs form in a special subset of haloes. The VL slope is reproduced once star formation occurs only above a threshold surface density, and the RL slope implies that the disc mass fraction is increasing with halo mass, consistent with feedback effects. A model that incorporates the above ingredients provides a simultaneous fit to all the observed features. In particular, the elimination of adiabatic contraction allows 80% disc contribution to the observed rotation velocity of bright discs at 2.2 disc scale lengths. The lack of halo contraction may indicate that disc formation is not as smooth as typically envisioned, but instead may involve clumpy, cold streams.

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