The Formation of Disk Galaxies

We present a scenario for the formation of disks that explains not only the properties of normal galaxies but also the properties of the population of low surface brightness galaxies (LSBs) as well. We use a gravitationally self-consistent model for disk collapse to calculate the observable properties of disk galaxies as a function of mass and angular momentum of the initial protogalaxy. The model naturally produces both smooth, asymptotically flat rotation curves and exponential surface brightness profiles over many disk scale lengths.

In this scenario, low-mass and/or high angular momentum halos naturally form low baryonic surface density disks, which will tend to be low surface brightness. Theoretical and numerical calculations suggest galaxy halos should form with a wide range of mass and angular momenta, and thus, the disks that form within these halos should have a wide range of surface brightnesses and scale lengths. We use theoretical predictions for the distribution of halo masses and angular momenta to calculate explicitly the expected number density of disk galaxies as a function of central surface brightness and disk scale length. The resulting distribution is compared to the observed properties of galactic disks and is shown to explain the range of observed disk properties, including the cutoff in the maximum disk scale length as a function of surface brightness. We also show that disk instabilities explain the observed lack of high surface density disks. The calculated distribution of disk properties also suggests that there are large numbers of galaxies that remain undetected owing to biases against galaxies with either low surface brightness or small scale length. We quantify this by calculating the difference between the intrinsic luminosity function and the luminosity function that would be measured in a galaxy survey with a given limiting surface brightness. We show that current measurements of the galaxy luminosity function may be missing more than half of all L_* galaxies, and an even larger fraction of faint galaxies, given the correlation between mass and surface brightness. The likely underestimate of the luminosity density is also expected to be large. We discuss how this affects observations of the ``faint blue galaxy'' population.

We also investigate the dynamics of galaxies as a function of surface brightness. We show that, in the absence of any systematic change in the ratio of disk mass to disk luminosity, galaxies of all surface brightnesses should lie on the same Tully-Fisher relation. Our models also show systematic changes in the shape of the rotation curve as a function of angular momentum, which leads to LSBs having slowly rising rotation curves. Furthermore, because high angular momentum LSB disks have their baryonic mass spread over a larger area than normal galaxies of comparable mass, LSB disks contribute very little to the observed dynamics of the galaxy. Thus, LSBs provide a very effective tracer of the shape and mass profile of the dark matter halo, out to proportionally larger radii than is possible to observe with normal galaxy rotation curves.