A simple model for the evolution of disc galaxies: the Milky Way

A simple model for the evolution of disc galaxies is presented. We adopt three numbers from observations of the Milky Way disc, Sigma(d) the local surface mass density, r(d) the stellar scalelength (of the assumed exponential disc), v(c), the amplitude of the (assumed flat) rotation curve, and physically, the (local) dynamical Kennicutt star formation prescription, standard chemical evolution equations assuming a Salpeter initial mass function and a model for spectral evolution of stellar populations. We can determine the detailed evolution of the model with only the addition of standard cosmological scalings with the time of the dimensional parameters. A surprising wealth of detailed specifications follows from this prescription including the gaseous infall rate as a function of radius and time, the distribution of stellar ages and metallicities with time and radius, surface brightness profiles at different wavelengths, colours, etc. Some of the detailed properties are as follows: the global gas infall rate and the global star formation rate are almost constant at 2-3 and 2-4 M-circle dot yr(-1) during the evolution of the disc. The present-day total masses in stars and in gas are 2.7 x 10(10) and 9.5 x 10(9) M-circle dot, respectively, and the disc has an absolute K-band magnitude of -23.2. The present-day stellar scalelength (normalized to 3 kpc) in the K band and is larger than at shorter wavelengths. At the solar neighbourhood stars started to form approximate to 10 Gyr ago at an increasing rate, peaking four billion years ago and then slowly declining in good agreement with observations. The mean age of long-lived stars at the solar neighbourhood is about 4 Gyr. The local surface densities of the stars and gas are 35 and 15 M-circle dot pc(-2), respectively. The metallicity distribution of the stars at the solar radius is narrow with a peak at [Z/Z(circle dot)] = -0.1. The present-day metallicity gradient is -0.046 dex kpc(-1) and has been significantly steeper in the past. Using a Chabrier initial mass function increases the luminosity of the model and results in a steeper metallicity gradient. The local metallicity distribution is only weakly affected. Different formulations for threshold densities for star formation have been tested and lead to a truncation of the stellar disc at about 12 kpc. Comparisons with the current and local fossil evidence provide support for the model, which can then be used to assess other local disc galaxies, the evolution of disc galaxies in deep optical surveys and also for theoretical investigations such as simulations of merging disc galaxies.