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, the local surface mass density, the stellar scale length (of the assumedly exponential disc) and the amplitude of the (assumedly flat) rotation curve, and physically, the (local) dynamical Kennicutt star formation prescription, standard chemical evolution equations assuming 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 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. At the solar neighbourhood stars start to form $\approx 10 Gyrs$ ago at an increasing rate peaking 4 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 $4 Gyrs$. The local surface density of the stars and gas are 35 and $15 M_{\odot}pc^{-2}$, respectively. The metallicity distribution of the stars at the solar radius is narrow with a peak at $[Z/Z_{\odot}] = -0.1$.Both a Salpeter IMF and a Chabrier IMF are consistent with observations. Comparisons with the current and local fossil evidence provides 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 (abbreviated).