A simple model for the evolution of disc galaxies is presented .
We adopt three numbers from observations of the Milky Way disc , \Sigma _ { \mathrm { d } } the local surface mass density , r _ { \mathrm { d } } the stellar scale length ( of the assumedly exponential disc ) and v _ { \mathrm { c } } the amplitude of the ( assumedly flat ) rotation curve , and physically , the ( local ) dynamical Kennicutt star formation prescription , standard chemical evolution equations assuming a Salpeter IMF 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 .
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 M _ { \odot } yr ^ { -1 } and 2 - 4 M _ { \odot } yr ^ { -1 } during the evolution of the disc .
The present day total mass in stars and in gas is 2.7 \times 10 ^ { 10 } M _ { \odot } and 9.5 \times 10 ^ { 9 } M _ { \odot } , respectively , and the disc has an absolute K-band magnitude of -23.2 .
The present day stellar scale length ( normalised to 3 kpc ) in the K-band and is larger than at shorter wavelengths .
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 .
The present day metallicity gradient is -0.046 dexkpc ^ { -1 } and has been significantly steeper in the past .
Using a Chabrier IMF increases the luminosity of the model and results in a steeper metallicity gradient .
The local metallicity distribution is only weakly affetcted .
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 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 .