We have used the self-consistent vertical disc models of the solar neighbourhood presented in Just & Jahreiss ( 19 ) , which are based on different star formation histories ( SFR ) and fit the local kinematics of main sequence stars equally well , to predict star counts towards the North Galactic Pole ( NGP ) .
We combined these four different models with the local main sequence in the filter system of the SDSS and predicted the star counts in the NGP field with b > 80 \deg .
All models fit the Hess diagrams in the F–K dwarf regime better than \pm 20 percent and the star number densities in the solar neighbourhood are consistent with the observed values .
The \chi ^ { 2 } analysis shows that model A is clearly preferred with systematic deviations of a few percent only .
The SFR of model A is characterised by a maximum at an age of 10 Gyr and a decline by a factor of four to the present day value of 1.4 M _ { \mathrm { \sun } } /pc ^ { 2 } /Gyr .
The thick disc can be modelled very well by an old isothermal simple stellar population .
The density profile can be approximated by a sech ^ { \alpha _ { \mathrm { t } } } function .
We found a power law index \alpha _ { \mathrm { t } } = 1.16 and a scale height h _ { \mathrm { t } } = 800 pc corresponding to a vertical velocity dispersion of \sigma _ { \mathrm { t } } = 45.3 km/s .
About 6 percent of the stars in the solar neighbourhood are thick disc stars .