Heating of galactic discs with realistic vertical potentials

The heating of galactic discs through scattering by molecular clouds and spiral waves is investigated by solving the orbit-averaged Fokker-Planck equation by Monte Carlo simulation. The vertical potential in the disc is handled in two ways: (i) by using a fixed and realistic anharmonic potential, or (ii) by generating the potential self-consistently, assuming that the disc can be approximated as a one-dimensional self-gravitating layer. The shape of the velocity ellipsoid is found to be little changed from earlier work in which a fixed harmonic potential was used. Self-consistent simulations have been run of coeval and star- forming discs with and without accretion. Predictions of the density distribution and the dependence of the vertical component of the velocity dispersion on height are made. It is found that the assumed strength of spiral heating does not significantly affect the shape of ρ(z) or σ_z_(Z). The age-velocity relation is derived for the accreting disc and a best fit is made to data from Wielen. Even with adiabatic heating due to accretion, the value of the cloud heating parameter required to fit Wielen's data is much higher than estimates of its current value from CO observations. The fit made to Stromgren's F stars, which are younger, gives a value of the cloud heating parameter which agrees with the observed value. It is found that the disc heating process modelled here, together with constant star formation, always leads to a closely isothermal population. By contrast, the density and velocity distributions of coeval stellar populations are expected to have significant sub-isothermal wings.