Simulations of the heating of the Galactic stellar disc

The velocity dispersion of nearby stars in the Galactic disc is well known to increase substantially with age; this is the so-called age-velocity relation, and is interpreted as a 'heating' of the disc as a function of time. We have studied the heating of the Galactic stellar disc caused by giant molecular clouds and halo black holes, via simulations of the orbits of tracer stars embedded in a patch of the local Galactic disc. We examine a range of masses and number densities of the giant molecular cloud and halo black hole perturbers. The heating of the stellar disc in the simulations is fitted with a simple power law of the form sigma proportional to t(alpha), where sigma is the velocity dispersion of the tracer stars as a function of time, t. We also fit this form to the best determinations of the increase in the velocity dispersion as a function of time as derived from stars in the solar neighbourhood for which ages can be reliably assigned. Observationally, alpha is found to lie in the range 0.3-0.6, i.e. it remains poorly constrained and its determination is probably still dominated by systematic errors. Better constrained observationally is the ratio of the velocity dispersions of the stars in the vertical z and horizontal x directions (i.e. towards the Galactic Centre), sigma(z)/sigma(x) = 0.5 +/- 0.1. For the heating of the stellar disc caused by giant molecular clouds (GMCs) we derive a heating sigma proportional to t(0.21), which differs somewhat from early (analytic) studies in which sigma proportional to t(1/4). This confirms the well-known results that there are insufficient GMCs to heat the Galactic disc appropriately. A range of dark halo black hole scenarios are verified to heat the stellar disc as sigma proportional to t(1/2) (as expected from analytical studies), and give sigma(z)/sigma(x) in the range 0.5-0.6, which is consistent with observations. Black holes with a mass of 10(7) M. are our favoured disc heaters, although they are only marginally consistent with observations. Simulations featuring a combination of giant molecular clouds and halo black holes can explain the observed heating of the stellar disc, but since other perturbing mechanisms, such as spiral arms, are yet to be included, we regard this solution as being ad hoc.