Closed orbits for actions of maximal tori on homogeneous spaces

Let G be a real algebraic group defined over Q, let (gamma) be an arithmetic subgroup, and let T be any torus containing a maximal Rsplit torus. We prove that the closed orbits for the action of T on G/(gamma) admit a simple algebraic description. In particular, we show that if G is reductive, an orbit Tx(gamma) is closed if and only if x^-1Tx is a product of a compact torus and a torus defined over Q, and it is divergent if and only if the maximal R-split subtorus of X^-1Tx is defined over Q and Q-split. Our analysis also yields the following:there is a compact K(subset of)G/(gamma) which intersects every T-orbit;if rankQ G(less than) rankR G, there are no divergent orbits for T.