SIMBAD references

We study the dynamics of a twisted tilted disc under the influence of an external radiation field. Assuming the effect of absorption and re-emission/scattering is that a pressure is applied to the disc surface where the local optical depth is of the order of unity, we determine the response of the vertical structure and the influence it has on the possibility of instability to warping.

We derive a pair of equations describing the evolution of a small tilt as a function of radius in the small-amplitude regime that applies to both the diffusive and the bending wave regimes. We also study the non-linear vertical response of the disc numerically using an analogous one-dimensional slab model. For global warps, we find that in order for the disc vertical structure to respond as a quasi-uniform shift or tilt, as has been assumed in previous work, the product of the ratio of the external radiation momentum flux to the local disc mid-plane pressure, where it is absorbed, with the disc aspect ratio should be significantly less than unity. Namely, this quantity should be of the order of or smaller than the ratio of the disc gas density corresponding to the layer intercepting radiation to the mid-plane density, λ ≪ 1.

When this condition is not satisfied, the disc surface tends to adjust so that the local normal becomes perpendicular to the radiation propagation direction. In this case, dynamical quantities determined by the disc twist and warp tend to oscillate with a large characteristic period T_*∼ λ^–1T_K_, where T_K is some `typical' orbital period of a gas element in the disc. The possibility of warping instability then becomes significantly reduced.

In addition, when the vertical response is non-uniform, the possible production of shocks may lead to an important dissipation mechanism.