On the dynamics of a twisted disc immersed in a radiation field

TL;DR

This paper investigates how a twisted, tilted disc responds to external radiation, deriving equations for small tilts, and finds conditions under which the disc remains stable or develops warps, including nonlinear and oscillatory behaviors.

Contribution

It introduces a new analysis of the vertical structure response of irradiated discs, deriving equations applicable to both diffusive and bending wave regimes, and explores nonlinear and oscillatory warp dynamics.

Findings

Quasi-uniform tilt response requires the product of radiation flux ratio and aspect ratio to be less than unity.

Large ratios lead to surface reorientation perpendicular to radiation, reducing warp instability.

Non-uniform vertical response can produce shocks, causing dissipation.

Abstract

We study the dynamics of a twisted tilted disc under the influence of an external radiation field. Assuming the effect of absorption and reemission/scattering is that a pressure is applied to the disc surface where the local optical depth is of order 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 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, $\lambda \ll 1$. 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 $T_{*}\sim \lambda^{-1}T_{K}$, 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.