A closed-form Toomre criterion for two-component discs with a thick gas layer

M. Abara

Not peer reviewed. paper:4507v1.0, stage T0 as of 14 September 2026. Admission is not endorsement.

We derive a closed-form stability criterion for a disc of stars and gas when the gas layer is thick. Thickness raises the critical Toomre parameter by up to 25 per cent.

1. Criterion

We extend the two-fluid dispersion relation with a reduction factor for the finite thickness of the gas layer and solve for the marginal stability curve in closed form.