Gravitational coupling between young planets and their parent disks is often explored using numerical simulations , which typically treat the disk thermodynamics in a highly simplified manner .
In particular , many studies adopt the locally isothermal approximation , in which the disk temperature is a fixed function of the stellocentric distance .
We explore the dynamics of planet-driven density waves in disks with more general thermodynamics , in which the temperature is relaxed towards an equilibrium profile on a finite cooling timescale t _ { c } .
We use both linear perturbation theory and direct numerical simulations to examine the global structure of density waves launched by planets in such disks .
A key diagnostic used in this study is the behavior of the wave angular momentum flux ( AMF ) , which directly determines the evolution of the underlying disk .
The AMF of free waves is constant for slowly cooling ( adiabatic ) disks , but scales with the disk temperature for rapidly cooling ( and locally isothermal ) disks .
However , cooling must be extremely fast , with \beta = \Omega t _ { c } \lesssim 10 ^ { -3 } for the locally isothermal approximation to provide a good description of density wave dynamics in the linear regime ( relaxing to \beta \lesssim 10 ^ { -2 } when nonlinear effects are important ) .
For intermediate cooling timescales , density waves are subject to a strong linear damping .
This modifies the appearance of planet-driven spiral arms and the characteristics of axisymmetric structures produced by massive planets : in disks with \beta \approx 0.1 – 1 , a near-thermal mass planet opens only a single wide gap around its orbit , in contrast to the several narrow gaps produced when cooling is either faster or slower .