Planet-disk interaction in disks with cooling: basic theory. (arXiv:1911.01428v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Miranda_R/0/1/0/all/0/1">Ryan Miranda</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Rafikov_R/0/1/0/all/0/1">Roman R. Rafikov</a> (1,2) ((1) IAS, (2) DAMTP, Cambridge)

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 $t_{rm c}$. 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 $beta = Omega t_{rm c} lesssim 10^{-3}$ 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.

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 $t_{rm c}$. 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 $beta = Omega t_{rm c} lesssim 10^{-3}$ 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.

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