Eccentric Modes in Disks With Pressure and Self-Gravity. (arXiv:1811.11758v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Lee_W/0/1/0/all/0/1">Wing-Kit Lee</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Dempsey_A/0/1/0/all/0/1">Adam M. Dempsey</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Lithwick_Y/0/1/0/all/0/1">Yoram Lithwick</a> (1) ((1) Northwestern)
Accretion disks around stars, or other central massive bodies, can support Accretion disks around stars, or other central massive bodies, can support http://arxiv.org/icons/sfx.gif
long-lived, slowly precessing $m=1$ disturbances in which the fluid motion is
nearly Keplerian with non-zero eccentricity. We study such `slow modes’ in
disks that are subject to both pressure and self-gravity forces. We derive a
second-order WKB dispersion relation that describes the dynamics quite
accurately, and show that the apparently complicated nature of the various
modes can be understood in a simple way with the help of a graphical method. We
also solve the linearized fluid equations numerically, and show that the
results agree with the theory. We find that when self-gravity is weak
($Qgtrsim 1/h$, where $Q$ is Toomre’s parameter, and $h$ is the disk aspect
ratio) the modes are pressure dominated. But when self-gravity is strong
($1
long-lived, slowly precessing $m=1$ disturbances in which the fluid motion is
nearly Keplerian with non-zero eccentricity. We study such `slow modes’ in
disks that are subject to both pressure and self-gravity forces. We derive a
second-order WKB dispersion relation that describes the dynamics quite
accurately, and show that the apparently complicated nature of the various
modes can be understood in a simple way with the help of a graphical method. We
also solve the linearized fluid equations numerically, and show that the
results agree with the theory. We find that when self-gravity is weak
($Qgtrsim 1/h$, where $Q$ is Toomre’s parameter, and $h$ is the disk aspect
ratio) the modes are pressure dominated. But when self-gravity is strong
($1<Qlesssim 1/h$), two kinds of gravity-dominated modes appear: one is an
aligned elliptical pattern and the other is a one-armed spiral. In the context
of protoplanetary disks, we suggest that if the radial eccentricity profile can
be measured, it could be used to determine the total disk mass.
