Multiple Spiral Arms in Protoplanetary Disks: Linear Theory. (arXiv:1811.09628v1 [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)
Recent observations of protoplanetary disks, as well as simulations of
planet-disk interaction, have suggested that a single planet may excite
multiple spiral arms in the disk, in contrast to the previous expectations
based on linear theory (predicting a one-armed density wave). We re-assess the
origin of multiple arms in the framework of linear theory, by solving for the
global two-dimensional disk response to an orbiting planet. We show that the
formation of a secondary arm in the inner disk, at about half of the orbital
radius of the planet, is a robust prediction of linear theory. This arm becomes
stronger than the primary spiral at several tenths of the orbital radius of the
planet. Several additional, weaker spiral arms may also form in the inner disk.
On the contrary, a secondary spiral arm is unlikely to form in the outer disk.
Our linear calculations, fully accounting for the global behavior of both the
phases and amplitudes of perturbations, generally support the recently proposed
WKB phase argument for the secondary arm origin (as caused by the intricacy of
constructive interference of azimuthal harmonics of the perturbation at
different radii). We provide analytical arguments showing that the process of a
single spiral wake splitting up into multiple arms is a generic linear outcome
of wave propagation in differentially rotating disks. It is not unique to
planet-driven waves and occurs also in linear calculations of spiral wakes
freely propagating with no external torques. These results are relevant for
understanding formation of multiple rings and gaps in protoplanetary disks.
Recent observations of protoplanetary disks, as well as simulations of
planet-disk interaction, have suggested that a single planet may excite
multiple spiral arms in the disk, in contrast to the previous expectations
based on linear theory (predicting a one-armed density wave). We re-assess the
origin of multiple arms in the framework of linear theory, by solving for the
global two-dimensional disk response to an orbiting planet. We show that the
formation of a secondary arm in the inner disk, at about half of the orbital
radius of the planet, is a robust prediction of linear theory. This arm becomes
stronger than the primary spiral at several tenths of the orbital radius of the
planet. Several additional, weaker spiral arms may also form in the inner disk.
On the contrary, a secondary spiral arm is unlikely to form in the outer disk.
Our linear calculations, fully accounting for the global behavior of both the
phases and amplitudes of perturbations, generally support the recently proposed
WKB phase argument for the secondary arm origin (as caused by the intricacy of
constructive interference of azimuthal harmonics of the perturbation at
different radii). We provide analytical arguments showing that the process of a
single spiral wake splitting up into multiple arms is a generic linear outcome
of wave propagation in differentially rotating disks. It is not unique to
planet-driven waves and occurs also in linear calculations of spiral wakes
freely propagating with no external torques. These results are relevant for
understanding formation of multiple rings and gaps in protoplanetary disks.
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