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(Left) The linear summation of perturbations driven by individual azimuthal components of the Fourier decomposed potential of a 3 Earth-mass planet, from to . (Right) The perturbation driven by the full potential of the planet. See more details here.

The evolution of disk surface density with a Jupiter-mass planet at . The planet opens a main gap around its orbit, but also two other gaps interior to its orbit. These additional gaps open through shocks from the secondary and tertiary arms. See more details here.

Three-dimensional density distribution showing the destabilization of two-armed spirals via the spiral wave instability. The simulation was carried out in cylindrical coordinates, but displayed in cartesian coordinates for visualization purpose only. See more details here.

 

(Left) The two-dimensional distribution of disk surface density over the course of an accretion outburst driven by the gravitational instability. (Middle) Same as the left panel but shows the disk temperature distribution. (Right) The time history of the mass accretion rate measured at the disk inner boundary during the outburst. See more details here.