Circumstellar asymmetries such as central warps have recently been shown to cast shadows on outer disks. We investigate the hydrodynamical consequences of such variable illumination on the outer regions of a transition disk, and the development of spiral arms. Using 2D simulations, we follow the evolution of a gaseous disk passively heated by the central star, under the periodic forcing of shadows with an opening angle of $sim$28$^circ$. With a lower pressure under the shadows, each crossing results in a variable azimuthal acceleration, which in time develops into spiral density waves. Their pitch angles evolve from $Pi sim 15^circ-22^circ$ at the onset, to $sim$11$^circ$-14$^circ$, over $sim$65~AU to 150~AU. Self-gravity enhances the density contrast of the spiral waves, as also reported previously for spirals launched by planets. Our control simulations with unshadowed irradiation do not develop structures, except for a different form of spiral waves seen at later times only in the gravitationally unstable control case. Scattered light predictions in the $H$-band show that such illumination spirals should be observable. We suggest that spiral arms in the case-study transition disk HD~142527 could be explained as a result of shadowing from the tilted inner disk.
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