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As spiral waves driven by a planet in a gaseous disk steepen into a shock,they deposit angular momentum, opening a gap in the disk. This has been wellstudied using both linear theory and numerical simulations, but so far, onlyfor the primary spiral arm -- the one directly attached to the planet. Usingtwo-dimensional hydrodynamic simulations, we show that the secondary andtertiary arms driven by a planet can also open gaps as they steepen intoshocks. The depths of the secondary/tertiary gaps in surface density grow withtime in a low viscosity disk ($\alpha = 5\times10^{-5}$), so even low-massplanets (e.g., super-Earth or mini-Neptune-mass) embedded in the disk can openmultiple observable gaps, provided that sufficient time has passed. Applyingour results to the HL Tau disk, we show that a single 30 Earth-mass planetembedded in the ring at 68.8~au (B5) can reasonably well reproduce thepositions of the two major gaps at 13.2 and 32.3 au (D1 and D2), and roughlyreproduce two other major gaps at 64.2 and 74.7 au (D5 and D6) seen in the mmcontinuum. The positions of secondary/tertiary gaps are found to be sensitiveto the planetary mass and the disk temperature profile, so with accurateobservational measurements of the temperature structure the positions ofmultiple gaps can be used to constrain the mass of the planet. We also commenton the gaps seen in the TW Hya and HD~163296 disk.

On the formation of multiple concentric rings and gaps in protoplanetary disks