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 well studied using both linear theory and numerical simulations , but so far , only for the primary spiral arm – the one directly attached to the planet .
Using two-dimensional hydrodynamic simulations , we show that the secondary and tertiary arms driven by a planet can also open gaps as they steepen into shocks .
The depths of the secondary/tertiary gaps in surface density grow with time in a low viscosity disk ( \alpha = 5 \times 10 ^ { -5 } ) , so even low-mass planets ( e.g. , super-Earth or mini-Neptune-mass ) embedded in the disk can open multiple observable gaps , provided that sufficient time has passed .
Applying our results to the HL Tau disk , we show that a single 30 Earth-mass planet embedded in the ring at 68.8 au ( B5 ) can reasonably well reproduce the positions of the two major gaps at 13.2 and 32.3 au ( D1 and D2 ) , and roughly reproduce two other major gaps at 64.2 and 74.7 au ( D5 and D6 ) seen in the mm continuum .
The positions of secondary/tertiary gaps are found to be sensitive to the planetary mass and the disk temperature profile , so with accurate observational measurements of the temperature structure the positions of multiple gaps can be used to constrain the mass of the planet .
We also comment on the gaps seen in the TW Hya and HD 163296 disk .