Mass constraint for a planet in a protoplanetary disk from the gap width

A giant planet creates a gap in a protoplanetary disk, which might explain the observed gaps in protoplanetary disks. The width and depth of the gaps depend on the planet mass and disk properties. We have performed two-dimensional hydrodynamic simulations for various planet masses, disk aspect ratios, and viscosities, to obtain an empirical formula for the gap width. The gap width is proportional to the square root of the planet mass, −3/4 the power of the disk aspect ratio and −1/4 the power of the viscosity. This empirical formula enables us to estimate the mass of a planet embedded in the disk from the width of an observed gap. We have applied the empirical formula for the gap width to the disk around HL Tau, assuming that each gap observed by the Atacama Large Millimeter/submillimeter Array (ALMA) observations is produced by planets, and discussed the planet masses within the gaps. The estimate of planet masses from the gap widths is less affected by the observational resolution and dust filtration than that by the gap depth.