Spiral Arms in Gravitationally Unstable Protoplanetary Disks as Imaged in Scattered Light

Combining 3D smoothed-particle hydrodynamics and Monte Carlo radiative transfer calculations, we examine the morphology of spiral density waves induced by gravitational instability (GI) in protoplanetary disks, as they would appear in direct images at near-infrared (NIR) wavelengths. We find that systems with disk-to-star-mass ratios q=M_disk/M_star that are ~0.25 or more may produce prominent spiral arms in NIR imaging, remarkably resembling features observed in the MWC 758 and SAO 206462 systems. The contrast of GI-induced arms at NIR wavelengths can reach a factor of ~3, and their pitch angles are about 10-15 degree. The dominant azimuthal wavenumber of GI-induced spiral arms roughly obeys m~1/q in the range 2<~1/q<~8. In particular, a massive disk with q~0.5 can exhibit grand-design m=2 spirals. GI-induced arms are in approximate corotation with the local disk, and may therefore trap dust particles by pressure drag. Although GI can produce NIR spiral arms with morphologies, contrasts, and pitch angles similar to those reported in recent observations, it also makes other demands that may or may not be satisfied in any given system. A GI origin requires that the spirals be relatively compact, on scales <~100 AU; that the disk be massive, q>~0.25; and that the accretion rate Mdot be high, on the order of 1e-6 solar mass per year.