Protoplanetary Disk Heating and Evolution Driven by the Spiral Density Waves

Abstract

High-resolution imaging of some protoplanetary disks in scattered light reveals presence of the global spiral arms of significant amplitude, likely excited by massive planets or stellar companions. Assuming that these arms are density waves, evolving into spiral shocks, we assess their effect on the thermodynamics, accretion, and global evolution of the disk. We derive analytical expressions for the direct (irreversible) heating, angular momentum transport, and mass accretion rate induced by the disk shocks of arbitrary strength. We find these processes to be very sensitive to the shock amplitude. Focusing on the waves of moderate strength (density jump at the shock $ΔΣ/Σ\sim 1$) we show the associated disk heating to be negligible (contributing at $\sim 1\%$ level to the energy budget) in passive, irradiated protoplanetary disks on $\sim 100$ AU scales, but becoming important within several AU from the star. At the same time, shock heating can be a significant (or even dominant) energy source in disks of cataclysmic variables, stellar X-ray binaries, and supermassive black hole binaries, heated mainly by viscous dissipation. Mass accretion induced by the global spiral shocks is comparable to (or exceeds) the mass inflow due to viscous stresses. Protoplanetary disks featuring prominent global spirals must be evolving rapidly, in $\lesssim 0.5$ Myr at $\sim 100$ AU. A direct upper limit on the disk evolution timescale can be established via the measurement of the gravitational torque due to the spiral arms from the imaging data. Our findings suggest that, regardless of their origin, global spiral waves must be important agents of the protoplanetary disk evolution. They may serve as an effective mechanism of disk dispersal and could be related to the transitional disk phenomenon.