Asymmetric Temperature Variations In Protoplanetary disks: I. Linear Theory, Corotating Spirals, and Ring Formation

Protoplanetary disks can exhibit asymmetric temperature variations due to phenomena such as shadows cast by the inner disk or localized heating by young planets. We investigate the disk features induced by these asymmetric temperature variations. We find that spirals are initially excited, then break into two and reconnect to form rings. By carrying out linear analyses, we first study the spiral launching mechanism, and find that the effects of azimuthal temperature variations share similarities with effects of external potentials. Specifically, rotating temperature variations launch steady spiral structures at Lindblad resonances, which corotate with the temperature patterns. When the cooling time exceeds the orbital period, these spiral structures are significantly weakened, and a checkerboard pattern may appear. A temperature variation of about 10\% can induce spirals with order unity density perturbations, comparable to those generated by a thermal mass planet. We then study ring formation and find it is related to the coupling between azimuthal temperature variations and spirals outside the resonances. Such coupling leads to a radially varying angular momentum flux, which produces anomalous wave-driven accretion and forms dense rings separated by the wavelength of the waves. Finally, we speculate that spirals induced by temperature variations may contribute to disk accretion through non-linear wave steepening and dissipation. Overall, considering that irradiation determines the temperature structure of protoplanetary disks, the change of irradiation both spatially or/and temporarily may produce observable effects in protoplanetary disks, especially spirals and rings in outer disks beyond tens of AU.