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Register a new userMultiple Spiral Arms in Protoplanetary Disks: Linear Theory
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Ryan Miranda IAS
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Recent observations of protoplanetary disks, as well as simulations of planet-disk interaction, have suggested that a single planet may excite multiple spiral arms in the disk, in contrast to the previous expectations based on linear theory (predicting a one-armed density wave). We re-assess the origin of multiple arms in the framework of linear theory, by solving for the global two-dimensional response of a non-barotropic disk to an orbiting planet. We show that the formation of a secondary arm in the inner disk, at about half of the orbital radius of the planet, is a robust prediction of linear theory. This arm becomes stronger than the primary spiral at several tenths of the orbital radius of the planet. Several additional, weaker spiral arms may also form in the inner disk. On the contrary, a secondary spiral arm is unlikely to form in the outer disk. Our linear calculations, fully accounting for the global behavior of both the phases and amplitudes of perturbations, generally support the recently proposed WKB phase argument for the secondary arm origin (as caused by the intricacy of constructive interference of azimuthal harmonics of the perturbation at different radii). We provide analytical arguments showing that the process of a single spiral wake splitting up into multiple arms is a generic linear outcome of wave propagation in differentially rotating disks. It is not unique to planet-driven waves and occurs also in linear calculations of spiral wakes freely propagating with no external torques. These results are relevant for understanding formation of multiple rings and gaps in protoplanetary disks.
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High-resolution imaging of protoplanetary disks has unveiled a rich diversity of spiral structure, some of which may arise from disk-planet interaction. Using 3D hydrodynamics with $beta$-cooling to a vertically-stratified background, as well as radiative-transfer modeling, we investigate the temperature rise in planet-driven spirals. In rapidly cooling disks, the temperature rise is dominated by a contribution from stellar irradiation, 0.3-3% inside the planet radius but always <0.5% outside. When cooling time equals or exceeds dynamical time, however, this is overwhelmed by hydrodynamic PdV work, which introduces a 10-20% perturbation within a factor of 2 from the planets orbital radius. We devise an empirical fit of the spiral amplitude $Delta (T)$ to take into account both effects. Where cooling is slow, we find also that temperature perturbations from buoyancy spirals -- a strictly 3D, non-isothermal phenomenon -- become nearly as strong as those from Lindblad spirals, which are amenable to 2D and isothermal studies. Our findings may help explain observed thermal features in disks like TW Hydrae and CQ Tauri, and underscore that 3D effects have a qualitatively important effect on disk structure.
Spiral arms have been observed in nearly a dozen protoplanetary discs in near-infrared scattered light and recently also in the sub-millimetre continuum. While one of the most compelling explanations is that they are driven by planetary or stellar companions, in all but one cases such companions have not yet been detected and there is even ambiguity on whether the planet should be located inside or outside the spirals. Here we use 3D hydrodynamic simulations to study the morphology of spiral density waves launched by embedded planets taking into account the vertical temperature gradient, a natural consequence of stellar irradiation. Our simulations show that the pitch angle of the spirals in thermally stratified discs is the lowest in the disc mid-plane and increases towards the disc surface. We combine the hydrodynamic simulations with 3D radiative transfer calculations to predict that the pitch-angle of planetary spirals observed in the near-infrared is higher than in the sub-millimetre. We also find that in both cases the spirals converge towards the planet. This provides a new powerful observational method to determine if the perturbing planet is inside our outside the spirals, as well as map the thermal stratification of the disc.
We present the first images of the transition disk around the close binary system HD 34700A in polarized scattered light using the Gemini Planet Imager instrument on Gemini South. The J and H band images reveal multiple spiral-arm structures outside a large (R = 0.49 = 175 au) cavity along with a bluish spiral structure inside the cavity. The cavity wall shows a strong discontinuity and we clearly see significant non-azimuthal polarization Uphi consistent with multiple scattering within a disk at an inferred inclination ~42deg. Radiative transfer modeling along with a new Gaia distance suggest HD 37400A is a young (~5 Myr) system consisting of two intermediate-mass (~2Msun) stars surrounded by a transitional disk and not a solar-mass binary with a debris disk as previously classified. Conventional assumptions of the dust-to-gas ratio would rule out a gravitational instability origin to the spirals while hydrodynamical models using the known external companion or a hypothetical massive protoplanet in the cavity both have trouble reproducing the relatively large spiral arm pitch angles (~30deg) without fine tuning of gas temperature. We explore the possibility that material surrounding a massive protoplanet could explain the rim discontinuity after also considering effects of shadowing by an inner disk. Analysis of archival Hubble Space Telescope data suggests the disk is rotating counterclockwise as expected from the spiral arm structure and revealed a new low-mass companion at 6.45 separation. We include an appendix which sets out clear definitions of Q, U, Qphi, Uphi, correcting some confusion and errors in the literature.
[Full abstract in the paper] In recent years, protoplanetary disks with spiral structures have been detected in scattered light, millimeter continuum, and CO gas emission. The mechanisms causing these structures are still under debate. A popular scenario to drive the spiral arms is the one of a planet perturbing the material in the disk. However, if the disk is massive, gravitational instability is usually the favored explanation. Multiwavelength studies could be helpful to distinguish between the two scenarios. So far, only a handful of disks with spiral arms have been observed in both scattered light and millimeter continuum. We aim to perform an in-depth characterization of the protoplanetary disk morphology around WaOph 6 analyzing data obtained at different wavelengths, as well as to investigate the origin of the spiral features in the disk. We present the first near-infrared polarimetric observations of WaOph 6 obtained with SPHERE at the VLT and compare them to archival millimeter continuum ALMA observations. We traced the spiral features in both data sets and estimated the respective pitch angles. We discuss the different scenarios that can give rise to the spiral arms in WaOph 6. We tested the planetary perturber hypothesis by performing hydrodynamical and radiative transfer simulations to compare them with scattered light and millimeter continuum observations.
One of the striking discoveries of protoplanetary disc research in recent years are the spiral arms seen in several transitional discs in polarised scattered light. An interesting interpretation of the observed spiral features is that they are density waves launched by one or more embedded (proto-)planets in the disc. In this paper we investigate whether planets can be held responsible for the excitation mechanism of the observed spirals. We use locally isothermal hydrodynamic simulations as well as analytic formulae to model the spiral waves launched by planets. Then H-band scattered light images are calculated using a 3D continuum radiative transfer code to study the effect of surface density and pressure scale height perturbation on the detectability of the spirals. We find that a relative change of about 3.5 in the surface density is required for the spirals to be detected with current telescopes in the near-infrared for sources at the distance of typical star-forming regions (140pc). This value is a factor of eight higher than what is seen in hydrodynamic simulations. We also find that a relative change of only 0.2 in pressure scale height is sufficient to create detectable signatures under the same conditions. Therefore, we suggest that the spiral arms observed to date in protoplanetary discs are the results of changes in the vertical structure of the disc (e.g. pressure scale height perturbation) instead of surface density perturbations.
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