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تسجيل مستخدم جديدSpiral arms in thermally stratified protoplanetary discs
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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.
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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 densit
y 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.
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 (predicti
ng 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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[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 scen
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