Abstract: We study classes of locally biholomorphic mappings defined in the polydisk P-n that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes.

Abstract: Disk solids are critical in many planet formation processes; however, their effect on planet migration remains largely unexplored. Here we assess this important issue for the first time by building on the systematic measurements of dust torques on an embedded planet by Benitez-Llambay & Pessah. Adopting standard models for the gaseous disk and its solid content, we quantify the impact of the dust torque for a wide range of conditions describing the disk/planet system. We show that the total torque can be positive and reverse inward planet migration for planetary cores with M (p) & LSIM; 10 M (& OPLUS;). We compute formation tracks for low-mass embryos for conditions usually invoked when modeling planet formation processes. Our most important conclusion is that dust torques can have a significant impact on the migration and formation history of planetary embryos. The most important implications of our findings are as follows. (i) For nominal dust-to-gas mass ratios & epsilon; & SIME; 0.01, low-mass planets migrate outwards beyond the water ice-line if most of the mass in the solids is in particles with Stokes numbers St & SIME;0.1. (ii) For & epsilon; & GSIM; 0.02-0.05, solids with small Stokes numbers, St & SIME; 0.01, can play a dominant role if most of the mass is in those particles. (iii) Dust torques have the potential to enable low-mass planetary cores formed in the inner disk to migrate outwards and act as the seed for massive planets at distances of tens of au.

Abstract: We present MDIRK: a multifluid second-order diagonally implicit Runge-Kutta method to study momentum transfer between gas and an arbitrary number (N) of dust species. The method integrates the equations of hydrodynamics with an implicit-explicit scheme and solves the stiff source term in the momentum equation with a diagonally implicit, asymptotically stable Runge-Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with O(N) operations, instead of standard matrix inversion, which is O(N)3 . Therefore, the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multifluid dusty Jeans instability, and a steady-state gas-dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order, asymptotically stable multifluid methods.

Abstract: Planet formation imprints signatures on the physical structures of disks. In this paper, we present high-resolution (similar to 50 mas, 8 au) Atacama Large Millimeter/submillimeter Array observations of 1.3 mm dust continuum and CO line emission toward the disk around the M3.5 star 2MASSJ04124068+2438157. The dust disk consists of only two narrow rings at radial distances of 0 47 and 0 78 (similar to 70 and 116 au), with Gaussian sigma widths of 5.6 and 8.5 au, respectively. The width of the outer ring is smaller than the estimated pressure scale height by similar to 25%, suggesting dust trapping in a radial pressure bump. The dust disk size, set by the location of the outermost ring, is significantly larger (by 3 sigma) than other disks with similar millimeter luminosity, which can be explained by an early formation of local pressure bump to stop radial drift of millimeter dust grains. After considering the disk's physical structure and accretion properties, we prefer planet-disk interaction over dead zone or photoevaporation models to explain the observed dust disk morphology. We carry out high-contrast imaging at the L' band using Keck/NIRC2 to search for potential young planets, but do not identify any source above 5 sigma. Within the dust gap between the two rings, we reach a contrast level of similar to 7 mag, constraining the possible planet below similar to 2-4M(Jup). Analyses of the gap/ring properties suggest that an approximately Saturn-mass planet at similar to 90 au is likely responsible for the formation of the outer ring, which can potentially be revealed with JWST.

Abstract: Context. The C/O ratio as traced with C2H emission in protoplanetary disks is fundamental for constraining the formation mechanisms of exoplanets and for our understanding of volatile depletion in disks, but current C2H observations show an apparent bimodal distribution that is not well understood, indicating that the C/O distribution is not described by a simple radial dependence. Aims. The transport of icy pebbles has been suggested to alter the local elemental abundances in protoplanetary disks through settling, drift, and trapping in pressure bumps, resulting in a depletion of volatiles in the surface layer and an increase in the elemental C/O. Methods. We combine all disks with spatially resolved ALMA C2H observations with high-resolution continuum images and constraints on the CO snow line to determine if the C2H emission is indeed related to the location of the icy pebbles. Results. We report a possible correlation between the presence of a significant CO-ice dust reservoir and high C2H emission, which is only found in disks with dust rings outside the CO snow line. In contrast, compact dust disks (without pressure bumps) and warm transition disks (with their dust ring inside the CO snow line) are not detected in C2H, suggesting that such disks may have never contained a significant CO ice reservoir. Conclusions. This correlation provides evidence for the regulation of the C/O profile by the complex interplay of CO snow line and pressure bump locations in the disk. These results demonstrate the importance of including dust transport in chemical disk models for a proper interpretation of exoplanet atmospheric compositions and a better understanding of volatile depletion in disks, in particular the use of CO isotopologs to determine gas surface densities.