We present Atacama Large Millimeter and Submillimeter Array observations of the protoplanetary disk around the Herbig Ae star HD 163296 that trace the spatial distribution of millimeter-sized particles and cold molecular gas on spatial scales as small as 25 astronomical units (A.U.). The image of the disk recorded in the 1.3 mm continuum emission reveals three dark concentric rings that indicate the presence of dust depleted gaps at about 60, 100, and 160 A.U. from the central star. The maps of the 12 CO, 13 CO, and C 18 O J ¼ 2 − 1 emission do not show such structures but reveal a change in the slope of the radial intensity profile across the positions of the dark rings in the continuum image. By comparing the observations with theoretical models for the disk emission, we find that the density of CO molecules is reduced inside the middle and outer dust gaps. However, in the inner ring there is no evidence of CO depletion. From the measurements of the dust and gas densities, we deduce that the gas-to-dust ratio varies across the disk and, in particular, it increases by at least a factor 5 within the inner dust gap compared to adjacent regions of the disk. The depletion of both dust and gas suggests that the middle and outer rings could be due to the gravitational torque exerted by two Saturn-mass planets orbiting at 100 and 160 A.U. from the star. On the other hand, the inner dust gap could result from dust accumulation at the edge of a magnetorotational instability dead zone, or from dust opacity variations at the edge of the CO frost line. Observations of the dust emission at higher angular resolution and of molecules that probe dense gas are required to establish more precisely the origins of the dark rings observed in the HD 163296 disk.

An adjoint sensitivity method is presented for parameter-dependent differentialalgebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In addition, it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system.

We present two-dimensional inviscid hydrodynamic simulations of a protoplanetary disk with an embedded planet, emphasizing the evolution of potential vorticity (the ratio of vorticity to density) and its dependence on numerical resolutions. By analyzing the structure of spiral shocks made by the planet, we show that progressive changes of the potential vorticity caused by spiral shocks ultimately lead to the excitation of a secondary instability. We also demonstrate that very high numerical resolution is required to both follow the potential vorticity changes and identify the location where the secondary instability is first excited. Low-resolution results are shown to give the wrong location. We establish the robustness of a secondary instability and its impact on the planet's torque. After the saturation of the instability, the disk shows large-scale nonaxisymmetry, causing the torque on the planet to oscillate with large amplitude. The impact of the oscillating torque on the protoplanet's migration remains to be investigated.

We suggest a new approach that could be used for modeling both the large-scale behavior of astrophysical jets and the magnetically dominated explosions in astrophysics. We describe a method for modeling the injection of magnetic fields and their subsequent evolution in a regime where the free energy is magnetically dominated. The injected magnetic fields, along with their associated currents, have both poloidal and toroidal components, and they are not force free. The dynamic expansion driven by the Lorentz force of the injected fields is studied using threedimensional ideal magnetohydrodynamic simulations. The generic behavior of magnetic field expansion, the interactions with the background medium, and the dependence on various parameters are investigated.

We present self-consistent cosmological magnetohydrodynamic (MHD) simulations that simultaneously follow the formation of a galaxy cluster and the magnetic field ejection by an active galactic nucleus (AGN). We find that the magnetic fields ejected by the AGNs, though initially distributed in relatively small volumes, can be transported throughout the cluster and be further amplified by the intracluster medium (ICM) turbulence during the cluster formation process. The ICM turbulence is shown to be generated and sustained by the frequent mergers of smaller halos. Furthermore, a cluster-wide dynamo process is shown to exist in the ICM and amplify the magnetic field energy and flux. The total magnetic energy in the cluster can reach ∼10 61 erg while micro Gauss (μG) fields can distribute over ∼ Mpc scales throughout the whole cluster. This finding shows that magnetic fields from AGNs, being further amplified by the ICM turbulence through small-scale dynamo processes, can be the origin of cluster-wide magnetic fields.