Model of Angular Momentum Transport at the Protoplane-tary Disk Evolution and Disk Surface Density

We consider how the tidal effect of a protoplanetary disk interaction can be incorporated into calculations of its viscous evolution. The evolution of the disk occurs under the action of both internal viscous torques and external torques resulting from the presence of one or more embedded planets. The planets migrate under the effect of their tidal interaction with the disk (in the type-II migration regime). Torques on a planet are caused by its gravitational interaction with the density waves which occupy the Lindblad resonances in the disk. Our model simplifies the functional form of the rate of injection of the angular momentum Λ(r) to construct and solve the evolution equation for a disk and an embedded protoplanet. The functional Λ(r) depends on the tidal dissipation distribution in the disk which is concentrated in a vicinity of the protoplanet’s orbit. We have found an analytic solution for the disk surface density.

3D MHD simulation of a pulsationally-driven MRI decretion disc

We explore the pulsationally driven orbital mass ejection mechanism for Be star disc formation using isothermal, 3D magnetohydrodynamic (MHD) and hydrodynamic simulations. Non-radial pulsations are added to a star rotating at 95 per cent of critical as an inner boundary condition that feeds gas into the domain. In MHD, the initial magnetic field within the star is weak. The hydrodynamics simulation has limited angular momentum transport, resulting in repeating cycles of mass accumulation into a rotationally-supported disc at small radii followed by fall-back on to the star. The MHD simulation, conversely, has efficient (Maxwell αM ∼ 0.04) angular momentum transport provided by both of turbulent and coherent magnetic fields; a slowly decreting midplane driven by the magnetorotational instability and a supersonic wind on the surface of the disc driven by global magnetic torques. The angle and time-averaged properties near the midplane agree reasonably well with a 1D viscous decretion disc model with a modified $\tilde{\alpha }=0.5$, in which the gas transitions from a subsonic thin disc to a supersonic spherical wind at the critical point. 1D models, however, cannot capture the multi-phase decretion/angular structure seen in our simulations. Our results demonstrate that, at least under certain conditions, non-radial pulsations on the surface of a rapidly rotating, weakly magnetized star can drive a Keplerian disc with the basic properties of the viscous decretion disc paradigm, albeit coupled to a laminar wind away from the midplane. Future modeling of Be star discs should consider the possible existence of such a surface wind.

Aerodynamic Functional Diagnostics Based on Angular Momentum Transport Lines

In analogy with the classical concept of mass-flux-based streamlines, we define angular momentum transport (AMT) lines as an aerodynamic functional diagnostic tool. The AMT lines are the ones whose tangents are given by the average angular momentum flux. The mathematical and physical properties of these AMT lines are exploited to study the generation, removal, and transport of angular momentum in turbomachinery components. We illustrate the concept by visualizing AMT lines in two relatively simple flows, namely, vaneless incompressible diffuser and von Karman flow (a model of centrifugal compressors). Next, we apply the proposed diagnostic tool to flow in a return channel. A return channel is a part of a multistage centrifugal compressor stage. Its principal function is to remove angular momentum. In this work, we apply the diagnostic tool of AMT lines to a Reynolds-averaged Navier Stokes (RANS) simulation and a wall-modeled large eddy simulation (LES) of flow in the return channel. We show that AMT lines give us insights into the AMT process that are otherwise not available with conventional visualization tools.

Aerodynamic Functional Diagnostics Based on Angular Momentum Transport Lines

In analogy with the classical concept of mass-flux-based streamlines, we define Angular Momentum Transport (AMT) lines as an aerodynamic functional diagnostic tool. The AMT lines are the ones whose tangents are given by the average angular momentum flux. The mathematical and physical properties of these AMT lines are exploited to study the generation, removal, and transport of angular momentum in turbomachinery components. We illustrate the concept by visualizing AMT lines in two relatively simple flows, namely, vaneless incompressible diffuser and von Karman flow (a model of centrifugal compressors). Next, we apply the proposed diagnostic tool to flow in a return channel. A return channel is a part of a multistage centrifugal compressor stage. Its principal function is to remove angular momentum. In this work, we apply the diagnostic tool of AMT lines to a Reynolds averaged Navier Stokes simulation (RANS) and a wall-modeled large eddy simulation (LES) of flow in the return channel. We show that AMT lines give us insights into the angular momentum transport process that are otherwise not available with conventional visualization tools.

Magnetic field transport in compact binaries

Context. Dwarf novæ (DNe) and low mass X-ray binaries (LMXBs) show eruptions that are thought to be due to a thermal-viscous instability in their accretion disk. These eruptions provide constraints on angular momentum transport mechanisms. Aims. We explore the idea that angular momentum transport could be controlled by the dynamical evolution of the large-scale magnetic field. We study the impact of different prescriptions for the magnetic field evolution on the dynamics of the disk. This is a first step in confronting the theory of magnetic field transport with observations. Methods. We developed a version of the disk instability model that evolves the density, the temperature, and the large-scale vertical magnetic flux simultaneously. We took into account the accretion driven by turbulence or by a magnetized outflow with prescriptions taken, respectively, from shearing box simulations or self-similar solutions of magnetized outflows. To evolve the magnetic flux, we used a toy model with physically motivated prescriptions that depend mainly on the local magnetization β, where β is the ratio of thermal pressure to magnetic pressure. Results. We find that allowing magnetic flux to be advected inwards provides the best agreement with DNe light curves. This leads to a hybrid configuration with an inner magnetized disk, driven by angular momentum losses to an MHD outflow, sharply transiting to an outer weakly-magnetized turbulent disk where the eruptions are triggered. The dynamical impact is equivalent to truncating a viscous disk so that it does not extend down to the compact object, with the truncation radius dependent on the magnetic flux and evolving as Ṁ−2/3. Conclusions. Models of DNe and LMXB light curves typically require the outer, viscous disk to be truncated in order to match the observations. There is no generic explanation for this truncation. We propose that it is a natural outcome of the presence of large-scale magnetic fields in both DNe and LMXBs, with the magnetic flux accumulating towards the center to produce a magnetized disk with a fast accretion timescale.

Seismic evidence for near solid-body rotation in two Kepler subgiants and implications for angular momentum transport

Context. Asteroseismic measurements of the internal rotation of subgiants and red giants all show the need for invoking a more efficient transport of angular momentum than theoretically predicted. Constraints on the core rotation rate are available starting from the base of the red giant branch (RGB) and we are still lacking information on the internal rotation of less evolved subgiants. Aims. We identify two young Kepler subgiants, KIC 8524425 and KIC 5955122, whose mixed modes are clearly split by rotation. We aim to probe their internal rotation profile and assess the efficiency of the angular momentum transport during this phase of the evolution. Methods. Using the full Kepler data set, we extracted the mode frequencies and rotational splittings for the two stars using a Bayesian approach. We then performed a detailed seismic modeling of both targets and used the rotational kernels to invert their internal rotation profiles using the MOLA inversion method. We thus obtained estimates of the average rotation rates in the g-mode cavity (⟨Ω⟩g) and in the p-mode cavity (⟨Ω⟩p). Results. We found that both stars are rotating nearly as solid bodies, with core-envelope contrasts of ⟨Ω⟩g/⟨Ω⟩p = 0.68 ± 0.47 for KIC 8524425 and ⟨Ω⟩g/⟨Ω⟩p = 0.72 ± 0.37 for KIC 5955122. This result shows that the internal transport of angular momentum has to occur faster than the timescale at which differential rotation is forced in these stars (between 300 Myr and 600 Myr). By modeling the additional transport of angular momentum as a diffusive process with a constant viscosity νadd, we found that values of νadd > 5 × 104 cm2 s−1 are required to account for the internal rotation of KIC 8524425, and νadd > 1.5 × 105 cm2 s−1 for KIC 5955122. These values are lower than or comparable to the efficiency of the core-envelope coupling during the main sequence, as given by the surface rotation of stars in open clusters. On the other hand, they are higher than the viscosity needed to reproduce the rotation of subgiants near the base of the RGB. Conclusions. Our results yield further evidence that the efficiency of the internal redistribution of angular momentum decreases during the subgiant phase. We thus bring new constraints that will need to be accounted for by mechanisms that are proposed as candidates for angular momentum transport in subgiants and red giants.