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1st-principles-discs Report Summary

Project ID: 306614
Funded under: FP7-IDEAS-ERC
Country: Denmark

Mid-Term Report Summary - 1ST-PRINCIPLES-DISCS (A First Principles Approach to Accretion Discs)

Most celestial bodies, from planets and stars to the most compact objects in the Universe, such as neutron stars and black holes; gain mass throughout their evolution by means of an accretion disc. As matter in the disc loses angular momentum and migrates inwards, it radiates part of its gravitational energy, giving rise to distinct observable phenomena. Understanding the physical processes that determine the rate at which gravitating bodies accrete mass and radiate energy is vital for unraveling the formation, evolution, and fate of almost every type of object in the Universe. The majority of astrophysical questions that depend on the details of how disc accretion proceeds are still being addressed using the “standard” paradigm developed in the early 70’s, where magnetic fields (known to play a fundamental role since the early 90’s) do not appear explicitly. This projects has two main objectives: 1) Develop effective models of magnetohydrodynamic turbulence and its related transport properties in order to develop more realistic models of accretion disks. 2) Investigate kinetic processes in hot, dilute regions of the accretion disk where the magnetohydrodynamic approximation breaks down. There has been substantial progress in both of these endeavors, as described below.

Regarding objective 1: We have developed a new way to characterize magnetohydrodynamic turbulence in accretion disks. Our results suggest that a first-principles theory to describe fully developed turbulence will likely have to consider the anisotropic nature of the flow at a fundamental level. This will have an impact on the development of theoretical models of magnetohydrodynamic turbulence in disks. We have developed the "vertically global shearing box". This is a generalization of the standard shearing box that has been a workhorse for investigating astrophysical disk dynamics in local settings for over two decades. We have extended the shearing-box framework to model non-barotropic disks in domains that are radially local, but vertically global. This new framework will allow us to investigate instabilities and turbulence in astrophysical disks in novel ways. We have used the test field method to characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale magnetic fields in accretion disks. We studied in a systematic way the scaling of the various dynamo coefficients with shear rate and magnetic flux. These scalings allow us to predict, in a quantitative manner, the cycle period of the dynamo waves observed in numerical simulations of accretion disks. This lends new support to the importance of the alpha-Omega mechanism in determining the evolution of large-scale magnetic fields in turbulent accretion disks. We have carried out a detail study of the stability of radially and vertically stratified hydrodynamic disks. We have found that sound waves in disks with a radial thermal structure can become overstable. We found that these modes have similar growth rates, but different characteristics, than the vertical shear instability, which has dominated recent attention for alternative mechanisms to drive turbulence in unmagnetized disks. Our analysis has also provided a more coherent picture of how several instabilities can dominate the disk dynamics depending on the cooling time used in the model for thermal relaxation.

Regarding objective 2: In order to simulate weakly-collisional plasmas in the dynamical background of a disk, we are developing a Vlasov-fluid hybrid approach in which the ions are considered as particles but the electrons (which are much lighter and therefore have less inertia) can be approximated as a fluid. We have developed a new integration scheme that enables the exact integration of the background shear flow. We have already run several successful tests and are beginning to run full simulations. The advantage of the approach that we are undertaking is that this new version of the code not only takes full advantage of the computer cluster with accelerator hardware (Xeon-Phi) acquired with the ERC, but it will also run efficiently in the largest European facilities with many thousands of processors. We have also developed a new method to deal with the explosive increase/decrease of computational macro-particles in particle-in-cell codes used to simulate weakly-collisional plasmas, such as found in accretion disk coronae. Our approach is to compute an optimal representation of the global particle phase space structure while decreasing or increasing the entire particle population, based on k-means clustering of the data. In essence, the procedure amounts to merging or splitting particles by statistical means, throughout the entire simulation volume, while minimizing a 6-dimensional total distance measure to preserve the most relevant physical properties of the plasma. This new development will be useful when dealing, for example, with non-thermal radiative processes in weakly-collisional accretion disk coronae.

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