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Beyond the Standard Accretion Disk Model: Theoretical Foundations and Observational Implications

Final Report Summary - BEYOND-STANDARD-DISK (Beyond the Standard Accretion Disk Model: Theoretical Foundations and Observational Implications)

Background and Introduction

Most celestial bodies, ranging from planets to stars to black holes, gain mass during their lives by gravitationally attracting matter from their environments. This accretion process takes place via a disk-like structure around the gravitating object. Understanding the physical processes that determine the rate at which matter accretes and energy is radiated in these disks is vital for unraveling the formation, evolution, and fate of almost every type of object in the Universe. Despite the fact that magnetic fields have been known to play a fundamental role in accretion disks since the early 90's, the majority of astrophysical questions that depend on the details of how disk accretion proceeds are still being addressed using the 'standard' accretion disk model (developed in the early 70's), where magnetic fields do not appear explicitly. This has produced a profound disconnect between observations, usually interpreted with the standard paradigm, and modern accretion disk theory and numerical simulations, where magnetic turbulence is crucial.

Summary Description of the Project Objectives

The goal of this proposal is to go beyond the state of the art by building accretion disk models from first principles. This entails deepening our understanding of the physical building blocks that need to be brought together and by assembling them in order to investigate the global physical and observational properties of the resulting models. This undertaking involves understanding and modeling the interplay between the generation of magnetized turbulence, the global structure of the accretion disk, and the radiative processes that take place in the disk and its corona. This research proposal has two main objectives:

I. To build on the researcher's previous work with the goal of developing the theoretical framework that will incorporate magnetic fields into self-consistent disk models.

II. To investigate the transport processes in the low-density regions of accretion disks, where the observed non-thermal radiation originates.

Description of the work performed since the beginning of the project and description of the main results achieved

Work performed towards Objective I.

The current paradigm, supported by numerical simulations, suggests that magnetic fields play an essential role in driving the turbulence responsible for angular momentum transport, which enables matter in accretion disks to spiral into the central objects. The vast majority of this work has been developed in the framework provided by magneto-hydrodynamics (MHD) in which the plasma is assumed to behave as a magnetized fluid. During this first period of the Marie Curie Fellowship, the researcher has made progress along several lines of work related to understanding the dynamics of magnetic fields in accretion disks around stars and black holes.

- In collaboration with Gareth Murphy, a postdoc at the Niels Bohr International Academy, the researcher carried out numerical simulations to gain insight into the nonlinear evolution of the secondary (parasitic) instabilities thought to be responsible for the saturation of the magnetorotational instability (MRI) in the MHD regime, which is valid in the bulk of the accretion disk. These simulations were performed with the publicly available Pluto code, developed by Prof. Andrea Mignone at the University of Torino.

Results: The researcher has shown that there is good agreement between the numerical simulations and the analytical results that he had derived in Pessah, 2010, ApJ, 716, 1012. This part of the project has also allowed the researcher to build physical intuition which is very valuable to understand the numerical simulations of the magnetorotational instability in the collison-less regime, which are already underway in connection with Objective II.
- In collaboration with Chi-kwan Chan, a postdoc at NORDITA and now working at the University of Arizona, the researcher has carried out an extensive suite of numerical simulations to investigate the transport of angular momentum in disk regions where the angular velocity differs significantly from Keplerian rotation laws. This is the case in the boundary layer that forms close to the stellar surface in accretion disks surrounding weakly magnetized stars. In order to achieve this goal the researcher modified the publicly available code Athena, developed by Prof. Jim Stone in Princeton University.

Results:
This work resulted in a refereed publication in the Astrophysical Journal (Pessah M.E. and C.K. Chan, 2012, ApJ, 751, 48). This paper shows that the accretion disk boundary layer is prone to the excitation of MHD waves, whose energy can grow significantly without generating much stress, rendering them an inefficient mechanism to transport significant angular momentum (inward). This suggests that the detailed structure of turbulent MHD accretion disk boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity. This can have important observational consequences that will be explored by the researcher in future work.

- In collaboration with Colin McNally, a postdoc at the Niels Bohr International Academy, The researcher is developing the formalism to be able to produce more realistic simulations of a region of an accretion disk that is local in the radial and azimuthal direction but that can extend up to several scale heights in the vertical direction.

Results:
The set of equations that the researcher has derived will be useful for many astrophysicists in high energy astrophysics, protoplanetary disks, and galactic dynamics. For instance, this formalism will allow us to study the launching of disk winds in an unprecedented manner. This project has picked up the interest of many group members in Copenhagen and we have also initiated a collaboration with Oliver Gressel at NORDITA, in Stockholm, on a related problem.

Work performed towards Objective II.

The MHD approximation, breaks down in low-density disk regions such as the inner disk and the disk coronae, where the plasma becomes collision-less. The researcher is pioneering the study of the processes that lead to angular momentum transport in the uncharted regime where the plasma dynamics needs to be studied at the kinetic level. In order to achieve the long-term goal of modeling these disk regions in the collision-less regime, the researcher has been actively collaborating with the Computational Astrophysics Group at the Niels Bohr Institute.

- In collaboration with Gareth Murphy and Troels Haugboelle, both postdocs at the Niels Bohr Institute, the researcher is working towards the ambitious goal of running particle-in-cell simulations of the magnetorotational instability (MRI) with the Photon-Plasma code developed in Copenhagen. Before running the full MRI experiments, we are simulating the 2D and 3D evolution of velocity and current density profiles that vary sinusoidally in the z-coordinate (perpendicular to the disk midplane). This setup mimics the 'background flows' induced by an MRI-unstable mode. The subsequent development of the expected Kelvin-Helmholtz and Tearing Mode-type instabilities in this kind of configuration is interesting on its own right since there have been no previous PIC attempts to simulate this. Furthermore, analyzing these experiments will provide valuable insight into the outcome of the 2D and 3D MRI-runs, in the next stages of this program.

All of these initial numerical studies have been performed with local resources, including the use of powerful personal computing equipment acquired with the funding devoted to research-related expenses. For the next step in this ambitious program we have secured computing time in one of the largest compute clusters in Europe, the Juqueen machine in Julich.

While at the Niels Bohr International Academy, the researcher had the opportunity to interact with other physicist with complementary expertise. This lead to a spin-off project with Sagar Chakraborty, a postdoc at the Niels Bohr International Academy (now a Professor at the Indian Institute of Technology in Kanpur). While pondering about the physics of dilute plasmas in low density regions of accretion disks, the researcher became aware of a very interesting problem in the context of low-density plasmas in a constant gravitational field. This has naturally led him to learn about the magneto-thermal instability (MTI) and the heat-flux-buoyancy instability (HBI), which have been shown to play a key role in galaxy clusters in recent years. His work with Sagar Chakraborty resulted in a thorough paper on the physics of dilute plasmas in the Astrophysical Journal (Pessah M.E. and S. Chakraborty, 2013, ApJ, 764, 13). The knowledge that the researcher has acquired while working on this problem has helped him to understand much better the physics of dilute plasmas which is proving to be extremely valuable to achieve the goals set forth by the Objective II of this research plan.

Expected final results and their potential impact and use

The work carried out under this Marie Curie Fellowship constitutes significant progress towards the long sought goal of moving beyond the standard paradigm proposed almost 40 years ago. Given the fundamental importance of accretion disks in a wide variety of astronomical systems, many fields across astrophysics will benefit from the outcome of this research program. In particular, it will provide a new framework for investigating the global structure and observational signatures of accretion disks in a wide variety of astrophysical systems. These models will thus directly benefit at least two areas of research that are extremely active in Europe, and the rest of the world, right now: planet formation and supermassive black hole feedback on galaxy evolution. To date, these problems have mostly been addressed within the standard framework, and thus ignoring the importance of magnetic fields. The high scientific profile of these subjects will enhance the international competitiveness of the European Research area in the interdisciplinary field of theoretical astrophysics.