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This study constitutes one part of our multi-disciplinary approach to the evolution of planet-forming disks. The goal is to establish the disks' thermal and mechanical properties as they grow by the infall of their parent interstellar clouds. Thus far, significant advances toward establishing the evolving surface density of such disks was made.
Planets form inside protostellar disks in a dead zone where the electrical resistivity of the gas is too high for magnetic forces to drive turbulence. We show that much of the dead zone nevertheless is active and flows toward the star while smooth, large-scale magnetic fields transfer the orbital angular momentum radially outward. Stellar X-ray and radionuclide ionization sustain a weak coupling of the dead zone gas to the magnetic fields, despite the rapid recombination of free charges on dust grains. Net radial magnetic fields are generated in the magnetorotational turbulence in the electrically conducting top and bottom surface layers of the disk, and reach the midplane by ohmic diffusion. A toroidal component to the fields is produced near the midplane by the orbital shear. The process is similar to the magnetization of the solar tachocline. The result is a laminar, magnetically driven accretion flow in the region where the planets form.
The status of theoretical work on protostellar disks is reviewed. Accretion disk theory and its application to models of the solar nebula and protostellar disks are discussed. A unified view of the process of star formation is presented, starting from the evolution of molecular clouds, and leading naturally to the formation of protostellar disks. The models used to describe this process are idealized, but are believed to provide good prototypes that well represent the essential hydromagnetic phenomena involved in star and disk formation. Several possible evolutionary paths and final configurations are qualitatively discussed, showing how the outcomes depend on the relative efficiencies of various angular momentum transport processes.
Formation of protoplanets and binary stars in a protostellar disk modifies the structure of the disk. Through tidal interactions, energy and angular momentum are transferred between the disk and protostellar or protoplanetary companion. We summarize recent progress in theoretical investigations of the disk-companion tidal interaction. We show that low-mass protoplanets excite density waves at their Lindblad resonances and that these waves are likely to be dissipated locally. When a protoplanet acquires sufficient mass, its tidal torque induces the formation of a gap in the vicinity of its orbit. Gap formation leads to the termination of protoplanetary growth by accretion. For proto-Jupiter to attain its present mass, we require that (1) the primordial solar nebula is heated by viscous dissipation; (2) the viscous evolution time scale of the nebula is comparable to the age of typical T Tauri stars with circumstellar disks; and (3) the mass distribution in the nebula is comparable to that estimated from a minimum-mass nebula model.
This program implements a spectral line, radiative transfer tool for interpreting Spitzer Space Telescope observations by matching them with models of protostellar disks for improved understanding of planet and star formation. The Spitzer Space Telescope detects gas phase molecules in the infrared spectra of protostellar disks, with spectral lines carrying information on the chemical composition of the material from which planets form. Input to the software includes chemical models developed at JPL. The products are synthetic images and spectra for comparison with Spitzer measurements. Radiative transfer in a protostellar disk is primarily affected by absorption and emission processes in the dust and in molecular gases such as H2, CO, and HCO. The magnitude of the optical absorption and emission is determined by the population of the electronic, vibrational, and rotational energy levels. The population of the molecular level is in turn determined by the intensity of the radiation field. Therefore, the intensity of the radiation field and the population of the molecular levels are inter-dependent quantities. To meet the computational challenges of solving for the coupled radiation field and electronic level populations in disks having wide ranges of optical depths and spatial scales, the tool runs in parallel on the JPL Dell Cluster supercomputer with C++ and Fortran compiler with a Message Passing Interface. Because this software has been developed on a distributed computing platform, the modeling of systems previously beyond the reach of available computational resources is possible.
The proposal achieved many of its objectives. The main area of investigation was the interaction of young planets with surrounding protostellar disks. The topics of interest include: 1) Simulations of Planet-Disk Interactions; 2) Secular Interactions Between Inclined Planets and a Gaseous Disk; 3) On the Tilting of Protostellar Disks by Resonant Tidal Effects; 4) Three-Dimensional Waves in Thermally Stratified Disks; and 5) Predictions of the Distribution of Planets. A list of publications resulting from this grant is also presented.
We present the first evidence for the process of terminating accretion in protostellar disks through the interaction between infall and a very wide opeining angle outflow.
An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion of a rotating gas cloud. Streamline equations for the flow onto the disk are derived, including the special case where the disk is very thin. For the radial structure of the disk, detailed equations of conservation of mass, momentum, angular momentum, and energy are given. Exact solutions are found for the case of no internal viscosity. For the more general case where there is viscous stress, hypotheses are formulated with the objective of discovering the main qualitative characteristics of a turbulent system and to estimate the magnitude of the turbulent stress. Solutions are also found for boundary conditions, and the large and small viscosity limits. The relation of energy balance to disk thermal structure is detailed. Finally, trends in the collapse of the dust cloud are discussed in the light of the solutions given.
Fragmentation in a gravitationally unstable accretion disk can be an important pathway for forming stellar/planetary companions. To characterize quantitatively the condition for and outcome of fragmentation under realistic thermodynamics, we perform global 3D simulations of gravitationally unstable disks at various cooling rates and cooling types, including the first global simulations of gravitational instability that employ full radiation transport. We find that fragmentation is a stochastic process, with the fragment generation rate per disk area p frag showing an exponential dependence on the parameter β ≡ Ω K t cool , where Ω K is the Keplerian rotation frequency, and t cool is the average cooling timescale. Compared to a prescribed constant β, radiative cooling in the optically thin/thick regime makes p frag decrease slower/faster in β; the critical β corresponding to ∼1 fragment per orbit is ≈3, 5, and 2 for constant β, optically thin, and optically thick cooling, respectively. The distribution function of the initial fragment mass is remarkably insensitive to disk thermodynamics. Regardless of cooling rate and optical depth, the typical initial fragment mass is m frag ≈ 40M tot h 3 , with M tot being the total (star+disk) mass and h = H/R being the disk aspect ratio. Applying this result to typical Class 0/I protostellar disks, we find m frag ∼ 20M J , suggesting that fragmentation more likely forms brown dwarfs. Given the finite width of the m frag distribution, forming massive planets is also possible.
An evolutionary model of dynamical processes in protostellar disks is described and illustrated with graphs of typical results. The effective transport mechanisms are discussed, including thermal convection, nonaxisymmetric gravitational instabilities in the outer regions of disks, and wave propagation. Consideration is then given to the stages of dynamical evolution, FU Ori outburst phenomena, unsteady accretion-disk flows, and nonlinear feedback as a mechanism to modulate mass transfer. The simulations show that mass redistribution is determined by angular-momentum transfer, which in turn is regulated by the effective viscosity generated by convectively driven turbulence. Significant mass transfer occurs as a result of mixing of infalling material with disk gas and is affected by the tidal torque associated with the growth of nonaxisymmetric disturbances in the outer disk. The time scale for disk evolution is found to be about 1 Myr.
The evolution and appearance of protostellar disks can be significantly altered by their UV environment. We follow the evolution after the external UV radiation source has been turned on.
The thermal structure of a wind that is centrifugally driven from the surface of a protostellar disk is studied. A generalized version of the Blandford and Payne self-similar wind model is introduced, and the temperature and ionization distributions in the outflow are investigated. For the evolution of atomic winds, the heat equation and the rate equations that describe the ionization and excitation state of hydrogen are solved self-consistently. Ambipolar diffusion is found to be a robust mechanism for heating the gas. In the more powerful outflows, molecular hydrogen is collisionally dissociated close to the disk surface, and hydrogen is mainly atomic within a few astronomical units from the central source. It is also demonstrated that these outflows have enough momentum to lift dust grains from the disk surface.
The project achieved many of its objectives. The main area of investigation was the interaction of young binary stars with surrounding protostellar disks. A secondary objective was the interaction of young planets with their central stars and surrounding disks. The grant funds were used to support visits by coinvestigators and visitors: Pawel Artymowicz, James Pringle, and Gordon Ogilvie. Funds were also used to support travel to meetings by Lubow and to provide partial salary support.
This grant final report contains bibliographic citations for eight papers published through support of NAG5-10732, "Properties of Planet-Forming Protostellar Disks."
2D, N-body simulations of the nonlinear development of long-wavelength instabilities predicted to occur early in the formation stage of protostellar disks forming single stars are presented under conditions of controlled energy loss. It is found that the thermodynamics and long-term evolution of gravitationally unstable disks are intimately coupled: the global evolution rate is linearly proportional to the rate at which dissipated energy reaches and escapes from the surfaces of the disk. An upper limit is obtained to the rate at which energy is lost if it is assumed that the disk maintains vertical isothermality.
We report the detection of emission from methanol in a compact source coincident with the position of the L1157 infrared source, which we attribute to molecules in the disk surrounding this young, Class O protostellar object. In addition, we identify a spectral feature in the outflow corresponding to an ethanol transition. Using the Caltech Owens Valley Millimeter Array with a synthesized beam size of 2", we detect spatially unresolved methanol in the 2(sub k) - 1(sub k) transitions at 3mm, which is coincident in position with the peak of the continuum emission. The gas phase methanol could be located in the central region (< 100 AU radius) of a flat disk, or in an extended heated surface layer (approx. 200 AU radius) of a flared disk. The fractional abundance of methanol X(CH3OH) is approx. 2 x l0(exp -8) in the flat disk model, and 3 x l0(exp -7) for the flared disk. The fractional abundance is small in the disk as a whole, but considerably larger in the warm portions. This difference indicates that substantial chemical processing probably takes place in the disk via depletion and desorption. The methanol desorbed from the grains in the warm surface layers returns to the icy grain mantles in the cooler interior of the disk, where it is available to become part of the composition of solar system-like bodies, such as comets, formed in the outer circumstellar region. This first millimeter-wavelength detection of a complex organic molecule in a young protostellar disk has implications for disk structure and chemical evolution and for potential use as a temperature probe. The research of TV and WL was conducted at the Jet Propulsion Laboratory, California Institute of Technology with support from the National Aeronautics and Space Administration.
The evolution and appearance of circumstellar disks in star forming regions can be influenced strongly by the radiation from nearby hot stars. Here we describe the results of numerical simulations of the evolution of protostellar disks and their immediate surroundings under the influence of external UV radiation.
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