Theoretical model for determining the turbulence state of protoplanetary disks from high spatial resolution radio observations
(Taku Takeuchi / Tokyo Institute of Technology)

 

Planetary formation is the process in a protoplanetary disk by which approximately 1 mm dust particles aggregate and grow to a size of 10,000 km or more in diameter. The part of the planetary formation process which is most wrapped in mystery is the initial stage, in which planetesimals approximately 1 km in diameter are formed. Only 1% of a protoplanetary disk is composed of solid matter, and it is constantly subjected to the dynamic effects of the disk gas. Particularly when dust aggregates are small, their motions are largely controlled by the disk gas. When considering how planetesimals are formed, it is extremely important to know the conditions of the disk gas, and in particular whether the gas flow is laminar or turbulent.
At present, high-resolution observation of protoplanetary disks is being carried out by the Subaru, ALMA, and other telescopes, and it is expected that these observations will allow us to determine the conditions of the disk gas. In particular, whether or not the disk gas is turbulent is an extremely important question for understanding planetesimal formation. ALMA is able to determine the disk structure to a scale of 1 AU, and it is hoped that this will provide some kind of answer to the question of disk turbulence. Present theories of planetesimal formation have to assume some disk gas conditions, however when this question is answered, it will become possible to construct a theory based on the actual conditions of the disk gas. This study intends to construct a theoretical model for disk turbulence conditions which can be compared with the ALMA dust continuum observations. With ALMA, there is the possibility that the disk gas velocity field can be detected directly from the width of the molecular spectrum lines, and this is of great importance for turbulence studies. However it is possible that there are large differences in the turbulence speed between the disk equatorial plane and the top layers. Moreover, the molecular spectrum lines do not necessarily trace the disk equatorial plane, and higher-resolution spatial structures can be obtained by continuum observation. When these issues are considered, then for the purpose of the zeroth-order question of “whether or not there is turbulence,” we should use the surface density structures of the disk that were obtained by dust continuum observations. Dust continuum observations can see through to the disk equatorial plane and are advantageous when searching for disk accretion.

This study has the following objectives. 1. Construct a theoretical model for obtaining information about disk turbulence based on dust continuum observations of the disk. 2. Compare the model in 1 with ALMA observation data and identify the conditions of gas turbulence. In the ALMA disk observations, it is expected that the number of observed astronomical bodies will be much larger for continuum observations to determine surface density distributions than the number observed for molecular spectrum line observations that are focused on turbulence. The purpose of the study is to carry out an effective comparison study using this data.

The most effective mechanism for sustaining turbulence in protoplanetary disks is magneto-rotational instability. In areas of the disk distant from the central star (farther than several AU to several tens of AU), turbulence will be produced due to the strong coupling between the magnetic field and gas. However in the inner parts of the disk, the magnetic field is not coupled to the gas and a laminar flow occurs. Gas which accretes from the outer part of the disk accumulates in the inner part, increasing the density in the inner part of the disk. In other words, differences in turbulence appear as differences in density. Here, because the strength of the turbulence is dependent on the strength of the magnetic field that passes vertically through the disk, it is necessary to also determine the strength of the magnetic field in order to theoretically compute the disk density structure. To solve this problem, we are conducting a new study which will also determine how the magnetic field and disk evolve. We first successfully derived a solution for steady-state problems. Using the steady-state problem results, it is possible to discuss the disk density structure, magnetic field, and turbulence conditions in quantitative terms. The boundary between the outer part of the disk (turbulent flow area) and the inner part (laminar flow area) should appear as a sudden change in density, and this can be detected by ALMA high-resolution observations of the dust continuum. In order to obtain turbulence information from the results of observing the density structure, we construct a theoretical model which can predict 2 features: the location of the boundary between the turbulent and laminar flows (several AU to several tens of AU), and the density contrast between the turbulent part and laminar flow part. Because the model predictions are focused on just these 2 numbers, if the ALMA observations find a sudden density change, then it can immediately be compared with the results of this study and discussed. This will make it possible to estimate the strength of the magnetic field passing through the disk and the strength of the gas turbulence. We are also currently studying the question of how the disk and magnetic field develop over time. The magnetic field is dragged by the accreting gas and accumulates to the central star. When this dragging works effectively, the magnetic field in the inner part of the disk becomes extremely strong. This increases the rate of gas accretion in the inner part of the disk and forms a hole in the inner disk. We will verify whether or not this phenomenon could be the mechanism which forms the so-called transition disks.

Finally, we will work to solve the problem of planetesimal formation based on an evolutionary model of the disk gas and magnetic field described here – a model for the evolution of protoplanetary disks that is based on the latest theories and observations.

 

Figure 1: Evolution of surface density in a protoplanetary disk. A hole gradually opens and expands in the center part. This occurs because the magnetic field is carried toward the disk center, increasing the strength of the magnetic field in the inner part of the disk and increasing the rate of gas accretion. At 105 to 7×106 years, a sudden increase in density is also seen at the outer edge of the dead zone (10 AU).

 

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