Research Introduction

	COMPUTATIONAL FLUID DYNAMICS
		MAGNETOHYDRODYNAMICS
in ASIAA

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Computational Fluid Dynamics & MagnetoHydroDynamics (CFD-MHD) in Astrophysics

INTRODUCTION:

CFD-MHD initiative has been a joint research project of the Institute of Astronomy and Astrophysics (ASIAA) and the Institute of Mathematics (ASIM) of the Academia Sinica, and the Department of Mathematics of the National Taiwan University. Its main goal is to develop high-performance codes of computational fluid dynamics and magnetohydrodynamics (CFD-MHD) for astrophysical problems. Over the last 4 years, we have successfully developed a set of 2-D Godunov codes based on exact Reimann solver. They are featured with self-gravitation and characteristics decomposition on the boundary, guaranteed non-reflection. At present we are applying these codes to the study of two main problems: the structure and evolution of gas disks in spiral galaxies and the planet migration in protostellar disks.

The structure and evolution of gas disks in galaxies:
The central regions of disk galaxies contain a large amount of gas and can be approximated as either isothermal or polytropic gas disks. We apply the Antares codes to simulate the evolution of these gas disks under the influence of different external force fields. Our present focus is on the potential due to a bar and spiral potential rotating at a constant angular speed. Theories explaining the spiral structures in galaxies have been around for a few decades by now, among which the density wave theory is perhaps the best motivated and most widely accepted. The theory, however, only address the structure of galaxies and cannot answer the evolution of galaxies. With our simulations we hope to be able to lend further support to it and fill in details of the evolution of galaxies.

In Fig. 1 is shown our simulation results for the 3-kpc arm in the Milky Way, which is believed to be a spiral galaxy. We conjecture that this 3-kpc arm is generated by density waves excited by a central bar potential. In our simulations we have considered two different sets of conditions, the main difference between those being the presence or absence of the self-gravity of the gas. The evolution of the resulting surface density distributions are shown from left to right. The upper panel corresponds to the case in which self-gravity is absent, while the opposite is true for the lower panel. The spiral structures for the two cases are clearly different. In particular, nearly chaotic behavior ensues only when self-gravity is considered.

Fig. 1

Similar simulations of a gas disk driven by a fast bar in a galaxy with nearly flat roatation curve gives rise to the starburst ring at the outer Lindblad resonance (OLR) outside, a stable circumnuclear dense molecular disk in the center (ILR, inner Lindblad resonance), and a general gas depletion region in between. All these are commonly seen in the nearby galaxies. In addition, a diamond shape feature is formed, resulting from the interaction between waves excited at OLR and ILR. A comparison with NGC6782 is shown in Figure 2.


Fig. 2

In the major-bar galaxies NGC1097 and NGC 1300 (Figure 3), there are a pair of very straight dust lanes in the major bar which end up to form a starburst ring in the galactic center. Similar morphology is observed in many not so overwhelming bar galaxies as well. We find that this type of structure can be reproduced in our numerical simulations. Preliminary results are shown in Fig. 4


Fig. 3 Two bar-spiral galaxies: NGC1097(left) and NGC1300 (right).

Fig. 4

The structure and evolution of protostellar disks:
Star formation has been one of the hottest topics in astronomy in recent years. Thanks to rapid progress in observational technology, many breakthroughs have been made. One of the most important of these discoveries is that of the protostellar disk, which plays a significant role in the process of the formation of the planetary system. To understand the process of formation of the planet and its subsequent migration, we consider a realistic model of the protostellar disk and calculate the planet and disk interaction. It has been found that many Jupiter-like giant planets are very close to their suns. In fact many of their distances from their sun are shorter than the earth-sun distance. However, according to the current theories of planet formation, these Jupiter-like planets could not have been formed so close to their suns. It is generally believed that they were more likely formed farther away and moved inwards as a result of their gravitational interaction with the protostellar disks.

Fig. 5 shows part of the results of our simulation for this problem. It can be seen in this figure that planets in protostellar disks do indeed migrate inwards. We have also found that self-gravity of the protostellar disks will affect their own surface density distributions, slow down the inward migration of the planets and make the orbits of planets more eccentric. These phenomena are even more noticeable when the disk has a high initial surface density.

Fig. 5: The protostellar disks in the first and second rows have higher initial surface densities than those in the third and fourth rows. Those in the first and third rows do not self-gravitate, while the opposite is true for those shown in the second and fourth rows.