Modeling Planetary Accretion

Questions
1. Isaacman and Sagan (1977) say that any model of solar system formation should be able to account for three main solar system characteristics. What are these characteristics? (3 points)

2. In the ACRETE model, the nebular cloud is filled with dust and gas molecules, after which an accretion nucleus is released into the nebular cloud. The dust and gas molecules can stick to the accretion nucleus, but do not stick together on their own. This a way of saving the computational cost of tracking thousands of interactions between dust grains and molecules.

  • a. Explain how the ACRETE model determines whether a particular dust grain sticks to an accretion nucleus. Include any relevant mathematical expressions in your answer, and define the variables used. (3 points)
  • b. What additional requirement is necessary for the accretion nucleus to collect gas? (2 points)

3. The ACRETE model is able to reproduce the distinction between terrestrial and Jovian planets without accounting for the chemical segregation that results from the condensation sequence or the effects of the T-Tauri wind. Carry out the steps below to explain how the model is able to accomplish this.

  • a. Begin by calculating the value of x (see point 6, Isaacman 8. Sagan, 1977, p. 513) for two accretion nuclei. Both have a mass of 3 = 10.M., but one H 1 AU from the centre of the nebula, and the other is 3 AU from the centre of the nebula. Show your work. (4 points)
  • b. Compare the two values of 0, and use this information to explain why the model generates terrestrial and Jovian planets. (4 points)

4. Describe and explain the results of varying the ratio of gas to dust K. (3 points)

5. The density of dust in the ACRETE nebula is highest at the centre of the nebula and decreases toward the edges of the nebula. ACRETE uses a mathematical expression, p, = Aexp(-arfi), to describe how rapidly the density of dust (pt) falls off with distance from the centre of the nebula (r).

  • a. According to !seaman and Sagan (1977), to what is a change in the parameter A equivalent? (2 points)
  • b. Isaacman and Sagan (1977) find that the model produces solar systems that look like ours when values of A correspond to a range of nebular masses between 0.02 M. and 0.2 M.. Why is the nebular mass of 0.02 M. the lower limit? What happens at nebular masses below 0.02 Me? Why is 0.2 M. the upper limit? (4 points)
  • c. The range of nebular mass from 0.02 M. to 0.2 M. is much smaller than the nebular mass of 1 M., which is used by astronomers studying the earlier history of the solar system. Why do Isaacman and Sagan not find this discrepancy problematic? (3 points)

6. Describe and explain the outcome of changing the eccentricity (r) of the dust particles in the nebula. (5 points)

7. Would you say that the model is sensitive or insensitive to changes in the distribution of density in the nebula? Support your conclusion with examples from the paper. (5 points)

8. Isaacman and Sagan (1977) find that the model produces planetary spacings that appear to be consistent with Trout-Bode-type laws, even for very unusual planetary systems. How do the authors interpret this outcome? (2 points)