課程名稱︰星系天文物理
課程性質︰天文所必修
課程教師︰闕志鴻
開課學院：理學院
開課系所︰天文物理所
考試日期（年月日）︰104/01/14
考試時限（分鐘）：110(+15)
試題 :
1. For a system of collisionless particles, (a)what is the main difference of
it from a system of fluid(collisional particles)?(10%)
For a spherical configuration of such collisionless particles, there is an
effect due to velocity anisotropy that enters the force balance equation.
(b)How do you derive this velocity anisotropy force?
2. The polytrope models of a collisionless system are the simplest models,
which yield Lane-Emden equation. The polytrope model assumes the
distribution function as const*E^(n-3/2), where E is the energy. Please
derive the Lane-Emden equation for the collisionless system.(15%)
Among the polytrope models, the Plummer's model is often used by
astronomers to describe a system of bound stars. What is n for the
Plummer's model?(5%)
What is the asymptotic behavior of the Plummer's model when r approaches
infinity?(5%)
3. (a)How do you derive the Jeans length from the Jeans analysis?(5%)
The stability of a uniformly rotating, self-gravitating disk of infinite
extent can be analyzed relatively straightforwardly, but the stability
criterion differs very much from that of the Jeans analysis.
(b)How do you to derive the stability criterion for a disk?(15%) How do
you compare the two stability criteria?(10%)
4. For a spherically symmetric configuration, how do you show the squared
frequency ω^2 is real for the fluid system(15%), and for the collisionless
system?(10%)