課程名稱︰恆星天文物理 課程性質︰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）︰2017年11月17日 考試時限（分鐘）：120分鐘 試題 : Stellar Astrophysics, fall 2017 midterm exam (1) Set up the radiation equation describing the balance of photons with the Einstein coefficients A21, B21 and B12. (10%) In thermal equilibrium, using this equation you can derive two relations to relate these three coefficients. How do you derive them? (15%) (2) In non-relativistic limit, we have the Larmor formula that describes how radiation is emitted by the acceleration of a charge particle. What is the Larmor formula? (5%) How much power is lost to radiation from the accelerated particle? (5%) From this information, how do you derive the radiation back-reaction force? (10%) Is there any simple physical reason, from the space-time invariance viewpoint, this back-reaction force should depend on the second time derivative, and not on the zero time derivative, of the velocity? (5%) (3) In free-free (Bremsstrahlung) emission, how do you calculate the acceleration of a weakly colliding particle for a given impact parameter b and a given incoming velocity v? (10%) Of cource, the collision occurs only in a finite time interval, how do you compute/estimate the frequency Fourier components of this collision (5%). Since both b and v are so far given, how do you obtain the total thermal free-free emission power density per frequency when intergrating the impact parameter b and averaging over velocity? (15%) (4) How do you derive the virial condition for a isolaterd gas sphere? (10%) How do you estimate the central pressure of a star, assuming that you know the stellar mass and radius? (10%) --

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