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%)