ASTR 498N                   Things to Know & Review

 

From Within

 

Here are shorthand reminders of things you should know (or be able to re-derive quickly) without reference to notes.  Please refer to the text or lecture notes for definitions of symbols.

 

Constants

There is no point in remembering any numerical quantity to better than two significant figures. 

c        speed of light                   (m s^–1)

pc      parsec                                        (m)

M  Mass of the Sun               (kg)

R   Radius of the Sun            (m)

L    Luminosity of the Sun     (W)

 

Magnitudes and such

Magnitude scale                

Apparent vs. absolute       

Effective temperature        

 

Radiative transfer

 

   or     where  and  

 

Cross section                       

Mean free path                  

 

Boltzmann & Saha        

Boltzmann                         

Saha                                  

Mean molecular weight

Number density of free particles         

Fully ionized hydrogen gas                   

Fully ionized helium gas                       

 

Thermodynamics

Fundamental relationship                      

 

Adiabatic processes

For ideal gas                                             

From  and the ideal gas law , you should be able to derive the companion relations  and .

 

Miscellaneous      

Characteristic dynamical time                

 

 

Equations of static stellar structure

 

                    conservation of mass

 

                  hydrostatic equilibrium

 

    conservation of energy

 

                   radiative energy transport

 

                          convective energy transport

 

You should be able to derive the first three equations using physical arguments.  Note that, in the energy conservation equation,  is the rate that the subsystem (mass shell) absorbs heat, consistent with the thermodynamic sign convention.  So the net rate of energy generation in the mass shell is  (all you need to remember).

 

Other Concepts To Review         

 

Virial Theorem

 

  nonrelativistic          relativistic          always

 

Three-Fold Way of quasistatic gravitational contraction:

1.     The star gets hotter

2.     Energy is liberated from the system.

3.     The total energy of the system decreases (star is more tightly bound).

 

Thermodynamics

 

·       In a system with a constant number of particles and no applied fields, we can choose any two state variables (T, P, V, U, S, …) to characterize the system.

·       The various thermodynamic potentials (U, F, G, H) reflect the fact that we can choose the two independent variables as we like.  Combinations of more than two variables are always related by equations, such as the fundamental relations (e.g.,   ), equations of state (e.g.,  ), or Maxwell relations (e.g.,  ).

 

Particle statistics and degeneracy

 

Occupation index    

 

C =   0          Maxwell-Boltzmann (classical)

C = +1         Fermi-Dirac

C = –1          Bose-Einstein

 

Remind yourself of the graphs of the M-B and F-D occupation indices as a function of particle energy, ε_p .  Review the criterion for complete degeneracy (  ) and the sense in which a degenerate gas is “cold.”  Be able to explain to define Fermi momentum using words and a diagram.  Why does a degenerate electron gas have high thermal conductivity?

 

Sources of opacity

 

Be able to describe physically what we mean by bound-bound, bound-free, free-free, and electron scattering opacity.  Have a general idea of their temperature dependence (e.g., electron scattering tends to dominate at high temperatures unless the gas is also highly degenerate).