ASTR 498N                   Things to Know & Review for the Final

 

(online at www.astro.umd.edu/~drabin/)

 

All right, I get it.

      Buffy

 

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From the Mid-Term

 

Please review (briefly) “Things to Know and Review.”  

 

Sample Questions

 

For a definition-type question, you’ll receive more credit for being quantitative (e.g., using an equation or diagram if appropriate) and illustrating why the concept is important for stellar structure.  Thus, defining the superadiabatic gradient as “the degree to which the temperature gradient exceeds the adiabatic gradient” is not worth full credit; you should define the adiabatic gradient, explain the consequences of exceeding it, and say how the superadiabatic gradient relates to convective energy flux.

 

Similarly, for an essay-type question, you’ll maximize credit by going beyond simple description and explaining why things happen.

 

Definition questions

Define and explain the stellar context of the following terms.

       1.        asymptotic giant branch

       2.        horizontal branch

       3.        helium core flash

       4.        Eddington luminosity

       5.        Chandrasekhar limit

       6.        Schönberg-Chandrasekhar limit

       7.        superadiabatic gradient

       8.        Gamow energy, Gamow peak

       9.        Fermi momentum

   10.        opacity, Rosseland mean opacity

   11.        Boltzmann and Saha equations

   12.        Stefan-Boltzmann law, stellar effective temperature

   13.        free-fall time, Jeans mass, Jeans radius

   14.        Kelvin-Helmholtz timescale

 

Short-answer questions

       1.        Define mean molecular weight μ.  Write a general expression for μ-1 in terms of XZ, NZ, and AZ, where XZ is the fraction by mass for the element with atomic number Z, NZ is the number of free particles contributed by each atom of element Z, and AZ is atomic weight.  Particularize this expression for a completely ionized gas composed of mass fractions X of hydrogen, Y of helium, and Z΄ = 1 – X – Y of heavier elements.  Assume AZ = 2Z + 2 for Z > 2.  What is μ for pure ionized hydrogen?  pure ionized helium?  typical Population I composition?

       2.        Write the formula for the electrostatic potential energy between two nuclei of charges ZA and ZB separated by a distance r.  Give an approximate numerical value for this energy (in MeV) at a head-on turn-around distance of 1 fm.

       3.        Write the three reactions that constitute the dominant branch of the proton-proton chain.  Which is the slowest of these reactions, how slow, and why?

       4.        Complete the following reactions:

 

 


What is the name of this reaction chain?  What is the significance of the * in 12C*?

       5.        Write the virial theorem, relating the kinetic energy and gravitational potential energy of a near-equilibrium, self-gravitating system, for the two limiting cases of a nonrelativistic gas and an ultrarelativistic gas.  Write corresponding equations involving the total energy.  Use the nonrelativistic equations to demonstrate three important consequences of quasistatic gravitational contraction of a gas sphere.  [Lecture 5]

       6.        Complete the stellar structure equations:

 

 

 

   (radiative transport)

   (convective transport)

 

Essay questions

1.     Using a diagram, describe the evolutionary path of a 0.1 M (or 1 M or 10 M) star in the (Tc, ρc) [central temperature and density] plane from the pre-main-sequence to final destiny.  Label the logarithmic axes with approximate values.  Identify major nuclear burning stages.  Demarcate areas of the plane that are dominated by the pressure of an ideal gas, radiation, nonrelativistic degenerate electrons, or relativistic degenerate electrons.  [Lecture 15.]

2.     Discuss the structure and evolution of a star of mass 1 M from (and including) the ZAMS through the planetary nebular phase.  Relevant factors include path in the HRD, sources of energy and specific nuclear reactions, locations of radiative and convective zones, opacity, and equation of state.  [Lectures 4 and 15; O&C Ch. 13]

3.     Discuss the structure and evolution of a star of mass 10 M from (and including) the ZAMS through the supernova event.  Relevant factors include path in the HRD, sources of energy and specific nuclear reactions, locations of radiative and convective zones, opacity, and equation of state.

4.     Discuss the importance of degenerate electron pressure in stellar structure and evolution.  Possible subtopics include:  origin of degeneracy, origin of relativistic degeneracy, temperature and density dependence of degeneracy pressure (nonrelativistic and relativistic), what parts of what stars become degenerate and when, physical consequences of degeneracy for nuclear burning and for the masses of white dwarfs.