SOLUTIONS TO PROBLEM 2 HW 3

      NOTE: I have included the H- ion in my calculations, which is a
      sink for free electrons; thus the fractional electron
      contribution is negative! You are NOT being asked to include the
      H- ion, so you can ignore it in Table 3.  Since, at T=6000, the
      abundance of the H- ion is roughly 10 orders of magnitude below
      that of HI, the effects are neglgible...  however, my numbers
      may be *very slightly* different than yours because of my
      inclusion of the H- ion.


      Table 1. Gas Constraint Properties

      X        = 0.71        assumed hydrogen mass fraction
      Y        = 0.27        assumed helium mass fraction
      Z        = 0.02        assumed metal mass fraction
      Pgas     = 100.        assumed gas pressure
      T        = 6.0000E+03  assumed temperature
      alpha_H  = 0.912016    abundance fraction of H
      alpha_He = 0.087337    abundance fraction of He
      alpha_Ca = 0.000646    abundance fraction of Ca
      ntot     = 1.2072E+14  total particle number density  


      Table 2. Equilibrium Gas Quantities

      nN       = 1.1996E+14  number density of nuclear matter
      ne       = 7.5754E+11  number density of free electrons
      muN      = 1.2947E+00  mean mol weight of nuclear matter
      mue      = 2.2235E+02  mean mol weight of free electrons
      mutot    = 1.2872E+00  total mean mol weight 
      rhoN     = 2.5790E-10  mass density of nuclear matter
      rhoe     = 6.9007E-16  mass density of free electrons
      rhotot   = 2.5790E-10  total mass density from densities
      Pe       = 6.2754E-01  electron pressure
      Pe/Ptot  = 6.2754E-03  ratio of electron to total pressure


      Table 3. Ionization Conditions

      In below table "density" is the number density [cm^-3]

      Hydrogen    H          HI-         HI          HII
      -------- ----------  ----------  ----------  ----------
      density  1.0940E+14  7.9110E+04  1.0879E+14  6.1195E+11  
      ion frac             7.2310E-10  9.9441E-01  5.5935E-03 
      frac ne             -1.0443E-07  0.0000E+00  8.0780E-01  
      log10(Phi)           2.1018E+01  9.6295E+00  ...
      log10(U)             0.0000E+00  3.0075E-01  0.0000E+00
      -------- ----------  ----------  ----------  ----------

      Helium      He          HeI        HeII        HeIII
      -------- ----------  ----------  ----------  ----------
      density  1.0477E+13  1.0477E+13  1.3895E+02  4.0739E-35  
      ion frac             1.0000E+00  1.3263E-11  3.8885E-48  
      frac ne              0.0000E+00  1.8342E-10  1.0756E-46  
      log10(Phi)           1.0020E+00 -2.4653E+01  ...
      log10(U)             0.0000E+00  3.0100E-01  0.0000E+00
      -------- ----------  ----------  ----------  ----------

      Calcium    Ca          CaI        CaII        CaIII
      -------- ----------  ----------  ----------  ----------
      density  7.7505E+10  1.8228E+06  6.8446E+10  9.0575E+09  
      ion frac             2.3519E-05  8.8311E-01  1.1686E-01  
      frac ne              0.0000E+00  9.0353E-02  2.3913E-02  
      log10(Phi)           1.6454E+01  1.1001E+01  ...
      log10(U)             1.4230E-01  3.7942E-01  0.0000E+00
      -------- ----------  ----------  ----------  ----------