STARMODL: Main Sequence Modeling.
Report_File=starmodl.txt.
An MR Modeler Report.    James A. Green, Greenwood Research
This model star features R=1.1*R_sun, with L_nuclear/L_star = 1, pretty nearly, a Zero Age Main Sequence requirement. The model star has a barely depleted core, and is quite young. However, the real ZAMS Sun was perhaps brighter at a smaller radius R such that R_sun < R < 1.1*R_sun: we merely tried L_observed = L_sun with R=1.1*R_sun. However, if the mass-luminosity law is strictly true at all times, R=1.1*R_sun gives the initial solar radius. This report answers the question: if the Sun were expanded at constant luminosity until L_nuclear/L_star = 1, how large would it be? Note that we may lower L_nuclear until it equals L_observed at the present radius only by lowering the core abundance of hydrogen, which enables us to compute the age of the star, but at the Zero Age star time we may lower L_nuclear until it matches L_observed from the mass-luminosity law only by increasing the radius to lower the central density and temperature. Then the central temperature comes down to 12.1615 million degrees K from over 13.33 million degrees as we expand the star to its state 4.5 to 5.5 billion years ago at a 1.1*R_sun initial radius prior to major hydrogen consumption. Subsequently the precise cross-over radius was found at 1.1039289*R_sun. Our stellar-evolution analysis in the earlier listing for the Sun based on spheres in equilibrium with gas plus radiation pressure and having H-depleted core structure with simplified molecular weight-based radial deformation accounted at most for 28% of the R_original/R_now = 1.1039289 radius transformation predicted by STARMODL, when taken over the entire lifetime of the Sun. Keeping the luminosity constant and taking the fractional abundance of hydrogen by weight equal to 0.005 to model the time just prior to core collapse yields a radius of 0.74928*R_sun, with a surface temperature of 6,665 degrees K, type F5.

Wed Jun 19 12:52:25 2002

1 models processed in this run, 0-0.

MODEL = 0 INPUT VARIABLES:
Starname = oldsun.
Assumed polytropic structure: n=3, gamma=4/3.
Distance = 1.000000e+00 LY,
         = 3.067485e-01 parsecs,
         = 9.460000e+15 meters,
         = 3.261865e+00 arc-seconds of parallax.
Visual magnitude = -2.704746.
Surface temperature was specified as = 5.501479e+03 deg.Kelvin.
Spectral type deduced from surface temp entry:
Henry Draper OBAFGKM Spectral type = G8.0 V [dwarf, regular].
Spectrum: Ca II strong, Fe & other metals strong, H weaker.
Wavelength at emission maximum = 527.130964 nanometers.
X[H] = 0.593141, Y[He] = 0.379610, Z[hvy] = 0.027249.
Chiu L/L_sun = 9.146336e-01, Clayton L/L_sun = 1.027382e+00, .
Chiu L/L_star = 9.153799e-01, Clayton L/L_star = 1.028220e+00, .
X[H] for L_Chiu_nuc/Lstar = 1 via H-burning core X(H) variation = 0.620204, .
X[H] for L_Clayton_nuc/Lstar = 1 via H-burning core X(H) variation = 0.585183, .
Detailed model abundances X(Z), by weight, for screening,
with heavy element abundance shaped like Aller,1961 - Clayton.
 1->H,                                                        2->He,
 3->Li, 4->Be, 5->B,  6->C, 7->N,  8->O, 9->F,               10->Ne,
11->Na,12->Mg,13->Al,14->Si,15->P,16->S, 17->Cl,             18->Ar,
19->K ,20->Ca,21->Sc,22->Ti,23->V,24->Cr,25->Mn,26->Fe,27->Co,28->Ni
ELEM. 0 <=  X(Z) <=  1,  and  Parts by weight
 H  chem[1] = 0.593141      1000.000000
He  chem[2] = 0.379610      640.000000
Li  chem[3] = 0.000000      0.000000
Be  chem[4] = 0.000000      0.000000
 B  chem[5] = 0.000000      0.000000
 C  chem[6] = 0.008541      14.400000
 N  chem[7] = 0.002669      4.500000
 O  chem[8] = 0.008304      14.000000
 F  chem[9] = 0.000012      0.020000
Ne  chem[10] = 0.005931      10.000000
Na  chem[11] = 0.000030      0.050000
Mg  chem[12] = 0.000356      0.600000
Al  chem[13] = 0.000030      0.050000
Si  chem[14] = 0.000534      0.900000
 P  chem[15] = 0.000000      0.000000
 S  chem[16] = 0.000415      0.700000
Cl  chem[17] = 0.000042      0.070000
Ar  chem[18] = 0.000178      0.300000
 K  chem[19] = 0.000000      0.000000
Ca  chem[20] = 0.000047      0.080000
Sc  chem[21] = 0.000000      0.000000
Ti  chem[22] = 0.000000      0.000000
 V  chem[23] = 0.000000      0.000000
Cr  chem[24] = 0.000000      0.000000
Mn  chem[25] = 0.000000      0.000000
Fe  chem[26] = 0.000119      0.200000
Co  chem[27] = 0.000000      0.000000
Ni  chem[28] = 0.000036      0.060000
>Ni chem[29] = 0.000006      0.010000
X_CNO = 0.011210.
Molecular weight mu = 0.673576.

Stellar Photosphere Ionization Ratios from the Saha Equation:
     n(Na+)/n(Na) = 5.448256e+07 n(H+)/n(H),
     n(He+)/n(He) = 7.861409e-11 n(H+)/n(H)

MODEL = 0 OUTPUT VARIABLES
Star Name = oldsun:
Zombeck bolometric corrections used.
Absolute magnitude before bolometric correction: M = 4.861342.
Absolute magnitude after correction: M + B.C = 4.762062.
Bolometric Correction = -0.099281.

L/Lsun, M/Msun, R/Rsun, prior to bolometric correction:
L/Lsun = 0.911871, M/Msun = 0.973300, R/Rsun = 1.050411.

After bolometric corrections, these quantities are:
L/Lsun = 0.999185, M/Msun = 0.999761, R/Rsun = 1.099552.

Radius = 7.652879e+08 meters.
Mass   = 1.988724e+30 kilograms.
Average density = 1.059283e+03 kg/m**3.
Central density = 5.739458e+04 kg/m**3.
   Central number density = 5.087700e+31 particles/m**3.
   Crit central g_s*N_Q quantum concentration = 8.926537e+36 particles/m**3.
   g_s*N_Q/n = 1.754533e+05, number_for_elec.degen(Tc)/actual_n, Phillips,p50.
   Compare with competing criteria electron degeneracy code results below.
Central pressure = 8.547126e+15 Newtons/m**3.
fbeta = [1-b]/b**4 = 6.470092e-04.  beta = 9.993667e-01.
Central gas pressure = 8.541713e+15 Newtons/m**2.
Central radiation pressure = 5.413180e+12 Newtons/m**2.
Ratio radiation_pressure/gas_pressure = 6.337347e-04.
Central temperature = 1.216150e+07 degrees Kelvin.
    Central photon density = 3.651382e+28 photons/m**3.
    Central photon energy density = 1.654845e+13 J/m**3.
Typical Phillips internal temp T_i = 4.721362e+06 degrees K.
    Typical photon density = 2.136476e+27 photons/m**3.
    Typical photon energy density = 3.759051e+11 J/m**3.
Stellar gravitational Binding Energy = 5.170605e+41 Joules.
 
The star oldsun,
   M/Msun = 9.997608e-01 < 6.23 Msun,
   is not a Type II supernova progenitor.
Stellar M.S. lifetime = 12.88x10**9[Msun/M]**2.409 = 1.288743e+10 yrs.
Zombeck lifetime = 13.0x10**9[Msun/M]**2.5 = 1.300778e+10 yrs.
Green's 1st M.S.lifetime = 9.92x10**9[Msun/M]**2 = 9.924748e+09 yrs.
Helmholtz-Kelvin gamma=4/3 contraction lifetime = 2.122835e+07 yrs,
   an upper limit to the star formation time.
   Initial star formation ionized radius R/R_solar = 4.900278e+01
   T_average at initial ionized radius = 30,000 deg. K.
Phillips freefall pulse time scale = 3.402831e+01 min
   = 5.671385e-01 hrs = 2.363077e-02 days = 6.467097e-05 years.
   Cepheid - typ 10 days, RR Lyrae - typ 0.5 to 1 day,
   both in F-G range, Red supergiants 100 days to several years.
Critical breakup angular rotation = 5.440176e-04 radians/sec.
    or 8.658317e-05 rev/sec = 5.194990e-03 rev/min
    = 7.480297e+00 rev/day, Surface velocity = 4.163301e+02 km/sec.
Photon mean free path = 1.410826e-03 meters = 1.410826e+00 mm
Photon random-walk escape time = 1.384711e+12 sec = 4.387550e+04 years.

AUX LUMINOSITIES - Estimates

L_stellar_wind(R) = 4.366631e+20 Joules
L_stellar_wind(R)/L_sun = 1.131251e-06 = 0.000113 percent
  Mass loss = 2.519248e+09 kg/sec = 3.996174e-14 solar masses/year
neutrinos = 6.883026e+14 neutrinos/sec per m**2 at 1 AU.
neutrinosH = 5.775648e+14 H(p,beta+,nu)D2 neutrinos/sec per m**2 at 1 AU.
neutrinosppe = 1.476539e+12 ppe neutrinos/sec-m**2 at 1 AU.
neutrinosBe = 9.400868e+13 Be7(e-,nu)Li7 neutrinos/sec-m**2 at 1 AU.
neutrinosB = 1.294322e+11 B8(beta+,nu)Be8 neutrinos/sec-m**2 at 1 AU.
neutrinosN = 8.174668e+12 N13(beta+,nu)C13 neutrinos/sec-m**2 at 1 AU.
neutrinosO = 6.948468e+12 O15(beta+,nu)N15 neutrinos/sec-m**2 at 1 AU.
L_neutrino       = 7.082516e+24 Watts
L_neutrino/L_sun = 1.834849e-02 = 1.834849 percent.

VARIABLES FROM CENTER TO SURFACE I
n=3, gamma=4/3, oldsun.
Radius           Density       Temperature   Pressure   Degeneracy
 r/Rstar         kg/m**3       deg. Kelvin    Newtons/m**2  Code
 0.000000e+00   5.739458e+04   1.216150e+07   8.547126e+15  2
 1.449044e-02   5.710851e+04   1.214126e+07   8.490371e+15  0
 2.898089e-02   5.626108e+04   1.208091e+07   8.322804e+15  0
 4.347133e-02   5.488376e+04   1.198151e+07   8.052252e+15  0
 5.796177e-02   5.302636e+04   1.184479e+07   7.690975e+15  0
 7.245222e-02   5.075351e+04   1.167308e+07   7.254603e+15  0
 8.694266e-02   4.814010e+04   1.146918e+07   6.760854e+15  0
 1.014331e-01   4.526659e+04   1.123628e+07   6.228202e+15  0
 1.159235e-01   4.221442e+04   1.097784e+07   5.674662e+15  0
 1.304140e-01   3.906175e+04   1.069746e+07   5.116754e+15  0
 1.449044e-01   3.588035e+04   1.039878e+07   4.568790e+15  0
 1.738853e-01   2.967256e+04   9.760719e+06   3.546492e+15  0
 2.028662e-01   2.396862e+04   9.090291e+06   2.667982e+15  0
 2.318471e-01   1.898149e+04   8.410211e+06   1.954787e+15  0
 2.608280e-01   1.478686e+04   7.738476e+06   1.401179e+15  0
 2.898089e-01   1.136429e+04   7.088336e+06   9.863903e+14  0
 3.187898e-01   8.637300e+03   6.468786e+06   6.841683e+14  0
 3.477706e-01   6.504480e+03   5.885287e+06   4.687512e+14  0
 3.767515e-01   4.860365e+03   5.340556e+06   3.178465e+14  0
 4.057324e-01   3.607231e+03   4.835278e+06   2.135785e+14  0
 4.347133e-01   2.660587e+03   4.368737e+06   1.423297e+14  0
 5.071655e-01   1.210148e+03   3.359771e+06   4.978636e+13  0
 5.796177e-01   5.260858e+02   2.545163e+06   1.639587e+13  0
 6.520700e-01   2.140042e+02   1.885837e+06   4.941840e+12  0
 7.245222e-01   7.810237e+01   1.347674e+06   1.288876e+12  0
 7.969744e-01   2.352205e+01   9.033482e+05   2.601911e+11  0
 8.694266e-01   4.799539e+00   5.318183e+05   3.125539e+10  0
 9.418788e-01   3.267883e-01   2.171629e+05   8.689889e+08  0
Degeneracy Code
  = 0 -> no electron degeneracy.
  = 1 -> relativistic electron degeneracy.
  = 2 -> non-relativistic electron degeneracy.

CONVECTION: VARIABLES FROM CENTER TO SURFACE I-B
Opacity includes bound-free, free-free, & electron scattering .
   If condition true, then convection is allowed.
r/r_star,                dT/dr  <   ((gam - 1)/gam)*(T/P)*(dP/dr)  true/false
r/r_star = 7.245222e-03, dT/dr = -3.650195e-03, -3.650183e-03 True,convection.
r/r_star = 2.173567e-02, dT/dr = -1.088500e-02, -1.088467e-02 True,convection.
r/r_star = 3.622611e-02, dT/dr = -1.792702e-02, -1.792549e-02 True,convection.
r/r_star = 5.071655e-02, dT/dr = -2.465691e-02, -2.465286e-02 True,convection.
r/r_star = 6.520700e-02, dT/dr = -3.096854e-02, -3.096028e-02 True,convection.
r/r_star = 7.969744e-02, dT/dr = -3.677371e-02, -3.675944e-02 True,convection.
r/r_star = 9.418788e-02, dT/dr = -4.200379e-02, -4.198170e-02 True,convection.
r/r_star = 1.086783e-01, dT/dr = -4.661051e-02, -4.657899e-02 True,convection.
r/r_star = 1.231688e-01, dT/dr = -5.056799e-02, -5.052573e-02 True,convection.
r/r_star = 1.376592e-01, dT/dr = -5.386813e-02, -5.381420e-02 True,convection.
r/r_star = 1.593949e-01, dT/dr = -5.753806e-02, -5.725153e-02 True,convection.
r/r_star = 1.883758e-01, dT/dr = -6.045688e-02, -6.007733e-02 True,convection.
r/r_star = 2.173567e-01, dT/dr = -6.132721e-02, -6.086816e-02 True,convection.
r/r_star = 2.463375e-01, dT/dr = -6.057478e-02, -6.005592e-02 True,convection.
r/r_star = 2.753184e-01, dT/dr = -5.862740e-02, -5.806999e-02 True,convection.
r/r_star = 3.042993e-01, dT/dr = -5.586880e-02, -5.529240e-02 True,convection.
r/r_star = 3.332802e-01, dT/dr = -5.261791e-02, -5.203851e-02 True,convection.
r/r_star = 3.622611e-01, dT/dr = -4.912202e-02, -4.855148e-02 True,convection.
r/r_star = 3.912420e-01, dT/dr = -4.556416e-02, -4.501037e-02 True,convection.
r/r_star = 4.202229e-01, dT/dr = -4.207101e-02, -4.153847e-02 True,convection.
r/r_star = 4.709394e-01, dT/dr = -3.639404e-02, -3.357149e-02 True,convection.
r/r_star = 5.433916e-01, dT/dr = -2.938339e-02, -2.686520e-02 True,convection.
r/r_star = 6.158439e-01, dT/dr = -2.378229e-02, -2.144894e-02 True,convection.
r/r_star = 6.882961e-01, dT/dr = -1.941188e-02, -1.709524e-02 True,convection.
r/r_star = 7.607483e-01, dT/dr = -1.602710e-02, -1.347986e-02 True,convection.
r/r_star = 8.332005e-01, dT/dr = -1.340131e-02, -1.016601e-02 True,convection.
r/r_star = 9.056527e-01, dT/dr = -1.134981e-02, -6.388648e-03 True,convection.


VARIABLES FROM CENTER TO SURFACE II
n=3, gamma=4/3, oldsun.
Opacityflag 1, bound-free, free-free, electron scattering incl.
Luminosity Partition in units of solar luminosity Lsun
Radius    L_nuclear = L_radiative + L_conduction + L_convection
 r/Rstar               [Maximum]
0.000000   0.001489  2.075239e-06   1.010954e-45   0.001487
0.014490   0.011216  9.312730e-06   4.484649e-45   0.011207
0.028981   0.036452  2.585675e-05   1.210799e-44   0.036426
0.043471   0.081052  5.077206e-05   2.274701e-44   0.081001
0.057962   0.145296  8.427511e-05   3.555531e-44   0.145212
0.072452   0.226202  1.267002e-04   4.956680e-44   0.226075
0.086943   0.318492  1.784995e-04   6.379756e-44   0.318313
0.101433   0.415857  2.402429e-04   7.733827e-44   0.415616
0.115924   0.512153  3.126299e-04   8.943013e-44   0.511840
0.130414   0.602296  3.964776e-04   9.950486e-44   0.601900
0.144904   0.760192  1.039700e-03   2.197118e-43   0.759153
0.173885   0.868782  1.504943e-03   2.306916e-43   0.867277
0.202866   0.934226  2.093514e-03   2.242213e-43   0.932132
0.231847   0.969527  2.830903e-03   2.053005e-43   0.966696
0.260828   0.986842  3.748669e-03   1.793824e-43   0.983094
0.289809   0.994661  4.885619e-03   1.510475e-43   0.989776
0.318790   0.997943  6.289573e-03   1.235074e-43   0.991653
0.347771   0.999232  8.019507e-03   9.864379e-44   0.991213
0.376752   0.999709  1.014883e-02   7.730691e-44   0.989560
0.405732   0.999875  1.276922e-02   5.965275e-44   0.987105
0.434713   0.999994  3.618062e-02   9.341121e-44   0.963813
0.507166   1.000000  6.177540e-02   4.440348e-44   0.938224
0.579618   1.000000  1.050137e-01   1.986750e-44   0.894986
0.652070   1.000000  1.792062e-01   8.245052e-45   0.820794
0.724522   1.000000  3.076961e-01   3.042356e-45   0.692304
0.796974   1.000000  5.223791e-01   9.043093e-46   0.477621
Last 2 table entries omitted.

NUCLEAR REACTIONS MAP, oldsun
nucmixflag = 1
Structure: n=3, gamma = 4/3.
The star is assumed homogeneously mixed, mu=6.735758e-01.
Threshold:10**7 K    10**8 K  5x10**8 K  10**9 2x10**9 3x10**9
[approx.] Hydrogen   Helium   Carbon     Neon  Oxygen  Silicon
          burns to  to C & O  O,Ne,Na,   O,Mg  Mg-S    to Iron.
r/Rstar   Helium              Mg                   
0.000000e+00, H->He [T=1.216150e+07 K]        
1.449044e-02, H->He [T=1.214126e+07 K]        
2.898089e-02, H->He [T=1.208091e+07 K]        
4.347133e-02, H->He [T=1.198151e+07 K]        
5.796177e-02, H->He [T=1.184479e+07 K]        
7.245222e-02, H->He [T=1.167308e+07 K]        
8.694266e-02, H->He [T=1.146918e+07 K]        
1.014331e-01, H->He [T=1.123628e+07 K]        
1.159235e-01, H->He [T=1.097784e+07 K]        
1.304140e-01, H->He [T=1.069746e+07 K]        
1.449044e-01, H->He [T=1.039878e+07 K]        
1.738853e-01, weak  [T=9.760719e+06 K]        
2.028662e-01, weak  [T=9.090291e+06 K]        
2.318471e-01, weak  [T=8.410211e+06 K]        
2.608280e-01, weak  [T=7.738476e+06 K]        
2.898089e-01, weak  [T=7.088336e+06 K]        
3.187898e-01, weak  [T=6.468786e+06 K]        
3.477706e-01, weak  [T=5.885287e+06 K]        
3.767515e-01, weak  [T=5.340556e+06 K]        
4.057324e-01, weak  [T=4.835278e+06 K]        
4.347133e-01, weak  [T=4.368737e+06 K]        
5.071655e-01, weak  [T=3.359771e+06 K]        
5.796177e-01, weak  [T=2.545163e+06 K]        
6.520700e-01, weak  [T=1.885837e+06 K]        
7.245222e-01, weak  [T=1.347674e+06 K]        
7.969744e-01, weak  [T=9.033482e+05 K]        
8.694266e-01, weak  [T=5.318183e+05 K]        
9.418788e-01, weak  [T=2.171629e+05 K]        
Central degeneracy non-relativistic.


  STAR AGE ESTIMATION & MODEL PERTURBATION ANALYSIS

Chiu Star age = 0.000000e+00 yr based on the H-burning core
  depletion required to normalize L_nuclear(R) for Chiu p-p fusion.
  10**7 K H-burning core radius = 0.16 solar radii = 0.14 star radius.
  Mantle: X=0.593141, Y=0.379610, Z=0.027249, mu=0.673576.
  Core:   X=0.593141, Y=0.379610, Z=0.027249, mu=0.673576.
  Core_Mass = 3.958150e+29 kg , = 0.198982 M_sun , M_core/M_star = 0.199030.
  Core gravitational potential energy = 2.214396e+20 Joules.
  1)Perturbation analysis based on nuclear energy gen & volume-avg mu. Disfavored.
    Old T_c = 1.216150e+07 K, Perturbed (mu_avg/mu_old)*T_c = 1.216150e+07 K
    Radial expansion perturbation delta_R/R_star < 0.000000.
  2)Polytropic analysis based on gas plus radiation laws. Since formation:
    Pressure and Temp drop in core as mu rises, R_star decreases.
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R) = -0.000000.
      delta_T/T = -(del_mu/mu) = -0.000000.
      delta_P/P = -(4/3)(del_mu/mu) = -0.000000.
    When the core has exhausted its hydrogen, mu = 1.345555, and
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.026523.
      delta_T/T = -(del_mu/mu) = -0.499407.
      delta_P/P = -(4/3)(del_mu/mu) = -0.665876.

Clayton Star age = 1.679706e+08 yr based on the H-burning core
  depletion required to normalize L_nuclear(R) for Clayton p-p fusion.
  10**7 K H-burning core radius = 0.16 solar radii = 0.14 star radius.
  Mantle: X=0.593141, Y=0.379610, Z=0.027249, mu=0.673576.
  Core:   X=0.584897, Y=0.387855, Z=0.027249, mu=0.678284.
  H-burningCoreMass = 3.958150e+29 kg , = 0.198982 Msun , Mcore/Mstar = 0.199030.
  Core gravitational potential energy = 2.214396e+20 Joules.
  1)Perturbation analysis based on nuclear energy gen & volume-avg mu. Disfavored.
    Old T_c = 1.216150e+07 K, Perturbed (mu_avg/mu_old)*T_c = 1.216176e+07 K
    Radial expansion perturbation delta_R/R_star < 0.000014.
  2)Polytropic analysis based on gas plus radiation laws. Since formation:
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.000369.
      delta_T/T = -(del_mu/mu) = -0.006942.
      delta_P/P = -(4/3)(del_mu/mu) = -0.009255.
    When the core has exhausted its hydrogen, mu = 1.345555, and
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.026523.
      delta_T/T = -(del_mu/mu) = -0.499407.
      delta_P/P = -(4/3)(del_mu/mu) = -0.665876.

THE HYDROGEN-BURNING CORE - COLLAPSE & ENVELOPE EJECTION PROBLEM

The smallest white dwarf in the Chandrasekhar Table has a mass
of 0.22 solar masses. Sun core mass is 0.279565 solar masses.
Bowers & Deeming: All stars < 4 solar masses form a white dwarf.
Smallest observed white dwarfs: M/Msun = 0.36 for 40 Eri B.
                                M/Msun = 0.39 for W 1346.
                                M/Msun = 0.01 for Van Maanen 2.
Two radial measures are used below for the collapsed core:
  1) Theoretical, after table by Chandrasekhar with 1.44 Msun limit.
  2) Experimental curve-fit, dwarf mass-radius, from Bowers & Deeming.
Hydrogen-burning core mass = 0.198982 solar masses.
  M_core/M_star = 0.199030 , if > 0.12, H-depleted core can collapse.
  M_core/M_star > M_Schoenberg-Chandrasekhar/M_star for collapse =.12.
  Core gravitational potential energy = 2.214396e+20 Joules.
  White dwarf approx. remnant potential energy = 6.450120e+41 Joules.
   using 2nd radius measure: remnant potential energy = 5.704801e+41 Joules.
  Stellar envelope launch energy for infinity = 2.954631e+41 Joules.
  Questionable:assumes half of the collapse energy is locked into dwarf thermal E_th, ala
  the virial theorem, then available E_total/2 divided between envelope E_th & kinetic E_kin.
  Total_available_collapse_energy/envelope_launch energy = 1.091527
   2nd r-measure Total_avail_collapse_energy/envelope_launch energy = 0.965400
  Assume virial theorem applies in a reciprocal form, so that half of the
  available collapse energy E_total/4 can expand the shell kinetically. Then:
  Too little energy is present to expand the envelope to infinity.
  Too little energy is present to expand the envelope to infinity.
  Half of the core collapse energy goes to heat the core,(virial th.)
  the other half is available to heat the envelope and eject it.
  Assume 1/2 of this available core collapse energy goes to heat the envelope.
  Then the max temperature rise in the envelope =5.514911e+06 K.
  Half of the core collapse energy goes to heat the core,(virial th.)
  the other half is available to heat the envelope and eject it.
  Assume 1/2 of this available core collapse energy goes to heat the envelope.
  Then the max temperature rise in the envelope =4.877657e+06 K, 2nd.
  The core collapse time controls the vigor of the shell expansion.
  Helmholtz-Kelvin model core collapse time =2.649523e+07 yr,
    but observationally planetary nebula ejection lasts < 3,000 yr,
    and the nebula clears away in say, 25,000 yrs.
  Core freefall time = 4.207306e+00 min
     = 7.012176e-02 hrs = 2.921740e-03 days = 7.996005e-06 years.
  Stellar photon random-walk escape time = 1.384711e+12 sec
    = 4.387550e+04 years.
Time from now to core collapse in H-burning core: = 1.191669e+10 yr.
Total Main-Sequence Lifetime until core collapse: = 1.208466e+10 yr,
   according to our simplistic H-burning core collapse theory.
                   H-burning_lifetime/Zombeck_Age = 0.929033
             H-burning_lifetime/Schwarzschild_Age = 0.937709
       H-burning_lifetime/Greens_Main_Seq.Lifeime = 1.217629
    H-burning_lifetime/Helmholtz_contraction_time = 569.269599


May 4, 2004
Our starz stellar evolution code, when pointed at the Sun, assumes that the Sun's exhausted helium core may implode (perhaps after a slow Helmholtz-Kelvin core contraction and a subsequent phase transformation), exploding the envelope like a planetary nebula, and computes an expansion velocity of about 161 km/sec for the solar debris (0.72 solar masses) comparable with the typical expansion velocities observed in such structures from the energy available for contraction to the density associated with support via a sea of degenerate electrons alone. The expanding shell of debris would reach the Earth 10 days after core implosion, leaving a white dwarf of 0.28 solar masses behind. [1], [2], [3], [4], [5]. Inspection of Hertzsprung-Russell Diagrams for various clusters shows that the slow Helmholtz contraction is associated with the formation of a Red Giant, which persists because a fusion reaction of helium to carbon takes place in the core, which can only collapse the rest of the way after the helium is exhausted, finally driving off the planetary nebula at the velocity of about 161 km/sec after the phase transformation of helium to carbon.

FUSION - NUCLEAR LUMINOSITY MEASURES,
nucmixflag = 1
gamma = 4/3, n=3, oldsun
Non-Normalized, Official Fusion Functions integrated
over the polytrope from the center to the surface.
Chiu luminosity includes electrostatic screening.
Clayton luminosity also includes electrostatic screening.
In solar luminosity units.
   [M/Msun]**4 = Max[L/Lsun] = 9.990435e-01,[Upper bound].
Computed observed     L/Lsun = 9.991847e-01,[from distance & m]*.
   [M/Msun]**3 = Min[L/Lsun] = 9.992825e-01,[Lower bound.]
P-P chain luminosity  L/Lsun = 1.000000e+00,[Clayton,scrnd&normd]
P-P chain luminosity  L/Lsun = 2.416618e-01,[Clayton,unscreened.]
P-P chain luminosity  L/Lsun = 1.027382e+00,[Clayton,screened.]
P-P chain luminosity  L/Lsun = 9.146336e-01,[Chiu,screened.]
P-P chain luminosity  L/Lsun = 3.788158e-01,[Chiu,unscreened.]
P-P chain luminosity  L/Lsun = 1.000000e+00,[Chiu,scrnd & normd]
P-P chain luminosity  L/Lsun = 2.303600e-01,[M. Scharzschild, unscr.]
P-P fusion luminosity L/Lsun = 2.629622e-01,[A.C.Phillips, unscr.]
Carbon cycle only L_CNO/Lsun = 1.690825e-04,[CNO cycle, M.Schw.,unscr.]
Triple-Alpha cyc.  L_He/Lsun = 1.043098e-144,[Helium burning,unscr.]
Total H-burning  L_Htot/Lsun = 1.027551e+00,[H-burning, PP + CNO.]
Total nuclear L:  L_tot/Lsun = 1.027551e+00,[Total, PP+CNO+He.]

In units of L_star oldsun.
   [M/Msun]**4 = Max[L/Lstar] = 9.998586e-01,[Upper bound].
Computed observed     L/Lstar = 1.000000e+00,[from distance & m]*.
   [M/Msun]**3 = Min[L/Lstar] = 1.000098e+00,[Lower bound.]
P-P chain luminosity  L/Lstar = 1.000816e+00,[Clayton,scrnd&normd]
P-P chain luminosity  L/Lstar = 2.418590e-01,[Clayton,unscreened.]
P-P chain luminosity  L/Lstar = 1.028220e+00,[Clayton,screened.]
P-P chain luminosity  L/Lstar = 9.153799e-01,[Chiu,screened.]
P-P chain luminosity  L/Lstar = 3.791249e-01,[Chiu,unscreened.]
P-P chain luminosity  L/Lstar = 1.000816e+00,[Chiu,scrnd & normd]
P-P chain luminosity  L/Lstar = 2.305479e-01,[M. Scharzschild, unscr.]
P-P fusion luminosity L/Lstar = 2.631767e-01,[A.C.Phillips, unscr.]
Carbon cycle only L_CNO/Lstar = 1.692205e-04,[CNO cycle, M.Schw.,unscr.]
Triple-Alpha cyc.  L_He/Lstar = 1.043949e-144,[Helium burning,unscr.]
Total H-burning  L_Htot/Lstar = 1.028390e+00,[H-burning, PP + CNO.]
Total nuclear L:  L_tot/Lstar = 1.028390e+00,[Total, PP+CNO+He.]

4th power L/Lsun-Max/[L/Lsun-obs]     = 9.998586e-01,
L/Lsun-observed/[L/Lsun-obs]          = 1.000000e+00, *
3rd power L/Lsun-Min/[L/Lsun-obs]     = 1.000098e+00,
L/Lsun_Clayton_unscreened/[L/Lsun]    = 2.418590e-01,
L/Lsun_Clayton_screened/[L/Lsun]      = 1.028220e+00,
L/Lsun_Clayton_scr-normalized/[L/Lsun]= 1.000816e+00,
L/Lsun_Chiu_screened/[L/Lsun]         = 9.153799e-01,
L/Lsun_Chiu_unscreened/[L/Lsun]       = 3.791249e-01,
L/Lsun_Chiu_scr-normalized/[L/Lsun]   = 1.000816e+00,
L/Lsun_Schwarzschild/[L/Lsun]         = 2.305479e-01,
L/Lsun_Phillips/[L/Lsun-observed]     = 2.631767e-01.
L_CNO/Lsun/[L/Lsun-observed]          = 1.692205e-04.
L_He/Lsun/[L/Lsun-observed]           = 1.043949e-144.
 

GREAT BALLS OF GAS!
Green's Paper on Big Bang Abundances
GM/R in Cosmic Sign Language

Proside: Free Stellar Structure Software at The Lost Chord
"Ram Dass" as a mythic archetype. [1] Behold the Spirit:
When I published my papers on Big Bang abundances, these images appeared at the same time over the Midwest.
Angelside: Shamanistic Humour
GM/R**2 Two! The Force!

DERIVATION OF THE BIG BANG HELIUM ABUNDANCE, Including a
Descriptive Analysis of Crunch-Bang or "Squeeze-Boom" Cosmology

James A. Green, May 2002