STAR8: Main Sequence Structure Investigator. Report_File=star8.txt.
Sat Jun 29 19:10:40 2002    James A. Green, Greenwood Research | Free Stellar Structure Downloads

This model features a radiative core using 2nd-order abundance mapping, as shown at the bottom.

MODEL = 0 INPUT VARIABLES:
Starname = sun.
Assumed polytropic structure: n=3, gamma=4/3.
Distance = 1.581395e-05 LY,
         = 4.850906e-06 parsecs,
         = 1.496000e+11 meters,
         = 2.062650e+05 arc-seconds of parallax.
Visual magnitude = -26.740000.
Surface temperature was specified as = 5.770000e+03 deg.Kelvin.
Spectral type deduced from surface temp entry:
Henry Draper OBAFGKM Spectral type = G3.0 V [dwarf, regular].
Spectrum: Ca II strong, Fe & other metals strong, H weaker.
Wavelength at emission maximum = 502.599653 nanometers.
X[H] = 0.597607, Y[He] = 0.382469, Z[hvy] = 0.019924.
Clayton + carbon_cycle L/L_sun = 2.169536e+00, .
Clayton + carbon_cycle L/L_star = 2.171306e+00, .
X[H] for L_Clayton_nuc/Lstar = 1 via H-burning core X(H) variation = 0.405560, .
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] = 0.597607      1000.000000
He  chem[2] = 0.382469      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] = 0.002869      4.800000
 N  chem[7] = 0.000896      1.500000
 O  chem[8] = 0.008367      14.000000
 F  chem[9] = 0.000012      0.020000
Ne  chem[10] = 0.005976      10.000000
Na  chem[11] = 0.000030      0.050000
Mg  chem[12] = 0.000359      0.600000
Al  chem[13] = 0.000030      0.050000
Si  chem[14] = 0.000538      0.900000
 P  chem[15] = 0.000000      0.000000
 S  chem[16] = 0.000418      0.700000
Cl  chem[17] = 0.000042      0.070000
Ar  chem[18] = 0.000179      0.300000
 K  chem[19] = 0.000000      0.000000
Ca  chem[20] = 0.000048      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] = 0.000120      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 = 0.003765.
Molecular weight mu = 0.670229.

Stellar Photosphere Ionization Ratios from the Saha Equation:
     n(Na+)/n(Na) = 2.378111e+07 n(H+)/n(H),
     n(He+)/n(He) = 2.321334e-10 n(H+)/n(H)

MODEL = 0 OUTPUT VARIABLES
Star Name = sun:
Zombeck bolometric corrections used.
Absolute magnitude before bolometric correction: M = 4.830886.
Absolute magnitude after correction: M + B.C = 4.762062.
Bolometric Correction = -0.068824.

L/Lsun, M/Msun, R/Rsun, prior to bolometric correction:
L/Lsun = 0.937813, M/Msun = 0.981342, R/Rsun = 0.968407.


Note that the M_Sun > 0.74199 solar masses is heavy enough to burn helium.
This means that after the hydrogen in the core is exhausted, the Sun
does not collapse to a helium white dwarf, but undergoes helium flash,
igniting its helium fuel, consequently expanding into a red giant.
However, M_Sun < 2.481 solar masses, so that the core cannot burn carbon,
and the star ends its evolution by becoming a carbon white dwarf and
expelling a planetary nebula.

After bolometric corrections, the LMR quantities are:
L/Lsun = 0.999185, M/Msun = 0.999761, R/Rsun = 0.999592.

Radius = 6.957162e+08 meters.
Mass   = 1.988724e+30 kilograms.
Average density = 1.409905e+03 kg/m**3.
Central density = 7.639219e+04 kg/m**3.
   Central number density = 6.805545e+31 particles/m**3.
   Crit central g_s*N_Q quantum concentration = 1.014569e+37 particles/m**3.
   g_s*N_Q/n = 1.490798e+05, number_for_elec.degen(Tc)/actual_n, Phillips,p50.
   Compare with competing criteria electron degeneracy code results below.
Central pressure = 1.251385e+16 Newtons/m**3.
fbeta = [1-b]/b**4 = 6.342446e-04.  beta = 9.993667e-01.
Central gas pressure = 1.250592e+16 Newtons/m**2.
Central radiation pressure = 7.925437e+12 Newtons/m**2.
Ratio radiation_pressure/gas_pressure = 6.337347e-04.
Central temperature = 1.331117e+07 degrees Kelvin.
    Central photon density = 4.787901e+28 photons/m**3.
    Central photon energy density = 2.375059e+13 J/m**3.
Typical Phillips internal temp T_i = 5.167692e+06 degrees K.
    Typical photon density = 2.801469e+27 photons/m**3.
    Typical photon energy density = 5.395047e+11 J/m**3.
Stellar gravitational Binding Energy = 5.687666e+41 Joules.
 
The star sun,
   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 = 2.335119e+07 yrs,
   an upper limit to the star formation time.
   Initial star formation ionized radius R/R_solar = 4.905249e+01
   T_average at initial ionized radius = 30,000 deg. K.
Phillips freefall pulse time scale = 2.949520e+01 min
   = 4.915867e-01 hrs = 2.048278e-02 days = 5.605577e-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 = 6.276275e-04 radians/sec.
    or 9.989011e-05 rev/sec = 5.993407e-03 rev/min
    = 8.629941e+00 rev/day, Surface velocity = 4.366507e+02 km/sec.
Photon mean free path = 1.081307e-03 meters = 1.081307e+00 mm
Photon random-walk escape time = 1.493132e+12 sec = 4.731089e+04 years.

AUX LUMINOSITIES - Estimates

L_stellar_wind(R) = 4.803294e+20 Joules/sec
L_stellar_wind(R)/L_sun = 1.244377e-06 -> 0.000124 percent
  Mass loss = 2.519248e+09 kg/sec = 3.996174e-14 solar masses/year
neutrinos = 1.446928e+15 neutrinos/sec per m**2 at 1 AU.
neutrinosH = 1.270549e+15 H(p,beta+,nu)D2 neutrinos/sec per m**2 at 1 AU.
neutrinosppe = 3.248147e+12 ppe neutrinos/sec-m**2 at 1 AU.
neutrinosBe = 1.489620e+14 Be7(e-,nu)Li7 neutrinos/sec-m**2 at 1 AU.
neutrinosB = 2.050926e+11 B8(beta+,nu)Be8 neutrinos/sec-m**2 at 1 AU.
neutrinosN = 1.295322e+13 N13(beta+,nu)C13 neutrinos/sec-m**2 at 1 AU.
neutrinosO = 1.101023e+13 O15(beta+,nu)N15 neutrinos/sec-m**2 at 1 AU.
L_neutrino       = 1.558039e+25 Watts
L_neutrino/L_sun = 4.036370e-02 = 4.036370 percent.

VARIABLES FROM CENTER TO SURFACE I
n=3, gamma=4/3, sun.
Radius           Density       Temperature   Pressure   Degeneracy
 r/Rstar         kg/m**3       deg. Kelvin    Newtons/m**2  Code
 0.000000e+00   7.639219e+04   1.331117e+07   1.251385e+16  2
 1.449044e-02   7.601143e+04   1.328902e+07   1.243075e+16  0
 2.898089e-02   7.488350e+04   1.322296e+07   1.218542e+16  0
 4.347133e-02   7.305028e+04   1.311417e+07   1.178930e+16  0
 5.796177e-02   7.057809e+04   1.296453e+07   1.126036e+16  0
 7.245222e-02   6.755292e+04   1.277658e+07   1.062146e+16  0
 8.694266e-02   6.407447e+04   1.255341e+07   9.898566e+15  0
 1.014331e-01   6.024983e+04   1.229850e+07   9.118710e+15  0
 1.159235e-01   5.618739e+04   1.201562e+07   8.308273e+15  0
 1.304140e-01   5.199119e+04   1.170873e+07   7.491440e+15  0
 1.449044e-01   4.775675e+04   1.138182e+07   6.689165e+15  0
 1.738853e-01   3.949418e+04   1.068344e+07   5.192419e+15  0
 2.028662e-01   3.190223e+04   9.949633e+06   3.906192e+15  0
 2.318471e-01   2.526437e+04   9.205263e+06   2.862003e+15  0
 2.608280e-01   1.968131e+04   8.470025e+06   2.051465e+15  0
 2.898089e-01   1.512587e+04   7.758424e+06   1.444174e+15  0
 3.187898e-01   1.149625e+04   7.080307e+06   1.001691e+15  0
 3.477706e-01   8.657463e+03   6.441647e+06   6.862986e+14  0
 3.767515e-01   6.469146e+03   5.845420e+06   4.653591e+14  0
 4.057324e-01   4.801225e+03   5.292376e+06   3.127003e+14  0
 4.347133e-01   3.541241e+03   4.781732e+06   2.083849e+14  0
 5.071655e-01   1.610707e+03   3.677384e+06   7.289221e+13  0
 5.796177e-01   7.002202e+02   2.785768e+06   2.400519e+13  0
 6.520700e-01   2.848396e+02   2.064113e+06   7.235348e+12  0
 7.245222e-01   1.039542e+02   1.475075e+06   1.887044e+12  0
 7.969744e-01   3.130785e+01   9.887454e+05   3.809458e+11  0
 8.694266e-01   6.388186e+00   5.820932e+05   4.576102e+10  0
 9.418788e-01   4.349552e-01   2.376922e+05   1.272287e+09  0
Degeneracy Code
  = 0 -> no electron degeneracy.
  = 1 -> relativistic electron degeneracy.
  = 2 -> non-relativistic electron degeneracy.

OPACITY FROM CENTER TO SURFACE
n=3, gamma=4/3, sun.
Radius         Density      Total_opacity,    Bound-free,    Free-free,    Elec.Scat
 r/Rstar       kg/m**3         ktotal           kbf             kff            ke
 0.000000e+00  7.639219e+04  3.982577e-01  3.516388e-01  1.466673e-02  3.195214e-02
 1.449044e-02  7.601143e+04  4.007024e-01  3.539856e-01  1.476461e-02  3.195214e-02
 2.898089e-02  7.488350e+04  4.056211e-01  3.587074e-01  1.496155e-02  3.195214e-02
 4.347133e-02  7.305028e+04  4.130728e-01  3.658608e-01  1.525992e-02  3.195214e-02
 5.796177e-02  7.057809e+04  4.231468e-01  3.755314e-01  1.566327e-02  3.195214e-02
 7.245222e-02  6.755292e+04  4.359631e-01  3.878345e-01  1.617643e-02  3.195214e-02
 8.694266e-02  6.407447e+04  4.516743e-01  4.029166e-01  1.680550e-02  3.195214e-02
 1.014331e-01  6.024983e+04  4.704665e-01  4.209564e-01  1.755794e-02  3.195214e-02
 1.159235e-01  5.618739e+04  4.925615e-01  4.421667e-01  1.844261e-02  3.195214e-02
 1.304140e-01  5.199119e+04  5.182189e-01  4.667969e-01  1.946993e-02  3.195214e-02
 1.449044e-01  4.775675e+04  5.650984e-01  5.117993e-01  2.134696e-02  3.195214e-02
 1.738853e-01  3.949418e+04  6.419206e-01  5.855456e-01  2.442289e-02  3.195214e-02
 2.028662e-01  3.190223e+04  7.399545e-01  6.796543e-01  2.834813e-02  3.195214e-02
 2.318471e-01  2.526437e+04  8.637236e-01  7.984677e-01  3.330379e-02  3.195214e-02
 2.608280e-01  1.968131e+04  1.018930e+00  9.474601e-01  3.951821e-02  3.195214e-02
 2.898089e-01  1.512587e+04  1.212750e+00  1.133519e+00  4.727865e-02  3.195214e-02
 3.187898e-01  1.149625e+04  1.454223e+00  1.365323e+00  5.694714e-02  3.195214e-02
 3.477706e-01  8.657463e+03  1.754792e+00  1.653858e+00  6.898179e-02  3.195214e-02
 3.767515e-01  6.469146e+03  2.129030e+00  2.013111e+00  8.396613e-02  3.195214e-02
 4.057324e-01  4.801225e+03  2.595650e+00  2.461049e+00  1.026494e-01  3.195214e-02
 4.347133e-01  3.541241e+03  3.745519e+00  3.564877e+00  1.486897e-01  3.195214e-02
 5.071655e-01  1.610707e+03  6.411367e+00  6.123985e+00  2.554292e-01  3.195214e-02
 5.796177e-01  7.002202e+02  1.141125e+01  1.092367e+01  4.556223e-01  3.195214e-02
 6.520700e-01  2.848396e+02  2.156669e+01  2.067250e+01  8.622423e-01  3.195214e-02
 7.245222e-01  1.039542e+02  4.515508e+01  4.331641e+01  1.806712e+00  3.195214e-02
 7.969744e-01  3.130785e+01  1.151465e+02  1.105054e+02  4.609139e+00  3.195214e-02
 8.694266e-01  6.388186e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 9.418788e-01  4.349552e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
Abundance variations in the core are not yet included in the opacity.
Opacity Flag = 1.
  = 1 -> total opacity is kbb+kff+ke.

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 = -4.394789e-03, -4.394774e-03 True,convection.
r/r_star = 2.173567e-02, dT/dr = -1.310541e-02, -1.310500e-02 True,convection.
r/r_star = 3.622611e-02, dT/dr = -2.158390e-02, -2.158206e-02 True,convection.
r/r_star = 5.071655e-02, dT/dr = -2.968661e-02, -2.968173e-02 True,convection.
r/r_star = 6.520700e-02, dT/dr = -3.728573e-02, -3.727579e-02 True,convection.
r/r_star = 7.969744e-02, dT/dr = -4.427509e-02, -4.425791e-02 True,convection.
r/r_star = 9.418788e-02, dT/dr = -5.057203e-02, -5.054544e-02 True,convection.
r/r_star = 1.086783e-01, dT/dr = -5.611846e-02, -5.608052e-02 True,convection.
r/r_star = 1.231688e-01, dT/dr = -6.088323e-02, -6.083234e-02 True,convection.
r/r_star = 1.376592e-01, dT/dr = -6.485655e-02, -6.479162e-02 True,convection.
r/r_star = 1.593949e-01, dT/dr = -6.927510e-02, -6.893012e-02 True,convection.
r/r_star = 1.883758e-01, dT/dr = -7.278933e-02, -7.233234e-02 True,convection.
r/r_star = 2.173567e-01, dT/dr = -7.383719e-02, -7.328450e-02 True,convection.
r/r_star = 2.463375e-01, dT/dr = -7.293127e-02, -7.230657e-02 True,convection.
r/r_star = 2.753184e-01, dT/dr = -7.058665e-02, -6.991554e-02 True,convection.
r/r_star = 3.042993e-01, dT/dr = -6.726534e-02, -6.657135e-02 True,convection.
r/r_star = 3.332802e-01, dT/dr = -6.335130e-02, -6.265371e-02 True,convection.
r/r_star = 3.622611e-01, dT/dr = -5.914229e-02, -5.845537e-02 True,convection.
r/r_star = 3.912420e-01, dT/dr = -5.485868e-02, -5.419192e-02 True,convection.
r/r_star = 4.202229e-01, dT/dr = -5.065297e-02, -5.001180e-02 True,convection.
r/r_star = 4.709394e-01, dT/dr = -4.381797e-02, -4.041966e-02 True,convection.
r/r_star = 5.433916e-01, dT/dr = -3.537724e-02, -3.234536e-02 True,convection.
r/r_star = 6.158439e-01, dT/dr = -2.863358e-02, -2.582425e-02 True,convection.
r/r_star = 6.882961e-01, dT/dr = -2.337166e-02, -2.058246e-02 True,convection.
r/r_star = 7.607483e-01, dT/dr = -1.929643e-02, -1.622958e-02 True,convection.
r/r_star = 8.332005e-01, dT/dr = -1.613501e-02, -1.223975e-02 True,convection.
r/r_star = 9.056527e-01, dT/dr = -1.366503e-02, -7.691852e-03 True,convection.

NUCLEAR REACTIONS MAP, sun
nucmixflag = 4
Structure: n=3, gamma = 4/3.
The star is assumed homogeneously mixed, mu=6.702287e-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=1.331117e+07 K]        
1.449044e-02, H->He [T=1.328902e+07 K]        
2.898089e-02, H->He [T=1.322296e+07 K]        
4.347133e-02, H->He [T=1.311417e+07 K]        
5.796177e-02, H->He [T=1.296453e+07 K]        
7.245222e-02, H->He [T=1.277658e+07 K]        
8.694266e-02, H->He [T=1.255341e+07 K]        
1.014331e-01, H->He [T=1.229850e+07 K]        
1.159235e-01, H->He [T=1.201562e+07 K]        
1.304140e-01, H->He [T=1.170873e+07 K]        
1.449044e-01, H->He [T=1.138182e+07 K]        
1.738853e-01, H->He [T=1.068344e+07 K]        
2.028662e-01, weak  [T=9.949633e+06 K]        
2.318471e-01, weak  [T=9.205263e+06 K]        
2.608280e-01, weak  [T=8.470025e+06 K]        
2.898089e-01, weak  [T=7.758424e+06 K]        
3.187898e-01, weak  [T=7.080307e+06 K]        
3.477706e-01, weak  [T=6.441647e+06 K]        
3.767515e-01, weak  [T=5.845420e+06 K]        
4.057324e-01, weak  [T=5.292376e+06 K]        
4.347133e-01, weak  [T=4.781732e+06 K]        
5.071655e-01, weak  [T=3.677384e+06 K]        
5.796177e-01, weak  [T=2.785768e+06 K]        
6.520700e-01, weak  [T=2.064113e+06 K]        
7.245222e-01, weak  [T=1.475075e+06 K]        
7.969744e-01, weak  [T=9.887454e+05 K]        
8.694266e-01, weak  [T=5.820932e+05 K]        
9.418788e-01, weak  [T=2.376922e+05 K]        
Central degeneracy non-relativistic.

STAR AGE ESTIMATION & MODEL PERTURBATION ANALYSIS

Clayton Star age = 5.497348e+09 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 = 0.17 solar radii = 0.17 star radius.
  Mantle: X=0.597607, Y=0.382469, Z=0.019924, mu=0.670229.
  Core:   X=0.405560, Y=0.574516, Z=0.019924, mu=0.798742.
  H-burningCoreMass = 5.561109e+29 kg , = 0.279565 Msun , Mcore/Mstar = 0.279632.
  Core gravitational potential energy = 6.013470e-154 Joules.
  1)Perturbation analysis based on nuclear energy gen & volume-avg mu. Disfavored.
    Old T_c = 1.331117e+07 K, Perturbed (mu_avg/mu_old)*T_c = 1.332459e+07 K
    Radial expansion perturbation delta_R/R_star < 0.000672.
  2)Polytropic analysis based on gas plus radiation laws. Since formation:
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.009322.
      delta_T/T = -(del_mu/mu) = -0.160894.
      delta_P/P = -(4/3)(del_mu/mu) = -0.214526.
    When the core has exhausted its hydrogen, mu = 1.342248, and
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.029008.
      delta_T/T = -(del_mu/mu) = -0.500667.
      delta_P/P = -(4/3)(del_mu/mu) = -0.667556.

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 = 0.279565 solar masses.
  M_core/M_star = 0.279632 , if > 0.12, H-depleted core can collapse.
  M_core/M_star > M_Schoenberg-Chandrasekhar/M_star for collapse =.12.
  Core gravitational potential energy = 6.013470e-154 Joules.
  White dwarf approx. remnant potential energy = 1.375033e+42 Joules.
   using 2nd radius measure: remnant potential energy = 1.336554e+42 Joules.
  Stellar envelope launch energy for infinity = 3.250095e+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 = 2.115374
   2nd r-measure Total_avail_collapse_energy/envelope_launch energy = 2.056177
  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:
    The stellar shell expands to infinity when core forms white dwarf.
  Maximum velocity of ejectae at infinity = 1.617850e+05 m/sec,
                      = 36.470963 Astronomical_Units/year,
                      = 0.000577 LY/year, or  = 1733.853140 years/LY,
                      = 9.987397 days to reach 1 AU,
  assuming half energy is wasted in heating the envelope.
  72.036800 percent of the stellar mass is ejected.
    2nd r - The stellar shell expands to infinity when core forms white dwarf.
  2nd Maximum velocity of ejectae at infinity = 1.128918e+05 m/sec,
                      = 25.449048 Astronomical_Units/year 2nd,
                      = 0.000402 LY/year, 2nd, = 2484.780356 yr/LY,
                      = 14.312913 days to reach 1 AU, 2nd
  assuming half energy is wasted in heating the envelope, 2nd.
  72.036800 percent of the stellar mass is ejected.
  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 =1.300716e+07 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 =1.264317e+07 K, 2nd.
  The core collapse time controls the vigor of the shell expansion.
  Helmholtz-Kelvin model core collapse time =5.648240e+07 yr,
    but observationally planetary nebula ejection lasts < 3,000 yr,
    and the nebula clears away in say, 25,000 yrs.
  Core freefall time = 4.044383e+00 min
     = 6.740639e-02 hrs = 2.808599e-03 days = 7.686370e-06 years.
  Stellar photon random-walk escape time = 1.493132e+12 sec
    = 4.731089e+04 years.
Time from now to core collapse in H-burning core: = 1.160916e+10 yr.
Total Main-Sequence Lifetime until core collapse: = 1.710651e+10 yr,
   according to our simplistic H-burning core collapse theory.
                   H-burning_lifetime/Zombeck_Age = 1.315099
             H-burning_lifetime/Schwarzschild_Age = 1.327380
       H-burning_lifetime/Greens_Main_Seq.Lifeime = 1.723622
    H-burning_lifetime/Helmholtz_contraction_time = 732.575597

FUSION - NUCLEAR LUMINOSITY MEASURES,
nucmixflag = 4
gamma = 4/3, n=3, sun
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 = 5.071197e-01,[Clayton,unscreened.]
P-P chain luminosity  L/Lsun = 2.167080e+00,[Clayton,screened.]
Carbon cycle only L_CNO/Lsun = 2.375560e-03,[CNO cycle, Reeves,unscr.]
Carbon cycle only L_CNO/Lsun = 2.456091e-03,[CNO cycle, Reeves,scr.]
Triple-Alpha cyc.  L_He/Lsun = 6.066361e-131,[Helium burning,unscr.]
Total H-burning  L_Htot/Lsun = 2.169536e+00,[H-burning, PP+CNO(Reeves,scr).]
Total nuclear L:  L_tot/Lsun = 2.169536e+00,[Total, PP+CNO(Reeves,scr)+He.]

In units of L_star sun.
   [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 = 5.075335e-01,[Clayton,unscreened.]
P-P chain luminosity  L/Lstar = 2.168848e+00,[Clayton,screened.]
Carbon cycle only L_CNO/Lstar = 2.377498e-03,[CNO cycle, Reeves,unscr.]
Carbon cycle only L_CNO/Lstar = 2.458095e-03,[CNO cycle, Reeves,scr.]
Triple-Alpha cyc.  L_He/Lstar = 6.071310e-131,[Helium burning,unscr.]
Total H-burning  L_Htot/Lstar = 2.171306e+00,[H-burning, PP(Clayton,scr)+CNO(Reeves,scr).]
Total nuclear L:  L_tot/Lstar = 2.171306e+00,[Total, PP(Clayton,scr)+CNO(Reeves,scr)+He.]

4th NUCLEAR LUMINOSITY RECAL WITH re-renormalized XYZ(r)
after mu-scaling of the temperature to include mu-scaling
Screened Clayton luminosity    L/Lsun = 1.005349.
Screened Reeves CNO luminosity L/Lsun = 0.000235.
Total H-burning luminosity     L/Lsun = 1.005584.
Screened Clayton luminosity    L/Lstar = 1.006169.
Screened Reeves CNO luminosity L/Lstar = 0.000235.
Total H-burning luminosity     L/Lstar = 1.006404.

ABUNDANCES: 2nd order SELF-CONSISTENT RENORMALIZED MAP, sun
nucmixflag = 4 Variational deflection: delta*sin(pi*(r/corewidth)).
Structure: n=3, gamma = 4/3.
Envelope abundances    : X(H)=0.597607, Y(He)=0.382469, Z(hvy)=0.019924.
Nominal Core abundances: X(H)=0.405560, Y(He)=0.574516, Z(hvy)=0.019924.
                  relative    ------Abundances XYZ--------
Stellar           nuclear
Shell   position  reaction    xch     ych     chemz  molecular shell mass   cumulative
 k      r/Rstar   rate        X(H)    Y(He)   Z(hvy) weight    Mshell/Mstar mass M(r)/Mstar
 0      0.000000  0.13372  0.04686  0.93322  0.01992  1.24442  0.00016214    0.00016214
 1      0.014490  0.13094  0.06148  0.91860  0.01992  1.21674  0.00108094    0.00124308
 2      0.028981  0.12452  0.09365  0.88643  0.01992  1.15999  0.00294369    0.00418677
 3      0.043471  0.11536  0.14066  0.83941  0.01992  1.08596  0.00560171    0.00978848
 4      0.057962  0.10421  0.19904  0.78103  0.01992  1.00622  0.00890555    0.01869403
 5      0.072452  0.09188  0.26363  0.71644  0.01992  0.93061  0.01267699    0.03137102
 6      0.086943  0.07918  0.32851  0.65156  0.01992  0.86531  0.01672350    0.04809452
 7      0.101433  0.06677  0.38803  0.59205  0.01992  0.81297  0.02085253    0.06894706
 8      0.115924  0.05518  0.43768  0.54239  0.01992  0.77392  0.02488420    0.09383125
 9      0.130414  0.04475  0.47467  0.50540  0.01992  0.74718  0.02866128    0.12249253
10      0.144904  0.03338  0.50846  0.47162  0.01992  0.72433  0.06722486    0.18971739
11      0.173885  0.02010  0.54282  0.43726  0.01992  0.70247  0.07683118    0.26654857 **
12      0.202866  0.01141  0.55060  0.42948  0.01992  0.69771  0.08190290    0.34845147
13      0.231847  0.00615  0.57229  0.40778  0.01992  0.68475  0.08271041    0.43116188
14      0.260828  0.00315  0.58463  0.39545  0.01992  0.67760  0.08001115    0.51117303
15      0.289809  0.00154  0.59125  0.38883  0.01992  0.67382  0.07475766    0.58593069
16      0.318790  0.00072  0.59462  0.38545  0.01992  0.67191  0.06788677    0.65381745
17      0.347771  0.00033  0.59626  0.38381  0.01992  0.67098  0.06019994    0.71401740
18      0.376752  0.00014  0.59702  0.38305  0.01992  0.67056  0.05231668    0.76633408
19      0.405732  0.00006  0.59736  0.38271  0.01992  0.67036  0.04467503    0.81100911
20      0.434713  0.00002  0.59752  0.38256  0.01992  0.67028  0.08662688    0.89763599
21      0.507166  0.00000  0.59760  0.38248  0.01992  0.67023  0.05173248    0.94936847
22      0.579618  0.00000  0.59761  0.38247  0.01992  0.67023  0.02832402    0.97769250
23      0.652070  0.00000  0.59761  0.38247  0.01992  0.67023  0.01396436    0.99165686
24      0.724522  0.00000  0.59761  0.38247  0.01992  0.67023  0.00593484    0.99759170
25      0.796974  0.00000  0.59761  0.38247  0.01992  0.67023  0.00198402    0.99957572
26      0.869427  0.00000  0.59761  0.38247  0.01992  0.67023  0.00042429    1.00000000
27      0.941879  0.00000  0.59761  0.38247  0.01992  0.67023  0.00000000    1.00000000
** Marks last core shell 11, T > 10**7 deg.K.
Star mass = 1.988724e+30 kg, or 1.000 solar masses.

OPACITY FROM CENTER TO SURFACE using 2nd-order abundance map.
n=3, gamma=4/3, sun.
Radius         Density      Total_opacity,    Bound-free,    Free-free,    Elec.Scat
 r/Rstar       kg/m**3         ktotal           kbf             kff            ke
 0.000000e+00  7.639219e+04  6.175625e-01  5.859200e-01  1.070537e-02  2.093714e-02
 1.449044e-02  7.601143e+04  6.107159e-01  5.785556e-01  1.093079e-02  2.122954e-02
 2.898089e-02  7.488350e+04  5.961116e-01  5.628344e-01  1.140428e-02  2.187290e-02
 4.347133e-02  7.305028e+04  5.777497e-01  5.428509e-01  1.208558e-02  2.281325e-02
 5.796177e-02  7.057809e+04  5.595615e-01  5.226463e-01  1.293430e-02  2.398086e-02
 7.245222e-02  6.755292e+04  5.450366e-01  5.058547e-01  1.390924e-02  2.527266e-02
 8.694266e-02  6.407447e+04  5.365429e-01  4.949952e-01  1.497739e-02  2.657026e-02
 1.014331e-01  6.024983e+04  5.353834e-01  4.915061e-01  1.611674e-02  2.776059e-02
 1.159235e-01  5.618739e+04  5.421687e-01  4.960995e-01  1.731564e-02  2.875362e-02
 1.304140e-01  5.199119e+04  5.571746e-01  5.091099e-01  1.857127e-02  2.949349e-02
 1.449044e-01  4.775675e+04  5.952673e-01  5.444548e-01  2.064335e-02  3.016915e-02
 1.738853e-01  3.949418e+04  6.626336e-01  6.078416e-01  2.393560e-02  3.085640e-02
 2.028662e-01  3.190223e+04  7.605914e-01  7.017150e-01  2.786445e-02  3.101198e-02
 2.318471e-01  2.526437e+04  8.766236e-01  8.121772e-01  3.300057e-02  3.144582e-02
 2.608280e-01  1.968131e+04  1.026746e+00  9.557186e-01  3.933466e-02  3.169251e-02
 2.898089e-01  1.512587e+04  1.217330e+00  1.138333e+00  4.717137e-02  3.182495e-02
 3.187898e-01  1.149625e+04  1.456817e+00  1.368038e+00  5.688657e-02  3.189245e-02
 3.477706e-01  8.657463e+03  1.756211e+00  1.655337e+00  6.894877e-02  3.192525e-02
 3.767515e-01  6.469146e+03  2.129780e+00  2.013891e+00  8.394873e-02  3.194050e-02
 4.057324e-01  4.801225e+03  2.596033e+00  2.461445e+00  1.026406e-01  3.194730e-02
 4.347133e-01  3.541241e+03  3.745729e+00  3.565094e+00  1.486849e-01  3.195031e-02
 5.071655e-01  1.610707e+03  6.411398e+00  6.124017e+00  2.554285e-01  3.195199e-02
 5.796177e-01  7.002202e+02  1.141125e+01  1.092367e+01  4.556222e-01  3.195213e-02
 6.520700e-01  2.848396e+02  2.156669e+01  2.067250e+01  8.622423e-01  3.195214e-02
 7.245222e-01  1.039542e+02  4.515508e+01  4.331641e+01  1.806712e+00  3.195214e-02
 7.969744e-01  3.130785e+01  1.151465e+02  1.105054e+02  4.609139e+00  3.195214e-02
 8.694266e-01  6.388186e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 9.418788e-01  4.349552e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
Opacity Flag = 1.
  = 1 -> total opacity is kbb+kff+ke.

VARIABLES FROM CENTER TO SURFACE II - Uses 2nd order abundance map.
n=3, gamma=4/3, sun.
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   0.000023  2.303928e-05 * 6.001427e-46   0.000000 L_radiative > L_nuclear.
0.014490   0.000133  1.334830e-04 * 2.704032e-45   0.000000 L_radiative > L_nuclear.
0.028981   0.000834  6.398732e-04   7.573636e-45   0.000194
0.043471   0.003835  1.332147e-03   1.508859e-44   0.002503
0.057962   0.013265  2.358104e-03   2.552961e-44   0.010906
0.072452   0.036048  3.767776e-03   3.909115e-44   0.032280
0.086943   0.079975  5.580848e-03   5.556362e-44   0.074394
0.101433   0.149563  7.775777e-03   7.404052e-44   0.141787
0.115924   0.242385  1.029122e-02   9.285935e-44   0.232094
0.130414   0.348933  1.303677e-02   1.099013e-43   0.335897
0.144904   0.571318  3.320198e-02   2.569733e-43   0.538116
0.173885   0.752403  4.524605e-02   2.862467e-43   0.707157
0.202866   0.866097  5.724738e-02   2.820002e-43   0.808850
0.231847   0.934418  7.065060e-02   2.681728e-43   0.863767
0.260828   0.970240  8.405323e-02   2.394561e-43   0.886186
0.289809   0.987128  9.733897e-02   2.040035e-43   0.889789
0.318790   0.994434  1.104939e-01   1.678071e-43   0.883940
0.347771   0.997374  1.235623e-01   1.344153e-43   0.873812
0.376752   0.998485  1.366265e-01   1.054834e-43   0.861858
0.405732   0.998880  1.497923e-01   8.144375e-44   0.849088
0.434713   0.999169  3.411543e-01   1.275682e-43   0.658015
0.507166   0.999184  4.082283e-01   6.064918e-44   0.590956
0.579618   0.999185  4.839660e-01   2.713669e-44   0.515219
0.652070   0.999185  5.742717e-01   1.126179e-44   0.424913
0.724522   0.999185  6.858129e-01   4.155506e-45   0.313372
0.796974   0.999185  8.178079e-01   1.235182e-45   0.181377
Last 2 table entries omitted.
MAX(L_radiative) = 1.518426e+00 Lsun.
L_radiative saturated L_nuclear setting L_convective=0 at r/Rstar=0.000000.

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. A few minutes after I picked up the above pictures, the wind had twisted the Old Man into an image of a Lady with long hair and a pearl necklace, so that I could judge which I liked better, it seemed. R**2 -> From Ram Dass to Rammed Ass.

Angelside: Shamanistic HumourGM/R**2 Two! The Force!

See DERIVATION OF THE BIG BANG HELIUM ABUNDANCE
by James A. Green, May 2002 & May 2006


REFERENCES

[1] Visionary Memories: See The Joyous Cosmology by Alan Watts & Be Here Now by Ram Dass, Still Here by Ram Dass, and Thomas Byrom's translation of The Dhammapada: The Sayings of the Buddha with introduction by Ram Dass, for an introduction to spiritual treats and guidance provided by Ram Dass over the years. Ram Dass also provides audio tapes, which is perhaps why the cloudy spirit figure is so in a wrap.... Rap!
[2] See James A. Green, Thermonuclear Fusion in Stars, Greenwood Research, 2nd edition, available now in 2003.
[3] Clayton, Donald D., Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill, 1965.
[4] Chiu, Hong-Yee, Stellar Physics, Blaisdell Publishing Co., 1968.

Star8 Themes from Bob Dylan: Knockin' on Heavens Door, Its All Over Now, Baby Blue.

Einstein & WeatherVisions | the Lincoln Zone Casebook

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Galaxy Formation by James A. Green, Greenwood Research.
Thermonuclear Fusion in Stars by James A. Green, Greenwood Research.
Gravitation & the Electroform Model: From General Relativity to Unified Field Theory, 11th edition, by James A. Green, Greenwood Research.
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