STARMAN: Main Sequence Modeling. Report_File=starman.txt.
Tue Jun 11 08:29:26 2002  James A. Green  Greenwood Research
Free Stellar Structure Software with Source Code in C

1 models processed in this run, 0-0.

MODEL = 0 INPUT VARIABLES:
Starname = The_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.
Mu was varied with core of iron + H + He to optimize L_nuc:
X[H] = 0.597600, Y[He] = 0.382500, Z[hvy] = 0.019900.
Chiu L/L_sun = 1.845909e+00, Clayton L/L_sun = 2.166969e+00, .
Chiu L/L_star = 1.847415e+00, Clayton L/L_star = 2.168737e+00, .
X[H] for L_Chiu_nuc/Lstar = 1 via H-burning core X(H) variation = 0.439851, .
X[H] for L_Clayton_nuc/Lstar = 1 via H-burning core X(H) variation = 0.405961, .
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
   0 <=  X(Z) <=  1,  and  Parts by weight
 chem[1] = 0.597600      1000.000000
 chem[2] = 0.382500      640.060241
 chem[3] = 0.000000      0.000000
 chem[4] = 0.000000      0.000000
 chem[5] = 0.000000      0.000000
 chem[6] = 0.002865      4.794195
 chem[7] = 0.000895      1.498192
 chem[8] = 0.008356      13.983138
 chem[9] = 0.000012      0.019976
 chem[10] = 0.005969      9.988004
 chem[11] = 0.000030      0.049939
 chem[12] = 0.000358      0.599270
 chem[13] = 0.000030      0.049939
 chem[14] = 0.000537      0.898922
 chem[15] = 0.000000      0.000000
 chem[16] = 0.000418      0.699165
 chem[17] = 0.000042      0.069917
 chem[18] = 0.000179      0.299635
 chem[19] = 0.000000      0.000000
 chem[20] = 0.000048      0.079903
 chem[21] = 0.000000      0.000000
 chem[22] = 0.000000      0.000000
 chem[23] = 0.000000      0.000000
 chem[24] = 0.000000      0.000000
 chem[25] = 0.000000      0.000000
 chem[26] = 0.000119      0.199757
 chem[27] = 0.000000      0.000000
 chem[28] = 0.000036      0.059927
 chem[29] = 0.000006      0.009988
X_CNO = 0.008909.
Molecular weight mu = 0.670230.

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, The_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.

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


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.

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 = 6.805532e+31 particles/m**3.
   Crit central g_s*N_Q quantum concentration = 1.014575e+37 particles/m**3.
   g_s*N_Q/n = 1.490810e+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 = 6.342496e-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 = 1.331120e+07 degrees Kelvin.
    Central photon density = 4.787929e+28 photons/m**3.
    Central photon energy density = 2.375077e+13 J/m**3.
Typical Phillips internal temp T_i = 5.167702e+06 degrees K.
    Typical photon density = 2.801485e+27 photons/m**3.
    Typical photon energy density = 5.395090e+11 J/m**3.
Stellar gravitational Binding Energy = 5.687666e+41 Joules.
 
The star The_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 = 4.905241e+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 = 1.081299e-03 meters = 1.081299e+00 mm
Photon random-walk escape time = 1.493143e+12 sec = 4.731126e+04 years.

AUX LUMINOSITIES - Estimates

L_stellar_wind(R) = 4.803294e+20 Joules
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 = 6.675743e+14 neutrinos/sec per m**2 at 1 AU.
neutrinosH = 5.862815e+14 H(p,beta+,nu)D2 neutrinos/sec per m**2 at 1 AU.
neutrinosppe = 1.498823e+12 ppe neutrinos/sec-m**2 at 1 AU.
neutrinosBe = 6.865500e+13 Be7(e-,nu)Li7 neutrinos/sec-m**2 at 1 AU.
neutrinosB = 9.452500e+10 B8(beta+,nu)Be8 neutrinos/sec-m**2 at 1 AU.
neutrinosN = 5.970000e+12 N13(beta+,nu)C13 neutrinos/sec-m**2 at 1 AU.
neutrinosO = 5.074500e+12 O15(beta+,nu)N15 neutrinos/sec-m**2 at 1 AU.
L_neutrino       = 7.189405e+24 Watts
L_neutrino/L_sun = 1.862540e-02 = 1.862540 percent.

VARIABLES FROM CENTER TO SURFACE I
n=3, gamma=4/3, The_SUN.
Radius           Density       Temperature   Pressure   Degeneracy
 r/Rsun          kg/m**3       deg. Kelvin    Newtons/m**2  Code
 0.000000e+00   7.639219e+04   1.331120e+07   1.251385e+16  2
 1.448454e-02   7.601143e+04   1.328905e+07   1.243075e+16  0
 2.896907e-02   7.488350e+04   1.322299e+07   1.218542e+16  0
 4.345361e-02   7.305028e+04   1.311419e+07   1.178930e+16  0
 5.793814e-02   7.057809e+04   1.296455e+07   1.126036e+16  0
 7.242268e-02   6.755292e+04   1.277661e+07   1.062146e+16  0
 8.690721e-02   6.407447e+04   1.255343e+07   9.898566e+15  0
 1.013917e-01   6.024983e+04   1.229852e+07   9.118710e+15  0
 1.158763e-01   5.618739e+04   1.201565e+07   8.308273e+15  0
 1.303608e-01   5.199119e+04   1.170876e+07   7.491440e+15  0
 1.448454e-01   4.775675e+04   1.138184e+07   6.689165e+15  0
 1.738144e-01   3.949418e+04   1.068346e+07   5.192419e+15  0
 2.027835e-01   3.190223e+04   9.949652e+06   3.906192e+15  0
 2.317526e-01   2.526437e+04   9.205281e+06   2.862003e+15  0
 2.607216e-01   1.968131e+04   8.470042e+06   2.051465e+15  0
 2.896907e-01   1.512587e+04   7.758440e+06   1.444174e+15  0
 3.186598e-01   1.149625e+04   7.080320e+06   1.001691e+15  0
 3.476289e-01   8.657463e+03   6.441660e+06   6.862986e+14  0
 3.765979e-01   6.469146e+03   5.845431e+06   4.653591e+14  0
 4.055670e-01   4.801225e+03   5.292387e+06   3.127003e+14  0
 4.345361e-01   3.541241e+03   4.781741e+06   2.083849e+14  0
 5.069587e-01   1.610707e+03   3.677391e+06   7.289221e+13  0
 5.793814e-01   7.002202e+02   2.785773e+06   2.400519e+13  0
 6.518041e-01   2.848396e+02   2.064117e+06   7.235348e+12  0
 7.242268e-01   1.039542e+02   1.475078e+06   1.887044e+12  0
 7.966495e-01   3.130785e+01   9.887473e+05   3.809458e+11  0
 8.690721e-01   6.388186e+00   5.820944e+05   4.576102e+10  0
 9.414948e-01   4.349552e-01   2.376926e+05   1.272287e+09  0
Degeneracy Code
  = 0 -> no electron degeneracy.
  = 1 -> relativistic electron degeneracy -> gamma=4/3.
  = 2 -> non-relativistic electron degeneracy -> gamma=5/3.

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 = -4.394798e-03, -4.394783e-03 True,convection.
r/r_star = 2.173567e-02, dT/dr = -1.310543e-02, -1.310503e-02 True,convection.
r/r_star = 3.622611e-02, dT/dr = -2.158395e-02, -2.158210e-02 True,convection.
r/r_star = 5.071655e-02, dT/dr = -2.968667e-02, -2.968179e-02 True,convection.
r/r_star = 6.520700e-02, dT/dr = -3.728580e-02, -3.727587e-02 True,convection.
r/r_star = 7.969744e-02, dT/dr = -4.427517e-02, -4.425800e-02 True,convection.
r/r_star = 9.418788e-02, dT/dr = -5.057213e-02, -5.054554e-02 True,convection.
r/r_star = 1.086783e-01, dT/dr = -5.611857e-02, -5.608063e-02 True,convection.
r/r_star = 1.231688e-01, dT/dr = -6.088335e-02, -6.083246e-02 True,convection.
r/r_star = 1.376592e-01, dT/dr = -6.485668e-02, -6.479175e-02 True,convection.
r/r_star = 1.593949e-01, dT/dr = -6.927524e-02, -6.893026e-02 True,convection.
r/r_star = 1.883758e-01, dT/dr = -7.278947e-02, -7.233249e-02 True,convection.
r/r_star = 2.173567e-01, dT/dr = -7.383733e-02, -7.328465e-02 True,convection.
r/r_star = 2.463375e-01, dT/dr = -7.293141e-02, -7.230671e-02 True,convection.
r/r_star = 2.753184e-01, dT/dr = -7.058679e-02, -6.991567e-02 True,convection.
r/r_star = 3.042993e-01, dT/dr = -6.726547e-02, -6.657148e-02 True,convection.
r/r_star = 3.332802e-01, dT/dr = -6.335143e-02, -6.265383e-02 True,convection.
r/r_star = 3.622611e-01, dT/dr = -5.914241e-02, -5.845549e-02 True,convection.
r/r_star = 3.912420e-01, dT/dr = -5.485879e-02, -5.419203e-02 True,convection.
r/r_star = 4.202229e-01, dT/dr = -5.065307e-02, -5.001190e-02 True,convection.
r/r_star = 4.709394e-01, dT/dr = -4.381805e-02, -4.041973e-02 True,convection.
r/r_star = 5.433916e-01, dT/dr = -3.537730e-02, -3.234542e-02 True,convection.
r/r_star = 6.158439e-01, dT/dr = -2.863363e-02, -2.582430e-02 True,convection.
r/r_star = 6.882961e-01, dT/dr = -2.337171e-02, -2.058250e-02 True,convection.
r/r_star = 7.607483e-01, dT/dr = -1.929647e-02, -1.622962e-02 True,convection.
r/r_star = 8.332005e-01, dT/dr = -1.613504e-02, -1.223977e-02 True,convection.
r/r_star = 9.056527e-01, dT/dr = -1.366506e-02, -7.691867e-03 True,convection.


VARIABLES FROM CENTER TO SURFACE II
n=3, gamma=4/3, The_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/Rsun                [Maximum]
0.000000   0.001508  2.094260e-06   1.381257e-45   0.001506
0.014485   0.011356  9.398382e-06   6.127336e-45   0.011347
0.028969   0.036873  2.609620e-05   1.654304e-44   0.036847
0.043454   0.081886  5.124711e-05   3.107904e-44   0.081835
0.057938   0.146573  8.507448e-05   4.857890e-44   0.146488
0.072423   0.227819  1.279225e-04   6.772268e-44   0.227692
0.086907   0.320236  1.802568e-04   8.716604e-44   0.320056
0.101392   0.417465  2.426641e-04   1.056666e-43   0.417222
0.115876   0.513389  3.158655e-04   1.221876e-43   0.513073
0.130361   0.603008  4.007039e-04   1.359526e-43   0.602608
0.144845   0.759822  1.051344e-03   3.001903e-43   0.758770
0.173814   0.867753  1.523117e-03   3.151919e-43   0.866230
0.202783   0.933103  2.121049e-03   3.063516e-43   0.930982
0.231753   0.968644  2.871824e-03   2.805002e-43   0.965772
0.260722   0.986274  3.808700e-03   2.450886e-43   0.982466
0.289691   0.994344  4.972911e-03   2.063749e-43   0.989371
0.318660   0.997784  6.415725e-03   1.687471e-43   0.991368
0.347629   0.999158  8.201038e-03   1.347761e-43   0.990957
0.376598   0.999675  1.040930e-02   1.056237e-43   0.989265
0.405567   0.999858  1.314229e-02   8.150303e-44   0.986716
0.434536   0.999993  3.748391e-02   1.276269e-43   0.962509
0.506959   1.000000  6.493102e-02   6.066808e-44   0.935069
0.579381   1.000000  1.127521e-01   2.714479e-44   0.887248
0.651804   1.000000  1.985922e-01   1.126514e-44   0.801408
0.724227   1.000000  3.574711e-01   4.156744e-45   0.642529
0.796649   1.000000  6.506550e-01   1.235550e-45   0.349345
Last 2 table entries omitted.

NUCLEAR REACTIONS MAP, The_SUN
Structure: n=3, gamma = 4/3.
The star is assumed homogeneously mixed, mu=6.702301e-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/Rsun    Helium              Mg                   
0.000000e+00, H->He [T=1.331120e+07 K]        
1.448454e-02, H->He [T=1.328905e+07 K]        
2.896907e-02, H->He [T=1.322299e+07 K]        
4.345361e-02, H->He [T=1.311419e+07 K]        
5.793814e-02, H->He [T=1.296455e+07 K]        
7.242268e-02, H->He [T=1.277661e+07 K]        
8.690721e-02, H->He [T=1.255343e+07 K]        
1.013917e-01, H->He [T=1.229852e+07 K]        
1.158763e-01, H->He [T=1.201565e+07 K]        
1.303608e-01, H->He [T=1.170876e+07 K]        
1.448454e-01, H->He [T=1.138184e+07 K]        
1.738144e-01, H->He [T=1.068346e+07 K]        
2.027835e-01, weak  [T=9.949652e+06 K]        
2.317526e-01, weak  [T=9.205281e+06 K]        
2.607216e-01, weak  [T=8.470042e+06 K]        
2.896907e-01, weak  [T=7.758440e+06 K]        
3.186598e-01, weak  [T=7.080320e+06 K]        
3.476289e-01, weak  [T=6.441660e+06 K]        
3.765979e-01, weak  [T=5.845431e+06 K]        
4.055670e-01, weak  [T=5.292387e+06 K]        
4.345361e-01, weak  [T=4.781741e+06 K]        
5.069587e-01, weak  [T=3.677391e+06 K]        
5.793814e-01, weak  [T=2.785773e+06 K]        
6.518041e-01, weak  [T=2.064117e+06 K]        
7.242268e-01, weak  [T=1.475078e+06 K]        
7.966495e-01, weak  [T=9.887473e+05 K]        
8.690721e-01, weak  [T=5.820944e+05 K]        
9.414948e-01, weak  [T=2.376926e+05 K]        
Central degeneracy non-relativistic.


  STAR AGE ESTIMATION & MODEL PERTURBATION ANALYSIS

Chiu Star age = 4.524409e+09 yr based on the H-burning core
  depletion required to normalize L(R) for Chiu p-p fusion.
  10**7 K H-burning core radius = 0.17 solar radii = 0.17 star radius.
  Mantle: X=0.597600, Y=0.382500, Z=0.019900, mu=0.670230.
  Core:   X=0.439542, Y=0.540558, Z=0.019900, mu=0.772527.
  Core_Mass = 5.561109e+29 kg , = 0.279565 M_sun , M_core/M_star = 0.279632.
  Core gravitational potential energy = 4.685375e+11 Joules.
  1)Perturbation analysis based on nuclear energy gen & volume-avg mu. Disfavored.
    Old T_c = 1.331120e+07 K, Perturbed (mu_avg/mu_old)*T_c = 1.332188e+07 K
    Radial expansion perturbation delta_R/R_star < 0.000535.
  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) = -0.007672.
      delta_T/T = -(del_mu/mu) = -0.132419.
      delta_P/P = -(4/3)(del_mu/mu) = -0.176559.
    When the core has exhausted its hydrogen, mu = 1.342237, and
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.029007.
      delta_T/T = -(del_mu/mu) = -0.500662.
      delta_P/P = -(4/3)(del_mu/mu) = -0.667549.

Clayton Star age = 5.493321e+09 yr based on the H-burning core
  depletion required to normalize L(R) for Clayton p-p fusion.
  10**7 K H-burning core radius = 0.17 solar radii = 0.17 star radius.
  Mantle: X=0.597600, Y=0.382500, Z=0.019900, mu=0.670230.
  Core:   X=0.405694, Y=0.574406, Z=0.019900, mu=0.798631.
  H-burningCoreMass = 5.561109e+29 kg , = 0.279565 Msun , Mcore/Mstar = 0.279632.
  Core gravitational potential energy = 4.685375e+11 Joules.
  1)Perturbation analysis based on nuclear energy gen & volume-avg mu. Disfavored.
    Old T_c = 1.331120e+07 K, Perturbed (mu_avg/mu_old)*T_c = 1.332461e+07 K
    Radial expansion perturbation delta_R/R_star < 0.000671.
  2)Polytropic analysis based on gas plus radiation laws. Since formation:
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.009315.
      delta_T/T = -(del_mu/mu) = -0.160777.
      delta_P/P = -(4/3)(del_mu/mu) = -0.214369.
    When the core has exhausted its hydrogen, mu = 1.342237, and
      delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.029007.
      delta_T/T = -(del_mu/mu) = -0.500662.
      delta_P/P = -(4/3)(del_mu/mu) = -0.667549.

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 = 4.685375e+11 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 =1.300719e+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 =1.264319e+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 = 1.493143e+12 sec
    = 4.731126e+04 years.
Time from now to core collapse in H-burning core: = 1.161298e+10 yr.
Total Main-Sequence Lifetime until core collapse: = 1.710631e+10 yr,
   according to our simplistic H-burning core collapse theory.
                   H-burning_lifetime/Zombeck_Age = 1.315083
             H-burning_lifetime/Schwarzschild_Age = 1.327364
       H-burning_lifetime/Greens_Main_Seq.Lifeime = 1.723601
    H-burning_lifetime/Helmholtz_contraction_time = 732.566794

FUSION - NUCLEAR LUMINOSITY MEASURES,
gamma = 4/3, n=3, The_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 = 1.000000e+00,[Clayton,scrnd&normd]
P-P chain luminosity  L/Lsun = 5.071158e-01,[Clayton,unscreened.]
P-P chain luminosity  L/Lsun = 2.166969e+00,[Clayton,screened.]
P-P chain luminosity  L/Lsun = 1.845909e+00,[Chiu,screened.]
P-P chain luminosity  L/Lsun = 7.629492e-01,[Chiu,unscreened.]
P-P chain luminosity  L/Lsun = 1.000000e+00,[Chiu,scrnd & normd]
P-P chain luminosity  L/Lsun = 4.638922e-01,[M. Scharzschild, unscr.]
P-P fusion luminosity L/Lsun = 5.099143e-01,[A.C.Phillips, unscr.]
Carbon cycle only L_CNO/Lsun = 1.087435e-03,[CNO cycle, M.Schw.,unscr.]
Triple-Alpha cyc.  L_He/Lsun = 6.071762e-131,[Helium burning,unscr.]
Total H-burning  L_Htot/Lsun = 2.168056e+00,[H-burning, PP + CNO.]
Total nuclear L:  L_tot/Lsun = 2.168056e+00,[Total, PP+CNO+He.]

In units of the luminosity of the star The_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 = 1.000816e+00,[Clayton,scrnd&normd]
P-P chain luminosity  L/Lstar = 5.075296e-01,[Clayton,unscreened.]
P-P chain luminosity  L/Lstar = 2.168737e+00,[Clayton,screened.]
P-P chain luminosity  L/Lstar = 1.847415e+00,[Chiu,screened.]
P-P chain luminosity  L/Lstar = 7.635717e-01,[Chiu,unscreened.]
P-P chain luminosity  L/Lstar = 1.000816e+00,[Chiu,scrnd & normd]
P-P chain luminosity  L/Lstar = 4.642707e-01,[M. Scharzschild, unscr.]
P-P fusion luminosity L/Lstar = 5.103304e-01,[A.C.Phillips, unscr.]
Carbon cycle only L_CNO/Lstar = 1.088323e-03,[CNO cycle, M.Schw.,unscr.]
Triple-Alpha cyc.  L_He/Lstar = 6.076717e-131,[Helium burning,unscr.]
Total H-burning  L_Htot/Lstar = 2.169825e+00,[H-burning, PP + CNO.]
Total nuclear L:  L_tot/Lstar = 2.169825e+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]    = 5.075296e-01,
L/Lsun_Clayton_screened/[L/Lsun]      = 2.168737e+00,
L/Lsun_Clayton_scr-normalized/[L/Lsun]= 1.000816e+00,
L/Lsun_Chiu_screened/[L/Lsun]         = 1.847415e+00,
L/Lsun_Chiu_unscreened/[L/Lsun]       = 7.635717e-01,
L/Lsun_Chiu_scr-normalized/[L/Lsun]   = 1.000816e+00,
L/Lsun_Schwarzschild/[L/Lsun]         = 4.642707e-01,
L/Lsun_Phillips/[L/Lsun-observed]     = 5.103304e-01.
L_CNO/Lsun/[L/Lsun-observed]          = 1.088323e-03.
L_He/Lsun/[L/Lsun-observed]           = 6.076717e-131.
 

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.
Angelside: Shamanistic Humour
GM/R**2 Two! The Force!

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


Jim Green's Home Page