FUSION: Main Sequence Modeling. Report_File=fusion.txt. Sat Aug 23 13:35:12 2003 1 models processed in this run, 0-0. 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. 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 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 = 0.670230. 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 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. 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 = 6.805532e+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 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/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 = 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, Sun. Radius Density Temperature Pressure Degeneracy r/Rstar kg/m**3 deg. Kelvin Newtons/m**2 Code 0.000000e+00 7.639219e+04 1.331120e+07 1.251385e+16 2 1.449044e-02 7.601143e+04 1.328905e+07 1.243075e+16 0 2.898089e-02 7.488350e+04 1.322299e+07 1.218542e+16 0 4.347133e-02 7.305028e+04 1.311419e+07 1.178930e+16 0 5.796177e-02 7.057809e+04 1.296455e+07 1.126036e+16 0 7.245222e-02 6.755292e+04 1.277661e+07 1.062146e+16 0 8.694266e-02 6.407447e+04 1.255343e+07 9.898566e+15 0 1.014331e-01 6.024983e+04 1.229852e+07 9.118710e+15 0 1.159235e-01 5.618739e+04 1.201565e+07 8.308273e+15 0 1.304140e-01 5.199119e+04 1.170876e+07 7.491440e+15 0 1.449044e-01 4.775675e+04 1.138184e+07 6.689165e+15 0 1.738853e-01 3.949418e+04 1.068346e+07 5.192419e+15 0 2.028662e-01 3.190223e+04 9.949652e+06 3.906192e+15 0 2.318471e-01 2.526437e+04 9.205281e+06 2.862003e+15 0 2.608280e-01 1.968131e+04 8.470042e+06 2.051465e+15 0 2.898089e-01 1.512587e+04 7.758440e+06 1.444174e+15 0 3.187898e-01 1.149625e+04 7.080320e+06 1.001691e+15 0 3.477706e-01 8.657463e+03 6.441660e+06 6.862986e+14 0 3.767515e-01 6.469146e+03 5.845431e+06 4.653591e+14 0 4.057324e-01 4.801225e+03 5.292387e+06 3.127003e+14 0 4.347133e-01 3.541241e+03 4.781741e+06 2.083849e+14 0 5.071655e-01 1.610707e+03 3.677391e+06 7.289221e+13 0 5.796177e-01 7.002202e+02 2.785773e+06 2.400519e+13 0 6.520700e-01 2.848396e+02 2.064117e+06 7.235348e+12 0 7.245222e-01 1.039542e+02 1.475078e+06 1.887044e+12 0 7.969744e-01 3.130785e+01 9.887473e+05 3.809458e+11 0 8.694266e-01 6.388186e+00 5.820944e+05 4.576102e+10 0 9.418788e-01 4.349552e-01 2.376926e+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 3.978271e-01 3.512081e-01 1.466696e-02 3.195200e-02 1.449044e-02 7.601143e+04 4.002689e-01 3.535521e-01 1.476484e-02 3.195200e-02 2.898089e-02 7.488350e+04 4.051818e-01 3.582680e-01 1.496179e-02 3.195200e-02 4.347133e-02 7.305028e+04 4.126248e-01 3.654127e-01 1.526016e-02 3.195200e-02 5.796177e-02 7.057809e+04 4.226869e-01 3.750714e-01 1.566352e-02 3.195200e-02 7.245222e-02 6.755292e+04 4.354881e-01 3.873595e-01 1.617669e-02 3.195200e-02 8.694266e-02 6.407447e+04 4.511809e-01 4.024231e-01 1.680577e-02 3.195200e-02 1.014331e-01 6.024983e+04 4.699510e-01 4.204408e-01 1.755821e-02 3.195200e-02 1.159235e-01 5.618739e+04 4.920200e-01 4.416251e-01 1.844290e-02 3.195200e-02 1.304140e-01 5.199119e+04 5.176473e-01 4.662251e-01 1.947023e-02 3.195200e-02 1.449044e-01 4.775675e+04 5.644717e-01 5.111724e-01 2.134729e-02 3.195200e-02 1.738853e-01 3.949418e+04 6.412036e-01 5.848283e-01 2.442327e-02 3.195200e-02 2.028662e-01 3.190223e+04 7.391224e-01 6.788218e-01 2.834857e-02 3.195200e-02 2.318471e-01 2.526437e+04 8.627460e-01 7.974897e-01 3.330431e-02 3.195200e-02 2.608280e-01 1.968131e+04 1.017770e+00 9.462996e-01 3.951883e-02 3.195200e-02 2.898089e-01 1.512587e+04 1.211362e+00 1.132130e+00 4.727939e-02 3.195200e-02 3.187898e-01 1.149625e+04 1.452551e+00 1.363651e+00 5.694803e-02 3.195200e-02 3.477706e-01 8.657463e+03 1.752767e+00 1.651832e+00 6.898287e-02 3.195200e-02 3.767515e-01 6.469146e+03 2.126565e+00 2.010646e+00 8.396744e-02 3.195200e-02 4.057324e-01 4.801225e+03 2.592637e+00 2.458034e+00 1.026510e-01 3.195200e-02 4.347133e-01 3.541241e+03 3.741155e+00 3.560511e+00 1.486920e-01 3.195200e-02 5.071655e-01 1.610707e+03 6.403869e+00 6.116484e+00 2.554332e-01 3.195200e-02 5.796177e-01 7.002202e+02 1.139787e+01 1.091029e+01 4.556294e-01 3.195200e-02 6.520700e-01 2.848396e+02 2.154139e+01 2.064718e+01 8.622558e-01 3.195200e-02 7.245222e-01 1.039542e+02 4.510205e+01 4.326336e+01 1.806740e+00 3.195200e-02 7.969744e-01 3.130785e+01 1.150112e+02 1.103700e+02 4.609211e+00 3.195200e-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 = -4.394798e-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 - Uses screened Reeves cno. 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 0.001513 1.706431e-04 1.381257e-45 0.001342 0.014490 0.011389 7.624390e-04 6.127336e-45 0.010626 0.028981 0.036964 2.098592e-03 1.654304e-44 0.034866 0.043471 0.082053 4.067668e-03 3.107904e-44 0.077985 0.057962 0.146804 6.636827e-03 4.857890e-44 0.140167 0.072452 0.228076 9.767776e-03 6.772268e-44 0.218308 0.086943 0.320465 1.341782e-02 8.716604e-44 0.307047 0.101433 0.417616 1.754093e-02 1.056666e-43 0.400075 0.115924 0.513426 2.208966e-02 1.221876e-43 0.491336 0.130414 0.602914 2.701517e-02 1.359526e-43 0.575899 0.144904 0.759463 6.671400e-02 3.001903e-43 0.692749 0.173885 0.867194 8.818729e-02 3.151919e-43 0.779007 0.202866 0.932418 1.108544e-01 3.063516e-43 0.821563 0.231847 0.967890 1.342441e-01 2.805002e-43 0.833646 0.260828 0.985486 1.580143e-01 2.450886e-43 0.827472 0.289809 0.993540 1.819451e-01 2.063749e-43 0.811595 0.318790 0.996973 2.059301e-01 1.687471e-43 0.791043 0.347771 0.998344 2.299574e-01 1.347761e-43 0.768387 0.376752 0.998860 2.541017e-01 1.056237e-43 0.744758 0.405732 0.999043 2.785051e-01 8.150303e-44 0.720538 0.434713 0.999178 6.342178e-01 1.276269e-43 0.364960 0.507166 0.999184 7.588572e-01 6.066808e-44 0.240327 0.579618 0.999185 8.996428e-01 2.714479e-44 0.099542 0.652070 0.999185 9.991847e-01 * 1.126514e-44 0.000000 L_radiative > L_nuclear. 0.724522 0.999185 9.991847e-01 * 4.156744e-45 0.000000 L_radiative > L_nuclear. 0.796974 0.999185 9.991847e-01 * 1.235550e-45 0.000000 L_radiative > L_nuclear. Last 2 table entries omitted. MAX(L_radiative) = 1.520224e+00 Lsun. L_radiative saturated L_nuclear setting L_convective=0 at r/Rstar=0.652070, probably due to an error in the opacity model. Opacity errors modify convective vs. radiative energy transport ratios, not structure. NUCLEAR REACTIONS MAP, Sun nucmixflag = 4 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/Rstar Helium Mg 0.000000e+00, H->He [T=1.331120e+07 K] 1.449044e-02, H->He [T=1.328905e+07 K] 2.898089e-02, H->He [T=1.322299e+07 K] 4.347133e-02, H->He [T=1.311419e+07 K] 5.796177e-02, H->He [T=1.296455e+07 K] 7.245222e-02, H->He [T=1.277661e+07 K] 8.694266e-02, H->He [T=1.255343e+07 K] 1.014331e-01, H->He [T=1.229852e+07 K] 1.159235e-01, H->He [T=1.201565e+07 K] 1.304140e-01, H->He [T=1.170876e+07 K] 1.449044e-01, H->He [T=1.138184e+07 K] 1.738853e-01, H->He [T=1.068346e+07 K] 2.028662e-01, weak [T=9.949652e+06 K] 2.318471e-01, weak [T=9.205281e+06 K] 2.608280e-01, weak [T=8.470042e+06 K] 2.898089e-01, weak [T=7.758440e+06 K] 3.187898e-01, weak [T=7.080320e+06 K] 3.477706e-01, weak [T=6.441660e+06 K] 3.767515e-01, weak [T=5.845431e+06 K] 4.057324e-01, weak [T=5.292387e+06 K] 4.347133e-01, weak [T=4.781741e+06 K] 5.071655e-01, weak [T=3.677391e+06 K] 5.796177e-01, weak [T=2.785773e+06 K] 6.520700e-01, weak [T=2.064117e+06 K] 7.245222e-01, weak [T=1.475078e+06 K] 7.969744e-01, weak [T=9.887473e+05 K] 8.694266e-01, weak [T=5.820944e+05 K] 9.418788e-01, weak [T=2.376926e+05 K] Central degeneracy non-relativistic. STAR AGE ESTIMATION & MODEL PERTURBATION ANALYSIS Chiu Star age_BEST = 4.529068e+09 yr based on the H-burning core depletion required to normalize L_nuclear(R) for Chiu p-p fusion, assumes constant luminosity at present luminosity. Chiu Star age_ERR = 3.178435e+09 yr based on the H-burning core depletion required to normalize L_nuclear(R) for Chiu p-p fusion, uses 1st-order average luminosity since star formation, making erroneous constant-radius assumption. 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=0.439379, Y=0.540721, Z=0.019900, mu=0.772649. Core_Mass = 5.561109e+29 kg , = 0.279565 M_sun , M_core/M_star = 0.279632. Core gravitational potential energy = 3.003642e+20 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 = 1.332189e+07 K Radial expansion perturbation delta_R/R_star < 0.000536. 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) = -0.007680. delta_T/T = -(del_mu/mu) = -0.132555. delta_P/P = -(4/3)(del_mu/mu) = -0.176740. 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_BEST = 5.496985e+09 yr based on the H-burning core depletion required to normalize L_nuclear(R) for Clayton p-p fusion, assumes present luminosity since star formation. Clayton Star age_ERR = 3.466822e+09 yr based on the H-burning core depletion required to normalize L_nuclear(R) for Chiu p-p fusion, uses 1st order average luminosity since star formation, making erroneous constant radius assumption. 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=0.405566, Y=0.574534, Z=0.019900, mu=0.798733. H-burningCoreMass = 5.561109e+29 kg , = 0.279565 Msun , Mcore/Mstar = 0.279632. Core gravitational potential energy = 3.003642e+20 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 = 1.332462e+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)= -0.009321. delta_T/T = -(del_mu/mu) = -0.160884. delta_P/P = -(4/3)(del_mu/mu) = -0.214512. 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 = 3.003642e+20 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: = 1.160932e+10 yr. Total Main-Sequence Lifetime until core collapse: = 1.507614e+10 yr, according to our simplistic H-burning core collapse theory. H-burning_lifetime/Zombeck_Age = 1.159010 H-burning_lifetime/Schwarzschild_Age = 1.169834 H-burning_lifetime/Greens_Main_Seq.Lifeime = 1.519045 H-burning_lifetime/Helmholtz_contraction_time = 645.626362 ABUNDANCES: XYZ(r) ESTIMATE, Sun nucmixflag = 4 Structure: n=3, gamma = 4/3. Envelope abundances : X(H)=0.597600, Y(He)=0.382500, Z(hvy)=0.019900. Nominal Core abundances: X(H)=0.405961, Y(He)=0.574139, Z(hvy)=0.019900. 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 0.04802 0.93208 0.01990 1.24217 0.00016214 0.00016214 1 0.014490 0.13094 0.05944 0.92066 0.01990 1.22051 0.00108094 0.00124308 2 0.028981 0.12452 0.08583 0.89427 0.01990 1.17329 0.00294369 0.00418677 3 0.043471 0.11536 0.12348 0.85662 0.01990 1.11189 0.00560171 0.00978848 4 0.057962 0.10421 0.16932 0.81078 0.01990 1.04529 0.00890555 0.01869403 5 0.072452 0.09188 0.21997 0.76013 0.01990 0.98040 0.01267699 0.03137102 6 0.086943 0.07918 0.27218 0.70792 0.01990 0.92144 0.01672350 0.04809452 7 0.101433 0.06677 0.32317 0.65693 0.01990 0.87033 0.02085253 0.06894706 8 0.115924 0.05518 0.37081 0.60929 0.01990 0.82745 0.02488420 0.09383125 9 0.130414 0.04475 0.41369 0.56641 0.01990 0.79231 0.02866128 0.12249253 10 0.144904 0.03338 0.46043 0.51967 0.01990 0.75725 0.06722486 0.18971739 11 0.173885 0.02010 0.51501 0.46509 0.01990 0.72005 0.07683118 0.26654857 ** 12 0.202866 0.01141 0.55069 0.42941 0.01990 0.69765 0.08190290 0.34845147 13 0.231847 0.00615 0.57234 0.40776 0.01990 0.68472 0.08271041 0.43116188 14 0.260828 0.00315 0.58465 0.39545 0.01990 0.67758 0.08001115 0.51117303 15 0.289809 0.00154 0.59125 0.38885 0.01990 0.67381 0.07475766 0.58593069 16 0.318790 0.00072 0.59462 0.38548 0.01990 0.67191 0.06788677 0.65381745 17 0.347771 0.00033 0.59626 0.38384 0.01990 0.67098 0.06019994 0.71401740 18 0.376752 0.00014 0.59702 0.38308 0.01990 0.67056 0.05231668 0.76633408 19 0.405732 0.00006 0.59736 0.38274 0.01990 0.67037 0.04467503 0.81100911 20 0.434713 0.00002 0.59751 0.38259 0.01990 0.67028 0.08662688 0.89763599 21 0.507166 0.00000 0.59759 0.38251 0.01990 0.67023 0.05173248 0.94936847 22 0.579618 0.00000 0.59760 0.38250 0.01990 0.67023 0.02832402 0.97769250 23 0.652070 0.00000 0.59760 0.38250 0.01990 0.67023 0.01396436 0.99165686 24 0.724522 0.00000 0.59760 0.38250 0.01990 0.67023 0.00593484 0.99759170 25 0.796974 0.00000 0.59760 0.38250 0.01990 0.67023 0.00198402 0.99957572 26 0.869427 0.00000 0.59760 0.38250 0.01990 0.67023 0.00042429 1.00000000 27 0.941879 0.00000 0.59760 0.38250 0.01990 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. 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 = 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 = 4.595635e-04,[CNO cycle, M.Schw.,unscr.] Carbon cycle only L_CNO/Lsun = 2.375627e-03,[CNO cycle, Reeves,unscr.] Carbon cycle only L_CNO/Lsun = 2.456159e-03,[CNO cycle, Reeves,scr.] Triple-Alpha cyc. L_He/Lsun = 6.071762e-131,[Helium burning,unscr.] Total H-burning L_Htot/Lsun = 2.167428e+00,[H-burning, PP + CNO.] Total H-burning L_Htot/Lsun = 2.169425e+00,[H-burning, PP+CNO(Reeves,scr).] Total nuclear L: L_tot/Lsun = 2.167428e+00,[Total, PP+CNO(Sch)+He.] Total nuclear L: L_tot/Lsun = 2.169425e+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 = 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 = 4.599384e-04,[CNO cycle, M.Schw.,unscr.] Carbon cycle only L_CNO/Lstar = 2.377566e-03,[CNO cycle, Reeves,unscr.] Carbon cycle only L_CNO/Lstar = 2.458163e-03,[CNO cycle, Reeves,scr.] Triple-Alpha cyc. L_He/Lstar = 6.076717e-131,[Helium burning,unscr.] Total H-burning L_Htot/Lstar = 2.169197e+00,[H-burning, PP(Clayton,scr)+CNO(Schw,unscr.).] Total H-burning L_Htot/Lstar = 2.171195e+00,[H-burning, PP(Clayton,scr)+CNO(Reeves,scr).] Total nuclear L: L_tot/Lstar = 2.169197e+00,[Total, PP(Clayton,scr)+CNO(Schw)+He.] Total nuclear L: L_tot/Lstar = 2.171195e+00,[Total, PP(Clayton,scr)+CNO(Reeves,scr)+He.]