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This model for Sirius does not electrostatically screen the carbon cycle, so that
we have increased the abundances of carbon and nitrogen to x3 of their normal values
according to Aller 1961 in order to get L_nuc/L_star = 1, the ZAMS criterion, at 8.7 LY.
MODEL = 0 INPUT VARIABLES:
Starname = Sirius.
Assumed polytropic structure: n=3, gamma=4/3.
Distance = 8.700000e+00 LY,
= 2.668712e+00 parsecs,
= 8.230200e+16 meters,
= 3.749270e-01 arc-seconds of parallax.
Visual magnitude = -1.420000.
Surface temperature[spect.type] = 1.026500e+04 degrees Kelvin.
Spectral type specified at entry time:
Henry Draper OBAFGKM Spectral type = A1.0 V [dwarf, regular].
Spectrum: Very strong H, decreasing later, Ca II increasing.
Wavelength at emission maximum = 282.513395 nanometers.
Mu was varied with core of U238 + H + He to optimize L_nuc:
X[H] = 0.593141, Y[He] = 0.379610, Z[hvy] = 0.027249.
Chiu L/L_sun = 1.041466e+01, Clayton L/L_sun = 1.226571e+01, .
Chiu L/L_star = 3.588730e-01, Clayton L/L_star = 4.226573e-01, .
X[H] for L_Chiu_nuc/Lstar = 1 via H-burning core X(H) variation = 0.183796, .
X[H] for L_Clayton_nuc/Lstar = 1 via H-burning core X(H) variation = 0.169360, .
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) = 1.400269e+04 n(H+)/n(H),
n(He+)/n(He) = 3.841849e-06 n(H+)/n(H)
MODEL = 0 OUTPUT VARIABLES
Star Name = Sirius:
Zombeck bolometric corrections used.
Absolute magnitude before bolometric correction: M = 1.448492.
Absolute magnitude after correction: M + B.C = 1.104415.
Bolometric Correction = -0.344077.
L/Lsun, M/Msun, R/Rsun, prior to bolometric correction:
L/Lsun = 21.138475, M/Msun = 2.447364, R/Rsun = 1.452682.
After bolometric corrections, these quantities are:
L/Lsun = 29.020467, M/Msun = 2.685786, R/Rsun = 1.702103.
Radius = 1.184664e+09 meters.
Mass = 5.342565e+30 kilograms.
Average density = 7.671426e+02 kg/m**3.
Central density = 4.156571e+04 kg/m**3.
Central number density = 3.684561e+31 particles/m**3.
Crit central g_s*N_Q quantum concentration = 2.028615e+37 particles/m**3.
g_s*N_Q/n = 5.505717e+05, number_for_elec.degen(Tc)/actual_n, Phillips,p50.
Compare with competing criteria electron degeneracy code results below.
Central pressure = 1.074210e+16 Newtons/m**3.
fbeta = [1-b]/b**4 = 4.669400e-03. beta = 9.954000e-01.
Central gas pressure = 1.069269e+16 Newtons/m**2.
Central radiation pressure = 4.941368e+13 Newtons/m**2.
Ratio radiation_pressure/gas_pressure = 4.621258e-03.
Central temperature = 2.102155e+07 degrees Kelvin.
Central photon density = 1.885778e+29 photons/m**3.
Central photon energy density = 1.477298e+14 J/m**3.
Typical Phillips internal temp T_i = 8.193553e+06 degrees K.
Typical photon density = 1.116639e+28 photons/m**3.
Typical photon energy density = 3.409557e+12 J/m**3.
Stellar gravitational Binding Energy = 2.410580e+42 Joules.
The star Sirius,
M/Msun = 2.685786e+00 < 6.23 Msun,
is not a Type II supernova progenitor.
Stellar M.S. lifetime = 12.88x10**9[Msun/M]**2.409 = 1.192018e+09 yrs.
Zombeck lifetime = 13.0x10**9[Msun/M]**2.5 = 1.099676e+09 yrs.
Green's 1st M.S.lifetime = 9.92x10**9[Msun/M]**2 = 1.375210e+09 yrs.
Helmholtz-Kelvin gamma=4/3 contraction lifetime = 3.407516e+06 yrs,
an upper limit to the star formation time.
Initial star formation ionized radius R/R_solar = 1.316425e+02
T_average at initial ionized radius = 30,000 deg. K.
Phillips freefall pulse time scale = 3.998603e+01 min
= 6.664338e-01 hrs = 2.776807e-02 days = 7.599363e-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 = 4.629617e-04 radians/sec.
or 7.368271e-05 rev/sec = 4.420963e-03 rev/min
= 6.365770e+00 rev/day, Surface velocity = 5.484541e+02 km/sec.
Photon mean free path = 2.918380e-03 meters = 2.918380e+00 mm
Photon random-walk escape time = 1.604099e+12 sec = 5.082698e+04 years.
AUX LUMINOSITIES - Estimates
L_stellar_wind(R) = 3.946868e+22 Joules
L_stellar_wind(R)/L_sun = 1.022505e-04 = 0.010225 percent
Mass loss = 1.312115e+11 kg/sec = 2.081352e-12 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, Sirius.
Radius Density Temperature Pressure Degeneracy
r/Rstar kg/m**3 deg. Kelvin Newtons/m**2 Code
0.000000e+00 4.156571e+04 2.102155e+07 1.074210e+16 2
1.449044e-02 4.135853e+04 2.098657e+07 1.067077e+16 0
2.898089e-02 4.074482e+04 2.088225e+07 1.046017e+16 0
4.347133e-02 3.974734e+04 2.071043e+07 1.012014e+16 0
5.796177e-02 3.840220e+04 2.047412e+07 9.666085e+15 0
7.245222e-02 3.675618e+04 2.017731e+07 9.117650e+15 0
8.694266e-02 3.486352e+04 1.982486e+07 8.497101e+15 0
1.014331e-01 3.278250e+04 1.942229e+07 7.827659e+15 0
1.159235e-01 3.057209e+04 1.897557e+07 7.131965e+15 0
1.304140e-01 2.828890e+04 1.849092e+07 6.430782e+15 0
1.449044e-01 2.598490e+04 1.797464e+07 5.742096e+15 0
1.738853e-01 2.148915e+04 1.687173e+07 4.457263e+15 0
2.028662e-01 1.735830e+04 1.571287e+07 3.353143e+15 0
2.318471e-01 1.374658e+04 1.453733e+07 2.456793e+15 0
2.608280e-01 1.070878e+04 1.337621e+07 1.761014e+15 0
2.898089e-01 8.230130e+03 1.225242e+07 1.239704e+15 0
3.187898e-01 6.255216e+03 1.118151e+07 8.598687e+14 0
3.477706e-01 4.710607e+03 1.017291e+07 5.891307e+14 0
3.767515e-01 3.519923e+03 9.231328e+06 3.994723e+14 0
4.057324e-01 2.612391e+03 8.357939e+06 2.684274e+14 0
4.347133e-01 1.926823e+03 7.551508e+06 1.788812e+14 0
5.071655e-01 8.764010e+02 5.807476e+06 6.257194e+13 0
5.796177e-01 3.809964e+02 4.399399e+06 2.060647e+13 0
6.520700e-01 1.549839e+02 3.259733e+06 6.210948e+12 0
7.245222e-01 5.656248e+01 2.329499e+06 1.619871e+12 0
7.969744e-01 1.703489e+01 1.561467e+06 3.270105e+11 0
8.694266e-01 3.475872e+00 9.192656e+05 3.928205e+10 0
9.418788e-01 2.366632e-01 3.753733e+05 1.092153e+09 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 = -4.075900e-03, -4.075886e-03 True,convection.
r/r_star = 2.173567e-02, dT/dr = -1.215447e-02, -1.215409e-02 True,convection.
r/r_star = 3.622611e-02, dT/dr = -2.001776e-02, -2.001605e-02 True,convection.
r/r_star = 5.071655e-02, dT/dr = -2.753253e-02, -2.752800e-02 True,convection.
r/r_star = 6.520700e-02, dT/dr = -3.458025e-02, -3.457103e-02 True,convection.
r/r_star = 7.969744e-02, dT/dr = -4.106245e-02, -4.104652e-02 True,convection.
r/r_star = 9.418788e-02, dT/dr = -4.690248e-02, -4.687782e-02 True,convection.
r/r_star = 1.086783e-01, dT/dr = -5.204646e-02, -5.201127e-02 True,convection.
r/r_star = 1.231688e-01, dT/dr = -5.646549e-02, -5.641830e-02 True,convection.
r/r_star = 1.376592e-01, dT/dr = -6.015050e-02, -6.009029e-02 True,convection.
r/r_star = 1.593949e-01, dT/dr = -6.424845e-02, -6.392850e-02 True,convection.
r/r_star = 1.883758e-01, dT/dr = -6.750767e-02, -6.708385e-02 True,convection.
r/r_star = 2.173567e-01, dT/dr = -6.847950e-02, -6.796692e-02 True,convection.
r/r_star = 2.463375e-01, dT/dr = -6.763932e-02, -6.705995e-02 True,convection.
r/r_star = 2.753184e-01, dT/dr = -6.546482e-02, -6.484241e-02 True,convection.
r/r_star = 3.042993e-01, dT/dr = -6.238451e-02, -6.174088e-02 True,convection.
r/r_star = 3.332802e-01, dT/dr = -5.875448e-02, -5.810750e-02 True,convection.
r/r_star = 3.622611e-01, dT/dr = -5.485088e-02, -5.421380e-02 True,convection.
r/r_star = 3.912420e-01, dT/dr = -5.087809e-02, -5.025971e-02 True,convection.
r/r_star = 4.202229e-01, dT/dr = -4.697755e-02, -4.638290e-02 True,convection.
r/r_star = 4.709394e-01, dT/dr = -4.063850e-02, -3.748677e-02 True,convection.
r/r_star = 5.433916e-01, dT/dr = -3.281023e-02, -2.999836e-02 True,convection.
r/r_star = 6.158439e-01, dT/dr = -2.655590e-02, -2.395042e-02 True,convection.
r/r_star = 6.882961e-01, dT/dr = -2.167579e-02, -1.908898e-02 True,convection.
r/r_star = 7.607483e-01, dT/dr = -1.789627e-02, -1.505195e-02 True,convection.
r/r_star = 8.332005e-01, dT/dr = -1.496424e-02, -1.135162e-02 True,convection.
r/r_star = 9.056527e-01, dT/dr = -1.267349e-02, -7.133725e-03 True,convection.
VARIABLES FROM CENTER TO SURFACE II
n=3, gamma=4/3, Sirius.
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 0.001359 3.672353e-04 1.062609e-44 0.000992
0.014490 0.010272 1.647985e-03 4.713796e-44 0.008624
0.028981 0.033602 4.575614e-03 1.272666e-43 0.029027
0.043471 0.075406 8.984606e-03 2.390929e-43 0.066422
0.057962 0.136679 1.491322e-02 3.737204e-43 0.121766
0.072452 0.215377 2.242052e-02 5.209946e-43 0.192956
0.086943 0.306993 3.158639e-02 6.705736e-43 0.275407
0.101433 0.405521 4.251139e-02 8.128995e-43 0.363010
0.115924 0.504560 5.531896e-02 9.399965e-43 0.449241
0.130414 0.598344 7.015308e-02 1.045892e-42 0.528191
0.144904 0.760991 1.839553e-01 2.309382e-42 0.577035
0.173885 0.871525 2.662332e-01 2.424790e-42 0.605292
0.202866 0.936233 3.702749e-01 2.356781e-42 0.565958
0.231847 0.970157 5.005419e-01 2.157905e-42 0.469615
0.260828 0.986647 6.625407e-01 1.885481e-42 0.324106
0.289809 0.994247 8.630176e-01 1.587654e-42 0.131230
0.318790 0.997599 9.975993e-01 * 1.298182e-42 0.000000 L_radiative > L_nuclear.
0.347771 0.999016 9.990158e-01 * 1.036841e-42 0.000000 L_radiative > L_nuclear.
0.376752 0.999589 9.995886e-01 * 8.125698e-43 0.000000 L_radiative > L_nuclear.
0.405732 0.999810 9.998099e-01 * 6.270077e-43 0.000000 L_radiative > L_nuclear.
0.434713 0.999988 9.999877e-01 * 9.818415e-43 0.000000 L_radiative > L_nuclear.
0.507166 0.999999 9.999994e-01 * 4.667232e-43 0.000000 L_radiative > L_nuclear.
0.579618 1.000000 1.000000e+00 * 2.088265e-43 0.000000 L_radiative > L_nuclear.
0.652070 1.000000 1.000000e+00 * 8.666341e-44 0.000000 L_radiative > L_nuclear.
0.724522 1.000000 1.000000e+00 * 3.197808e-44 0.000000 L_radiative > L_nuclear.
0.796974 1.000000 1.000000e+00 * 9.505159e-45 0.000000 L_radiative > L_nuclear.
Last 2 table entries omitted.
L_radiative saturated L_nuclear setting L_convective=0 at r/Rstar=0.318790
NUCLEAR REACTIONS MAP, Sirius
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=2.102155e+07 K]
1.449044e-02, H->He [T=2.098657e+07 K]
2.898089e-02, H->He [T=2.088225e+07 K]
4.347133e-02, H->He [T=2.071043e+07 K]
5.796177e-02, H->He [T=2.047412e+07 K]
7.245222e-02, H->He [T=2.017731e+07 K]
8.694266e-02, H->He [T=1.982486e+07 K]
1.014331e-01, H->He [T=1.942229e+07 K]
1.159235e-01, H->He [T=1.897557e+07 K]
1.304140e-01, H->He [T=1.849092e+07 K]
1.449044e-01, H->He [T=1.797464e+07 K]
1.738853e-01, H->He [T=1.687173e+07 K]
2.028662e-01, H->He [T=1.571287e+07 K]
2.318471e-01, H->He [T=1.453733e+07 K]
2.608280e-01, H->He [T=1.337621e+07 K]
2.898089e-01, H->He [T=1.225242e+07 K]
3.187898e-01, H->He [T=1.118151e+07 K]
3.477706e-01, H->He [T=1.017291e+07 K]
3.767515e-01, weak [T=9.231328e+06 K]
4.057324e-01, weak [T=8.357939e+06 K]
4.347133e-01, weak [T=7.551508e+06 K]
5.071655e-01, weak [T=5.807476e+06 K]
5.796177e-01, weak [T=4.399399e+06 K]
6.520700e-01, weak [T=3.259733e+06 K]
7.245222e-01, weak [T=2.329499e+06 K]
7.969744e-01, weak [T=1.561467e+06 K]
8.694266e-01, weak [T=9.192656e+05 K]
9.418788e-01, weak [T=3.753733e+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 = 0.59 solar radii = 0.35 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 = 4.001927e+30 kg , = 2.011827 M_sun , M_core/M_star = 0.749065.
Core gravitational potential energy = 8.294000e+20 Joules.
1)Perturbation analysis based on nuclear energy gen & volume-avg mu. Disfavored.
Old T_c = 2.102155e+07 K, Perturbed (mu_avg/mu_old)*T_c = 2.102155e+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)= -0.098540.
delta_T/T = -(del_mu/mu) = -0.499407.
delta_P/P = -(4/3)(del_mu/mu) = -0.665876.
Clayton Star age = 6.393132e+07 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 = 0.59 solar radii = 0.35 star radius.
Mantle: X=0.593141, Y=0.379610, Z=0.027249, mu=0.673576.
Core: X=0.584127, Y=0.388624, Z=0.027249, mu=0.678727.
H-burningCoreMass = 4.001927e+30 kg , = 2.011827 Msun , Mcore/Mstar = 0.749065.
Core gravitational potential energy = 8.294000e+20 Joules.
1)Perturbation analysis based on nuclear energy gen & volume-avg mu. Disfavored.
Old T_c = 2.102155e+07 K, Perturbed (mu_avg/mu_old)*T_c = 2.102832e+07 K
Radial expansion perturbation delta_R/R_star < 0.000214.
2)Polytropic analysis based on gas plus radiation laws. Since formation:
delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.001498.
delta_T/T = -(del_mu/mu) = -0.007590.
delta_P/P = -(4/3)(del_mu/mu) = -0.010119.
When the core has exhausted its hydrogen, mu = 1.345555, and
delta_R/R = -(1/3)(del_mu/mu)(R_core/R)= -0.098540.
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 = 2.011827 solar masses.
Core > 0.64 solar masses -> Turns on Helium fusion to halt collapse. ELSE:
M_core/M_star = 0.749065 , if > 0.12, H-depleted core can collapse.
M_core/M_star > M_Schoenberg-Chandrasekhar/M_star for collapse =.12.
Core gravitational potential energy = 8.294000e+20 Joules.
White dwarf approx. remnant potential energy = 1.315552e+52 Joules.
using 2nd radius measure: remnant potential energy = 1.871033e+44 Joules.
Stellar envelope launch energy for infinity = 1.377474e+42 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 = 4775232647.618183
2nd r-measure Total_avail_collapse_energy/envelope_launch energy = 67.915329
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 = 7.004598e+10 m/sec,
= 15790365.127512 Astronomical_Units/year,
= 249.708100 LY/year, or = 0.004005 years/LY,
= 0.000023 days to reach 1 AU,
assuming half energy is wasted in heating the envelope.
25.093534 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 = 8.229608e+06 m/sec,
= 1855.188818 Astronomical_Units/year 2nd,
= 0.029338 LY/year, 2nd, = 34.085638 yr/LY,
= 0.196341 days to reach 1 AU, 2nd
assuming half energy is wasted in heating the envelope, 2nd.
25.093534 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 =1.336467e+17 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 =1.900778e+09 K, 2nd.
The core collapse time controls the vigor of the shell expansion.
Helmholtz-Kelvin model core collapse time =1.860584e+16 yr,
but observationally planetary nebula ejection lasts < 3,000 yr,
and the nebula clears away in say, 25,000 yrs.
Core freefall time = 9.475191e+00 min
= 1.579198e-01 hrs = 6.579994e-03 days = 1.800765e-05 years.
Stellar photon random-walk escape time = 1.604099e+12 sec
= 5.082698e+04 years.
Core > 0.64 Msun -> Turns on Helium fusion to halt core collapse,
possibly initiating radial stellar pulsations.
Time from now to core collapse in H-burning core: = 4.142876e+09 yr.
Total Main-Sequence Lifetime until core collapse: = 4.206808e+09 yr,
according to our simplistic H-burning core collapse theory.
H-burning_lifetime/Zombeck_Age = 3.825496
H-burning_lifetime/Schwarzschild_Age = 3.529147
H-burning_lifetime/Greens_Main_Seq.Lifeime = 3.059030
H-burning_lifetime/Helmholtz_contraction_time = 1234.567091
FUSION - NUCLEAR LUMINOSITY MEASURES,
nucmixflag = 1
gamma = 4/3, n=3, Sirius
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] = 5.203380e+01,[Upper bound].
Computed observed L/Lsun = 2.902047e+01,[from distance & m]*.
[M/Msun]**3 = Min[L/Lsun] = 1.937377e+01,[Lower bound.]
P-P chain luminosity L/Lsun = 1.000000e+00,[Clayton,scrnd&normd]
P-P chain luminosity L/Lsun = 7.135426e+00,[Clayton,unscreened.]
P-P chain luminosity L/Lsun = 1.226571e+01,[Clayton,screened.]
P-P chain luminosity L/Lsun = 1.041466e+01,[Chiu,screened.]
P-P chain luminosity L/Lsun = 6.808442e+00,[Chiu,unscreened.]
P-P chain luminosity L/Lsun = 1.000000e+00,[Chiu,scrnd & normd]
P-P chain luminosity L/Lsun = 4.137169e+00,[M. Scharzschild, unscr.]
P-P fusion luminosity L/Lsun = 4.567134e+00,[A.C.Phillips, unscr.]
Carbon cycle only L_CNO/Lsun = 1.765733e+01,[CNO cycle, M.Schw.,unscr.]
Triple-Alpha cyc. L_He/Lsun = 1.007689e-78,[Helium burning,unscr.]
Total H-burning L_Htot/Lsun = 2.992304e+01,[H-burning, PP + CNO.]
Total nuclear L: L_tot/Lsun = 2.992304e+01,[Total, PP+CNO+He.]
In units of L_star Sirius.
[M/Msun]**4 = Max[L/Lstar] = 1.793003e+00,[Upper bound].
Computed observed L/Lstar = 1.000000e+00,[from distance & m]*.
[M/Msun]**3 = Min[L/Lstar] = 6.675899e-01,[Lower bound.]
P-P chain luminosity L/Lstar = 3.445844e-02,[Clayton,scrnd&normd]
P-P chain luminosity L/Lstar = 2.458756e-01,[Clayton,unscreened.]
P-P chain luminosity L/Lstar = 4.226573e-01,[Clayton,screened.]
P-P chain luminosity L/Lstar = 3.588730e-01,[Chiu,screened.]
P-P chain luminosity L/Lstar = 2.346083e-01,[Chiu,unscreened.]
P-P chain luminosity L/Lstar = 3.445844e-02,[Chiu,scrnd & normd]
P-P chain luminosity L/Lstar = 1.425604e-01,[M. Scharzschild, unscr.]
P-P fusion luminosity L/Lstar = 1.573763e-01,[A.C.Phillips, unscr.]
Carbon cycle only L_CNO/Lstar = 6.084441e-01,[CNO cycle, M.Schw.,unscr.]
Triple-Alpha cyc. L_He/Lstar = 3.472339e-80,[Helium burning,unscr.]
Total H-burning L_Htot/Lstar = 1.031101e+00,[H-burning, PP + CNO.]
Total nuclear L: L_tot/Lstar = 1.031101e+00,[Total, PP+CNO+He.]
4th power L/Lsun-Max/[L/Lsun-obs] = 1.793003e+00,
L/Lsun-observed/[L/Lsun-obs] = 1.000000e+00, *
3rd power L/Lsun-Min/[L/Lsun-obs] = 6.675899e-01,
L/Lsun_Clayton_unscreened/[L/Lsun] = 2.458756e-01,
L/Lsun_Clayton_screened/[L/Lsun] = 4.226573e-01,
L/Lsun_Clayton_scr-normalized/[L/Lsun]= 3.445844e-02,
L/Lsun_Chiu_screened/[L/Lsun] = 3.588730e-01,
L/Lsun_Chiu_unscreened/[L/Lsun] = 2.346083e-01,
L/Lsun_Chiu_scr-normalized/[L/Lsun] = 3.445844e-02,
L/Lsun_Schwarzschild/[L/Lsun] = 1.425604e-01,
L/Lsun_Phillips/[L/Lsun-observed] = 1.573763e-01.
L_CNO/Lsun/[L/Lsun-observed] = 6.084441e-01.
L_He/Lsun/[L/Lsun-observed] = 3.472339e-80.
GM/R in Cosmic Sign Language
