PPN H Burn Simple Example¶
For stars a bit more massive than the sun($M\gtrsim2.5 M_\odot$) the CNO cycles dominate energy production during hydrogen burning. This examples uses a constant temperature of $T_9$ = 0.055 and density of $\rho$ = 100 $g/cm^{3}$, suggesting this is hydrigen shell burning. In this notebook we will take a look at the signatures of the CNO cycle at initial solar metallicities.
%pylab nbagg
import ppn
b = ppn.abu_vector('./')
Below are two abundance charts--one showing the initial abundances of lighter elements and the second shows the same plot at the end of the run for comparison.
ifig=0;close(ifig);figure(ifig)
b.abu_chart(0, plotaxis=[-1.5, 18.5, -1, 20])
ifig=38;close(ifig);figure(ifig)
b.abu_chart(38, plotaxis=[-1.5, 18.5, -1, 20])
While these two plots only show us the initial anf final states of the run we can infer the nucleosynthesis which has taken place. On the lowest end we start off with predominantly hydrogen then helium. By the end of the run much of the $^1$H and all of the $^2$H has been depleted, along with $^3$He as well. These have been converted into predominantly $^4$He via the p-p chain. We also can see marked transfer in the distribution of fractional number of isotopes in the range A = 12->27 due to the CNO, NeNa and MgAl cycles.
;close(ifig);figure(ifig)
b.abu_flux_chart(31,which_flux = 0,plotaxis=[3.5, 15, 5.25, 15])
Above is, on the left hand side, another abundance plot, and on the right is a flux plot showing the flux of charged particles during this timestep. From these two plots we can make a number of observations. For example, at this early time, t = 8.6288$\times$10$^2$yr ($<$ 0.1$t_{tot}$), isotopes $^{17}$F and $^{18}$F have yet to be exhausted through the $^{17}$F$(e^+,\nu)^{17}$O and $^{18}$F$(e^+,\nu)^{18}$O reactions. The most rapid reaction in this fux plot is the $^{15}$N$(p,\alpha)^{12}$C, due to its large cross section relative to other relevent p-capture reactions. There is clearly the presence of CNO and interestingly, here we can see the pipeline to the NeNa cycle(and subsequently, MgAl)which is the $^{19}$F$(p,\gamma)^{20}$Ne reaction.
#For the purpose of reproduction here are some important values one can compare:
#For step 0
data1 = np.loadtxt('./iso_massf00000.DAT', usecols=(0,4),skiprows = 7)
print data1[2,1] #Proton abundance. Expected value: 1.43094e-05 pm 1.43094e-06
print data1[10,1] #C12 abundance. Expected value: 0.00248278 pm 2.48278e-04
print data1[13,1] #N14 abundance. Expected value: 0.000734041 pm 17.34041 e-05
#For step 31
data = np.loadtxt('./iso_massf00031.DAT', usecols=(0,4),skiprows = 7)
print data[2,1] #Proton abundance. Expected value: 6.30669e-20 pm 6.30669e-21
print data[10,1] #C12 abundance. Expected value: 0.000128693 pm 1.28693e-05
print data1[13,1] #N14 abundance. Expected value: 0..000734041 pm 17.340414e-05
#For step 38
data1 = np.loadtxt('./iso_massf00038.DAT', usecols=(0,4),skiprows = 7)
print data1[2,1] #Proton abundance. Expected value: 5.84407e-24 pm 5.84407e-25
print data1[10,1] #C12 abundance. Expected value: 0.000128694 pm 1.28694e-05
print data1[13,1] #N14 abundance. Expected value: 0.00873581 pm 8.73581e-04