Creating an NSE table#

We can tabulate the NSE state on a grid \((\rho, T, Y_e)\), giving:

\(\bar{A}\) : the mean molecular weight
\(\langle B/A \rangle\) : the average binding energy per nucleon of the NSE state [MeV]
\(dY_e/dt\) : the time-evolution of \(Y_e\) due to weak reactions [1/s]
\(d\bar{A}/dt\) : the time-evolution of \(\bar{A}\) due to weak reactions [1/s]
\(d\langle B/A\rangle/dt\) : the time-evolution of the binding energy per nucleon due to weak reactions [MeV/s]
\(\epsilon_\nu\) : the energy loss due to neutrinos [erg / g / s]

import pynucastro as pyna
from pynucastro import Nucleus

First we’ll create a simple NSE network with a few nuclei. We’ll include tabulated weak rates so we can compute the change in the state due to electron/positron captures and decays.

nucs = [Nucleus("p"), Nucleus("n"), Nucleus("he4"),
        Nucleus("fe52"), Nucleus("fe53"), Nucleus("fe54"),
        Nucleus("fe55"), Nucleus("fe56"),
        Nucleus("co54"), Nucleus("co55"), Nucleus("co56"),
        Nucleus("ni56"), Nucleus("ni57")]

tl = pyna.TabularLibrary().linking_nuclei(nucs)
rl = pyna.ReacLibLibrary().linking_nuclei(nucs)
all_lib = tl + rl

warning: He4 was not able to be linked
warning: Fe53 was not able to be linked
warning: Fe52 was not able to be linked
warning: Ni57 was not able to be linked

dupes = all_lib.find_duplicate_links()
rates_to_remove = []
for d in dupes:
    rates_to_remove += [r for r in d if isinstance(r, pyna.rates.ReacLibRate)]

for r in rates_to_remove:
    all_lib.remove_rate(r)

nse = pyna.NSENetwork(libraries=[all_lib])

Now we’ll create a grid of temperature, density, and \(Y_e\) where we want to compute the NSE state

import numpy as np

Ts = np.logspace(9.6, 10.4, 3)
rhos = np.logspace(7, 10, 4)
yes = np.linspace(0.43, 0.5, 3)

Finally we can generate the table. This will compute the NSE state at each combination of \((\rho, T, Y_e)\). To help accelerate the convergence, it will start at the highest temperature and loop over \(\rho\) and \(Y_e\) and cache the values of the proton and neutron chemical potentials for the next temperature.

nse.generate_table(rho_values=rhos,
                   T_values=Ts,
                   Ye_values=yes)

The table is stored as nse.tbl

%cat nse.tbl

# NSE table generated by pynucastro 2.4.0.post45+g630df533
# original NSENetwork had 13 nuclei
#
#   log10(rho)       log10(T)           Ye             Abar            <B/A>          dYe/dt         dAbar/dt        d<B/A>/dt         e_nu       
0000000000    9.6000000000    0.5000000000   50.2051965167    8.6280555771  -4.3798684e-05              -0   2.3285948e-06   7.4765875e+13 
0000000000    9.6000000000    0.4650000000   55.7461181559    8.7870631885  -5.5253373e-09  -1.1145835e-21   3.9317237e-10   1.3980145e+10 
0000000000    9.6000000000    0.4300000000   11.0637644863    8.1412181124   0.00017699678  -2.9553154e-26  -1.8453759e-12   2.7707299e+14 
0000000000   10.0000000000    0.5000000000    1.2148721368    1.6682000987     0.084056593   -6.583548e-57   5.7350248e-41   7.8635828e+17 
0000000000   10.0000000000    0.4650000000    1.2129154977    1.6556759493      0.10066493  -5.9529967e-56   3.5220152e-41   8.3544455e+17 
0000000000   10.0000000000    0.4300000000    1.2071216016    1.6183519865       0.1178642    1.513528e-55   5.9197765e-42   8.8944343e+17 
0000000000   10.4000000000    0.5000000000    1.0000000000    0.0000000002       5.7463273  1.9226178e-218   6.744271e-203   2.3050257e+20 
0000000000   10.4000000000    0.4650000000    1.0000000000    0.0000000002       7.2542055 -7.0032754e-219  5.8190855e-203    2.360043e+20 
0000000000   10.4000000000    0.4300000000    1.0000000000    0.0000000002       8.7650901 -2.6690723e-219  3.8278045e-203   2.4155562e+20 
0000000000    9.6000000000    0.5000000000   54.3190287662    8.6383977879  -0.00084867596   3.1990002e-16   4.3696922e-05   1.4741939e+15 
0000000000    9.6000000000    0.4650000000   55.8970086078    8.7873938438  -4.9038114e-08  -2.6006588e-20    4.195729e-09   1.2981616e+11 
0000000000    9.6000000000    0.4300000000   11.0638264094    8.1412220464   9.2047376e-06  -3.3885397e-29  -5.6069146e-13   1.1254068e+13 
0000000000   10.0000000000    0.5000000000    2.5712548608    5.7636834391    -0.019589285   5.2225195e-34   1.7213902e-19   1.6310989e+17 
0000000000   10.0000000000    0.4650000000    2.5124367565    5.6778079210   -0.0041256863  -1.8948014e-33   2.1068176e-19   1.5065028e+17 
0000000000   10.0000000000    0.4300000000    2.3664071228    5.4461458125    0.0093041571  -2.1633157e-33   1.1443317e-19    1.616981e+17 
0000000000   10.4000000000    0.5000000000    1.0000000214    0.0000002024        1.213841  2.5731991e-165  9.8468142e-150   2.1894106e+20 
0000000000   10.4000000000    0.4650000000    1.0000000212    0.0000002004       2.8346072  9.3782403e-166  8.4165829e-150   2.2127881e+20 
0000000000   10.4000000000    0.4300000000    1.0000000206    0.0000001945       4.4726034  3.2632729e-166  5.4823209e-150   2.2397331e+20 
0000000000    9.6000000000    0.5000000000   55.5133155462    8.6413416287    -0.060150514              -0    0.0031209543   1.5551546e+17 
0000000000    9.6000000000    0.4650000000   55.9133553778    8.7874269700  -3.9837589e-06   7.4477304e-19   3.6045209e-07   1.0369016e+13 
0000000000    9.6000000000    0.4300000000   11.0638296395    8.1412222516   1.0225013e-08  -9.8140885e-34  -5.2463927e-15   1.1664591e+10 
0000000000   10.0000000000    0.5000000000    4.3121776451    7.1515970038     -0.10742171              -0   2.9758632e-05   4.7264474e+17 
0000000000   10.0000000000    0.4650000000    5.1247512774    7.3995936852    -0.019430688  -7.2863326e-20   3.3567893e-06    8.738192e+16 
0000000000   10.0000000000    0.4300000000    4.4162917436    7.0777667298   -0.0059568646   2.9604104e-21   5.1854462e-07   3.2607547e+16 
0000000000   10.4000000000    0.5000000000    1.0000214391    0.0002025496      -17.715252  2.0751102e-111   3.7269651e-96   2.7735801e+20 
0000000000   10.4000000000    0.4650000000    1.0000212299    0.0002005606      -15.005795 -5.4639132e-112   3.0828763e-96   2.5962747e+20 
0000000000   10.4000000000    0.4300000000    1.0000206076    0.0001946701      -12.327315  2.9766209e-112   1.9401569e-96   2.4324142e+20 
0000000000    9.6000000000    0.5000000000   55.8690710156    8.6423241378      -5.2274435              -0      0.27200888   2.9375322e+19 
0000000000    9.6000000000    0.4650000000   55.9152992533    8.7874248629  -0.00092936032  -1.9067515e-16     8.53828e-05   4.3024741e+15 
0000000000    9.6000000000    0.4300000000   11.0638297827    8.1412222607   5.0971987e-15  -9.3106432e-42  -6.8646472e-21       5801.4456 
0000000000   10.0000000000    0.5000000000   13.9373408169    8.2743569660      -5.5783268              -0      0.10960359   3.9379731e+19 
0000000000   10.0000000000    0.4650000000   28.2439837438    8.6492581227    -0.075077755   4.8295467e-16   0.00050735877   5.2201547e+17 
0000000000   10.0000000000    0.4300000000   10.2419481655    8.0844804259   -0.0025107086  -8.2806269e-20    1.107337e-06   1.7236325e+16 
0000000000   10.4000000000    0.5000000000    1.0197762664    0.1829102375      -196.64449  -8.6978104e-58   3.9060715e-42   2.3555843e+21 
0000000000   10.4000000000    0.4650000000    1.0195859199    0.1811835464       -167.5422  -8.2805369e-59   3.0444336e-42   1.9968627e+21 
0000000000   10.4000000000    0.4300000000    1.0190251346    0.1760927406      -140.99607   4.1357153e-58   1.8184629e-42   1.6720802e+21 

There are other options to the NSE table writing, including storing the mass fractions or a reduced composition constructed by binning the nuclei into the closest nuclei in a smaller set.