Creating an NSE table#

We can tabulate the NSE state on a grid $(ρ, T, Y_{e})$ , giving:

$\bar{A}$ : the mean molecular weight
$⟨ B / A ⟩$ : the average binding energy per nucleon of the NSE state [MeV]
$d Y_{e} / d t$ : the time-evolution of $Y_{e}$ due to weak reactions [1/s]
$d \bar{A} / d t$ : the time-evolution of $\bar{A}$ due to weak reactions [1/s]
$d ⟨ B / A ⟩ / d t$ : the time-evolution of the binding energy per nucleon due to weak reactions [MeV/s]
$ϵ_{ν}$ : 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 $(ρ, T, Y_{e})$ . To help accelerate the convergence, it will start at the highest temperature and loop over $ρ$ 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 2.5.0.post37+g50ff3873
# original NSENetwork had 13 nuclei
#
#   log10(rho)       log10(T)           Ye             Abar            <B/A>          dYe/dt         dAbar/dt        d<B/A>/dt         e_nu       
   7.0000000000    9.6000000000    0.5000000000   50.2051965063    8.6280555770  -4.3798684e-05              -0   2.3285948e-06   7.4765875e+13 
   7.0000000000    9.6000000000    0.4650000000   55.7461181554    8.7870631885  -5.5253373e-09   2.1689193e-21   3.9317237e-10   1.3980145e+10 
   7.0000000000    9.6000000000    0.4300000000   11.0637644863    8.1412181124   0.00017699678  -2.9553154e-26  -1.8453759e-12   2.7707299e+14 
   7.0000000000   10.0000000000    0.5000000000    1.2148721356    1.6682000908     0.084056593   1.1097981e-55   5.7350242e-41   7.8635828e+17 
   7.0000000000   10.0000000000    0.4650000000    1.2129154965    1.6556759416      0.10066493  -9.5154199e-56   3.5220148e-41   8.3544455e+17 
   7.0000000000   10.0000000000    0.4300000000    1.2071216004    1.6183519789       0.1178642  -1.8245905e-55   5.9197759e-42   8.8944343e+17 
   7.0000000000   10.4000000000    0.5000000000    1.0000000000    0.0000000002       5.7463273 -3.0282656e-218  6.7442697e-203   2.3050257e+20 
   7.0000000000   10.4000000000    0.4650000000    1.0000000000    0.0000000002       7.2542055 -1.4008643e-218  5.8190844e-203    2.360043e+20 
   7.0000000000   10.4000000000    0.4300000000    1.0000000000    0.0000000002       8.7650901  1.5660364e-218  3.8278038e-203   2.4155562e+20 
   8.0000000000    9.6000000000    0.5000000000   54.3190287633    8.6383977879  -0.00084867596              -0   4.3696922e-05   1.4741939e+15 
   8.0000000000    9.6000000000    0.4650000000   55.8970086077    8.7873938438  -4.9038114e-08   2.6652714e-20    4.195729e-09   1.2981616e+11 
   8.0000000000    9.6000000000    0.4300000000   11.0638264094    8.1412220464   9.2047376e-06  -3.3885398e-29  -5.6069146e-13   1.1254068e+13 
   8.0000000000   10.0000000000    0.5000000000    2.5712548585    5.7636834359    -0.019589285  -5.2722578e-34   1.7213901e-19   1.6310989e+17 
   8.0000000000   10.0000000000    0.4650000000    2.5124367545    5.6778079180   -0.0041256863  -3.8679592e-33   2.1068175e-19   1.5065028e+17 
   8.0000000000   10.0000000000    0.4300000000    2.3664071213    5.4461458099    0.0093041571   4.0022393e-35   1.1443316e-19    1.616981e+17 
   8.0000000000   10.4000000000    0.5000000000    1.0000000214    0.0000002024        1.213841 -1.9167604e-165  9.8468124e-150   2.1894106e+20 
   8.0000000000   10.4000000000    0.4650000000    1.0000000212    0.0000002004       2.8346072  1.4571224e-165  8.4165813e-150   2.2127881e+20 
   8.0000000000   10.4000000000    0.4300000000    1.0000000206    0.0000001945       4.4726034  2.0415049e-165  5.4823199e-150   2.2397331e+20 
   9.0000000000    9.6000000000    0.5000000000   55.5133155454    8.6413416287    -0.060150514              -0    0.0031209543   1.5551546e+17 
   9.0000000000    9.6000000000    0.4650000000   55.9133553778    8.7874269700  -3.9837589e-06   2.1308784e-18   3.6045209e-07   1.0369016e+13 
   9.0000000000    9.6000000000    0.4300000000   11.0638296395    8.1412222516   1.0225013e-08  -9.8140885e-34  -5.2463927e-15   1.1664591e+10 
   9.0000000000   10.0000000000    0.5000000000    4.3121776381    7.1515970010     -0.10742171  -8.6627599e-20   2.9758631e-05   4.7264474e+17 
   9.0000000000   10.0000000000    0.4650000000    5.1247512633    7.3995936810    -0.019430688   1.8465661e-19   3.3567893e-06   8.7381921e+16 
   9.0000000000   10.0000000000    0.4300000000    4.4162917338    7.0777667259   -0.0059568646  -9.8582877e-21   5.1854462e-07   3.2607547e+16 
   9.0000000000   10.4000000000    0.5000000000    1.0000214391    0.0002025496      -17.715252 -4.6659523e-112   3.7269644e-96   2.7735801e+20 
   9.0000000000   10.4000000000    0.4650000000    1.0000212299    0.0002005606      -15.005795 -5.0233078e-112   3.0828757e-96   2.5962747e+20 
   9.0000000000   10.4000000000    0.4300000000    1.0000206076    0.0001946701      -12.327315  9.4415328e-113   1.9401565e-96   2.4324142e+20 
  10.0000000000    9.6000000000    0.5000000000   55.8690710154    8.6423241378      -5.2274435              -0      0.27200888   2.9375322e+19 
  10.0000000000    9.6000000000    0.4650000000   55.9152992533    8.7874248629  -0.00092936032   -1.324133e-16     8.53828e-05   4.3024741e+15 
  10.0000000000    9.6000000000    0.4300000000   11.0638297820    8.1412222637   5.0971987e-15  -9.3106433e-42  -6.8646472e-21       5801.4456 
  10.0000000000   10.0000000000    0.5000000000   13.9373407965    8.2743569653      -5.5783268   2.1566023e-14      0.10960359   3.9379731e+19 
  10.0000000000   10.0000000000    0.4650000000   28.2439836979    8.6492581223    -0.075077755  -6.6877144e-16   0.00050735877   5.2201547e+17 
  10.0000000000   10.0000000000    0.4300000000   10.2419481623    8.0844804256   -0.0025107086  -3.0948296e-20    1.107337e-06   1.7236326e+16 
  10.0000000000   10.4000000000    0.5000000000    1.0197762662    0.1829102358      -196.64449  -9.9403547e-58   3.9060708e-42   2.3555843e+21 
  10.0000000000   10.4000000000    0.4650000000    1.0195859197    0.1811835447       -167.5422    -7.86651e-58    3.044433e-42   1.9968627e+21 
  10.0000000000   10.4000000000    0.4300000000    1.0190251344    0.1760927389      -140.99607  -1.6336075e-57   1.8184626e-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.