Overview of pynucastro

pynucastro is a set of python interfaces to nuclear reaction rates. It is meant for both interactive exploration of rates (through Jupyter notebooks) and to create reaction networks for use in simulation codes.

The preferred way of importing pynucastro is as follows:

import pynucastro as pyna

The main classes are:

• Nucleus: This is a single nucleus. It knows its proton number, Z, neutron number, N, weight, A, and binding energy, nucbind, as well as T-dependent partition function and ground state spin.

• Rate: This is a single rate. It knows the reactants and products and has methods that allow you to evaluate it at a specified temperature and plot its temperature dependence. A Rate also knows how to the generate code (C++ and python) needed to evaluate it.

  There are a few special rates derived from Rate:

  • ReacLibRate: This is a rate in the JINA ReacLib format, with the temperature dependence specified by an interpolant with 7 different coefficients.

  • TabularRate: This is a rate that is tabulated in terms of \((T, \rho Y_e)\). This is how the weak rate (electron captures and beta-decays) are stored. Interpolation is used to find the rate at any thermodynamic state.

  • ApproximateRate: An approximate rate groups together \(A(\alpha, \gamma)B\) and \(A(\alpha,p)X(p,\gamma)B\) into a single effective rate, assuming equilibrium of \(p\) and \(X\).

  • DerivedRate: A derived rate uses detailed balance to recompute a reverse rate from the forward rate.

• RatePair: For a single nuclear process, this holds the corresponding forward and reverse rates.

• Library: This is a collection of rates (for example, the entire ReacLib library). It provides methods for filtering out rates based on different sets of rules.

  There are two important subclasses:

  • ReacLibLibrary: The entire ReacLib rate library (> 80,000 rates)

  • TabularLibrary: A Library containing all known tabular weak rates.

• Composition: This is a collection of nuclei and their mass fractions. A Composition is used when evaluating the full rates in a network.

• RateCollection: This is the most basic form of a network. It is a collection of rates and nuclei, that knows about the connectivity of the nuclei through different reactions. This acts as the base class for different reaction networks. A RateCollection has methods to evaluate the rates and make a plot of the links between rates.

  There are a few important subclasses:

  • NSENetwork: This allows a user to find the nuclear statistical equilibrium state of a collection of nuclei.

  • PythonNetwork: This is a collection of rates with functions that know how to write python code to express the righthand side of the system of ODEs.

  • SimpleCxxNetwork: This is a simple C++ network that provides functions for computing the righthand side and Jacobian of a network. Not all pynucastro features are supported in this network.

  • AmrexAstroCxxNetwork: This is a C++ network of the form needed by the AMReX Astrophysics Microphysics library used by the Castro and MAESTROeX simulation codes.

Usage

There are two modes of usage for pynucastro.

• Within a Jupyter notebook, one can evaluate the rates and interactively visualize a network and see the flow between nuclei as connections colored by the rate linking them.

• You can use pynucastro to write the righthand side routine for the system of ODEs that must be integrated to evolve a reaction network. A reaction network takes the form:

  \[\frac{dY_i}{dt} = - \sum_{j,k} Y_i Y_j \lambda_{i(j,k)l} + \sum_{j,k} Y_l Y_k \lambda_{l(j,k)i}\]

  where the \(\lambda\)’s are the rates of destruction and creation of species i, represented by the molar fraction \(Y_i\) (see, e.g., Timmes [1999]). pynucastro will create the righthand sides of this system of ODEs (as python or C++ code) from the list of rates you provide. One can use this to add reaction networks to existing simulation codes, for example, the MAESTROeX and Castro codes.