Dealing with Duplicate Rates

Sometimes we combine multiple sources of rates into a RateCollection or network, and we run the risk of having the same rate sequence duplicated, even though the rate itself may be different (i.e., a different source or tabulated vs. ReacLib).

import pynucastro as pyna

rl = pyna.ReacLibLibrary()
wl = pyna.TabularLibrary()

Let’s create a set of nuclei that can describe basic C burning

nuclei = ["c12", "o16", "ne20",
          "na23", "mg23", "mg24",
          "p", "n", "a"]

We’ll pull rates in both from the ReacLib library and from our tabulated weak rates

lib = rl.linking_nuclei(nuclei) + wl.linking_nuclei(nuclei)

warning: C12 was not able to be linked
warning: He4 was not able to be linked
warning: O16 was not able to be linked
warning: Ne20 was not able to be linked
warning: Mg24 was not able to be linked

If we try to create a network or RateCollection now, it will fail:

rc = pyna.RateCollection(libraries=[lib])

/opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/pynucastro/networks/rate_collection.py:720: UserWarning: ReacLib neutron decay rate (<n_to_p_weak_wc12>) does not account for degeneracy at high densities. Consider using tabular rate from Langanke.
  warnings.warn(msg)

---------------------------------------------------------------------------
RateDuplicationError                      Traceback (most recent call last)
Cell In[5], line 1
----> 1 rc = pyna.RateCollection(libraries=[lib])

File /opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/pynucastro/networks/rate_collection.py:586, in RateCollection.__init__(self, rate_files, libraries, rates, inert_nuclei, symmetric_screening, do_screening)
    582         combined_library += lib
    584 self.rates = self.rates + combined_library.get_rates()
--> 586 self._build_collection()

File /opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/pynucastro/networks/rate_collection.py:731, in RateCollection._build_collection(self)
    728 # finally check for duplicate rates -- these are not
    729 # allowed
    730 if self.find_duplicate_links():
--> 731     raise RateDuplicationError("Duplicate rates found")

RateDuplicationError: Duplicate rates found

We see that we get a RateDuplicationError because one or more rates has a duplicate.

We can find the duplicates using the find_duplicate_links method. This will return a list of lists of rates that all provide the same link.

lib.find_duplicate_links()

[[n ⟶ p + e⁻ + 𝜈, n ⟶ p + e⁻ + 𝜈],
 [Mg23 ⟶ Na23 + e⁺ + 𝜈, Mg23 + e⁻ ⟶ Na23 + 𝜈]]

We see that the neutron decay and the decay of \({}^{23}\mathrm{Mg}\) are both duplicated. Let’s see if we can learn more:

for n, p in enumerate(lib.find_duplicate_links()):
    print(f"dupe {n}:")
    print(f"   rate 1: {p[0]} ({type(p[0])})")
    print(f"   rate 2: {p[1]} ({type(p[1])})")

dupe 0:
   rate 1: n ⟶ p + e⁻ + 𝜈 (<class 'pynucastro.rates.reaclib_rate.ReacLibRate'>)
   rate 2: n ⟶ p + e⁻ + 𝜈 (<class 'pynucastro.rates.tabular_rate.TabularRate'>)
dupe 1:
   rate 1: Mg23 ⟶ Na23 + e⁺ + 𝜈 (<class 'pynucastro.rates.reaclib_rate.ReacLibRate'>)
   rate 2: Mg23 + e⁻ ⟶ Na23 + 𝜈 (<class 'pynucastro.rates.tabular_rate.TabularRate'>)

In this case, we see that one is a ReacLibRate and the other is a TabularRate.

The first duplicate is neutron decay. ReacLib simply has the decay constant, with no density or temperature dependence. The tabulated rate in this case comes from the Langanke and Martínez-Pinedo [2001] and is accurate at high densities / temperatures when degeneracy effects are important.

For the second rate, note that in the TabularRate we combine the rates:

\[(Z, A) \rightarrow (Z -1, A) + e^+ + \nu_e\]

\[(Z, A) + e^- \rightarrow (Z - 1, A) + \bar{\nu}_e\]

into a single effective rate. This means that our TabularRate version of the \({}^{23}\mathrm{Mg}\) decay will contain both the \(\beta+\) decay and electron capture. Furthermore, the tabular rates have both the density and temperature dependence, and thus should be preferred to the ReacLibRates when we have a duplicate.

Here we loop over the duplicates and store the rates (the ReacLib versions) that we wish to remove in a list

rates_to_remove = []
for pair in lib.find_duplicate_links():
    for r in pair:
        if isinstance(r, pyna.rates.ReacLibRate):
            rates_to_remove.append(r)

Now we remove the duplicates from the list

for r in rates_to_remove:
    lib.remove_rate(r)

Finally, we can make the RateCollection without error:

rc = pyna.RateCollection(libraries=[lib])

fig = rc.plot(rotated=True)