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/3.11.11/x64/lib/python3.11/site-packages/pynucastro/networks/rate_collection.py:576: 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/3.11.11/x64/lib/python3.11/site-packages/pynucastro/networks/rate_collection.py:472, in RateCollection.__init__(self, rate_files, libraries, rates, inert_nuclei, symmetric_screening, do_screening)
    468         combined_library += lib
    470 self.rates = self.rates + combined_library.get_rates()
--> 472 self._build_collection()

File /opt/hostedtoolcache/Python/3.11.11/x64/lib/python3.11/site-packages/pynucastro/networks/rate_collection.py:586, in RateCollection._build_collection(self)
    583 # finally check for duplicate rates -- these are not
    584 # allowed
    585 if self.find_duplicate_links():
--> 586     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 tuples 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. For the tabular rates, we take the approach that the sequences:

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 paper 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)