Available Reaction Networks

A network defines the composition, which is needed by the equation of state and transport coefficient routines. Even if there are no reactions taking place, a network still needs to be defined, so Microphysics knows the properties of the fluid.

Tip

If reactions can be ignored, then the general_null network can be used — this simply defines a composition with no reactions.

Note

Many of the networks here are generated using pynucastro using the AmrexAstroCxxNetwork class.

general_null

general_null is a bare interface for a nuclear reaction network — no reactions are enabled. The data in the network is defined at compile type by specifying an inputs file. For example, networks/general_null/triple_alpha_plus_o.net would describe the triple-α reaction converting helium into carbon, as well as oxygen and iron. This has the form:

# name       short name    aion     zion
helium-4       He4          4.0      2.0
carbon-12      C12         12.0      6.0
oxygen-16      O16         16.0      8.0
iron-56        Fe56        56.0     26.0

The four columns give the long name of the species, the short form that will be used for plotfile variables, and the mass number, A, and proton number, Z.

The name of the inputs file by one of two make variables:

  • NETWORK_INPUTS : this is simply the name of the “.net” file, without any path. The build system will look for it in the current directory and then in $(MICROPHYSICS_HOME)/networks/general_null/.

    For the example above, we would set:

    NETWORK_INPUTS := triple_alpha_plus_o.net
    
  • GENERAL_NET_INPUTS : this is the full path to the file. For example we could set:

    GENERAL_NET_INPUTS := /path/to/file/triple_alpha_plus_o.net
    

At compile time, the “.net” file is parsed and a network header network_properties.H is written using the python script write_network.py. The make rule for this is contained in Microphysics/networks/Make.package.

iso7, aprox13, aprox19, and aprox21

These are alpha-chains (with some other nuclei) based on the original Fortran networks from Frank Timmes. These networks share common rates from Microphysics/rates and are implemented using the templated C++ network infrastructure.

These networks approximate a lot of the links, in particular, combining (α,p)(p,γ) and (α,γ) into a single effective rate.

The available networks are:

  • iso7 : contains 4He, 12C, 16O, 20Ne, 24Mg, 28Si, 56Ni and is based on [11].

  • aprox13 : adds 32S, 36Ar, 40Ca, 44Ti, 48Cr, 52Fe

  • aprox19 : adds 1H, 3He, 14N, 54Fe, p, n. Here, p participates only in the photodisintegration rates at high mass number, and is distinct from 1H.

  • aprox21 : adds 56Cr, 56Fe. This is designed to reach a lower Ye than the other networks, for use in massive star simulations. Note that the link to 56Cr is greatly approximated.

These networks store the total binding energy of the nucleus in MeV as bion(:). They then compute the mass of each nucleus in grams as:

Mk=(AkZk)mn+Zk(mp+me)Bk

where mn, mp, and me are the neutron, proton, and electron masses, Ak and Zk are the atomic weight and number, and Bk is the binding energy of the nucleus (converted to grams). Mk is stored as mion(:) in the network.

The energy release per gram is converted from the rates as:

ϵ=NAc2kdYkdtMkϵν

where NA is Avogadro’s number (to convert this to “per gram”) and ϵν is the neutrino loss term (see Neutrino Losses).

CNO_extras

This network replicates the popular MESA “cno_extras” network which is meant to study hot-CNO burning and the start of the breakout from CNO burning. This network is managed by pynucastro.

_images/cno_extras_hide_alpha.png

Note

We add 56Fe as an inert nucleus to allow this to be used for X-ray burst simulations (not shown in the network diagram above).

nova networks

The nova and nova2 networks both are intended for modeling classical novae.

  • nova focuses just on CNO/hot-CNO:

    _images/nova.png
  • nova2 expands nova by adding the pp-chain nuclei:

    _images/nova2.png

He-burning networks

This is a collection of networks meant to model He burning. The are inspired by the “aprox”-family of networks, but contain more nuclei/rates, and are managed by pynucastro.

One feature of these networks is that they include a bypass rate for 12C(α,γ)16O discussed in [12]. This is appropriate for explosive He burning. That paper discusses the sequences:

  • 14C(α,γ)18O(α,γ)22Ne at high temperatures (T > 1 GK). We don’t consider this.

  • 14N(α,γ)18F(α,p)21Ne is the one they consider important, since it produces protons that are then available for 12C(p,γ)13N(α,p)16O.

This leaves 21Ne as an endpoint, which we connect to the other nuclei by including 22Na.

For the 12C+12C, 12C+16O, and 16O+16O rates, we also need to include:

  • 12C(12C,n)23Mg(n,γ)24Mg

  • 16O(16O,n)31S(n,γ)32S

  • 16O(12C,n)27Si(n,γ)28Si

Since the neutron captures on those intermediate nuclei are so fast, we leave those out and take the forward rate to just be the first rate. We do not include reverse rates for these processes.

These networks also combine some of the A(α,p)X(p,γ)B links with A(α,γ)B, allowing us to drop the intermediate nucleus X. Some will approximate A(n,γ)X(n,γ)B into an effective A(nn,γ)B rate (double-neutron capture).

The networks are named with a descriptive name, the number of nuclei, and the letter a if they approximate (α,p)(p,γ), the letter n if they approximate double-neutron capture, and the letter p if they split the protons into two groups (one for photo-disintegration).

he-burn-18a

Note

This network was previously called subch_base.

This is the simplest network and is similar to aprox13, but includes a better description of 12C and 16O burning, as well as the bypass rate for 12C(α,γ)16O.

It has the following features / simplifications:

  • 35Cl, 39K, 43Sc, 47V, 51Mn, and 55Co are approximated out of the (α,p)(p,γ) links.

  • The nuclei 14N, 18F, 21Ne, and 22Na are not included. This means that we do not capture the 14N(α,γ)18F(α,p)21Ne rate sequence.

  • The reverse rates of 12C+12C, 12C+16O, 16O+16O are neglected since they’re not present in the original aprox13 network

  • The 12C+20Ne rate is removed

  • The (α,γ) links between 23Na, 27Al and between 27Al and 31P are removed, since they’re not in the original aprox13 network.

The network appears as:

_images/he-burn-18a.png

The nuclei in gray are those that have been approximated about, but the links are effectively accounted for in the approximate rates.

There are 2 runtime parameters that can be used to disable rates:

  • network.disable_p_c12__n13 : if set to 1, then the rate 12C(p,γ)13N and its inverse are disabled.

  • network.disable_he4_n13__p_o16 : if set to 1, then the rate 13N(α,p)16O and its inverse are disabled.

Together, these parameters allow us to turn off the sequence 12C(p,γ)13N(α,p)16O that acts as a bypass for 12C(α,γ)16O.

he-burn-22a

Note

This network was previously called subch_simple.

This builds on he-burn-18a by including the 14N(α,γ)18F(α,p)21Ne rate sequence, which allows an enhancement to the 12C(p,γ)13N(α,p)16O rate due to the additional proton release.

_images/he-burn-22a.png

Warning

Due to inclusion of the rate sequence, 14N(α,γ)18F(α,p)21Ne, there is an artificial end-point at 22Na.

Like he-burn-18a, there are 2 runtime parameters that can disable the rates for the 12C(p,γ)13N(α,p)16O sequence.

he-burn-31anp

This builds on he-burn-22a by adding some iron-peak nuclei. It no longer approximates out 51Mn or 55Co, and includes approximations to double-neutron capture. Finally, it splits the protons into two groups, with those participating in reactions with mass numbers > 48 treated as a separate group (for photo-disintegration reactions).

The iron group here resembles aprox21, but has the addition of stable 58Ni and doesn’t include the approximation to 56Cr.

_images/he-burn-31anp.png

he-burn-36a

This has the most complete iron-group, with nuclei up to 60Zn and no approximations to the neutron captures. This network can be quite slow.

_images/he-burn-36a.png

CNO_He_burn

This network is meant to study explosive H and He burning. It combines the CNO_extras network (with the exception of the inert 56Fe with the he-burn-22a network. This allows it to capture hot-CNO and He burning.

_images/cno-he-burn-33a.png

ECSN

ECSN is meant to model electron-capture supernovae in O-Ne white dwarfs. It includes various weak rates that are important to this process.

_images/ECSN.png

C-ignition networks

There are a number of networks that have been developed for exploring carbon burning in near-Chandrasekhar mass which dwarfs.

ignition_chamulak

This network was introduced in our paper on convection in white dwarfs as a model of Type Ia supernovae [13]. It models carbon burning in a regime appropriate for a simmering white dwarf, and captures the effects of a much larger network by setting the ash state and energetics to the values suggested in [14].

The binding energy, q, in this network is interpolated based on the density. It is stored as the binding energy (ergs/g) per nucleon, with a sign convention that binding energies are negative. The energy generation rate is then:

ϵ=qdX(12C)dt=qA12CdY(12C)dt

(this is positive since both q and dY/dt are negative)

ignition_reaclib

This contains several networks designed to model C burning in WDs. They include:

  • C-burn-simple : a version of ignition_simple built from ReacLib rates. This just includes the C+C rates and doesn’t group the endpoints together.

  • URCA-simple : a basic network for modeling convective Urca, containing the 23Na-23Ne Urca pair.

  • URCA-medium : a more extensive Urca network than URCA-simple, containing more extensive C burning rates.

ignition_simple

This is the original network used in our white dwarf convection studies [15]. It includes a single-step 12C(12C,γ)24Mg reaction. The carbon mass fraction equation appears as

DX(12C)Dt=112ρX(12C)2fCoul[NAσv]

where NAσv is evaluated using the reaction rate from (Caughlan and Fowler 1988). The Coulomb screening factor, fCoul, is evaluated using the general routine from the Kepler stellar evolution code (Weaver 1978), which implements the work of (Graboske 1973) for weak screening and the work of (Alastuey 1978 and Itoh 1979) for strong screening.

powerlaw

This is a simple single-step reaction rate. We will consider only two species, fuel, f, and ash, a, through the reaction: f+fa+γ. Baryon conservation requires that Af=Aa/2, and charge conservation requires that Zf=Za/2. We take our reaction rate to be a powerlaw in temperature. The standard way to write this is in terms of the number densities, in which case we have

dnfdt=2dnadt=r

with

r=r0nX2(TT0)ν

Here, r0 sets the overall rate, with units of [cm3 s1], T0 is a reference temperature scale, and ν is the temperature exponent, which will play a role in setting the reaction zone thickness. In terms of mass fractions, nf=ρXa/(Aamu), our rate equation is

dXfdt=r0muρXf21Af(TT0)νω˙fdXadt=12r0muρXf2AaAf2(TT0)ν=r0muρXf21Af(TT0)ν

We define a new rate constant, r~0 with units of [s1] as

r~0={r0muAfρ0if TTa0if T<Ta

where ρ0 is a reference density and Ta is an activation temperature, and then our mass fraction equation is:

dXfdt=r~0Xf2(ρρ0)(TT0)ν

Finally, for the energy generation, we take our reaction to release a specific energy, [erg g1], of qburn, and our energy source is

ϵ=qburndXfdt

There are a number of parameters we use to control the constants in this network. This is one of the few networks that was designed to work with gamma_law as the EOS.

rprox

This network contains 10 species, approximating hot CNO, triple-α, and rp-breakout burning up through 56Ni, using the ideas from [16], but with modern reaction rates from ReacLib [17] where available. This network was used for the X-ray burst studies in [18], [19], and more details are contained in those papers.

triple_alpha_plus_cago

This is a 2 reaction network for helium burning, capturing the 3-α reaction and 12C(α,γ)16O. Additionally, 56Fe is included as an inert species.