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Jakub Skowronski
Reaction atlas

Reaction atlas

Reaction rates: how fast, and what if?

Every reaction in a star has its own rate, climbing steeply with temperature. Choose a site, find the slowest step, then change a rate and see what comes out.

Where it burns

Centre of the Sun today · 16 million K · 150 g/cm3 · 1 billion years

BottleneckCentre of the Sun today: the slowest step of the chain is 1H(p,e+ν)2H, 6.1 billion years on average. Everything else waits for it. What if it were faster? ↓

1 · How fastHow the rates change with temperature

10−2210−1910−1610−1310−1010−710−410−11020.010.10.020.05Temperature (GK)NA⟨σv⟩ (cm3 mol−1 s−1)↑ faster15 M☉16 MK · ☉ Sun2H(p,γ)3He3He(3He,2p)4He1H(p,e+ν)2H
16 million K

Drag across the chart, or use the slider below it, to change the temperature.

Not plotted: decays, which hardly depend on temperature (laboratory half-lives), with two exceptions: 26Al, whose short-lived isomer, populated by the heat, speeds up its decay above about 0.1 GK, and 7Be's electron capture, which depends on the electron density. All are in the next chart.

How to read 1H(p,e+ν)2H: two protons fuse, emitting a positron and a neutrino, and become deuterium.

Three reactions are already coloured: clear one to colour another.

Why heat matters so much

For 1H(p,e+ν)2H: few nuclei are fast (grey falling curve), and only fast ones tunnel through the Coulomb barrier (grey rising curve). The reactions happen where the two overlap, the Gamow peak.

Gamow window0621Energy (keV)

how many nucleichance to tunnelreactions

Gamow peak: E0 = 6.1 keV ± 3.3 keV · kT = 1.4 keV

The window is where a smooth (non-resonant) cross section reacts most. A narrow resonance inside it dominates instead (24Mg(p,γ) at 300 million kelvin through its 214 keV resonance, 25Mg(p,γ) at 80 million kelvin): the rate then follows the resonance's energy, not the window.

2Who is slowest

How long does a nucleus wait?

At these conditions, how long a nucleus waits, on average, before each reaction turns it into something else. Each dot is one reaction, on a logarithmic time axis.

The flow goes 1H → 2H → 3He, and ends as 4He. About half the 3He (52%) fuses with another 3He (ppI); the other half (48%) captures 4He and goes on through 7Be (ppII and ppIII). Waiting times at the start of the burn (for a nova, at its peak), with the scenario's initial composition: as the partners of a reaction are used up or built up, the waits change. Here 3He starts at its protosolar value, so its waits are shorter than in the Sun today.

Where the matter flows

The path a nucleus takes, from the network itself: each arrow's width is how much matter went through that step during the burn; side arrows are leaks out of the path.

(α,γ)7Be 48%(p,e+ν)slowest(p,γ)(3He,2p)1H2H3He4He

Curiosities: what if a rate were twice as fast?

All 21 curiosities →

One rate doubled, one burn, one result: a nucleus, the energy or the neutrinos. Every number comes from the explorer's own calculation.

  • Curiosity☉ Sun

    If 1H(p,e+ν)2H were twice as fast, this model of the Sun's centre would end up with about a sixth less hydrogen (−15%).

    • Biggest knock-on effect: 3He (+26%).
    • Energy output +62%; the first 1% of the hydrogen burns 46% sooner.

    The Sun's slowest step, never measured. A real Sun would cool down to compensate.

    One-zone model at 16 MK over 1 billion years. Real stars adjust. The energy is that of this gas at the model's temperature, not the star's luminosity: a real star would adjust its temperature to keep its luminosity. Doubling is a what-if, not the rate's actual uncertainty. How well this rate is known: well known.

    Try itHow we know this rate

  • Curiosity☉ Sun

    If 3He(α,γ)7Be were twice as fast, this model of the Sun's centre would end up with about two fifths more beryllium‑7 (+37%).

    • Energy output +12%; the first 1% of the hydrogen burns 14% sooner.

    Beryllium‑7 gives off the Sun's 7Be neutrinos, which Borexino counted on Earth.

    One-zone model at 16 MK over 1 billion years. Real stars adjust. The energy is that of this gas at the model's temperature, not the star's luminosity: a real star would adjust its temperature to keep its luminosity. Doubling is a what-if, not the rate's actual uncertainty. How well this rate is known: improving.

    Try itHow we know this rate

  • Curiosity☉ Sun

    If 3He(3He,2p)4He were twice as fast, this model of the Sun's centre would give off about a fifth fewer boron‑8 neutrinos (−21%).

    • Energy output −6%; the first 1% of the hydrogen burns 8% later.

    Two helium‑3 nuclei fusing directly skip beryllium‑7, so fewer boron‑8 neutrinos reach Earth.

    One-zone model at 16 MK over 1 billion years. Real stars adjust. The neutrinos are those of this gas at the model's temperature: a real star would adjust its temperature to keep its luminosity. Doubling is a what-if, not the rate's actual uncertainty. How well this rate is known: well known.

    Try itHow we know this rate

3What if

What if a rate were different?

Every rate is known only within an uncertainty, from a few per cent to a factor of ten. Choose one, change it, and see which nuclei come out different at the end of the burn.

Choose a reaction to change

1H(p,e+ν)2H
×1

Your changes

No rate changed yet.

The burn ran for 1 billion years. Precomputed with the same solver; change anything to recalculate in your browser.

What changes most

Final mass fraction after 1 billion years, changed ÷ unchanged. Bars to the right: more of that nucleus.

Change a rate to see what it does: for now every nucleus ends as in the unchanged burn.

Energy

  • Energy output, mean over the burn: 13 erg g−1 s−1; neutrinos carry away 3.4% of the energy released
  • Time to burn the first 1% of the hydrogen: 43 million years

The power of one gram of gas at the burn's temperature, neutrinos excluded: not the star's luminosity. A real star would adjust its temperature to keep its luminosity.

Abundances during the burn

Mass fraction of each nucleus against time.

10−610−510−410−310−210−111 s1 h1 yr1 MyrTimeMass fraction4He1H3He

Energy during the burn

Energy generation rate ε (neutrinos excluded) against time.

101021031041051061071081 s1 h1 yr1 MyrTimeε (erg g⁻¹ s⁻¹)ε

Which rate matters most?

Every rate doubled in turn, at the scenario's own conditions: the colour says how much each nucleus at the end of the burn follows it. +1: it doubles with the rate; −1: it halves. The last columns do the same for the energy: the mean power, the time the fuel lasts and the neutrinos.

For specialists

What you are looking at

The rates come from REACLIB, the library of reaction rates maintained by JINA, as pynucastro distributes it: for each reaction a seven-parameter formula fitted to the measured or calculated rate, with its source. Your browser evaluates that same formula. For reactions between charged nuclei the steepness comes from the Coulomb barrier: only the nuclei in the Gamow window take part, and a hotter gas has many more of them.

A nucleus's waiting time is one over the chance per second that a reaction transforms it: it depends on the rate, on the density and on how many partners are around (protons, nearly always). For a decay it is the mean life, the half-life divided by ln 2. In a cycle the slowest step rules: 14N(p,γ)15O in the CNO cycle, the fusion of two protons in the pp chain. Where a nucleus can go two ways the faster one wins, so the slowest step is taken along the path the flow follows: in a nova, 13N captures a proton long before it decays.

“What if” reruns the burn in a one-zone model: fixed temperature and density, the scenario's initial composition, and the network integrated in time with an implicit method, in a separate thread of your browser. The result is compared with the burn at the original rates. A one-zone model shows which reactions matter, and how much; it does not replace a model of a star. Each scenario's values and their source are under “Where these numbers come from”.

Credits, licences and sources

Reaction rates: the JINA REACLIB database (Cyburt et al. 2010), snapshot of 30 March 2025 as distributed with pynucastro; each rate's own source is listed with it in the specialist tables. REACLIB is free to use with citation. reaclib.jinaweb.org

The networks, the rate sources, the solar composition and the screening were exported with pynucastro (Smith et al. 2023; Willcox & Zingale 2018), BSD 3-Clause licence. The browser's solver is checked against pynucastro's own integration of the same networks. github.com/pynucastro/pynucastro

References

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