Neutron Star Mergers and Heavy Element Synthesis

Jamie McCullough
March 20, 2022

Submitted as coursework for PH241, Stanford University, Winter 2021


Fig. 1: This depicts the binding energy per nucleon for different nuclei sizes. [8] (Source: Wikimedia Commons)

Everything that makes up what we touch, what we see, what we are, has a history. The study of cosmology is dedicated to understanding the history and future of our universe and all the contents within it. Most of what we interact with in our everyday life is known as baryonic matter that is, made up of protons and neutrons. In fact, despite the baryonic matter in the universe being mostly comprised of hydrogen and helium, the lightest of the elements, what we interact with on a daily basis tends to be what astronomers call metals or heavy elements with nuclei made up of many more protons and neutrons than hydrogen (which only has a single proton and electron). This essay will outline the origins of heavy elements, specifically discussing the processes that create them (so called nucleosynthesis), and what cosmic events are most responsible for generating these atoms.

Binding Energy and Nuclear Forces

The process of big bang nucleosynthesis is well established and accepted by the astronomical community, with the light element ratio observations supporting the idea that all particles in our universe originated from a hot, explosive beginning. This means that we generally believe the baryonic component of the very early universe, immediately following the big bang, to only be comprised of very light elements that could form before the temperatures cooled as the universe expanded. [1] This is leaves us with a starting point of roughly 75% hydrogen and 25% helium, around 14 billion years ago.

Naively, one might think that since nuclei are built from the same base particles, charged (proton) and uncharged (neutron) components might just naturally form nuclei of all sizes if they happen to run into each other. The real picture is complicated by a number of effects, the first of many being Coulombic forces, that is like-charges repelling one another, and the second being the strong force, which binds nucleons to one another at very short distances (and is also responsible for holding together the subatomic quarks that make up each nucleon). Protons within a nucleus will repel each other due to electrostatic forces, but will snap together if they are close enough to each other that the strong force dominates. This means that nuclei with larger radii are generally more loosely bound, because at these larger scales Coulombic forces become just as relevant as the strong force and work in opposition to it.

In everyday life, if we have something made of smaller building-blocks we can get the mass by summing all the pieces. This is not quite true for atomic nuclei, which tend to weigh less than the sum of their parts, and this is best explained by a non-zero binding energy of the nucleus, otherwise known as a mass defect. Since some nuclei can be more stable than others, the binding energy per nucleon changes considerably as the number of nucleons, the mass number A, increases as seen in Fig. 1.

This plot alone explains why nuclear fusion and fission can both release energy, as the elements on the left side become more stable (larger binding energy) with increasing A or fusing together, and the elements on the right become more stable by decreasing A or splitting apart. Iron-56 here sits at the peak of the plot, being the most stable. This binding energy is released when the nucleus forms so for example. Say that through fission some U-235 collides with a neutron to form Ba-144 and Kr-89, 215 MeV of energy will be released. This energy is released because Ba-144 and Kr-89 have higher binding energies than U-235. [2] It would take considerable energy to turn Ba-144 and Kr-89 into U-235 (the reverse reaction) for the same reason.

R-Process and S-Process: How Are Heavy Elements Made?

We know understand the basic idea of nuclear stability and the types of energy exchanges that can happen during fusion and fission. We've also established that chronologically, we start with only the lightest of elements. So how do they form?

Electrostatic forces generally repel protons from a nuclei at large distances because they are both positively charged. This is not true for the uncharged neutron. Increasing A (generating heavier nuclei) is therefore easier to do when adding neutrons, in a reaction like that below for some hypothetical element X with mass number A and atomic number (number of protons), Z: [1]

AXZ + n (A + 1)XZ + γ

This reaction might not result in a stable nucleus, and the resulting unstable nucleus can undergo something called beta decay, where it ejects an electron or positron. If a neutron undergoes beta decay, it ejects the electron and a neutrino (a very light, neutral particle) resulting in a leftover proton. Essentially, it is a mechanism that allows the nucleus to change its charge. If the beta decay reaction happens more quickly than the neutron-capture, the process is considered slow, or an s-process. This means that each nucleus likely has a chance to get into a stable state before adding another neutron. If neutron-capture is faster than the beta-decay, we call it rapid neutron capture, or the r-process. Some elements that require the r-process to be seen in the quantities we observe include Uranium and Gold alongside other heavy metals.

Where Does This Happen?

The conditions required for r-process involve large numbers of neutrons bombarding the nucleus. Consequently, the astronomical environments where it can happen are dense and energetic. The leading theory for some time was that exploding stars, supernovae, were responsible for most elements that could only be produced through the r-process. This idea is partly where Carl Sagan's famous "We are star stuff" quote originates, because most all of Earth and humanity is comprised of material that must have formed in stellar cores and ejected back into the universe at one point in time. Recent years has seen the r-process picture complicated by other potential contributors like black hole mergers, neutron star mergers, and to a much lesser degree, accretion disks around massive objects like black holes. [3]

Fig. 2: This figure shows the localization of the signal for GW170817 on the sky, near galaxy NGC 4993 (center of right panels) and a kilonova explosion that resulted from the collision of two neutron stars. The picture of this galaxy was taken on two separate occasions, the bottom panel being before the merger, and the top being taken shortly after. The joint optical, X-ray, IR and gravitational wave measurements of this event stand as one of the great feats of so-called "multi-messenger" astronomy. [4] (Source: Wikimedia Commons)

Neutron Stars

If stars explosively ejecting heavy fusion products into the universe do not account for the amounts of heavy elements we see in our galaxy, where could they come from? High energy events are required to generate the heaviest nuclei like Uranium, in regions where nuclei can be bombarded with neutrons on a very short timescale. The most massive compact objects in our universe are black holes, but material entering in a black hole by definition cannot escape for us to see and measure. Supernovae, on the other hand do tend to leave behind very dense remnants of degenerate matter, the spent stellar cores of massive stars. These are known by the moniker neutron stars because they are so dense that they are made almost entirely out of neutrons tightly packed together. In essence, the gravity has crushed the protons and electrons together, leaving the star as one giant nucleus of neutrons lined by heavy elements.

Neutron Star Mergers as the Main R-Process Contributor

The Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a binary merger event in August of 2017 by measuring the ripples in space time created by two objects spiraling inward. Previous events detected by LIGO were found to be black hole mergers, with the shape of the signal linked to the masses of the merging objects. As this initial detection provided a localization of where the merger happened on the sky, a gamma ray burst was independently measured with a short delay, and an optical counterpart was measured by several telescopes within an hour after the initial detection. More than a week later radio and x-ray astronomers detected counterparts in their own domains as well. [4] The gravitational wave signal indicated masses that were consistent with those of neutron stars, and the optical detection provided the first known visual data for a binary neutron star merger, producing a so called kilonova. In Fig. 2, we can see the optical follow up observations of the merger GW170817 that was first detected via LIGO, as well as the search area in the sky identified by the initial detection (seen from the contour plots). [4]

This detection was also able to disentangle r-process elements created from the event from those created in the s-process, by modeling the s-process created elements and ascribing the r-process to account for what was left over. The dynamical ejecta that produced the light seen in the kilonova was very well measured by many telescopes, and the event itself helped inform the merger rate for these kinds of objects. It was found that if more than 10% of the mass ejected during the merger was converted into r-process elements, that it could fully account for most r-process elements found in our galaxy. [5] It is important to note that our understanding of neutron star merger rates do spring from a single event, and at best our estimates of their frequency can only be thought of as first order.

With the advent of this measurement, neutron star mergers are thought to be both more common than previously expected as well as the main r-process contributor. [6] Supernovae are undoubtedly more common than neutron star mergers, but it seems that neutron star mergers produce a very large amount of heavy element ejecta. While another potential contributor to r-process elements could be neutron stars merging with black holes, it seems that this is a smaller factor in heavy metal creation than neutron star mergers alone. [7]

© Jamie McCullough. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] B. W. Carroll, An Introduction to Modern Astrophysics, 2nd Ed. (Cambridge University Press, 2017), pp. 542-543.

[2] J. F. Mulligan, Practical Physics: The Production and Conservation of Energy (McGraw Hill, 1980).

[3] L. Jin, "Constraints on R-Process Nucleosynthesis in Accretion Disks," Nature 350, 403 (1991).

[4] B. P. Abbott et al., "Multi-Messenger Observations of a Binary Neutron Star Merger," Asrophy. J. Lett. 848, L12 (2017).

[5] B. P. Abbott et al. "Estimating the Contribution of Dynamical Ejecta in the Kilonova Associated with GW170817," Astrophys. J. Lett. 850, L39 (2017).

[6] F.-K. Thielemann et al., "Neutron Star Mergers and Nucleosynthesis of Heavy Elements," Annu. Rev. Nucl. Part. Sci. 67, 253 (2017).

[7] H.-Y. Chen, S. Vitale, and F. Foucart, "The Relative Contribution to Heavy Metals Production from Binary Neutron Star Mergers and Neutron Star Black Hole Mergers," Astrophys. J. Lett. 920, L3 (2021).

[8] W. D. Loveland, D. J. Morrissey, and G. T. Seaborg, Modern Nuclear Chemistry, 2nd Ed. (Wiley, 2017), pp. 29-35.