Inferring the role of binary neutron star mergers in r-process nucleosynthesis with multi-messenger observations using Cosmic Explorer and Einstein Telescope

This paper proposes a method using third-generation gravitational-wave detectors (Cosmic Explorer and Einstein Telescope) to measure the fractional contribution of binary neutron star mergers to cosmic r-process nucleosynthesis by analyzing the redshift-dependent correlation between merger event rates and r-process abundances, achieving a precision of approximately 5–6% for both multi-messenger "bright-sirens" and "dark-sirens" scenarios.

The Gist

The Big Mystery: Where Do Heavy Elements Come From?

Imagine the universe as a giant kitchen. The "ingredients" for the heavy elements in our bodies (like gold, platinum, and uranium) are created in a process called the r-process. Scientists have known for a long time that this happens during violent cosmic events, but they are still arguing over which event is the main chef.

There are two main suspects:

1. Binary Neutron Star (BNS) Mergers: Two dead, super-dense stars crashing into each other.
2. Rare Supernovae: Exploding stars that spin incredibly fast or collapse into black holes.

We know the first suspect (neutron star mergers) can cook up these elements because we saw it happen once (the famous GW170817 event). However, we aren't sure if they do all the cooking, or just a small part of it. Some evidence suggests they might be too slow to explain why heavy elements existed in the very early universe.

The New Idea: A Cosmic "Receipt" Check

The authors of this paper propose a new way to solve this mystery. They suggest we stop looking at just one event and start looking at the entire history of the universe as a giant ledger.

Think of it like this:

• The Gravitational Wave (GW) Detector is a counter. It counts how many times two neutron stars crash into each other across the universe.
• The Telescope is a spectroscopist. It measures how much "heavy element soup" (r-process abundance) exists in galaxies at different times in the past.

The authors' method is to compare these two lists. If neutron star mergers are the only source of heavy elements, the number of crashes and the amount of heavy elements should rise and fall in perfect sync. If they are not the only source, the two lists will drift apart.

The Time Machine: Looking Back in Time

To do this, the scientists need to look far back in time. They propose using future, super-powerful "time machines" (telescopes and detectors) called Cosmic Explorer and the Einstein Telescope.

These machines will be able to:

1. Count the crashes: Detect thousands of neutron star collisions from billions of years ago (high redshift).
2. Taste the soup: Measure the heavy elements in galaxies that existed billions of years ago.

The paper simulates what would happen if we used these machines for one year of observation. They created a "mock" database (a fake universe) to test their math.

The Two Scenarios: Bright vs. Dark Sirens

The paper tests two different ways of gathering data, using a "siren" analogy:

1. The "Bright Siren" (The Ideal Case):

   • Imagine a crash happens, and it also sends out a flash of light (like a kilonova or a gamma-ray burst) that our telescopes can see.
   • This light tells us exactly where the crash happened and how far away it is. It's like seeing a car crash and the license plate clearly.
   • Result: This gives very precise data.

2. The "Dark Siren" (The Harder Case):

   • Imagine a crash happens, but there is no flash of light. We only hear the "sound" (gravitational waves) but can't see the source.
   • We have to guess the distance based on the sound alone, which is fuzzier. It's like hearing a crash in the dark and guessing where it happened.
   • Result: This is less precise, but the paper shows it still works well enough.

What Did They Find?

Using their mathematical "receipt check," the authors found that:

• Precision: Even in the "Dark Siren" scenario (without light), they could determine how much of the heavy elements come from neutron star mergers with about 94–95% accuracy (meaning a 5–6% margin of error).
• The "Delay" Factor: They could also figure out how long it takes for neutron stars to merge after they are born. Do they crash immediately, or do they wait billions of years? Their method can measure this "waiting time" quite well, though it's slightly harder than measuring the total amount of elements.
• The Verdict: If neutron star mergers are responsible for a significant chunk (more than 10%) of the universe's heavy elements, this method can prove it.

The Bottom Line

This paper doesn't claim to have solved the mystery yet because we don't have these super-telescopes built yet. Instead, it is a blueprint.

It says: "If we build these next-generation detectors and start measuring heavy elements in distant galaxies, we will finally be able to count exactly how much of the universe's gold and uranium comes from crashing neutron stars versus exploding stars."

It turns the question from "Who is the chef?" into a math problem we can actually solve by comparing the number of crashes to the amount of food on the table.

Technical Summary

Technical Summary: Inferring the Role of Binary Neutron Star Mergers in r-process Nucleosynthesis with Multi-messenger Observations

Problem Statement
The cosmic origin of rapid neutron-capture (r-process) elements remains a fundamental open question in astrophysics. While binary neutron star (BNS) mergers are confirmed r-process sites (e.g., GW170817), their exclusive dominance is challenged by chemical evolution studies. These studies highlight discrepancies regarding the delay times of BNS mergers relative to star formation, observed BNS rates by current gravitational-wave (GW) detectors, and retention issues in low-mass halos. Conversely, rare classes of core-collapse supernovae (CCSNe), such as magnetorotational SNe and collapsars, offer "prompt" enrichment but lack definitive observational signatures of r-process production. Current methods relying on local stellar archaeology or chemical evolution models face degeneracies between star formation history, merger rates, and yield assumptions.

Methodology
The authors propose a novel correlation technique to measure the fractional cumulative contribution of BNS mergers ($F_{\text{BNS},z_0}$) to the total cosmic r-process abundance. The method exploits the redshift-dependent correlation between the total number of observed BNS GW events ($N_{\text{GW}}$) and the average r-process abundances ($Ab_{\text{El}}$) of galaxies at redshifts $z \lesssim 1$.

1. Theoretical Framework: The method assumes that both $N_{\text{GW}}(z)$ and $Ab_{\text{El}}(z)$ are functions of the cosmic star formation history ($\psi_{\text{SF}}$). By defining a correlation function $K(\theta) = N_{\text{GW}}(z) / Ab_{\text{El}}(z)$, the dependence on the star formation history is eliminated, rendering the correlation sensitive primarily to the BNS delay-time distribution (DTD) parameters (minimum delay $t_{\text{min}}$ and power-law index $b$) and the fractional contribution $F_{\text{BNS},z_0}$.
2. Modeling:
   • GW Events: The BNS merger rate is modeled as a convolution of the star formation rate with a power-law DTD ($D(t) \propto t^b$ for $t > t_{\text{min}}$).
   • Abundances: A cosmic chemical evolution (CCE) model is employed, assuming r-process enrichment arises from two sources: BNS mergers (delayed) and "prompt" r-process CCSNe (rCCSNe).
   • Scenarios: The analysis considers two limiting observational scenarios for third-generation (3G) GW detectors (Cosmic Explorer and Einstein Telescope):
     • Bright Sirens: GW events with electromagnetic (EM) counterparts, allowing precise host galaxy redshift determination.
     • Dark Sirens: GW events without EM counterparts, relying on luminosity distance-redshift conversion with larger uncertainties.
3. Statistical Analysis: The authors employ Fisher information matrix forecasts to estimate the precision of parameter recovery. They generate mock data for $N_{\text{GW}}$ and $Ab_{\text{Eu}}$ (using Europium as a tracer) incorporating expected observational uncertainties, including counting statistics, redshift errors, and intrinsic scatter in abundance measurements.

Key Contributions and Results
Using Fisher forecasts with a fiducial scenario of two Cosmic Explorer (CE) detectors and one Einstein Telescope (ET) observing for one year, the paper demonstrates the following:

• Precision on $F_{\text{BNS},z_0}$: The method can estimate the fractional cumulative contribution of BNS mergers to the cosmic r-process with a precision of $\lesssim 5-6\%$ at $1\sigma$ for fiducial scenarios where $F_{\text{BNS},z_0} \gtrsim 0.1$. This precision holds for both bright-siren and dark-siren scenarios, as the estimation is dominated by the uncertainty in the abundance proxy rather than the GW redshift uncertainty.
• DTD Parameters: The method yields estimates for the DTD power-law index $b$ comparable to existing constraints from short gamma-ray burst (GRB) studies (precision $\lesssim 10-20\%$). However, the minimum delay time $t_{\text{min}}$ is less tightly constrained (uncertainty $\approx 100-150\%$) at the fiducial value of $t_{\text{min}} = 0.2$ Gyr, due to the weak sensitivity of the average delay time to $t_{\text{min}}$ when $t_{\text{min}} \ll t_{\text{max}}$.
• Redshift Requirements: The signal-to-noise ratio (SNR) for constraining $F_{\text{BNS},z_0}$ to within $\lesssim 20\%$ requires observations of r-process abundances and GWs out to $z \lesssim 0.7$. Constraints on the DTD parameters $b$ and $t_{\text{min}}$ improve with observations extending to $z \lesssim 1.0$.
• Independence from Star Formation History: The correlation technique is shown to be largely independent of the underlying cosmic star formation history, isolating the physics of the r-process sources.

Significance and Claims
The authors claim this method provides a robust, model-independent way to quantify the role of BNS mergers in cosmic r-process nucleosynthesis using future 3G GW and electromagnetic data.

• Resolving Degeneracies: Unlike previous chemical evolution studies that struggle with degeneracies between merger rates, yields, and star formation histories, this correlation method directly links the event rate to the chemical yield.
• Science Case for High-Redshift Abundances: The paper argues that while local stellar archaeology can reconstruct abundance trends, this method provides a compelling science case for identifying signatures of neutron-capture elements in galaxies beyond the local Universe ($z \gtrsim 0.1$).
• Broader Implications: Accurate determination of BNS DTD parameters via this method would improve the identification of host galaxies for multi-messenger follow-up, refine constraints on cosmological parameters via standard sirens, and inform models of BNS formation channels (e.g., common-envelope phases).

The authors remain modest regarding the feasibility of obtaining the necessary abundance data at high redshifts, noting that while progress in continuum spectroscopy and gas-phase abundance inference (e.g., via JWST) is promising, the realization of these measurements remains an open challenge. The method is presented as a tool to be applied once such data becomes available, or as a motivation to develop the necessary observational capabilities.