INTERACTIVE COMPANION · FIELD NOTES · GEOCHEMISTRY

The Assay Bench

A live model accompanying “The Core Is Leaking”

Nine parts per million. That is the whole claim. Hawaiian basalts carry more ruthenium-100 than mantle rock has any way to make, and exactly one reservoir on Earth has both the right isotopic composition and enough ruthenium in it to shift a rock's ratio by that much. It is the core, which geology spent a century describing as sealed.

Two calculators sit below. The first turns a measured isotope excess into a mass fraction of core metal. The second pushes that fraction through a mass balance and weighs the gold. Both are the club's own simplified model rather than the paper's analysis, and every number they print can be checked by hand against the equations printed beside them.

Model 1. How much core do you need?

Our first attempt was wrong. We divided the measured excess by the core's assumed composition, got 36%, and spent a happy four minutes admiring a Hawaiʻi made of one third liquid iron. The article keeps the wreckage in §5.

Isotope ratios do not mix by mass. They mix weighted by how much of the element each side brings to the pot. A kilogram of core metal carries roughly 800 times more ruthenium than a kilogram of mantle does, so the core's vote is 800 times louder than its weight. Written out, with $f$ the mass fraction of core, $C$ the ruthenium concentrations and $\varepsilon$ the compositions:

$$f \;=\; \frac{C_{m}\left(\varepsilon_{\text{obs}} - \varepsilon_{m}\right)}{C_{c}\left(\varepsilon_{c} - \varepsilon_{\text{obs}}\right) + C_{m}\left(\varepsilon_{\text{obs}} - \varepsilon_{m}\right)}$$

Put the ambient mantle at $\varepsilon_m = 0$, divide top and bottom by $C_m$, and the only chemistry left is the concentration ratio $C_c/C_m = 4000/5 = 800$. That single line of algebra is everything the plot draws. Notice that the curve bends. It has to. Add enough core metal and the mixture stops being mantle, so the ratio stops responding.

Measured ε¹⁰⁰Ru excess +9.0 ppm Start at the published Hawaiian mean of +9. Kīlauea Iki on its own reads +11, and the Napali Member on Kauaʻi reads +17. Try those. Watch how fast the answer climbs: doubling the excess more than doubles the core fraction, because the curve is steepest near the origin. Analytical 2σ 3.0 ppm 3 ppm is the error on a mean of many runs. Push it up to 13, the scatter on a single run, and watch the shaded band swallow the dashed measurement line. The verdict underneath refuses to make a claim once that happens. Core ε¹⁰⁰Ru +25 ppm Nobody has ever held a piece of the core, so this is an educated guess somewhere between +15 and +35. Drag it to 15 and watch the required core fraction nearly triple while the measurement stays put. This is the softest joint in the model. Tungsten cross-check Leave it on for now. It grades the ruthenium answer against a second isotope system that had no say in producing it. Switch it off to see how much weaker the argument gets on ruthenium alone.

core fraction f: – that is: – predicted μ¹⁸²W: –

–

Why the tungsten carries more weight than the ruthenium

Any single isotope anomaly has an escape route. Maybe the standard was contaminated. Maybe there is a mantle component nobody has named yet. What makes the core story awkward to dismiss is that a second, chemically unrelated system has to agree, because both signatures were set by the same event: metal draining to the centre of the planet before the late veneer of meteorites arrived.

So the mixing fraction you compute from ruthenium makes a prediction about tungsten, and nobody gets to adjust it afterwards. The tungsten arithmetic is the same equation with different numbers. The core holds about 36 times more tungsten than the mantle, at a μ¹⁸²W near −220 ppm. Feed the ruthenium answer in and the prediction comes out at about −5.5 ppm. Hawaiian basalts measure roughly −5 to −12. Two clocks, set independently, reading nearly the same time.

Drag the core composition slider and watch the two numbers move together. They are not free to disagree, and that is the point.

Model 2. The gold ledger

Ruthenium is only the tracer. It travels with company, and the company includes most of the planet's gold. If a fraction $f$ of core material rides the Hawaiian plume upward, gold arrives with it every year, and the amount is one multiplication:

$$\dot{M}_{\mathrm{Au}} \;=\; M_{\text{basalt}} \; f \; C^{\mathrm{Au}}_{c}$$

Basalt mass per year, times the core fraction from Model 1, times the gold concentration in core metal. Nothing clever happens here, and the ledger inherits every uncertainty sitting upstream of it. Change the excess in Model 1 and this one moves too.

Plume basalt output 0.43 ×10¹² kg/yr 0.43 is 0.15 km³ of magma a year at a density of 2,900 kg/m³. The bottom of the slider is roughly Kīlauea's measured supply on its own. Gold scales straight with this one, which is why the curve on the right of the panel is a straight line. Au in core metal 525 ppb Core gold is inferred from meteorites and from how metal and silicate share elements, never measured. 300 to 800 ppb covers the published spread. Run both ends and notice that the story survives either one. Hotspot lifetime 85 Myr This moves only the cumulative total at the bottom right. 85 Myr is the rough age of the Hawaiian–Emperor chain. Treat the running total as an order of magnitude, because output has grown several-fold along that chain. Melt scavenging The conservative setting assumes gold rides along passively. Switch to the second and the melt collects gold from 12.5 times its own mass of source rock. Everything multiplies by 12.5, which is why we do not quote it as the headline.

core metal: – core gold: – one wedding band every – over the hotspot's life: –

Club central estimate: 159 kg of core-derived gold per year
68% range: 90 to 301 kg/yr
Ring cadence: one 4 g band every 13.3 minutes
Over 85 Myr: about 13.5 million tonnes, or 61× all the gold ever mined
Core share of the gold: 17%, so most of it is still ordinary mantle gold

What would break this

The honest failure modes deserve naming. The core end-member composition is inferred rather than sampled, and there is no piece of the core to check it against. An unrecognised reservoir in the deep mantle carrying a core-like signature would explain the same data with no leakage at all. And the excess is small enough that a systematic analytical bias of the same size would wipe it out.

Try this. Push the analytical uncertainty in Model 1 up until the error bar swallows the signal, then read the verdict line. The measurement gets harder and the conclusion gets weaker, and you can see why this paper needed a decade of mass-spectrometry development before anyone could write it.

Then try the other one. Set the core composition to +15 ppm, its lowest permitted value. The required core fraction jumps from 0.070% to 0.187%, the gold ledger jumps with it, and the tungsten prediction slides toward the far edge of the observed window. A factor of 2.3 in a quantity nobody has measured moves the answer by a factor of 2.7. That is the weak joint, and hiding it would be the one dishonest thing this page could do.