Water that remembers how cold it was

The line beyond which ice counts as rock sat at about three astronomical units in the Sun’s disc, and the Earth formed well inside it, from material too warm to hold water as ice. Yet the Earth has oceans, a few times their mass again in its mantle, and an atmosphere that was once much wetter. The water came from somewhere beyond the line, and the question of where has stayed open: what a body is made of dates its formation rather than placing it, because the line itself moved, and the elemental ratios that might have located a birthplace turned out not to be unique.

There is a second kind of record, and it is not in the elements but in their isotopes. Hydrogen has a heavy form, deuterium, one atom in every fifty thousand or so in the gas the Sun formed from. In water the share is different from body to body, by up to a factor of fifty, and the differences were set by temperature: by how cold the water was when it formed, and whether it was ever hot enough afterwards to forget.

Where the line was #

The line in the figure is a snapshot. In the youngest, most actively accreting disc it sat several astronomical units out, swept inward as the disc’s own heating faded, and at any moment it divided the water that was vapour, and could exchange with the gas, from the water that was ice, and could not. A water molecule’s deuterium label records which side of that line it spent its last warm moment on. The ratio does not say where a body formed; it says how much of the water the body collected had been inside the line, and hot, at some point before it was locked up.

That is a weaker statement than a map, and a more useful one, because it is a quantity the disc’s physics predicts directly. A disc that mixed vigorously sent a lot of reset water outward and its outer bodies should have low ratios; a quiet disc kept its labels apart. The measured spread between the chondrites and the comets is therefore also a measurement of how well the Sun’s disc mixed.

Why cold water is heavy #

The chemistry that makes cold water rich in deuterium runs only in the cold. In a molecular cloud at ten or twenty kelvin, the ion that drives most of its chemistry, $\mathrm{H_3^+}$, swaps one of its hydrogens for a deuterium from HD, and the reverse reaction is suppressed because it needs a little energy — about two hundred kelvin’s worth — that the cold gas does not have. The deuterated ion passes its deuterium on to whatever it reacts with next, and the molecules that freeze onto grains as ice inherit the enrichment. Water ice in clouds that are forming stars ends up with a ratio of order a thousandth, fifty times the gas around it.

Heat undoes it. Water vapour in contact with hydrogen gas at a few hundred kelvin or more exchanges its hydrogen with the gas’s, and since there is vastly more hydrogen gas than water, the water’s ratio is pulled back towards the gas’s. Water that has been hot loses its cold label and takes on the protosolar one, about $2 \times 10^{-5}$, within a factor of a few. After that the ratio is fixed: ice freezing, rock forming, a body accreting, none of these changes it. Only escape does, because hydrogen leaves a planet more readily than deuterium does, and that is why Mars’s water, which has lost most of its hydrogen to space, is now several times richer than the Earth’s.

So a body’s ratio is a mixture of two labels — cold and inherited, or hot and reset — in the proportions in which its water had those two histories.

A mixture of two histories #

Read that way, each measurement places a body on a line.

On this reading the Earth’s oceans are about one-seventh inherited water and six-sevenths water that was once hot — and so are the carbonaceous chondrites. The comets that fell inward from the Oort cloud are about three-tenths inherited; 67P, a comet of the Jupiter family, over half. The numbers are relative rather than absolute, because both ends of the mixture are uncertain by factors of two — the cold end in particular, since the ratio in ice varies between clouds and with how cold each was. But the ordering is robust, and it says that the water in the inner solar system’s rocks and the water in its comets had different thermal histories, with the oceans firmly on the rocks’ side.

A ratio that rises outward #

The mixture becomes a map once the disc’s own structure is added. The inner disc was hot enough to reset water and the outer disc was not, and turbulence mixed the two.

In this simplest model, reprocessed water from the hot inner disc diffuses outward and mixes with the inherited ice, so the ratio rises steadily with distance from the Sun, and the place where it matches the oceans’ moves outward with time. During the first million years, when the asteroids were forming, it passes through the asteroid belt and the region just beyond the snow line — where the carbonaceous chondrites’ parent bodies grew. The comets, with their higher ratios, were assembled further out, where less of the water had ever been hot. The model’s numbers depend on the viscosity and on how fast water was carried inward again on drifting pebbles, which pulls the other way; its shape — a ratio that increases outward — is what the measurements show, from the rocks of the inner belt through the icy moons of Saturn to the Oort-cloud comets.

That makes the deuterium ratio, loosely, a thermometer for the history of a body’s water and a distance scale for where it was assembled — not because water was made differently at different distances, but because the fraction that had passed through the hot inner disc fell off outward.

How a comet’s ratio is measured #

The measurements are hard, and their difficulty is part of why the picture changed twice. A comet’s water is measured either remotely, from the faint emission lines of HDO molecules in its coma, or in place by a spacecraft flying through the coma with a mass spectrometer. The remote measurements need a bright comet and a sensitive telescope: Hartley 2’s was made with the Herschel space observatory in 2011, Wirtanen’s with an airborne telescope during its close pass in 2018. The in-place measurement of 67P was made by the Rosetta spacecraft’s spectrometer over two years in orbit around the comet, and it is the most precise ratio for any comet.

Both see the coma, not the nucleus, and the two need not be the same. Water sublimating from ice can fractionate slightly, and dust grains carry ice out into the coma where it sublimates later; Rosetta found the ratio in 67P’s coma varying with the comet’s activity, and later analysis suggested that the measured value may be biased upward by a few tens of per cent. The comets with ocean-like ratios are both hyperactive, shedding icy grains, which may mean their measured ratios are biased the other way. The scatter between comets is real, but its size is still being argued.

What escape does to the label #

The one process that changes a ratio after the fact is the loss of hydrogen to space, and two of the Earth’s neighbours show what it does. Hydrogen escapes a planet’s upper atmosphere more readily than deuterium, because it is half the mass and diffuses upward and out faster, so a planet that loses most of its hydrogen keeps a disproportionate share of its deuterium. Mars’s atmospheric water, measured by the Curiosity rover and from the Earth, has about six times the oceans’ ratio, and martian meteorites show the ratio rising through the planet’s history. Venus’s atmosphere has more than a hundred times the oceans’ ratio — the record of a planet that lost almost all its water to space, leaving the heavy fraction behind.

Read backwards, those ratios measure how much water each planet once had: the more enriched the remnant, the larger the fraction lost. The calculation depends on how fractionating the escape was, which depends on whether the hydrogen left as a gentle trickle or a blowing wind, and the inferred initial water of Venus ranges from a few metres to an ocean’s depth. But it means that the Earth’s own ratio may be a little above its source’s, and that a planet’s deuterium is a measurement of its atmosphere’s history as much as of its water’s origin.

The icy moons #

Enceladus, the small moon of Saturn whose south pole vents a plume of water from a subsurface ocean, has a ratio about twice the oceans’, like the Oort-cloud comets. Saturn’s moons formed far beyond the snow line, from material that had mostly kept its cold label, and their water — at least Enceladus’s — sits where the mixing picture would place it. The ratio of Saturn’s largest moon, Titan, is measured only in its methane rather than its water, and the moons of Jupiter, which formed closer in, have not been measured at all. A measurement of Europa’s or Ganymede’s water, which the spacecraft now on their way to Jupiter may make, would test the gradient in the one place between the asteroid belt and the comets where nothing is known.

Where the oceans came from #

The measurement’s sharpest use is to rule things out.

For most of the twentieth century the obvious source of the oceans was comets: icy bodies, rich in water, falling on the young Earth in large numbers. The deuterium measurements of Halley in 1986, and of Hyakutake and Hale–Bopp in the 1990s, all came out at about twice the oceans’ ratio, which means the oceans cannot be mostly cometary water of that kind — mixing comet water at twice the ratio with anything else can only bring the ratio down if the other source is lighter, and then the comets’ share is limited to the oceans’ excess over that source divided by the comets’ excess. With rocky water near the chondrites’ ratio, comets like Halley supplied at most a tenth or so.

The carbonaceous chondrites match. They contain up to a tenth of their mass as water bound in clay minerals, with a ratio within ten per cent of the oceans’, and they come from the outer asteroid belt, beyond the snow line but not far beyond it. An Earth that accreted a few per cent of its mass from such material would have received several oceans’ worth of water with the right label — and the Earth’s other volatile elements, nitrogen and the noble gases, point the same way.

Two discoveries complicated that. In 2011 the comet Hartley 2, from the Jupiter family, was measured at the oceans’ ratio, and in 2018 so was 46P/Wirtanen; meanwhile 67P, another Jupiter-family comet, came out at three and a half times it. The Jupiter-family comets are not one population with one label, and some of them could have supplied water indistinguishable from the oceans’. The question has moved to other isotopes: comets are rich in noble gases relative to water, and the Earth’s xenon carries a small cometary component — about a fifth of its atmospheric xenon — that limits the comets’ share of the water to well under a per cent by mass, because bringing more water would have brought more xenon than the atmosphere holds.

Other labels that agree #

Deuterium is not the only isotopic label water and its companions carry, and the agreement between them is what turned a suggestion into the standard picture. Nitrogen’s heavy isotope is enriched in comets’ ammonia and hydrogen cyanide, by factors of two or three over the Earth’s atmosphere, and the carbonaceous chondrites again sit close to the Earth’s value. The noble gases, especially xenon, show the cometary share is small. And the isotopes of rock-forming elements — chromium, titanium, molybdenum — divide every meteorite into two families that formed on opposite sides of a barrier, and the Earth’s mantle carries a small but measurable admixture of the outer family, consistent with a late delivery of a few per cent of its mass from beyond Jupiter.

Each label is set by a different process — deuterium by cold ion chemistry, nitrogen by self-shielding of light in the cloud’s outskirts, the rock-forming isotopes by which stellar debris was mixed into which part of the disc — and they disagree about almost nothing. Where the elemental ratios of the condensation staircase could not locate a birthplace uniquely, because more than one place gives the same mixture, several independent isotopic labels together narrow the possibilities to one region: the outer asteroid belt, and some of the Earth’s own building blocks.

A further complication from inside the Earth #

The oceans’ ratio is not necessarily the Earth’s. Water deep in the mantle, sampled by lavas from the deepest plumes, has been measured with a ratio about a quarter lower than the oceans’, closer to the chondrites at the low end and moving towards the protosolar value. That has been read as a sign that some of the Earth’s hydrogen came directly from the gas of the Sun’s disc, dissolved into a magma ocean while the young Earth was wrapped in a captured hydrogen atmosphere — an atmosphere whose survival depended on how fast the young Sun spun. The oceans may then be a mixture of three sources rather than two, and their ratio a little higher than their source’s because the light hydrogen escaped preferentially in the planet’s first hundred million years.

The enstatite chondrites add a fourth possibility. These are rocks from the inner solar system, formed at the same place and with the same isotopes as the Earth’s own building blocks, and long assumed to be dry. Measured carefully in 2020, they hold enough hydrogen to have given the Earth several oceans’ worth, with a ratio close to the mantle’s. If the Earth’s own building blocks were that wet, the water need not have been delivered from beyond the snow line at all.

What the ratio cannot say #

The ratio fixes how much of a body’s water was ever hot. It does not fix where the body formed, because the same ratio can be reached by a body near the snow line early or one further out later, as the moving curves of the third figure show. It cannot tell the outer asteroid belt from a population of comets with the same ratio, and Hartley 2 shows that such comets exist. And it is changed, after the fact, by escape: any body that has lost a large share of its hydrogen to space has a ratio higher than the one it started with, which is why the measurement is reliable for comets and asteroids, which hold their water as ice or minerals, and less so for planets with atmospheres.

Still open: how much of the Earth’s water was there from the start #

The deuterium ratio narrowed the question from “comets or asteroids” to “which asteroids, and how much from inside”, without settling it. If the Earth’s building blocks were as wet as the enstatite chondrites suggest, the oceans are mostly native and the late delivery from beyond the snow line was a topping up. If they were dry, the oceans were delivered, mostly from the outer belt, by bodies that crossed Jupiter’s orbit to reach the inner solar system. The two pictures predict different ratios for the deepest mantle water and different amounts of water for Mars and Venus, and the samples that would distinguish them — the oldest mantle reservoirs, and water from the inner planets measured before it escaped — are the ones that are hardest to reach.