Gal Science: The Ages of Things -The Toast

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As The Toast searches for its one true Gal Scientist, we will be running a ton of wonderful one-off pieces by female scientists of all shapes and sizes and fields and education levels, which we are sure you will enjoy. They’ll live here, so you can always find them. 

Last year, in response to this (really badly written) article and its title (Earth’s Water May Be Older Than Previously Thought), Mallory tweeted: “isn’t ALL water the same age??” and “this is probably a dumb question but i have the same question with rocks, they’re all from the same Earth, how do they have different ages?” 

This is, in fact, not dumb. Even other geoscientists who are not specialists in the ages of things ask similar questions; recently a colleague asked me why we don’t consider how old atoms already were when they joined our solar system, which is closely related.

It doesn’t help that the article in question is unnecessarily confusing, thanks to a combination of dumbing down way too much for a non-scientist audience, extreme abbreviation, a lack of useful citations and links, and straight-up bad explanations. So for better reference, here is the actual scientific article abstract (full text behind a paywall), and this is one of the official press releases.

A very brief (and clearer) summary of the research study: it is unclear when volatiles like hydrogen, which is very important in today’s planetary budget (see: oceans, life, etc.), became part of the early accreting Earth. This is a subject of active debate and current research. This particular study – which looks like a really interesting and well-done study, but I am sure not everyone will agree with its conclusions – found that the exact isotopic compositions of the stable elements O, H, and N in different types of meteorites and Earth are all similar. That suggests that the different types of meteorites formed from similar initial material. The researchers interpret this to mean that the volatile elements were not delivered to the later-forming solar system bodies separatel (i.e., later on in the process), but were already present during early planetary accretion. Also, if the O and H were present on the Earth’s surface at an early stage in its accretion, the conditions would have been right for them to make water molecules and an early ocean.

The terminology that is used when referring to the ages of substances in the solar system and on Earth can be confusing for non-specialist readers, because it includes a lot of shorthand and the assumption of background knowledge. This latest study is just one example. So my goal here is to lay it all out in more detail, and then perhaps everyone can have an easier time reading about studies like this one.

1. Ages of atoms

How old are atoms? Shortest answer: depends.

Matter likely formed in the universe during the Big Bang, about 14 billion years ago (that age comes from the rate of universe expansion). Subatomic particles formed first (as a quark-gluon plasma*), and within minutes the smallest atoms formed: hydrogen, helium, lithium, beryllium. Mostly the first two, especially hydrogen. That process altogether lasted maybe 20 minutes. Most of the primordial matter is still around, so any given hydrogen atom (including on Earth and in the sun) could easily be about 14 billion years old.

Everything else, all other atoms, have been built from those basic building blocks by nuclear fusion in stars: smash two hydrogen atoms together, make some more helium; keep smashing, make the rest. How far a star gets down the periodic table depends on the star’s size, because the mass of the collapsing nebula cloud determines its temperature (gravitational collapse into a protostar = conversion of potential energy to kinetic energy = heat. The more mass falling in, the hotter the star. Stars get hot through contraction first, and then the very high temperatures trigger the self-sustaining fusion reactions). Higher temperatures mean more and faster flying atoms, which means more collisions — so temperature basically determines how energetic the smashing gets. The more energetic and frequent the smashing, the bigger you can make your nuclides – basically because some of the intermediate building steps aren’t stable and will fall apart unless you smash them into something else real fast.**

So, big stars from early in the universe made the non-hydrogen and non-helium matter. The bigger the star, the more heavier elements it could make. Everything heavier than iron in the periodic table requires a supernova, which is a neutron-cascade-triggered runaway fusion reaction. It’s not energetically favorable to make anything bigger than iron, so runaway fusion is necessary to make them. Obviously, since we have elements bigger than Fe around, that happened some time in the past.

Our solar system started as a very dispersed cloud of dust, like all nebulae. The dust was the product of the Big Bang followed by fusion in now-dead stars. And if you disturb a diffuse dust cloud in space, some of the particles will wind up closer to some of the others, triggering them to move (fall) towards each other by gravitational attraction. Which will make a blob of dust, which will have a higher gravitational attraction and attract even more of the dust in the cloud. The inward collapse makes the cloud spin because of angular momentum, like an ice skater pulling their limbs in for a fast spin. So if a nebula is disturbed, it can collapse on itself, creating one or more protostars surrounded by a rotating dust disc; if it gets hot enough to start fusing, it’s a star. And the matter that goes into the star and circles around it has the same elemental makeup that the nebula cloud did. Eventually the star is going to make new atoms through fusion, but that is mostly trapped inside the star – aside from rare solar mass ejections and the solar wind of tiny particles, that material cannot escape. In other words, the material rotating around the star in the disc is composed of the dust that was already there. The age of those atoms is variable: some are probably 14 billion years old (primordial Big Bang particles); some are much younger, from dead stars that exploded as supernovae and sent their dust back out into the universe.

Some of the dust in our solar disc eventually collided and accreted to make the Earth (here is an example of how this happens). So how old are the atoms on Earth? Anywhere from 14 billion years old to, well, today: bombardment of the planet’s surface and atmosphere by solar and interstellar radiation still creates newly fused atoms, we fuse a lot of them in our nuclear reactors, and radioactive decay when an unstable nuclide breaks apart also creates a new, different atom. These are all continuous, ongoing processes on Earth. Newly arrived material on Earth is also variable in age: some interstellar dust could be extra-solar-system material of unknown origin and age; ejected solar particles could be brand new; and meteors and meteorites are from elsewhere in our solar system were therefore made from the same dust in the solar disc that Earth was.

We cannot know the ages of the atoms on Earth or in the solar system. There is no reference point for comparison except the Big Bang, and no way to date individual atoms of unknown origin.*** 

2. Ages of rocks and minerals and molecules

Atoms, of course, mostly aren’t floating around freely. They are bonded to things: isolated molecules like they teach you about in introductory chemistry classes, polymerized liquids, crystalline mineral atomic lattices, ionic solutions, trees, cats. It turns out that we can in many cases determine the time at which a substance’s atoms came together, like the age of a molecule or mineral or pile of organic goo, even though we have no idea how old the individual atoms themselves are.

The Earth is a big ball of chemically bonded atoms, on average, and so we can determine the age of it. Even if the atoms are bonded in different substances, we can determine an average age of joining (like for a big pile of rocks stuck together, or even all the minerals in a single rock). Geologists refer to large, chemically-bonded units of things “reservoirs,” i.e., places where atoms go and are stored in isolation together for a while, like a water reservoir. If you add or remove some of the atoms, the total composition has changed and so that marks the start of a new reservoir. You can determine the ages of reservoirs, whether the reservoir is the entire Earth, a layer within the Earth, like the upper mantle, or a section of the solar system. Smaller things aren’t usually called “reservoirs,” but the same concept applies: a magma cools to form a new rock full of new minerals, and that event has an age. A rock is subjected to very high pressures and temperatures and all its mineral components recrystallize as new grains, and that event also has an age. Or fluids infiltrate a rock and react with it to produce new mineral grains. The age of a substance that is bigger than a single atom is essentially the age-of-coming-togetherness. And you can compare any two such ages: which happened first, the formation of Earth as a whole planet through accretion of solar-system-nebula-dust, or the arrival of volatile elements like hydrogen?

There is, of course, a gap between the theoretically possible and actually measurable. To measure an age, there must be a clock ticking somewhere in the reservoir so we can back out how long it has been running. Sometimes there’s not a good clock for the reservoir you are interested in. The ticking clocks are usually radioactive isotopes, which are present in trace quantities and decay at predictable rates over time. That rate is actually determined by the probability that a less-than-stable atomic nucleus will spontaneously break down: the balance between the strong atomic force holding nucleons (protons and neutrons) together vs. the repellant force of lots of positively charged protons jammed up against each other is delicate, and some combinations are inherently unstable. But the degree to which they are unstable is dramatically variable. Some nuclides (atoms, isotopes) are so unstable that they break down in seconds or milliseconds or less. Others can stick around for billions of years before they spontaneously come apart, ejecting a particle to create a new proton+neutron combination (a new atom).

The chance that an individual atom will spontaneously decay is a probability function: there is a minute chance it will happen tomorrow, and a proportionally greater chance it will happen within the coming year, but we can’t predict exactly when it will actually happen. Some of the atoms will survive longer than they “should,” through sheer dumb luck. But if you have a big pile of those atoms, probability predicts the overall rate of decay extremely accurately: a specific percentage of those atoms will, definitely, for-sure break down between today and tomorrow. I can’t tell you which of them will be the ones to go, but I can tell you exactly how many.

This means that radioactive decay clocks aren’t linear: the number of atoms that decays today is not the same as the number that will decay tomorrow. But the fraction of them that decays today and tomorrow is constant: it’s just that because some of them will decay today, fewer will be left to work with in the future. The loss of 50% of a pile of 100 atoms would mean 50 atoms decaying today; but then there are only 50 left, so 50% loss will only cause 25 to decay tomorrow. This is why radioactive decay for a particular isotope is expressed as either the half-life (how much time it takes to lose half of the atoms – in my example, one day), or the decay constant (proportional to the inverse of the half-life). Decay constants are measurable in the laboratory and known very precisely for radioactive isotopes of interest.

Exponential Decay

Knowing this, all you have to do is find a naturally-occurring radioactive isotope that is present in high enough concentrations in your reservoir to be detectable with modern instrumentation, whose decay constant is well-known, and whose half-life is appropriate for the timescales you are measuring: you need to be able to detect the change, so it can’t be too slow; but if your reservoir ran out of the parent 100 million years ago, it isn’t going to do you much good. That’s like the batteries of a stopwatch dying halfway through your measurement. And of course, you need to know what the daughter is: the decayed parents are gone, but you can figure out how much there used to be by counting the daughters that remain.

There is a list of appropriate radioactive parent-daughter pairs that fit these criteria for a range of timescales of interest: that is, appropriate half-lives for the timescale, measurable at natural concentration levels in common Earth materials, and well-characterized decay rates. There are other considerations: could either the parent or the daughter element in question have been perturbed (added or removed) since the event you are trying to date, meaning you aren’t measuring what you think you are measuring? Are there instrumental interferences to worry about during analysis that might make the data collection extremely difficult? Can you extract the parent and/or daughter in the laboratory to measure them at all? And very importantly: was there already some of the daughter naturally present in your reservoir before the clock started ticking for your event of interest? (Hint: yes, and you’ll have to correct for that.) If you can account for those things, you can measure ages in substances.

Unfortunately, Earth is rather incompletely mixed as a whole reservoir. We don’t have any original primordial Earth rocks or even single minerals available at the surface. The oldest mineral grains we have ever dated are over 4 billion years old, but the Earth is a dynamic, tectonically active, constantly self-recycling and self-burying system, and even those are not as old as the Earth planetary mixture itself. So to determine the age of the planet and solar system, we measure the ages of meteorites.

Meteoritics research has demonstrated that there are many different kinds of meteorites, from all kinds of solar system reservoirs that have (happily) landed as fragments on Earth recently enough for us to find them. We have materials that condensed at different distances from the sun and therefore at different temperatures and compositions.**** We have stuff that accreted at different times and therefore from different starting materials. Some came from large protoplanet-sized bodies with fully-differentiated internal layers (cores, mantles) that were then broken apart. Or they contain tiny preserved droplets from the earliest dust in the disc, before larger accreted rocks even existed.

And they all give us ages: the age of the start of the solar system; the age at which the first rocky bodies formed; and the age of bodies big enough to form a core, like the Earth. We have pieces of the moon know when it formed. And we can compare ages of newer reservoirs on Earth to the age of the meteorites and the inferred age of the Earth. So when a science article says water on Earth is the same age as the Earth, it means that Earth’s volatile hydrogen reservoir is the same age as the end of the major phase of planetary accretion,***** rather than being added during the late arrival of comets and water-rich meteorites. And that is the answer to Mallory’s question. It’s not a dumb question.

* Plasma: the fourth state of matter, similar to a gas but the particles are highly charged. Quarks and gluons are types of subatomic particles.

** A rather crude but fun and basic example of how this works is the stellar fusion 2048 game, located here.

*** There are a few exceptions, like short-lived isotopes that can only be here if they recently formed, or else they would have decayed away already; or the daughters of radioactive decay from ancient parent isotopes whose half-lives were relatively short, so they are the parents are entirely gone now (extinct).

**** It’s hotter near the sun, and some elements condense at higher temperatures than others, so the solar system is compositionally stratified.

***** The Earth is struck by some 200+ objects per year, most of them small, mostly landing in unpopulated areas like the oceans or unpopulated parts of continents. Those objects are now part of Earth’s reservoir. Accretion is still happening, just much more slowly now than when the solar system was still forming its major planetary bodies.

Lynne explores how magma is made by studying the mineralogical, chemical, and isotopic makeup of igneous rocks. She also teaches geology, plays music, dances, and hangs out with her fabulous fluffy pets.

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