What Jupiter kept of the Sun's siblings

Three interstellar objects have been seen passing through the solar system — ʻOumuamua in 2017, Borisov in 2019 and a third in 2025 — and each arrived at tens of kilometres a second and left again. The essay on what Jupiter keeps worked out why. A flyby of Jupiter turns a body’s velocity relative to the planet without changing its size, and can remove at most a few kilometres a second from its speed relative to the Sun; a visitor arriving with more than that to spare cannot be kept. Today’s visitors move like the stars of the Galactic disc, at tens of kilometres a second relative to the Sun, and only the slowest fraction of a per cent are ever captured.

That essay ended on a different epoch. The Sun did not form alone. It formed in a cluster of a thousand or more stars moving together, within a few kilometres a second of one another, and while their planetary systems formed they ejected small bodies by the trillion — at speeds of a few kilometres a second, the very speeds at which Jupiter captures efficiently. Simulations of that phase have suggested that a large share of the Sun’s distant comets may have been captured from its siblings. The question this essay asks is narrower and can be answered with the same arithmetic as before: how much of that capturing could Jupiter have done?

The answer comes in two parts that point in opposite directions. Jupiter’s captures from the cluster outnumber everything it has captured since by a factor of hundreds. And they are still too few to matter.

Evidence that there were siblings #

The birth cluster is inferred rather than observed, and the inference rests on three kinds of evidence. Most stars form in clusters — the young stellar groups within a kiloparsec of the Sun hold hundreds to thousands of members — so a cluster birth is the default unless something argues against it. The Sun’s oldest solids carried short-lived radioactive elements, some of which are most easily explained by a nearby massive star’s winds or supernova within a few million years of their formation. And the outer solar system has orbits that the planets alone cannot make: Sedna’s perihelion lies at seventy-six astronomical units, far beyond Neptune’s reach, and the disc of small bodies beyond Neptune ends abruptly near fifty, both of which are natural outcomes of a passing star at a few hundred astronomical units — a close encounter that is likely in a cluster and almost impossible in the field today.

Together they suggest a cluster of a thousand to ten thousand stars, dense enough to have perturbed the Sun’s outer disc and short-lived enough not to have destroyed it. The figures below take a thousand stars per cubic parsec as the middle case and draw the others beside it.

The speeds of a crowd that was born together #

A body ejected from one of the Sun’s siblings passes the Sun at a speed set by two things: how fast its own star was moving relative to the Sun, and how fast it left that star.

The stars of a young cluster have a velocity dispersion of about a kilometre a second, set by their mutual gravity, and like any cluster it slowly boils itself away as encounters fling its lightest members out; the Sun’s left within a few hundred million years at most. The bodies their planets fling out leave with speeds comparable to the escape speeds from the planets that eject them — a few kilometres a second for giant planets at a few astronomical units — and once clear of their star they move through the cluster at roughly that speed plus their star’s. The combined distribution peaks at two or three kilometres a second. Nearly all of the siblings’ bodies arrive below five.

Today’s visitors are a different population. They have been released by stars throughout the Galaxy’s history, and they share their parent stars’ motions relative to the Sun — tens of kilometres a second, with a long tail. Fewer than one in two hundred arrives below five kilometres a second. The two distributions barely overlap, and the boundary between them is where Jupiter’s ability to keep a body ends.

How a flyby keeps anything at all #

The mechanism is worth restating, because everything in the calculation follows from it. A body falling into the solar system from interstellar space is on an orbit that has no period: a hyperbola about the Sun, with its speed at every point exceeding the local escape speed by an amount fixed far away. Jupiter can change that only by a close encounter, and an encounter is itself a hyperbola, this time about Jupiter. Relative to Jupiter the body arrives and leaves at the same speed; what the encounter does is turn its velocity, by an angle that depends on how close it passes — the geometry of aiming at a plane instead of at a planet, in which the miss distance decides everything.

Turning a velocity relative to Jupiter changes it relative to the Sun, because Jupiter is moving at thirteen kilometres a second. A turn that points the body’s velocity against Jupiter’s motion lowers its speed relative to the Sun, and if the speed falls below the local escape speed, the body is bound. This is the same exchange that lets a spacecraft steal speed from a planet, run backwards, and it has the same limit: the largest change Jupiter can make is about twice its own orbital speed times the sine of half the turn, and the turn is capped by how close the body can pass without hitting the planet. A body arriving with more excess speed than Jupiter can remove passes through untouched in every geometry.

So capture is a threshold phenomenon in speed, and the threshold is a few kilometres a second. Below it, a useful fraction of the bodies that reach Jupiter’s neighbourhood are kept; above it, almost none. The whole difference between the birth cluster and today is which side of that threshold the passing bodies were on.

Kept a thousand times more readily #

Capture depends on speed twice. A slow body is focused by the Sun’s gravity, so more of the slow bodies passing through the neighbourhood actually reach Jupiter’s orbit; and once there, a slow body needs only a small turn of its velocity to be left bound.

The capture rate per unit density — captures a year for each body per cubic astronomical unit of space — is a single number that turns a population’s density into a rate. For today’s visitors, averaged over their speed distribution, it is about four thousandths. For the siblings’ bodies it is about four: twelve hundred times larger. Most of the factor comes from the capture probability itself, which is a few tens of per cent at two kilometres a second against a fraction of a per cent at the slow edge of today’s visitors, and the rest from gravitational focusing, which multiplies the flux of slow bodies past Jupiter by the square of the ratio of the escape speed to the arrival speed.

That ratio is not a refinement. It is the reason the cluster matters at all. The same Monte Carlo of flybys that gives today’s rates, run at the cluster’s speeds, says that for a few tens of millions of years the Sun’s environment was arranged almost perfectly for Jupiter to keep what passed.

How crowded the cluster was with bodies #

A rate per unit density needs a density. The density of free bodies in the birth cluster depends on how many each star ejected, how densely the stars were packed, and how long an ejected body stayed in the cluster before leaving it.

The numbers of bodies ejected are not known directly, but they are constrained by the density of interstellar objects today. The three detected so far imply a density of about two tenths of a body of ʻOumuamua’s size per cubic astronomical unit of interstellar space — which, spread over the Galaxy’s volume and its stars, means each star has ejected something like $10^{15}$ to $10^{16}$ such bodies over its life. Most of that ejection happens while its giant planets are clearing their surroundings, in the first few tens of millions of years.

In the birth cluster those bodies were packed into a parsec. With a thousand stars per cubic parsec, each ejecting $10^{16}$ bodies over thirty million years, and each body crossing the cluster in half a million years, the free bodies passing the Sun numbered about nineteen per cubic astronomical unit — a hundred times today’s density. The field is the ejecta of every star the Galaxy has ever made, spread through its whole disc; the cluster was its own stars’ ejecta, concentrated for as long as they took to leave.

Almost every capture, from the siblings #

Multiply the two.

A density a hundred times higher and a capture rate per unit density twelve hundred times higher make a capture rate about a hundred thousand times today’s. Sustained for the thirty million years of the cluster phase, it amounts to some billions of captured bodies — against about three million captured from the field in all the time since. Whatever the cluster’s exact density, the conclusion is the same: almost everything Jupiter has ever captured, it captured from its siblings, in the first one per cent of its history.

That is the surprising half of the answer. Interstellar objects are now discovered as rare, fast curiosities, and a captured one would be a rarity among rarities. In the solar system’s first tens of millions of years they were neither rare nor fast, and Jupiter was a net collecting them at the rate of tens a year.

A crowd that came and went #

A capture by one flyby is not permanent. The captured orbit still crosses Jupiter’s, and the next close encounter, a few thousand or tens of thousands of years later, can throw the body out again or send it into the Sun.

So the captured population is a balance between capture and loss, and during the cluster phase it was large: with a survival time of a hundred thousand years, some eight million of the siblings’ bodies were on temporarily bound orbits through the planetary region at any moment, against perhaps seventy of today’s visitors now. The young solar system’s population of small bodies was being stirred continuously by bodies that had formed round other stars — passing through, being caught, being thrown out again.

That stirring had consequences that are easier to estimate than the captures themselves. Each captured body that later struck a planet delivered material from another star’s disc. The rate of such impacts during the cluster phase would have been tiny compared with the bombardment by the Sun’s own planetesimals, which were far more numerous; but it is a reminder that the solar system was not chemically closed while it formed.

Too few to matter beside the Sun’s own #

Billions of captures sounds large until it is compared with the Sun’s own small bodies.

The Sun’s distant cloud of comets holds, on the usual estimates, a few hundred billion bodies larger than a kilometre, and by the usual size distribution something like $10^{14}$ of ʻOumuamua’s size. Jupiter’s captures from the cluster, even if every one of them had survived, would be two parts in a hundred thousand of that. And they did not survive: a captured orbit that crosses Jupiter’s is short-lived, and only a small fraction of such bodies are scattered onto orbits that keep them, either in the distant cloud or in the scattered disc beyond Neptune. With a survival fraction of a per cent the siblings’ bodies left by Jupiter’s captures are a few tens of millions — undetectable among the Sun’s own by any test of composition yet devised.

The same arithmetic run for the Sun’s own disc shows why. The Sun’s planets ejected their own $10^{16}$ bodies during the same epoch, and kept a share of them in the distant cloud. The Sun kept a per cent or more of its own ejecta — some hundred trillion bodies — while Jupiter, catching the siblings’ bodies one flyby at a time, kept a few billion and lost most of those.

The route that could have worked #

None of this rules out the possibility that the Sun’s comets came partly from its siblings. It rules out Jupiter as the agent. The mechanism the simulations found works differently and on a different scale.

A body ejected slowly from one star, wandering through a cluster, can end up bound to another star not by a close encounter with a planet but by the cluster’s own gravity. As the cluster disperses, its mean field changes slowly, and bodies that happened to be within tens of thousands of astronomical units of a star, moving slowly relative to it, are left bound when the cluster’s gravity stops competing — captured into wide, loosely bound orbits like the distant cloud’s. That capture happens at distances a hundred thousand times larger than Jupiter’s orbit, where the volume swept is correspondingly enormous, and it needs no planet at all. Its efficiency depends on the cluster’s density and how quickly it dispersed, and the simulations found it could make the captured share of the distant cloud anything from small to most.

The Jupiter route and the cluster route are distinguishable by where they put their bodies. Jupiter’s captures sit on orbits crossing the planetary region, at semi-major axes of tens to hundreds of astronomical units, and are mostly lost within a million years; the cluster’s sit in the distant cloud and stay. Comets arriving from the distant cloud today, on their first passage through the planetary region, are the population in which any siblings’ bodies would now be found.

What the arithmetic assumes #

The cluster is uniform and steady. The density of free bodies is drawn for a uniform cluster with a constant ejection rate over thirty million years. Real clusters are clumpy, their stars form over a few million years, and they disperse; the number of bodies passing the Sun was higher in its densest years and lower later.

Every star ejects the same number. The ejected numbers are scaled from today’s interstellar density, which itself rests on three detections and on the census that each survey’s sensitivity draws. Stars without giant planets eject fewer bodies, and the figure’s middle case could be off by a factor of ten in either direction.

The captured orbits are drawn from today’s planets. A captured body’s later history — whether it is thrown out, hits a planet, or is passed outward to Saturn and the planets beyond in a chain of encounters that keeps its Tisserand parameter nearly fixed — depends on the planets’ arrangement during the cluster phase, which may not have been today’s. The survival fractions used are therefore ranges, not calculations.

Capture is by one flyby of Jupiter. The capture rates come from single patched-conic encounters with Jupiter on a circular orbit, with Saturn, the other planets and the Sun’s own disc of planetesimals ignored. During the cluster phase the giant planets may not yet have reached their present orbits, and the gas disc may still have been present for the first few million years.

The comparison population is an estimate. The number of the Sun’s own bodies of ʻOumuamua’s size is extrapolated from the population of comets larger than a kilometre, which is itself known only to within a factor of several.

Still open: whether any comet came from elsewhere #

Jupiter’s role in the Sun’s earliest environment was large and brief: it captured almost all the interstellar bodies it will ever capture in the cluster’s first tens of millions of years, and almost all of them left again. What the arithmetic leaves undecided is the larger question the simulations raised — what fraction of the distant cloud the cluster’s own gravity contributed — because that depends on how dense the birth cluster was and how quickly it came apart, which are measured only indirectly, from the orbits of the most distant bodies beyond Neptune and from the short-lived radioactive elements the Sun’s oldest solids carried.

The test is chemical. Comets formed round other stars, in discs with different compositions and temperatures, should differ in their isotopic ratios and volatile abundances from comets formed round the Sun. The comets that come in from the distant cloud for the first time, measured spectroscopically as they brighten, are the sample in which a sibling’s comet would be found. None has yet been identified as one. If a population of them is, the Sun’s distant cloud will turn out to be partly a collection — and Jupiter, for all the billions it caught, will have had almost nothing to do with it.