A stream that points the wrong way

A stellar stream is a record of an orbit. A globular cluster or a dwarf galaxy orbiting in the Milky Way’s halo is stripped by the Galaxy’s tide, and its stars spread out ahead of it and behind it along almost the same path. A stream is not quite the orbit it came from — its stars leave with small offsets in energy and drift onto neighbouring orbits — but it is close, and a stream’s shape on the sky, its distances and its stars’ motions together constrain the potential the stream moves in. That is how streams measure the mass and shape of the dark halo.

The method has a premise that was stated and set aside in the essay that introduced it: the halo holds still. The potential is taken to be fixed in time, so that the stream’s stars, all moving in the same potential, trace orbits that can be fitted. The Milky Way’s halo is not fixed. Its most massive satellite, the Large Magellanic Cloud, is falling in for what appears to be the first time, it is massive enough to matter, and it is fifty kiloparsecs away — close to many of the streams that are used to measure the halo.

This essay is about what the Cloud does to a stream, and why the effect has turned from a nuisance into a measurement.

Two ways a satellite pulls #

A satellite affects a stream in two ways, and both matter.

The obvious one is direct: the Cloud’s gravity pulls on each star of the stream, more strongly on the stars that pass close to it, and deflects them. A stream passing within a few tens of kiloparsecs of a Cloud of a hundred billion solar masses has its nearest stars pulled sideways by a few tens of kilometres a second over a few hundred million years — comparable to their motion across the stream.

The less obvious one is indirect. The Cloud also pulls on the Milky Way — on its disc, its inner halo, its centre — and the Galaxy’s centre accelerates towards the Cloud. Every measurement of a stream is made from the Sun, inside the Galaxy, and every model of a stream is computed in a frame centred on the Galaxy. In that frame, which is accelerating, every star feels an extra, uniform acceleration in the direction away from the Cloud: the reflex. Stars far out in the halo, which the Cloud’s pull on the inner Galaxy does not reach directly, appear to be pulled the other way.

The model treats the Galaxy’s centre as a single point accelerated by the Cloud, which exaggerates the effect: in reality the inner Galaxy responds as an extended body and its outer parts lag. But the direction and the timing are robust. The acceleration began in earnest only a few hundred million years ago, which is short compared with the orbital periods of stars in the outer halo, so the outer halo has not had time to follow. In the Galaxy’s frame, the outer halo is moving.

One stream, with and without the Cloud #

The model stream is stripped from a dwarf galaxy on a polar orbit about thirty-five kiloparsecs from the Galactic centre, in a plane that contains the Cloud’s present position, and released over two billion years. Its stars feel the Galaxy’s halo, the Cloud’s gravity, and the reflex.

The model is deliberately one that passes close: a stream far from the Cloud’s path is barely affected, and the real streams that have been used for the measurement were chosen because they are not. What the picture shows is how large the effect can be. A stream is a dynamically cold structure — its stars move together to within a few kilometres a second — and an external perturbation that would be negligible for the halo as a whole is large compared with the stream’s own internal motions.

Velocities that stop pointing along the stream #

The diagnostic that has turned the effect into a measurement is simple to state. In a static halo, a stream’s stars move along the stream: their proper motions on the sky point along its track, to within the few degrees by which the stream differs from its progenitor’s orbit. A perturbation that pushes the stream sideways moves its stars’ positions faster than it changes their velocities — the positions integrate the velocity change — so for a while after the push, the stars move in one direction while the stream lies in another.

That misalignment is the observable. It needs positions and proper motions along the stream, which the Gaia satellite supplies for every bright stream star, and radial velocities and distances, which spectroscopic surveys supply. It does not need the stream’s progenitor to be known or the stream’s age to be fitted. A misalignment of tens of degrees cannot be produced by a static potential of any shape; it requires something that changed recently.

The same stars with a lighter and a heavier Cloud make the dependence visible directly.

A measurement of the Cloud’s mass #

Run the model at a range of masses and the misalignment becomes a calibration.

The real case is the Orphan stream, a long, thin stream of stars that stretches across much of the northern and southern sky at twenty to sixty kiloparsecs, and whose southern part passes close to the Magellanic Clouds. When its stars’ proper motions were measured with Gaia in 2019, they were found to be misaligned with the stream’s track, by up to tens of degrees, in the southern part — the part nearest the Cloud. Models of the stream in a halo containing the Cloud reproduced the misalignment only for a Cloud of about 1.4 × 10¹¹ solar masses, with an uncertainty of about twenty per cent. Those models found, as the figure does, that the Galaxy’s reflex motion had to be included.

That mass is about a tenth of the Milky Way’s, and ten times what the Cloud’s stars and gas account for. It is a dark-matter halo of its own, and it is larger than the Cloud’s rotation curve suggested — because a rotation curve measures the mass inside the radius where the gas is, and the Cloud’s halo extends far beyond it. The stream weighs the whole of it.

The Cloud has been weighed several ways #

The stream is not the only measurement, and the agreement among them is the strongest argument that the Cloud is as massive as the stream says.

The Cloud’s effect on other streams — several thin streams pass at different distances and angles — has been modelled in the same way, and gives consistent masses. The Galaxy’s reflex has been detected directly: the distant stars of the outer halo, beyond about forty kiloparsecs, show a coherent velocity relative to the inner Galaxy, of a few tens of kilometres a second, in the direction the Cloud’s pull predicts. And the Cloud raises a wake in the halo behind it — a drag with nothing to drag against, the dynamical friction overdensity, drawn out over tens of kiloparsecs — whose signature has been seen as an excess of distant halo stars along the Cloud’s past orbit.

So the Milky Way’s halo is now known to be out of equilibrium, measurably, in a way that every analysis of its outer parts has to take into account. Streams used to measure the halo’s mass and shape have to be fitted with the Cloud included, and the halo’s mass from the motions of its distant stars has to be corrected for the reflex.

A stream on the far side #

Not every stream is so affected, and the ones that are not are useful for a different reason.

So the streams sort themselves by their geometry relative to the Cloud’s orbit. Streams that passed close to it measure the Cloud; streams far from it measure the halo, corrected for the Galaxy’s motion; and a joint fit of many streams, each with its own geometry, separates the two. That is the programme the Gaia data have made possible, with dozens of streams now mapped in six dimensions.

Why first infall #

The figures put the Cloud on its first approach, and that is itself a result of the measurements. The Cloud’s present velocity, measured from the proper motions of its stars by the Hubble Space Telescope and later Gaia, is about 320 kilometres a second relative to the Galaxy — close to the escape speed at its distance for any plausible Milky Way mass. Integrated backwards in a static Galaxy, it either escapes entirely or swings out to hundreds of kiloparsecs on an orbit lasting many billions of years. Either way, it has not been this close before.

Whether two galaxies merge is a ratio of two times: the time dynamical friction takes to drain their relative orbit, against the time they spend near each other. For the Cloud, with a tenth of the Galaxy’s mass, friction is strong, and run forward, the models bring it back in a second passage within a few billion years and into a merger with the Galaxy after that — an event that will scatter the Galaxy’s outer halo and perhaps grow its central black hole. The first-infall geometry is what makes the present moment unusual: the Galaxy has been disturbed recently and has not had time to settle, which is exactly why the streams show it.

Why the halo’s shape depended on it #

Before the Cloud was included, fits of the Orphan stream and others in static haloes gave halo shapes that disagreed with each other — one stream preferring a halo flattened one way, another the other. A shell of mass outside a stream turns nothing by the shell theorem, so each stream measures the halo’s shape only inside its own orbit, and disagreements between streams at different radii could in principle be real variations of shape with radius. Some of them were the Cloud: a static-halo fit to a stream perturbed by the Cloud absorbs the perturbation into whatever shape parameters it has, and different streams, perturbed differently, absorb it differently.

With the Cloud included, the streams’ preferred shapes come closer together. The halo’s shape is still uncertain, but the uncertainty is now a statement about the halo rather than a symptom of a missing satellite.

What this does to the subhalo search #

Streams were also meant to count the small dark-matter clumps — subhaloes — that cold dark matter predicts, through the gaps a passing clump opens and the spectrum of density fluctuations many clumps make together. The Cloud complicates that too. It perturbs a stream on large scales, and its own subhaloes — a satellite of a hundred billion solar masses brings its own population of dark clumps — perturb streams that pass near it on small ones.

The large-scale perturbation is separable from the small-scale signal, in principle, because it has a different scale and a different pattern along the stream. But a stream that the Cloud has wrenched sideways, as in the model, has had its density structure reshaped as well, and gaps opened by subhaloes long ago can be stretched, compressed or erased. Streams far from the Cloud’s path are the cleaner subhalo detectors, which turns the Cloud’s orbit into a criterion for which streams to trust for which question.

The other perturbers #

The Cloud is the largest disturbance in the Milky Way’s halo now, and not the only one. The Sagittarius dwarf galaxy, currently passing through the Galactic disc on the far side of the centre, was once perhaps as massive as a few tens of billions of solar masses and has been shedding its own spectacular stream for billions of years; its passages through the disc are thought to have set the disc ringing in ways that Gaia’s maps of stellar motions near the Sun record. The Small Magellanic Cloud, bound to the Large one, adds its own smaller pull. And the Galaxy’s own bar, rotating at its centre, perturbs streams whose orbits come close enough to feel it.

Each leaves a different signature on a stream, because each acts at a different place and time. The bar acts repeatedly, at every pericentre, and opens gaps and fans in streams that pass inside a few kiloparsecs. Sagittarius acts briefly, at each disc crossing, on streams near its path. The Cloud acts once, recently, on a large scale. A stream is a long, thin record of everything that has disturbed it along its length, and separating the perturbers is a matter of matching each disturbance’s timing and geometry to the stream’s.

On a still longer view, the Galaxy as a whole is falling towards Andromeda, and whether the two collide is decided by a speed across the sky that is measured, like the Cloud’s mass, from proper motions. The Large Magellanic Cloud enters that measurement too: the Galaxy’s reflex motion towards the Cloud is a few tens of kilometres a second, comparable to the tangential velocity of Andromeda that decides the outcome, and the frame in which Andromeda’s motion is measured has to be corrected for it.

Where the model stops #

A point-mass Galaxy centre. The reflex is applied as a uniform acceleration equal to the Cloud’s pull on the Galactic centre. The real Galaxy responds as an extended body, its inner parts moving with the centre and its outer parts lagging, and the reflex felt by a star depends on its distance from the centre. The model’s reflex is therefore an overestimate at large radii.

A rigid Cloud. The Cloud is a Plummer sphere of fixed mass and size. It is being tidally stripped as it falls in, and its mass profile, which sets how it pulls on nearby stars, is uncertain beyond the region where its stars are.

A spherical, static halo. Apart from the Cloud, the Galaxy’s halo is a fixed logarithmic potential. The real halo responds to the Cloud with its own wake and its own reflex, which a full model includes by simulating the halo as particles.

A dwarf progenitor without self-gravity. The model stream’s stars are released at a fixed distance either side of the progenitor and then feel no gravity from it. Real progenitors hold their stars until they escape and continue to perturb the stream near them.

One stream at one orientation. The model stream was placed to pass near the Cloud. The size of the misalignment depends strongly on how close a stream passes and when, and the calibration of misalignment against mass has to be done stream by stream, with each stream’s own orbit.

The surprising connection #

The misalignment between a stream’s track and its stars’ motions is the same diagnostic the encounter between two galaxies leaves in their tidal tails, at a smaller scale. A tail drawn out by a passing companion is a record of the encounter’s geometry, and its stars’ velocities lag behind the shape the encounter impressed on them; reading the lag is how the encounter is reconstructed. The Orphan stream is a tidal tail of a dwarf galaxy, drawn out by the Milky Way, then bent by a third galaxy passing near it — and the bend is fresh enough that the velocities have not caught up. A record of a three-body encounter between galaxies is being read from the angle between two directions on the sky.

Still open: how the Galaxy itself is responding #

The Cloud’s mass is now known to about twenty per cent from streams and the reflex together, but the response of the Milky Way to it — how its disc is being warped, how its inner and outer halo are moving relative to each other, whether the Galaxy’s centre and the Sun are moving together — is only beginning to be measured. The Galaxy’s disc shows a warp, and the outer halo a velocity, both in directions the Cloud predicts, but how much of each the Cloud has caused, and how much is older history, depends on a model of the Galaxy that is itself out of equilibrium. Whether the halo can be fitted as a static potential plus a perturbation, or has to be treated from the start as a structure in motion, decides whether the methods that measured the Galaxy’s mass from its outer stars still apply, or have to be rebuilt around a Galaxy that is being pulled sideways.