A flow too quiet for the lumps it runs between

The law that the universe is expanding was found in the worst possible place to look for it. Every galaxy in the 1929 diagram that first showed recession growing with distance lay within about twenty megaparsecs of the Milky Way, and most of them much closer. That is the region where the Milky Way’s own neighbourhood — its group, the dwarfs scattered round it, the larger groups a few megaparsecs away and the Virgo cluster beyond — ought to dominate every motion. Distances there are small, so the expansion velocities are small, a few hundred kilometres a second at most, and any galaxy pulled about by a nearby mass should wander from the law by an amount comparable to the law itself.

It does not. When the distances to the galaxies of the Local Volume were measured precisely, a few decades later, from the brightness at which the red giants run out, the scatter about the Hubble law came out between about thirty and sixty kilometres a second, depending on the sample and on what is subtracted first. Allan Sandage drew attention to the oddity in 1986 and it has been argued about since. The galaxies near the Local Group recede in an orderly line through a region whose matter is anything but orderly, and they do it more quietly than linear theory, run for an ordinary place in a standard universe, says they should.

The difficulty in the two values of the expansion rate that disagree is about precision at a few per cent and distances of hundreds of megaparsecs, where an ordinary local fluctuation changes the local rate by about half a per cent. This essay is about the other end of the scale: the first ten megaparsecs, where the flow is not a few per cent off the law but should be tens of per cent off it, and is not.

The flow that the group’s mass should bend #

The expectation can be made exact for the simplest model. Treat the Local Group as a lump of extra mass sitting in an otherwise uniform universe with the cosmological constant, and follow the shells of matter round it from the time when everything was nearly smooth. A shell close to the group feels the group’s extra pull; it is slowed, eventually turned round, and falls in. A shell far away hardly notices and recedes at the Hubble rate. In between, at some radius, a shell is turning round today: it is momentarily at rest relative to the group’s centre, and that radius is the zero-velocity surface.

For a group of two trillion solar masses the shells turn round at a megaparsec, which is close to where the outermost dwarf galaxies of the Local Group sit and to where the zero-velocity radius has been measured. The same physics was already used to weigh the group from Andromeda’s approach, where the radius of turnaround and the age of the universe fix the mass inside it. Outside the surface the curves show the shape the flow should have: recession that starts at zero and climbs back towards the Hubble line over the next two or three megaparsecs, below it all the way. At a megaparsec and a half the two-trillion group holds a galaxy back to fifty-seven kilometres a second against a hundred for an undisturbed flow.

The figure is the flow as it would be if the group were the only lump. That is the first thing it gets wrong about the real neighbourhood, and the reason it is still worth drawing is that the departures from it are where the information is.

What a quiet flow looks like, and what a noisy one would #

A galaxy’s measured velocity is the curve’s value at its distance plus whatever random motion it has acquired from everything else, and its measured distance carries an error of its own — five to ten per cent for the red-giant method, which sits near the bottom of a chain in which every distance is calibrated by the one before. Those two noises together decide what a diagram of the nearby galaxies can be made to say.

At forty kilometres a second the picture is close to what the Local Volume actually looks like. The innermost points sit on the falling part of the curve, the zero crossing is legible, and beyond two megaparsecs the galaxies hug the line closely enough that the slope of the flow — a local Hubble constant — can be read to within a few per cent from a few dozen of them. The local slope measured this way comes out close to the global value, which is itself a small surprise: nothing obliges the expansion inside a ten-megaparsec region full of structure to match the average over the universe so well.

The same flow with the random motions turned up to three hundred kilometres a second — the size galaxies typically have relative to their neighbours in redshift surveys of the wider universe — looks quite different.

The law survives in the sense that the cloud of points still rises to the right. But inside three megaparsecs individual galaxies scatter by more than their entire expected velocity, half of them appear to be approaching, and the turnaround of the group’s own surroundings cannot be located. Had the nearby universe been like this, Hubble’s twenty-four galaxies would have shown a much weaker trend, and nothing about the Local Group’s mass could have been learned from its surroundings. The quiet of the local flow is what turned the nearby galaxies into an instrument.

How faint the group’s own signature is #

That instrument turns out to be blunt, and the reason is instructive. Draw the infall curves for groups of different masses and subtract one from another, and the difference they make outside the zero-velocity surface is small.

Halving the group’s mass speeds the flow at a megaparsec and a half by eighteen kilometres a second; doubling it slows it by twenty-eight. Both are smaller than a single galaxy’s random motion even in a flow as cold as the observed one. The group’s pull is written into the first megaparsec or two outside the zero-velocity surface and then fades as the inverse square of distance against a Hubble velocity that grows linearly with it, so its fractional effect falls as the cube.

The consequence is that the mass of the Local Group cannot be read from any one neighbour, only from an average. To tell one trillion solar masses from two at the level of a couple of standard errors requires a mean velocity good to about eight kilometres a second at a megaparsec and a half, which with forty kilometres a second of scatter per galaxy means a couple of dozen galaxies in a shell one or two megaparsecs out. The Local Volume has roughly that many with good distances there. With three hundred kilometres a second of scatter it would need about a thousand, and the shell does not hold a thousand galaxies. The coldness of the flow is not a curiosity beside the measurement of the group’s mass from its surroundings; it is the reason that measurement is possible at all, and it sets how good it can be.

It also means the zero-velocity radius is the better handle of the two. The crossing point moves by a quarter of a megaparsec between one and two trillion solar masses, which is a change in where the galaxies with zero velocity sit rather than a change of a few kilometres a second in how fast the outer ones recede. Distances to the dwarfs near the surface are what fix it, and distances are what the red giants supply.

What an ordinary place should show #

The natural comparison for the observed scatter is what a typical observer in a standard universe would see. Linear theory gives a lower bound. The density fluctuations measured in the microwave background and in galaxy surveys, grown to the present, produce peculiar velocities whose total size is about three hundred kilometres a second — consistent with the speed at which the Local Group itself moves through the background radiation, which is about six hundred. Most of that comes from long wavelengths, which move a whole region together over scales larger than any survey maps. What matters for scatter about a local Hubble law is the part left over after the common motion of a region is removed.

Over a sphere of eight megaparsecs — roughly the region over which the cold-flow measurements are made — linear theory expects random motions relative to the region’s mean of about a hundred and ten kilometres a second. The observed scatter is two to three times smaller. And linear theory is the generous comparison, because it leaves out the non-linear motions that matter most on these scales: the orbital speeds of galaxies inside groups, the infall onto filaments, the splashback of material that has passed through a group and come out the other side. In the redshift surveys those motions bring the dispersion of galaxy pairs a megaparsec apart to three hundred or more. By either measure the neighbourhood is quiet.

The comparison has a caveat that the figure cannot show. The observed number is a scatter about the Hubble line for galaxies that have reliable distances, and those are predominantly dwarfs outside groups, chosen because they can be resolved into stars. Galaxies inside the nearby groups — the members of the Centaurus A group, of M81’s, of the Sculptor filament — move within their groups at a hundred kilometres a second or more, and a scatter quoted for the whole volume depends on whether group members are counted once at the group’s mean velocity or individually. The quiet is a property of the flow between groups, and that is still the striking part.

A sheet that is moving and a flow that is still #

There is an obvious objection to calling anything near the Milky Way quiet. The Local Group moves through the microwave background at about six hundred kilometres a second, a speed that the background’s dipole measures to a fraction of a per cent. Nothing about that is cold. The resolution is that the coldness is a statement about relative motion.

The Milky Way and the galaxies round it belong to a thin, flattened structure, the Local Sheet, a few megaparsecs across and less than one thick, and the sheet as a whole is moving: about two hundred and sixty kilometres a second away from the Local Void, the great underdense region on one side of it, which expands faster than the universe around it and pushes its walls outward, as measured from the galaxies’ distances and velocities. To an observer inside the sheet that motion is invisible in the Hubble diagram, because the observer shares it. Subtract the observer’s own velocity and the sheet’s members recede in a nearly perfect line. Measure every velocity against the background radiation instead and each galaxy acquires the common motion projected onto its line of sight, which is a smooth dipole across the sky rather than scatter, and which a fit would remove as a term of its own.

So the neighbourhood is fast and quiet at once, in the sense that matters: the large-scale field has moved the whole sheet coherently, and the small-scale field has barely stirred the galaxies within it. In terms of the linear calculation, the long wavelengths that carry most of the velocity are present with roughly the expected amplitude, and the short ones that would produce scatter are weak here.

Three explanations and what each requires #

The first explanation offered was the cosmological constant. A repulsion that grows with distance accelerates every shell outside the group, and it was argued that this pulls the flow towards the Hubble line sooner and smooths it. The objection is the one that applies to any claim that the expansion itself pushes: a pattern of velocities exerts no force, and only the constant’s acceleration term enters a shell’s motion. The infall solution includes it, and its effect on the curve is real but modest: on one to three megaparsecs it is comparable to the difference between the group masses, tens of kilometres a second in the mean, and it does nothing to suppress random motions that are set by the structure the galaxies formed in. Simulations without the cosmological constant produce cold local flows in some places and hot ones in others, which is the sign that the constant is not what decides.

The second is geometry. A galaxy forming in a flattened sheet that sits beside a large void acquires most of its peculiar velocity along the direction perpendicular to the sheet, as the void expands and pushes the sheet away, and little within the sheet’s plane. The Local Volume’s galaxies lie mostly in the sheet, so their velocity relative to each other is mostly in-plane, and the in-plane motions are small. In this reading the coldness is the signature of the sheet: the region’s matter has collapsed in one dimension and not yet in the other two, and one-dimensional collapse stirs up little random motion in the directions that have not collapsed.

The third is selection of the place. Computer simulations of a standard universe produce regions as quiet as this one, but not around a randomly chosen galaxy like the Milky Way. They appear when the comparison is restricted to pairs of large galaxies with an environment like the Local Group’s — an isolated pair, no massive cluster within several megaparsecs, a large void next door. In those environments the simulated flows are frequently as cold as the observed one. That is not an explanation of why the Milky Way lives in such a place; it is an argument that once it does, the quiet follows.

The second and third are the same answer stated twice, and they are where the evidence points: the Milky Way’s neighbourhood is a low-density sheet on the edge of a void, its mass in the space between groups is small, and small mass between groups means small random motion between them.

What the quiet is used for #

The cold flow is not only a puzzle; it has been put to work. It is what allows the low-redshift side of the Hubble diagram to be used at all for calibrating distance methods against each other, since a galaxy whose velocity is dominated by random motion carries no information about its distance. It made the zero-velocity radius of the Local Group, and of the groups round M81 and Centaurus A, measurable as numbers with errors rather than as rough estimates, because the turnaround shows up as a crossing rather than a smear. And it limits how much mass can lie between the groups, since any substantial matter there would stir the flow.

That last use is the one with consequences. If the Local Volume’s mass were dominated by groups whose total masses match their measured turnaround radii, and by little else, then the mean density of matter within ten megaparsecs comes out well below the cosmic mean — a few tenths of it. A low density between groups is what makes a cold flow natural. It is also a statement that the Milky Way’s surroundings are not a fair sample of the universe on these scales, which matters for every measurement that treats a local number as a global one.

The deviation that the law was found through #

There is a historical irony in all this that is worth stating directly. Hubble’s 1929 distances were too short by a factor of about seven, because the brightest stars and Cepheids he used were miscalibrated, so the slope he quoted, five hundred kilometres a second per megaparsec, was too large by the same factor. The velocities, from the redshifts, were accurate. The law came through anyway because the galaxies he used were in a quiet region. A flow with the random motions typical of the wider universe, imposed on his small sample at those small velocities, would have left the trend far less convincing, and the first claim of an expanding universe would have had to wait for galaxies further away, where velocities are large enough that random motions are a small fraction of them.

The nearby galaxies, in other words, were not a fair test of the law and did not need to be. They were an unusually clean one.

What a sphere round the Local Group leaves out #

Every curve here assumes spherical symmetry round the Local Group, and the real neighbourhood has none. The group is two large galaxies and their satellites, not a point; the sheet is flat; the void is on one side; the Virgo cluster, sixteen megaparsecs away, pulls the whole region towards it at a couple of hundred kilometres a second. The spherical model is used for the zero-velocity radius because the dwarfs near that radius are close enough to the group that its pull dominates, and it degrades outwards. The synthetic diagrams use random motions drawn from a single Gaussian, while real ones have tails from galaxies that have fallen through a group. And the linear-theory comparison stands in for what is really a question for simulations, in which the answer depends on how galaxies are matched to dark-matter halos and how the observed sample was selected.

What does not depend on any of those is the measurement: two to three times colder than linear theory expects for an average place, and several times colder than the pairwise motions in the wider universe.

Still open: whether the quiet extends to the dark matter #

The cold flow is a statement about galaxies, and galaxies trace matter only where matter has managed to form them. A sheet of dark matter between the groups that never formed galaxies would stir the flow without appearing in any count; its absence in the scatter is evidence that it is not there, but evidence weighted by how faithfully the dwarfs with distances sample the velocity field. Two tests are coming within reach. Distances good to a few per cent for many more faint dwarfs, from the next generation of space telescopes resolving red giants out to ten megaparsecs and beyond, will measure whether the scatter stays cold as fainter, more numerous galaxies are added. And weak lensing of background galaxies by the mass in the Local Volume, which is a measurement of matter rather than of light, is now at the edge of being possible for the nearest groups. If the quiet flow and the lensing mass agree that the space between the groups is nearly empty, the neighbourhood is a void-edge sheet and the puzzle is closed. If lensing finds mass there that the flow does not feel, the coldness becomes a problem about how dark matter moves rather than about where the Milky Way lives.