A halo the telescope paints on every galaxy

The faintest light measured in astronomy is not the light of the most distant objects but the outskirts of nearby galaxies. Around a disc galaxy like the Milky Way, beyond the edge of its visible disc, lies a stellar halo — a diffuse spheroid of old stars, the debris of the small galaxies it has eaten — and its surface brightness is around thirty magnitudes per square arcsecond, a ten-thousandth of the night sky. Measuring light that faint is a problem of subtraction: the sky is ten thousand times brighter, and every photon of it has to be modelled and removed before the halo appears.

A second problem is less obvious and, at these depths, larger. A flat field that contains scattered light corrupts a faint measurement additively, which is the first lesson of deep imaging. The second is that the galaxy’s own light is scattered too. Every telescope spreads the light of a point into a pattern, the point-spread function, and the pattern has two parts: a core, the sharp dot whose width is set by the atmosphere and the optics, and a wing, a faint glow that falls off slowly and extends to arcminutes. The core holds nearly all the light. The wing holds a few per cent, spread over an area millions of times larger. Around a bright galaxy, a few per cent of a lot of light is a great deal of faint light, and it lands exactly where the halo is being looked for.

The wing nobody measures #

The wing is made of several things. Dust on the mirrors and the microscopic roughness of their polished surfaces scatter a small fraction of light at every angle; aerosols in the atmosphere do the same; reflections between the surfaces of filters, windows and the detector send ghosts of bright objects across the field. Each process scatters only a fraction of a per cent of the light, but the fractions add, and they add with a characteristic shape: the scattered light falls off roughly as the inverse square of the distance from its source, out to many arcminutes.

The inverse-square wing has a property that makes it treacherous. Its light per square arcsecond falls rapidly, but the area of each annulus grows as the radius, so the light per annulus falls only as the inverse of the radius, and the total light in the wing grows logarithmically with the radius it reaches. A wing that extends to ten arcminutes holds almost as much light beyond one arcminute as within it. The point-spread function’s shape near its core — what a photometrist calls the seeing — is measured from faint stars, which are bright enough to show the core and nowhere near bright enough to show the wing. The wing has to be measured separately, from the brightest stars in the sky, saturated in their centres and traced outward over tens of arcminutes, and most observations never do it.

A halo that was red for the wrong reason #

The wing has a colour, and the colour has a history. In the 2000s, images of hundreds of edge-on disc galaxies from a large sky survey were stacked to reach depths no single image could, and the stack showed a faint, very red halo around the average disc — redder than any normal population of old stars could make, which suggested an exotic population of very low-mass stars or something stranger. A few years later the red halo was traced to the detectors. The silicon of a thinned CCD is nearly transparent to the reddest light it records, so red photons penetrate it, reflect from its back surface and are absorbed some distance from where they arrived. The detector adds its own extended wing to the point-spread function, and the wing is far stronger in the red than in the blue. Stacked around a disc, it made a red halo out of nothing.

That episode is the reason the wing is now modelled band by band. It is also a reminder that a point-spread function is not one function: it differs between telescopes, between filters on one telescope, and between nights, and the core that sets what a large mirror can resolve tells nothing about the wing that decides what it can see at thirty magnitudes per square arcsecond.

A profile that bends up #

The opening figure shows what the wing does to a galaxy. An exponential disc falls by 1.086 magnitudes per square arcsecond for every scale length, so ten scale lengths out it is eleven magnitudes fainter than its centre — at thirty-one magnitudes per square arcsecond for a disc whose centre is at twenty. The wing takes a few per cent of the light from every point of the disc and spreads it over a region much larger than the disc. Near the centre the scattered light is swamped by the disc’s own. Far out, where the disc has faded by a factor of twenty thousand, it is not.

The result is a profile that falls straight and then bends up. With five per cent of the light in the wing, the observed profile rises three-quarters of a magnitude above the disc’s own beyond about nine scale lengths, at twenty-nine magnitudes per square arcsecond, and from there it falls slowly — the shallow component that a deep image of a disc galaxy reports as its stellar halo. With two per cent the bend comes half a magnitude fainter and a scale length further out. Nothing in the profile marks the bend as an artefact; a real halo would produce the same shape. The shallow outer slope does not help either. A stellar halo’s light falls with radius as a power law, roughly as the inverse cube of distance in the Milky Way’s, which on a magnitude plot against linear radius is exactly the kind of slow, curving decline the scattered light produces; the two are separated only by their amplitudes and by how they vary from galaxy to galaxy.

Up-bending profiles are common in deep images, and they are reported as haloes, as the outer discs of galaxies that have been stirred by interactions, or as the outskirts of a galaxy that has two profiles. Some of them are those things. The analyses that have modelled their telescopes’ wings carefully, using bright stars in the same images, have found that a substantial share of what had been called a halo in earlier work, in many galaxies, was scattered light.

The same depth for every galaxy #

The wing’s inverse-square shape has a second consequence, which is the clearest way to tell its halo from a real one.

Take two discs with the same central surface brightness, one twice as large on the sky as the other. The larger disc holds four times as much light, so its wing holds four times as much scattered light. At the same multiple of its scale length it is twice as far from its centre in arcseconds, and an inverse-square wing is four times fainter there. The two factors cancel. Where the wing falls as the inverse square of distance, the scattered light at a given number of scale lengths is the same for every disc, whatever its angular size, and the false halo appears at the same surface brightness around every galaxy.

That is a sharp test. A real stellar halo’s surface brightness at a given multiple of its disc’s scale length depends on the galaxy’s history — how much it accreted and when — and varies from galaxy to galaxy by factors of several. A false halo does not vary at all, beyond what the central surface brightness and the wing fraction set. A sample of galaxies whose haloes all appear at twenty-nine and a half magnitudes per square arcsecond, at ten scale lengths, whatever their distance and size, is a sample measuring its telescope. The test needs no model of the wing at all, only a sample spanning a range of angular sizes, which every survey has.

How much light the false halo holds #

The false halo is not a small effect compared with the real one.

The stellar halo of the Milky Way, counted star by star, holds about one per cent of its light; the Andromeda galaxy’s, a few per cent. A telescope with five per cent of its light in its wings makes a false halo holding a little over one per cent of a disc’s light beyond six scale lengths — as large as the Milky Way’s real one. The relation is nearly linear in the wing fraction, because the false halo is simply the wing’s share of the disc’s light that happens to land outside six scale lengths, and for a wing extending to arcminutes, most of it does.

That is why the comparison of stellar haloes between galaxies, which is one of the main tests of how galaxies were assembled, has had a troubled history in integrated light. Models of galaxy formation predict haloes holding from a fraction of a per cent to ten per cent of a galaxy’s light, depending on how many satellites it accreted; a telescope’s wing can add a per cent to any of them. Haloes measured by counting their resolved stars — possible only for the nearest galaxies, where individual red giants can be seen — are free of the wing, and they are the calibration that integrated-light measurements have to match.

A thick disc made from a thin one #

The same effect acts on a disc seen edge-on, where it produces a different illusion.

An edge-on thin disc falls away from its midplane steeply, by more than two magnitudes per scale height far out. The scattered light from the bright midplane does not fall so fast; it is spread over arcminutes. From about four scale heights the observed vertical profile turns over into a shallow component, and fitted with two discs, a thin and a thick, the shallow part reads as a thick disc several times thicker than the thin one and holding a few per cent of the light. That is exactly the description of the thick discs found in edge-on galaxies, and of the Milky Way’s own, which is known from star counts to be real.

In external galaxies it is not always real. Thick discs reported in deep images of edge-on galaxies were re-examined after the importance of the wings was recognised, and for several the thick component weakened or disappeared once the scattered light was modelled. Others survived — thick discs are common, and the Milky Way’s is beyond doubt — but the wing is an unavoidable first suspect in any shallow component found near twenty-eight to thirty magnitudes per square arcsecond.

Correcting for the wings #

The remedy is to model the wing and subtract its contribution, and the figure shows what that remedy depends on.

An exact model of the wing recovers the disc perfectly, straight to fourteen scale lengths. A model whose wing is twenty per cent too faint leaves a fifth of the false halo behind, a residual that still reads as a halo, half a magnitude above the disc at ten scale lengths. A model twenty per cent too bright subtracts some of the disc’s own light along with the scattered light, and the profile turns down into an apparent truncation — an edge to the disc that is not there. Truncated discs are also reported in deep images, and the figure says that a wing model slightly too strong would create them.

So the outskirts measured below about twenty-nine magnitudes per square arcsecond are as much a measurement of the wing model as of the galaxy.

Two features make the problem worse in practice than in the figure. The wing’s amplitude is measured from bright stars, which saturate the detector in their cores, so the inner part of the wing — the part that matters most for galaxies a few arcminutes across — has to be stitched together from stars of different brightness, each covering a different range of radius. And the wing changes with time: dust accumulates on the mirrors between cleanings, the atmosphere’s aerosol content varies from night to night, and a stack of exposures taken over months averages over wings of different strengths. The wing model is a measurement in its own right, with errors of its own, and those errors are what the corrected outskirts inherit. A wing model good to twenty per cent is a good wing model; it requires tracing bright stars out to tens of arcminutes in the same images, at the same colours, with the same instrument configuration, because the wing changes with the cleanliness of the mirrors and the state of the atmosphere. Telescopes built specifically for low surface-brightness work — arrays of commercial camera lenses with no secondary mirrors, minimal surfaces and coated optics — exist precisely to make the wing small enough that this correction is minor rather than dominant.

Why the inverse square #

The wing’s shape is not arbitrary, and the cancellation that puts every false halo at the same depth depends on it. Light scattered by a rough surface goes into angles set by the roughness’s spatial structure: a surface whose irregularities span a wide range of scales, with more power in the larger ones in a particular proportion, scatters light into a pattern falling roughly as the inverse square of the angle. Polished mirrors have roughness of that kind, and so does a layer of dust grains of mixed sizes; atmospheric aerosols scatter more steeply forward. The sum of these processes gives the inverse-square shape over a wide range of angles, with a steeper fall at the largest angles where the telescope’s own baffles cut it off.

A wing that falls faster than the inverse square breaks the cancellation in favour of large galaxies, whose outskirts are further from their centres in arcseconds; one that falls more slowly breaks it against them. Measured wings from different telescopes have slopes between about minus two and minus three, so the cancellation is approximate rather than exact — the false halo depends weakly on a galaxy’s angular size, more weakly than any real halo is expected to. The test of a constant depth survives as a test of a nearly constant one.

What the model leaves out #

The wing here is a single power law with one amplitude, identical at every point of the field and every colour. Real wings change across the field, with the optics’ aberrations; they differ between colours, so that the false halo has a colour that is not the galaxy’s and can masquerade as a population of old red stars; and they include ghosts — reflections that put a faint displaced copy of a bright galaxy somewhere else in the field — which are not power laws at all. The disc here is a perfect exponential, and real discs have spiral arms, bars and bright cores whose scattered light is distributed accordingly.

None of this weakens the main argument, which depends on two facts only: that the wing holds a few per cent of the light, and that it extends far beyond the galaxy. Both are measured facts about every large telescope that has looked.

Still open: how faint the faintest light really is #

The deep imaging of galaxies has reached the surface brightnesses at which their haloes, streams and faint outer discs should be seen, and at those depths a telescope’s wings put a halo on every galaxy, thicken every edge-on disc, and can truncate every profile, depending on how well they are modelled. The tests are clear: a false halo has the same surface brightness around every galaxy, it has the colour of the wing rather than of a stellar population, and it vanishes when the wing is subtracted correctly.

What is not settled is how much of the faint structure already reported survives those tests, because many of the deepest images were taken before the wing was routinely measured. The galaxies whose haloes can be checked against resolved star counts are few and near. The streams around them, which are narrow and lumpy and cannot be mimicked by a smooth wing, are the most robust features of all — and their shapes carry information of their own, down to the pull of a passing satellite. The diffuse haloes — the features most directly predicted by models of how galaxies grow — are the most exposed, and the question of how faint they really are is a question about scattered light before it is a question about galaxies.