Two colours, and almost nothing between

A colour is a ratio of two fluxes, so it is free of distance and cheap to measure. Plot a large sample of galaxies by colour against absolute magnitude and something happens that a smooth population would not produce: the points collect into two groups.

What a galaxy’s colour is measuring #

For a single star, colour is a thermometer: the ratio of fluxes in two bands fixes the temperature of the surface emitting them.

For a galaxy, the light is the sum of billions of stars of every temperature, and the integrated colour is dominated by whichever population contributes most in the two bands. Because massive stars are enormously more luminous and enormously shorter-lived, that comes to a simple statement: a galaxy’s colour measures how recently it last formed stars.

A galaxy forming stars now contains O and B stars, which are blue and outshine everything else; it is blue. A galaxy that stopped a billion years ago has none of them left, and its light comes from cooler main-sequence stars and from red giants; it is red. The clock is fast at first and then slow. Most of the reddening happens in the first billion years after star formation stops, and after that the colour changes only slowly with age. That non-linearity matters for the argument below.

Why the red sequence is tilted, and why it is tight #

The red group is not a blob; it is a narrow band with a definite slope, brighter galaxies being redder.

The slope is not an age effect. It is metallicity: more massive galaxies retain their heavy elements more effectively, because their deeper potential wells make it harder for supernova-driven winds to expel enriched gas. More metals means more line blanketing in the blue part of the spectrum, so the integrated colour reddens. The relation between mass and metallicity is measured independently, from the spectra, and it predicts the observed tilt.

The tightness is the more striking property. The scatter about the red sequence is small — under a tenth of a magnitude in the best-measured samples — which means the galaxies on it have similar ages as well as a systematic metallicity trend. Since colour changes slowly at old ages, a small scatter in colour permits a large scatter in age, so this is a weaker constraint than it looks; but it is a constraint, and it says that the red galaxies at a given mass stopped forming stars at broadly similar times.

The red sequence is also useful as a tool. Its tightness makes it possible to find galaxy clusters by looking for an over-density of galaxies sharing one colour, and to estimate their redshifts photometrically from where that colour sits.

What an empty gap means #

The valley between the two populations is the informative part, and its interpretation is the same reasoning the radius valley in the exoplanet census required.

A galaxy that is transforming from blue to red must pass through intermediate colours. The number of galaxies found at those colours is proportional to the rate at which galaxies transform, times the time each spends in transit. So an underpopulated region means a short crossing time — not that galaxies avoid it, but that they do not linger.

Quantitatively, if a few per cent of the population sits in the valley and the total has been transforming steadily over ten billion years, the crossing takes a few hundred million years. That is fast compared with the age of the galaxies and comparable with a single orbit at the disc’s edge.

So the emptiness of the green valley is a measurement of a timescale, and it rules out slow processes. A galaxy that gradually exhausted its gas over several billion years would spend that long in the valley and the valley would be full. Whatever ends star formation, it acts quickly once it begins.

What might act that quickly #

Several candidates match the timescale and probably all of them operate.

Gas removal in a cluster. Ram-pressure stripping by the intracluster medium removes a galaxy’s gas in one crossing of the cluster core, a few hundred million years. This is efficient, and it explains why the red fraction rises with local density.

Energy from the central black hole. An accreting supermassive black hole can inject enough energy to heat or expel a galaxy’s gas, and the correlation between black-hole mass and bulge properties suggests the two are connected. This mechanism is the leading explanation for why the most massive galaxies are red, since they are not usually in clusters.

A merger. Two gas-rich galaxies colliding drive their gas to the centre, burn it in a burst, and leave a spheroid with nothing left to form stars from. The burst itself is short, and the remnant is red.

The colour of a population, computed #

It is worth seeing where a galaxy’s colour comes from quantitatively, because the answer explains both the speed of the reddening and its eventual slowness.

Take a population formed in a single burst. Immediately afterwards its light is dominated by stars of twenty to sixty solar masses, whose surface temperatures are thirty to forty thousand kelvin. Those stars are gone within ten million years. After a hundred million years the hottest stars remaining are of about six solar masses, at fifteen thousand kelvin; after a billion, about two solar masses at nine thousand; after ten billion, one solar mass at six thousand.

The colour difference between the first and second of those states is large; between the third and fourth it is small. The clock therefore runs fast for the first few hundred million years and then nearly stops, which is exactly the property that makes the red sequence tight and the green valley informative.

The observation behind the number #

The bimodality was known in fragments for decades and was established beyond argument by the Sloan Digital Sky Survey, which measured colours and redshifts for hundreds of thousands of galaxies in five bands.

Three points about that measurement matter.

The colour must be corrected for redshift. A filter samples a different part of the rest-frame spectrum for a galaxy at $z=0.1$ than for one at $z=0$, and the correction depends on the spectrum being corrected — which is the thing being measured. The corrections are done iteratively and are a leading systematic.

Dust reddens too. An inclined spiral, full of dust and forming stars vigorously, can be as red as a quiescent elliptical. Separating the two requires more than a colour: an infrared measurement, or a spectral feature, or the ultraviolet slope. A good fraction of the apparent green valley is dusty star-forming galaxies seen edge-on.

And absolute magnitude requires a distance, so the horizontal axis of the diagram inherits the redshift survey underneath it.

What the fraction does with mass #

The bimodality is not a fifty-fifty split, and how the balance shifts with galaxy mass is one of the more useful regularities in the census.

Below about $10^{10}$ solar masses in stars, galaxies are overwhelmingly blue and forming stars. Above about $3\times10^{10}$, they are overwhelmingly red and quiescent. The transition is not gradual across the whole range — it is fairly sharp, and the mass at which it occurs is close to the mass above which a galaxy’s halo is hot enough to shock-heat infalling gas rather than let it stream in cold.

That coincidence is the basis for one of the standard accounts of quenching: below the threshold, gas reaches the disc cold and forms stars; above it, the gas is shock-heated to the halo’s virial temperature and can be kept hot by a modest energy input from the centre. The account is attractive because it explains a mass scale rather than assuming one.

Mass is only half of what sets the balance, and the other half is where the galaxy is. At fixed stellar mass the red fraction is higher in a cluster than in the field, by enough to be the dominant term for dwarf galaxies and a minor one for the most massive — which is the sense in which the third of the figures above is a cluster and the second is a low-mass field population, rather than the same distribution drawn twice. The two dependences are separable in the data and they are not the same mechanism: mass-driven quenching acts through the halo’s own gas, and environment-driven quenching acts by removing gas the galaxy brought with it. A census that reports one red fraction has averaged over both.

It also connects the two halves of this field’s census. A luminosity function with a knee requires a mechanism that suppresses galaxy growth above a particular mass, and the mass at which galaxies turn red is close to the mass at which the counts turn over. Two independent features of the census pointing at the same scale is the kind of agreement worth building on.

The galaxies that are red for the wrong reason #

The colour is being read as an age indicator, and there is a second way for a galaxy to be red that has nothing to do with age.

Dust absorbs blue light more efficiently than red, so a galaxy full of dust is reddened — and a galaxy full of dust is generally a galaxy busily forming stars, since the dust and the star formation come from the same gas. So the reddest objects in a colour-selected sample include some of the most actively star-forming ones, sitting on the red sequence for a reason opposite to everything the sequence is supposed to mean.

The effect is largest for spirals seen edge-on, where the line of sight passes through the whole disc, and it is not a small contamination: dusty star-forming galaxies make up a substantial fraction of a red-selected sample, and the fraction rises with redshift as the population becomes gas-rich.

Three things separate them, and all of them need information beyond one colour.

Morphology. A dusty spiral looks like a disc and a quenched galaxy looks like a spheroid, so a resolved image distinguishes them where the colour cannot.

The infrared. Absorbed starlight is re-emitted in the far infrared, so a dusty galaxy is enormously bright there and a genuinely old one is not. That is the cleanest discriminant and it needs a different telescope.

A second colour. Dust reddening and ageing move a galaxy along slightly different directions in a plane of two colours, so a pair of colours separates them partially — which is why the standard diagnostic diagrams have two colours rather than one.

A bimodality measured in one colour is therefore a mixture of three populations rather than two, and the size of the third is the leading systematic in every quantitative statement about the red fraction.

It is also the reason the cleanest versions of this measurement are made in the rest-frame ultraviolet and infrared rather than in the optical: the first is where the young stars dominate and the second is where the dust re-radiates, so the pair brackets the confusion instead of sitting inside it.

Neither is available for the large samples the statistics need, which is the usual trade: the measurement that removes the systematic exists, and it exists for a hundredth as many objects as the measurement that has it.

Where the picture stops #

The model in the first figure is two Gaussians. It reproduces the observed shape and it is not a derivation of it: the widths and the fraction are chosen to match the data, and the figure’s purpose is to show what a deficit between two populations looks like and how much of the sample lands in it.

Colour is degenerate between age and metallicity. An old, metal-poor population and a younger, metal-rich one can have the same broad-band colour. Breaking that degeneracy needs spectral features — the strength of the Balmer absorption lines against the metal lines — and the resulting ages carry uncertainties of gigayears.

The valley’s width depends on the bands. Measured in optical colours the gap is shallow; measured with an ultraviolet band against an infrared one it is much deeper, because the ultraviolet responds to star formation on a timescale of a hundred million years rather than a billion. The same population therefore looks more or less bimodal depending on which two filters are divided, and any statement about the depth of the valley has to name them.

And the diagram is a snapshot. A population that is bimodal now says nothing directly about how individual galaxies moved through it, and there is more than one history that produces the same instantaneous distribution. Following the bimodality to higher redshift is how that is attacked: the red sequence is in place by $z \approx 1$ and thins out beyond $z \approx 2$, which brackets when most of the quenching happened.

Where the two populations came from #

The final question the diagram poses is genetic rather than instantaneous: are the red galaxies the descendants of the blue ones, or two populations with separate histories?

The evidence favours descent, with qualifications. The total stellar mass on the red sequence has roughly doubled since $z \approx 1$, while the mass in the blue cloud has stayed nearly flat — so galaxies have been arriving on the red sequence continuously, and they must be coming from somewhere. The blue cloud is the only available supplier.

But the arrivals do not simply change colour and stay put. A galaxy that quenches at a given mass lands at the faint end of the red sequence; the bright end has grown by a different route, through mergers of red galaxies with each other, which add mass without adding any new stars. Those “dry” mergers are the reason the most massive galaxies are red, enormous, and have surprisingly old stellar populations for their size.

So the diagram records two processes running at once — quenching, which moves galaxies across the gap, and merging, which moves them along the sequence. Disentangling the two is the substance of a large part of the field, and every technique for doing it comes back to the two axes of this one plot.

It is worth noting what the diagram does not divide galaxies by, because the omission is informative.

Morphology — spiral against elliptical — correlates with colour and is not the same cut. There are red spirals, which have kept their structure and lost their gas, and blue ellipticals, usually recent mergers with a burst still fading. A classification by shape and one by colour agree perhaps eighty per cent of the time, and the disagreements are the interesting galaxies, because they are the ones caught between two states. That the colour cut is the sharper of the two is itself a result: what happens to a galaxy’s gas is more decisive, and happens faster, than what happens to its shape.

The generalisation #

The reasoning here is one of this collection’s recurring shapes, and it is worth stating in its general form: a gap in a distribution is a statement about a rate.

In a steady state, the number of objects observed in any interval of a variable is proportional to the time an object spends there. So a sparsely populated region means either that few objects enter it — which the two full populations on either side rule out — or that they cross it quickly.

That single argument is what makes the Hertzsprung gap in the stellar colour–magnitude diagram a statement about how fast a star crosses it, the radius valley a statement about how fast a planet loses its envelope, and the green valley a statement about how fast star formation stops. In each case a deficit has been converted into a time, using nothing but the assumption that the population is in a steady state — which is the assumption to examine when the conclusion looks surprising.

One more reading shows what a steeper faint-end slope does to the same bimodality.

The valley between the two colours is a statement about how quickly galaxies cross it, and its emptiness is therefore a timescale rather than a preference — whatever turns a blue galaxy red does it faster than the galaxies arrive.

Where the ladder goes next #

The next rung is the mechanism itself: what actually stops star formation, at which galaxy masses, and why the answer appears to differ between the field and the cluster.

Later rungs on this anchor: the morphology–density relation and environmental quenching; feedback from active nuclei as the mass-dependent mechanism; the evolution of the red fraction with redshift; dust as a contaminant and how it is removed; the green valley resolved with ultraviolet data, which changes its apparent width considerably; and the stellar mass function of each population separately, which is a sharper statement than the colour distribution alone.