Astronomy & Celestial Mechanics
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Galaxies

Two ways to stop that do not interact

A galaxy's chance of having stopped forming stars depends on its mass and on where it is, and the census says the two dependences multiply. The efficiency with which environment quenches a galaxy is the same number at every mass, across two and a half decades of it — which is surprising, because both mechanisms work on the same gas.

Assumes Galaxy populations, Clusters and Star formation.

15 min read 5 figures Scales that defeat intuitionLight is the only messenger

Two colours, and almost nothing between established that galaxies come in two colours with almost nothing between, and that the emptiness of the gap is a statement about how fast the transition happens. It named three candidate mechanisms and left the question of which operates where.

The census can answer a version of that question, and the answer has a structure nobody predicted.

Two ways to stop, and the same curve shifted. The fraction of galaxies that have stopped forming stars, against their stellar mass, at four local densities. Two things are happening at once. Mass quenching turns the curve upward above about 10^10.6 solar masses, and it does so at the same mass whatever the environment — the curves rise in step. Environment quenching lifts the whole curve, and it does so by the same fraction of what is left at every mass, which is why the four curves look like one curve with its floor raised rather than like four different shapes. At 10⁹·⁵ solar masses the red fraction runs from 13 per cent in the field to 97 in a cluster core, and almost all of that difference is environmental; at 10¹¹·⁵ almost everything is red everywhere and the environment has nothing left to do. The two mechanisms are separable, which is the census's central quantitative result and the thing any account of either one has to explain.
Fig. 1 The fraction of galaxies that have stopped forming stars, against stellar mass, at four local densities. Two things happen at once: the curve turns upward above about ten and a half in the logarithm of the stellar mass, at the same mass in every environment, and the whole curve lifts as the density rises. The lifting is by the same fraction of what is left at every mass, which is why the four look like one curve with its floor raised rather than like four different shapes.

The question the two-dimensional census asks

A galaxy has a stellar mass and it has a local density of neighbours. Both correlate with whether it is red. The useful question is not which correlates more strongly but whether the two dependences can be separated — whether, holding one fixed, the other behaves the same way at every value of the first.

Write the red fraction as a function of both, fred(M,ρ)f_{\rm red}(M, \rho), and define the environmental quenching efficiency as the excess red fraction over the lowest-density bin, divided by the fraction of galaxies still blue there:

εenv(M,ρ)=fred(M,ρ)−fred(M,ρmin)1−fred(M,ρmin).\varepsilon_{\rm env}(M, \rho) = \frac{f_{\rm red}(M,\rho) - f_{\rm red}(M,\rho_{\rm min})}{1 - f_{\rm red}(M,\rho_{\rm min})}.

The denominator is what makes this a useful quantity rather than a difference of two fractions. At high mass almost everything is already red, so an environment that quenched with perfect efficiency could still only raise the red fraction by a little — and a raw difference would call that a weak environmental effect when it is a saturated one.

An efficiency that does not know the mass. The efficiency with which environment quenches a galaxy — the excess red fraction over the field, divided by the number of galaxies still blue in the field and therefore available to be quenched — against stellar mass, at three densities. Every curve is exactly flat. That is not a feature of the data being fitted but a consequence of the model: if the two mechanisms act independently, the probability of surviving both is the product of the probabilities of surviving each, and the environmental term factors out of the mass dependence entirely. The observed version of this plot is flat too, across two and a half decades of stellar mass and three of local density, and that flatness is the strongest statement the census makes about quenching. It says the mechanism that acts on a galaxy because of where it is does not care how massive the galaxy is, and the mechanism that acts because of its mass does not care where it is — which is surprising, because every physical account of either one involves gas, and there is only one supply of it.
Fig. 2 That quantity, against stellar mass, at three densities. Every curve is flat, and in the drawn model it is flat identically: if the two mechanisms act independently, the probability of surviving both is the product of the probabilities of surviving each, so the environmental term factors out of the mass dependence entirely. The observed version of this plot is flat too, and that is the measurement.

What separability means

If the efficiency is independent of mass, then

1−fred(M,ρ)=[1−fmass(M)][1−fenv(ρ)],1 - f_{\rm red}(M,\rho) = \left[1 - f_{\rm mass}(M)\right]\left[1 - f_{\rm env}(\rho)\right],

which reads: the probability that a galaxy is still forming stars is the probability that it escaped mass quenching times the probability that it escaped environmental quenching, as though the two were independent trials.

That is a strong statement and it is not obviously true. Both mechanisms work by removing or heating the same gas, and there is only one supply of it in each galaxy. A galaxy that has already lost half its gas to one process ought to be easier for the other to finish off, which would make the two dependences interact and the efficiency rise with mass.

It does not. Across the range where both effects are measurable — roughly 10910^{9} to 101110^{11} solar masses, and from the field to a cluster core — the efficiency is constant to within the errors.

Two ways to stop, and the same curve shifted. The fraction of galaxies that have stopped forming stars, against their stellar mass, at four local densities. Two things are happening at once. Mass quenching turns the curve upward above about 10^10.6 solar masses, and it does so at the same mass whatever the environment — the curves rise in step. Environment quenching lifts the whole curve, and it does so by the same fraction of what is left at every mass, which is why the four curves look like one curve with its floor raised rather than like four different shapes. At 10⁹·⁵ solar masses the red fraction runs from 16 per cent in the field to 97 in a cluster core, and almost all of that difference is environmental; at 10¹¹·⁵ almost everything is red everywhere and the environment has nothing left to do. The two mechanisms are separable, which is the census's central quantitative result and the thing any account of either one has to explain.
Fig. 3 The same construction with a shallower dependence on density and a higher threshold. The shapes change and the separability does not, because it is a property of the form rather than of the parameters. What a measurement establishes is that the data have this form, and the useful content of the model is that it has one free function of mass and one of density rather than a free function of both.

Which accounts survive it

Separability is a constraint on mechanisms, and it is a sharp one.

Ram-pressure stripping — the intracluster medium blowing a galaxy’s gas out as it falls through — depends on the galaxy’s own gravity holding the gas in, which depends on its mass. A stripping-dominated account predicts an efficiency that falls with mass, because a massive galaxy holds its gas better. That is not what is seen at the masses where both effects operate, though stripping is certainly happening: it is observed directly, as tails of gas behind galaxies in clusters.

Strangulation — the galaxy loses access to fresh gas when it becomes a satellite, and simply uses up what it has — is closer to what the data want. The supply is cut off by an event that has nothing to do with the galaxy’s mass, and the galaxy then consumes its remaining gas at whatever rate its mass sets. The timescale is the gas depletion time, a few billion years, and the gas running out before the galaxy does is exactly the process.

And mass quenching — whatever holds gas hot in a massive halo — has to be a function of mass alone, which the leading accounts are: a halo above a threshold mass shock-heats infalling gas, and an accreting nucleus supplies enough energy to keep it hot.

The separability therefore points at an account in which the environmental process is a switch thrown by an event — becoming a satellite — and the mass process is a threshold in a property the galaxy carries with it. Two things of different kinds, which is why they multiply rather than interfere.

The complication the separability hides

There is a population the clean picture does not fit, and naming it is more useful than the picture.

At the lowest masses — below about 10910^{9} solar masses — the red fraction in the field is essentially zero and the red fraction in a cluster is high, so the efficiency is nearly one and its mass dependence cannot be measured: there is nothing to divide by. The dwarfs are quenched almost entirely by environment, and almost every isolated dwarf is still forming stars — which is the clearest environmental signal in the whole census and the one where the efficiency cannot be measured.

At the highest masses the reverse happens. Above 101110^{11} the field fraction is already above ninety per cent, so environment has almost nothing left to act on, and the efficiency is again measured as a small difference of two numbers near one.

The separability is therefore established in the middle of the range and assumed at both ends, where the quantity it is about is poorly determined by construction. That is a normal situation and it is worth saying out loud, because the flatness of the drawn curve is exact and the flatness of the measured one is a statement with error bars that grow at both edges.

There is a second complication and it is about what “environment” means. Local density is a proxy, and what it is a proxy for is the mass of the halo the galaxy lives in and how long it has lived there. Two galaxies at the same local density can be a recent arrival in a large cluster and a long-term resident of a small group, and their histories are not the same. Analyses that use halo mass and the time since infall in place of density find a cleaner picture — and they require a model to assign both.

Two populations, and the valley between them. 420 model galaxies, 70 per cent of them drawn from a tight red sequence tilted by -0.08 magnitudes of colour per magnitude of brightness, the rest from a broad blue cloud. Only 1.9 per cent land in the band of width 0.20 magnitudes midway between the two sequences, against 8 per cent in the same band laid on the blue cloud and 49 per cent on the red sequence. The bimodality is the strongest statement the galaxy census makes: a galaxy is usually forming stars or has stopped, rarely in between, and since colour tracks the age of the newest stars, the emptiness of the middle is a statement about a timescale — whatever ends star formation does it in a few hundred million years, not a few billion.
Fig. 4 What the separability produces in the colour–magnitude diagram itself. A cluster’s population is seventy per cent red against a field’s forty; the two sequences do not move and the valley between them does not fill in. The separable model says exactly this: environment changes how many galaxies have been through the transition and nothing about the transition itself, which is why the shape of the diagram is the same everywhere and only the weights differ.

A timescale from the separability

The separable form contains a number that a mechanism has to reproduce, and extracting it is the most useful thing the census does.

The environmental efficiency is the fraction of satellites that have been quenched by their environment. If becoming a satellite starts a clock and quenching happens when the clock runs out, then the efficiency is the fraction of satellites whose clocks have run out — which, given a distribution of infall times from a cosmological simulation, converts directly into the clock’s length.

The answer is between two and five billion years, depending on the galaxy’s mass and on the halo’s, and it is long. A galaxy falling into a cluster crosses it in about a billion years, so a satellite typically survives a crossing or two with its star formation intact before stopping.

That length rules things out. Ram-pressure stripping in a cluster core acts in a few hundred million years, which is far too fast — a stripping-dominated account would give an efficiency that saturated almost immediately after infall, and the observed one rises gradually. Whatever sets the clock acts on the timescale a galaxy takes to use up the gas it already has, which is the depletion time, which is a few billion years.

There is a wrinkle that makes the number more interesting rather than less. The delay is longer for lower-mass satellites in absolute terms, and it is roughly the same in units of each galaxy’s own gas depletion time. The clock is the galaxy’s own, started by an external event — which is exactly the structure the separability required, arrived at from an entirely different direction.

An efficiency that does not know the mass. The efficiency with which environment quenches a galaxy — the excess red fraction over the field, divided by the number of galaxies still blue in the field and therefore available to be quenched — against stellar mass, at three densities. Every curve is exactly flat. That is not a feature of the data being fitted but a consequence of the model: if the two mechanisms act independently, the probability of surviving both is the product of the probabilities of surviving each, and the environmental term factors out of the mass dependence entirely. The observed version of this plot is flat too, across two and a half decades of stellar mass and three of local density, and that flatness is the strongest statement the census makes about quenching. It says the mechanism that acts on a galaxy because of where it is does not care how massive the galaxy is, and the mechanism that acts because of its mass does not care where it is — which is surprising, because every physical account of either one involves gas, and there is only one supply of it.
Fig. 5 The efficiency at four densities under a different parameterisation, to show what the flatness is and is not. The level of each curve is a fit — it is the fraction of satellites at that density whose clocks have run out, and it is what converts into a timescale. The flatness is not a fit: it is the separability, and it holds whatever the levels are. Reading the level as the measurement and the flatness as the result is the right way round.

What was actually measured

A survey with redshifts, from which three quantities are derived and none is observed directly.

The stellar mass comes from fitting a stellar population model to the broadband colours, or from a single colour and a mass-to-light ratio. It carries a systematic of about a factor of 1.5 from the assumed distribution of stellar masses at birth, and that systematic is common to the whole sample — so it shifts the mass axis without distorting it, which is the best kind of systematic to have in a plot about a shape — the same consolation a luminosity function’s knee offers.

The local density comes from the distance to the nth nearest neighbour within a redshift slice, and it depends on n, on the slice’s thickness and on the survey’s completeness. Different choices give densities that correlate well and are not the same number, so the density axis is a rank rather than a measurement.

And “red” is a cut. Some analyses split on colour, some on a spectral index, some on a fitted star-formation rate. The three do not agree on individual galaxies — a dusty star-forming galaxy is red in colour and blue in the others — so the red fraction depends on the definition by several per cent, which is comparable with the effects being separated.

The honest summary is that the separability has been found with every combination of those choices that has been tried, which is a stronger statement than any one analysis makes.

What the shape of the mass term is trying to say

The environmental half of the separation is an event with a clock. The mass half is a threshold, and where the threshold sits is a number worth taking seriously because two unrelated arguments produce nearly the same one.

The red fraction turns upward at a stellar mass of about 3×10103\times10^{10} solar masses, which for a typical stellar-to-halo mass ratio is a halo of around 101210^{12}. That is close to the mass above which infalling gas is shock-heated to the halo’s virial temperature rather than streaming in cold — a transition computed from the cooling function and the shock’s stability, with no galaxies in it at all.

It is also close to the mass at which the luminosity function’s knee sits, and to the mass above which galaxies are predominantly spheroidal rather than discs. Three features of three different statistics, at one scale.

Whether that is one mechanism or a coincidence of three is the central open question of the subject, and the honest position is that the agreement is suggestive and the arguments connecting them are not yet tight. What can be said is narrower and still useful: the mass term in the separation is a threshold rather than a gradual rise, its position is measured to about a factor of two, and any account of it has to produce a scale rather than take one.

The alternative account — that the mass dependence is not about the halo at all but about the black hole, whose mass correlates with the bulge and whose energy output scales steeply with it — predicts a threshold in the bulge mass rather than the total. Those two are hard to separate in a survey, because bulge mass and total mass correlate, and the analyses that have tried find bulge mass the better predictor. That is a real result and it is not decisive, since the better predictor of a correlated pair is partly a statement about which was measured better.

Where the model stops

The model here is a form, not a derivation. The exponential shapes for the two quenching probabilities are chosen because they are simple and because the data are consistent with them. Nothing in this essay derives either one, and the separability would hold for many other pairs of functions — it is a statement about the structure of the dependence rather than about its shape.

Time is missing. The census is a snapshot, and quenching is a process. A separable red fraction today is consistent with several different histories, including ones in which the two processes did interfere at earlier epochs and the interference has been erased. Following the separability to higher redshift is how that is attacked, and the answer so far is that it weakens.

Dust is still the leading contaminant, for the reason the colour census gives: a dusty star-forming galaxy is red, dusty galaxies are more common in dense environments, and a colour-selected red fraction therefore overstates environmental quenching by an amount that has to be modelled.

And the causal direction is not established. A galaxy in a dense environment today may have been in a dense environment when it formed, so a correlation with density is partly a correlation with when and where a galaxy was assembled. Disentangling “quenched by its environment” from “formed early because it is in a place that collapsed early” is the hardest part of the subject and nothing in a snapshot settles it.

The central galaxy is a third case

Everything above splits galaxies into two categories by density, and the real division is into three: a galaxy that dominates its own halo, a galaxy that orbits inside somebody else’s, and — the case the density proxy cannot see — a galaxy that used to be a satellite and has been ejected back out.

Centrals and satellites behave differently at fixed mass and fixed density, and the difference is not small. At 101010^{10} solar masses a central in the field is quenched perhaps fifteen per cent of the time and a satellite of the same mass in the same measured density perhaps forty. So the density-based analysis is averaging over two populations whose quenching has different causes, and the separability it finds is a separability of the average.

Splitting them properly requires a group catalogue — an algorithm that decides which galaxies share a halo and which of them is the central — and every such catalogue has misclassifications at the ten to twenty per cent level. A satellite called a central drags the central’s quenched fraction up; a central called a satellite does the reverse. The corrections are made with mock catalogues run through the same algorithm, which is the same feed-a-known-signal-to-the-pipeline discipline that high-contrast imaging arrived at.

The ejected population is the awkward one. Simulations find that a substantial fraction of galaxies now outside a cluster’s virial radius have been inside it — thrown back out by three-body interactions during infall — and they carry their quenching with them. They are counted as field galaxies, they are red, and they inflate the field’s quenched fraction in exactly the mass range where the environmental efficiency is being measured against it.

The reference population is contaminated by the population it is a reference for, which is a difficulty that no amount of survey volume removes, and which is one of the two or three reasons the quoted efficiencies differ between analyses by more than their error bars.

The generalisation

The shape to carry is that a two-variable dependence which factorises is a much stronger claim than a two-variable dependence that merely exists, and that the test for it is the ratio rather than the difference.

The quantity that made this measurable is the efficiency — an excess divided by what was available to be affected. Differences of fractions are misleading whenever a fraction can saturate, and almost every fraction can. Normalising by what was left to change turns a saturating quantity into one that can be compared across a range, and it is the same move that makes a survival curve readable, a completeness correction honest, and a conditional probability the right thing to plot.

The second reading is about what independence means physically. Two processes that act on the same resource are not obviously independent, and finding that they behave as though they are says something about their kinds: they are independent when one is an event and the other a threshold, because an event does not consult the threshold and a threshold does not know about the event. Separability is evidence about the type of each mechanism rather than about its strength, and it is the sort of evidence that is available from a census and from almost nothing else.

Still open: what the gap’s width is measuring

What comes next returns to the valley itself. Its emptiness was read as a crossing time in one colour; the crossing time that comes out depends on which colour, because each passband remembers star formation for a different length of time. In the ultraviolet the same population looks different enough that the quantity being inferred is not obviously the same quantity.

Beside it lies the morphology–density relation, which is the same census cut by shape rather than by colour — and which agrees with the colour cut about eighty per cent of the time. The twenty per cent is where the galaxies caught between two states are.

Where this goes next

Two populations, and the valley between them. 420 model galaxies, 42 per cent of them drawn from a tight red sequence tilted by -0.08 magnitudes of colour per magnitude of brightness, the rest from a broad blue cloud. Only 3.3 per cent land in the band of width 0.20 magnitudes midway between the two sequences, against 17 per cent in the same band laid on the blue cloud and 27 per cent on the red sequence. The bimodality is the strongest statement the galaxy census makes: a galaxy is usually forming stars or has stopped, rarely in between, and since colour tracks the age of the newest stars, the emptiness of the middle is a statement about a timescale — whatever ends star formation does it in a few hundred million years, not a few billion. Two colours, and almost nothing between Plot a few hundred thousand galaxies by colour and brightness and they do not fill the plane. They pile into a tight red sequence and a broad blue cloud with a near-empty gap between, and an empty gap is a statement about how fast something happens. A cluster weighed three ways, and its stars weighed once. A cluster of galaxies with a velocity dispersion of 1000 km/s, gas at 8 keV and a strong-lensing Einstein radius of 25 arcseconds, each turned into a mass inside 1.5 Mpc by its own relation and nothing else: 7.0, 8.9 and 15.2 × 10¹⁴ M☉. The three assume, respectively, that the galaxies are in equilibrium, that the gas is, and nothing whatever — so their agreement to within a factor of 2.2 is not three restatements of one assumption. The lensing bar is the loosest of the three and is drawn that way deliberately: it measures the mass inside a cylinder of radius 109 kpc, 1.11×10¹⁴ M☉, and carrying that out to 1.5 Mpc as though it were a sphere overstates it. The stars are 2.9 per cent of it. A cluster weighed three ways The speeds of a cluster's galaxies, the temperature of its gas and the bending of light behind it are three measurements with almost nothing in common. They agree within a factor of two, and all three exceed the mass of the stars by about a hundred. The star-formation law, and the clock inside it. 46 model discs on the Kennicutt–Schmidt plane, built from Σ_SFR = 2.5e-4 Σ_gas^1.4 with 0.28 dex of scatter, with the exponent then fitted back off the drawn points at 1.42. The diagonal dashed lines are constant depletion times: gas divided by the rate consuming it. Every disc on this plane consumes its gas within a few gigayears, and a galaxy that has been forming stars for ten of them therefore cannot have been working from the gas it started with. The slope steeper than one is what makes the depletion time shorter where the gas is richer, which is the opposite of the intuition that a full tank lasts longer. The gas runs out before the galaxy does Divide a disc's gas by the rate it is turning that gas into stars and the answer is about two billion years — a seventh of the age of the disc. Every spiral still forming stars is therefore being fed from outside, and the star-formation law says the richer the disc, the sooner it starves.

About the same objects

Not linked from either essay — found by the objects both name.

What links here

Essays that link to this one from their own argument.

The objects this essay names

Each one links to every other essay that touches it.

FeedbackHalo massMorphology density relationQuenchingQuenching efficiencyRam pressure strippingRed sequenceSatellite galaxySeparabilityStrangulation