A lifetime read from how gas and stars sit apart

A giant molecular cloud has a mass of a hundred thousand to a few million Suns, a size of tens of parsecs, internal motions of a few kilometres a second, and a lifetime nobody has measured by watching. Its free-fall time — how long it would take to collapse if nothing held it up — is a few million years, a thousand times longer than the history of the observations. So every cloud is seen once, at one moment of its life, and nothing in a single cloud says which moment.

The essay on the motions that both support a cloud and seed its stars ended on exactly that problem. Two accounts of molecular clouds fit every static measurement: in one, clouds are long-lived structures held near equilibrium for tens of free-fall times, slowly forming stars; in the other, they are transient, assembled and dispersed within a free-fall time or two, forming stars quickly and inefficiently before their young stars blow them apart. The linewidths, virial parameters and filaments look the same either way. What separates them is how long the state lasts, and duration is not in a snapshot of one cloud.

It is in a snapshot of many. A galaxy holds thousands of clouds at every stage of their lives at once, and if every cloud goes through the same sequence — gas, then gas with young stars embedded, then young stars with the gas cleared — then the number of clouds caught in each stage is proportional to how long the stage lasts. That idea is old. The modern version turns it into a measurement by asking not how many clouds are in each stage, but how the gas and the young stars are arranged on the sky relative to each other.

Two pictures with a history #

The long-lived picture came first. In the 1970s and 1980s, clouds were treated as gravitationally bound objects supported against collapse — by turbulence, which cannot hold a cloud up indefinitely unless it is driven, and by magnetic fields, whose support cannot be squeezed away by compression and has to be lost by the slow drift of neutral gas past the ions. A cloud held up by a field that leaks out on the drift timescale would live tens of millions of years, form stars slowly in cores that lose their support first, and be gradually dispersed. Lifetimes of a hundred million years were proposed on the grounds that clouds are found between the spiral arms as well as in them.

The transient picture arrived around 2000, from two directions. The young stars in nearby clouds are almost all younger than a few million years, with few older ones still embedded, which suggests clouds form stars quickly and do not linger after doing so. And simulations of turbulent clouds showed structures assembled by converging flows and dispersed within a crossing time. On this view a cloud is not an object but an event — a passing concentration in a turbulent medium, which collapses where its own Jeans mass is exceeded and is gone before the rest of it has time to.

The two pictures predict lifetimes a factor of ten apart, and for thirty years the argument between them was conducted with indirect evidence: the ages of stars, the presence of clouds between arms, the energetics of feedback. Each piece of evidence was compatible with both pictures with enough adjustment. The question needed a measurement of duration that did not depend on interpreting any one cloud.

What a count can say #

The simplest version is a census. Classify the clouds of a galaxy by whether they contain young massive stars, and the fraction without them is the starless stage’s share of a cloud’s life.

The Large Magellanic Cloud, near enough and face-on enough for every cloud to be catalogued, was surveyed this way in the 2000s. About a quarter of its giant molecular clouds have no massive young stars, about half have ionised regions round young stars, and about a quarter have exposed young clusters as well. Converted with the ages of the clusters, that gave lifetimes of twenty to thirty million years.

The conversion is where the difficulty lies. A census measures ratios of durations, never a duration. A quarter of clouds starless means the starless stage is a third as long as the stage with stars; it says nothing about how long either is until one of them is fixed from outside. If stars appear only in the last two million years of a cloud’s life, a quarter starless means clouds live less than three million years. If they appear in the last twenty, it means twenty-seven. The figure is the whole problem in one picture: the same count, read through different assumptions about how long gas and stars coexist, gives answers a factor of ten apart.

Pointing the aperture at the gas, then at the stars #

The improvement, proposed by Diederik Kruijssen and Steven Longmore in 2014, replaces the classification of individual clouds with a statistic of two maps: one of molecular gas, from carbon monoxide emission, and one of young massive stars, from the Hα light of the gas they ionise. Choose apertures of some size, centre them on the brightest peaks of the gas map, and measure the ratio of gas to Hα inside them, relative to the whole galaxy’s ratio. Then do the same with apertures centred on the Hα peaks. Repeat for apertures of every size.

On large scales, both branches give the galaxy’s average. An aperture a kiloparsec across contains dozens of star-forming regions at every stage, and it does not matter where it is centred. On small scales, an aperture contains one region, at one stage, chosen by where the aperture was pointed. Centred on a gas peak, it holds a cloud, and that cloud contains young stars only if it is caught in the overlap — the short time between the first massive stars switching on and the gas being cleared. Centred on an Hα peak, it holds young stars, and their surrounding gas is still there only if they too are caught in the overlap. So the two branches split into a fork, gas-rich above and gas-poor below.

The fork’s shape carries three numbers. The upper branch at small scales is the Hα phase’s length divided by the overlap. The lower branch is the overlap divided by the cloud lifetime. And the scale at which the fork closes is the typical distance between independent regions — the size of the cells the galaxy’s star formation is divided into.

The branch that reads the lifetime #

Varying the cloud lifetime shows which branch carries it.

The upper branches barely move: a cloud picked out by its gas contains young stars for the overlap time, whatever happens before that, so the gas-peak branch knows only the overlap. The lower branch is the one that measures the cloud’s life. A young region picked out by its Hα has gas left only during the overlap, and the gas it has then is compared with the galaxy’s average gas — which is large if clouds live a long time, because long-lived clouds accumulate in the census. Clouds of eighty million years make the lower branch dip forty times below the galaxy’s ratio; clouds of five million years, two and a half times.

The calibration is the Hα phase. Hα is emitted by gas ionised by stars more massive than about fifteen Suns, and those stars live a few million years; the time over which a newborn population emits Hα, averaged over the initial mass function, is about four million years, and it is computed from stellar evolution rather than inferred from clouds. Everything else in the fork is measured in units of it. That is what a census lacked: a duration fixed independently, against which the ratios become times.

Resolution sets what can be read #

The fork is opened only on scales smaller than the separation between regions. A measurement whose resolution is coarser than that separation sees only the part of the fork that has already closed.

For regions 150 parsecs apart, a resolution of 300 parsecs leaves only the outer part of the fork visible, where the branches have nearly converged. The lifetime can still be fitted, because the shape of the closing branches depends on it, but the fit leans on the model’s assumptions about the regions — that they are independent, that they all follow the same sequence, that their spacing is uniform. At a resolution of fifty parsecs or better, the fork’s open end is seen directly. That is why the method needed interferometric maps of molecular gas at tens of parsecs across whole galaxies, which have been made only in the last decade, for dozens of nearby discs. At a distance of ten megaparsecs, one arcsecond is fifty parsecs, so resolving the fork’s open end in a typical nearby spiral needs a resolution of an arcsecond or better in carbon monoxide and in Hα over a whole disc — routine for optical imaging, and demanding for millimetre interferometry, which reaches it only with long baselines and many hours per galaxy. The farther galaxies, and the ones seen nearly edge-on, where regions overlap along the line of sight, can be measured only through the closing part of the fork.

The results, across those galaxies, are lifetimes of ten to thirty million years, overlaps of one to five million years, and region separations of one to a few hundred parsecs. The overlap is the time massive stars take to disperse their clouds, and its shortness is itself a result: a cloud is cleared within a few million years of its first massive stars switching on, before the most massive of them have exploded as supernovae, so the clearing is done by their radiation, winds and expanding ionised gas.

A lifetime in free-fall times #

A lifetime in years means little until it is compared with the time a cloud would take to collapse.

At the mean density of a giant molecular cloud averaged over its whole volume — about a hundred hydrogen molecules per cubic centimetre — the free-fall time is about three million years, and a cloud of twenty million years lives six or seven of them. That is neither of the two pictures in its pure form. It is longer than the one or two free-fall times of a cloud dispersed as fast as gravity can assemble it, and shorter than the tens of free-fall times a quasi-equilibrium structure would last. The comparison with the galaxies’ own clocks makes the same point: the lifetimes are comparable with the time a disc takes to rotate through a spiral arm or to shear a cloud apart, about one dynamical time of the disc, which is what a picture of clouds assembled and torn apart by the galaxy’s large-scale motions predicts.

The density matters. The dense clumps within a cloud, at ten thousand molecules per cubic centimetre, have free-fall times of three hundred thousand years, and a cloud of twenty million years contains clumps that have lived many of their own free-fall times — or that were assembled late. A lifetime in free-fall times is a statement about a particular density, and the measurement gives it at the clouds’ mean.

A short life and a low efficiency #

The lifetime connects to the oldest puzzle about molecular clouds. If all the molecular gas in the Milky Way collapsed in a free-fall time and turned into stars, the Galaxy would form stars at a few hundred solar masses a year. It forms one or two. Benjamin Zuckerman and Neal Evans pointed this out in 1974, and the deficit has been the central fact of star formation ever since: the gas runs out far more slowly than gravity alone would empty it.

The two pictures explain the deficit differently. In the long-lived picture, clouds form stars slowly for a long time — support by turbulence and magnetic fields keeps the rate per free-fall time low. In the transient picture, clouds form stars at whatever rate they like but are destroyed before they convert much of their gas. The measured numbers make them the same statement. Dense-gas tracers give an efficiency of about one per cent per free-fall time; a lifetime of a few free-fall times then turns a few per cent of each cloud into stars before it is dispersed; and the integrated efficiencies inferred from the stellar masses of the clusters that clouds leave behind are a few per cent to ten. The low efficiency is the short life multiplied by the slow rate, and both are needed.

The clearing itself is fast for a reason. The overlap of one to five million years is shorter than the lives of most stars that explode as supernovae, so the clouds are dispersed before most of their supernovae go off. The radiation of the most massive stars ionises the gas round them, heating it from about twenty kelvin to ten thousand; the ionised gas, at five hundred times the pressure of the cold gas round it, expands at about ten kilometres a second and pushes the remaining molecular gas away. A cloud a few tens of parsecs across is cleared by that expansion in a few million years, which is the overlap the fork measures. That the measured overlap matches this arithmetic is a check of the method as well as a result: the clouds are destroyed by the first generation of their own massive stars, and the supernovae that follow explode into gas that has already been cleared, heating the diffuse medium between clouds rather than the clouds themselves.

So the clouds are neither long-lived reservoirs nor single free-fall collapses. They form stars inefficiently for a few free-fall times, at a rate that is low per free-fall time for reasons the turbulence and the field supply, and are then cleared within a few million years by the stars they made — and most of their gas returns to the diffuse medium to become molecular again in a later cloud.

What the statistic assumes #

Every region follows the same sequence. The fork is computed for a population whose members all go from gas to stars to cleared, with the same durations. Real clouds differ in mass and environment, and the measured lifetime is an average weighted by how the regions contribute to the two maps’ peaks. Clouds that never form massive stars contribute to the gas map but never to the Hα map, and are counted as a long starless phase rather than as a separate population.

The tracers are what they are assumed to be. Carbon monoxide misses molecular gas where it is photodissociated or where the metallicity is low, and Hα is absorbed by dust in the youngest, most embedded regions. Both biases shorten the overlap and change the lower branch. The Hα clock itself depends on the initial mass function’s upper end, which is what converts light into a birth rate in the first place.

The regions are independent and evenly spaced. Clustering of regions — along spiral arms, for example — makes the fork close on a scale set by the arm’s width as well as the regions’ separation. The full method fits a distribution of separations; the figures here use one.

Star formation is assumed steady. The count of regions in each stage measures each stage’s duration only if regions are being born at a constant rate over the past few tens of millions of years. A galaxy whose star formation rose or fell over that time — after an interaction, or as a spiral arm swept through — has its census skewed towards the stages that were being produced fastest, and the lifetime inferred from it is biased by an amount that depends on how fast the rate changed relative to the lifetime being measured.

The figures use the simplest model. The branches drawn are expectations, without the scatter that small numbers of peaks introduce in real maps, and without the corrections the full method makes for the peaks’ own detection threshold.

Still open: whether the lifetime depends on where the cloud is #

The statistical lifetimes have answered the question the snapshot could not: clouds live ten to thirty million years, a few free-fall times at their mean density, and are cleared within a few million years of making massive stars. That is the first measurement of a cloud’s age that does not depend on watching one, and it agrees with the cluster-age census of the Magellanic Cloud once the overlap is fixed by the fork rather than assumed.

What remains open is how the lifetime depends on the environment. The clouds near a galaxy’s centre, where the disc’s shear is strong and the pressure high, and the clouds in its outskirts, where both are weak, are measured with the same method and do not all give the same answer; whether the lifetime tracks the local dynamical time — the galaxy’s rotation and shear — or the clouds’ own free-fall time, or the time their stars take to clear them, decides what controls star formation on the scale of clouds. The maps that would decide it, at tens of parsecs across the whole range of environments in one galaxy, are now being made.