Fast and inefficient star formation due to short-lived molecular clouds and rapid feedback

The physics of star formation and the deposition of mass, momentum, and energy into the interstellar medium by massive stars ("feedback") are the main uncertainties in cosmological simulations of galaxy formation and evolution. These processes determine the properties of galaxies, but are poorly understood on the ~100 pc scale of molecular clouds resolved in modern galaxy formation simulations. The key missing ingredient has been an empirical census of the evolutionary cycling between molecular clouds, star formation, and feedback.
Fast and inefficient star formation due to short-lived molecular clouds and rapid feedback

By analysing data from the new ALMA telescope with novel analysis techniques, it is finally possible to directly measure the evolutionary timeline on the scales of molecular clouds in nearby galaxies. This has now been done for the first time in the nearby flocculent spiral galaxy NGC300.

On the evening of February 4, 2013, I was walking home after work from the metro in Munich with my neighbour and colleague Steve Longmore. Both of us had been working on the formation of massive stars and stellar clusters for several years, and we were discussing a puzzling discovery from a field somewhat disconnected to ours. On the scales of entire galaxies, there exists a well-known relation between the (molecular) gas surface density and the star formation rate (SFR) surface density: the so-called "Schmidt-Kennicutt relation", or "star formation relation" (which I will use hereafter). A series of papers had just shown that the star formation relation breaks down on small (<500 pc) spatial scales; the scatter on the correlation increases rapidly until the correlation vanishes altogether on scales of ~100 pc.

As we were discussing this finding, both of us quickly realised it made perfect sense. On the scales of individual sites of star formation, it matters when exactly you observe a star-forming region. Too early, and all you see is gas. Too late, and the feedback from massive stars has dispersed the molecular cloud from which they formed. For any evolutionary timeline describing star formation within molecular clouds, an individual region only ever reflects a single moment on that timeline. To get a systematic correlation between gas and star formation, you need a large number of regions spanning the full range of evolutionary ages. This can be achieved either by integrating in time or in space; these are degenerate quantities.

"It is an uncertainty principle," I exclaimed. "But with different variables than the quantum-mechanical one." Steve nodded immediately; this was one of these analogies that hardly required explaining. The spatial scale over which the molecular gas surface density and the SFR surface density are measured should be large enough to contain at least one region bright in each tracer used, otherwise there can be no correlation between them. But whether at least one region is bright in each tracer depends on their relative lifetimes. If one tracer lives 100 times longer than the other, statistically speaking about 100 regions are required to have one of them be bright in the short-lived tracer. This can be quantified such that the product of the spatial scale (Δx) and the square-root of the lifetime of the shortest-lived tracer (Δt) should exceed the product of the mean separation length between regions (λ) and the square-root of the total duration of the evolutionary timeline connecting both tracers (τ):

I am still a bit disappointed about the square-root, but that is the inevitable result of looking at the two-dimensional structure of a star-forming galaxy disc rather than a one- or three-dimensional one. If this "uncertainty principle for star formation" is satisfied, the scatter on the star formation relation should be small. If it is not satisfied, the relation should vanish.

That same evening, I wrote Steve a long email summarising our conversation. Some details would turn out to be wrong, but the ideas were there. Within ten minutes, he replied "have you submitted it yet?" We wouldn't. At least not for a while. Instead, we decided other projects had priority.

Coming from a different field, we thought our idea was so simple that somebody must have published it already. It was only two months later that we learned we were not just wrong, but that our colleagues working on galactic-scale star formation were very interested in trying to explain why the star formation relation breaks down on small spatial scales, and in particular what the quantitative details of that breakdown can say about the cloud-scale physics of star formation and stellar feedback. We sprang back to life and in a matter of days drafted a paper that explored two quantitative implications of our "uncertainty principle". First, it explained why the star formation relation breaks down on small spatial scales and predicted how the scatter on the relation varies continuously as a function of spatial scale. Second, it demonstrated that the details of how exactly the star formation relation breaks down are a direct probe of the cloud-scale physics of star formation and feedback. We had not realised this implication during our initial conversation in February, but it worked remarkably well.

When evaluating the star formation relation on a certain spatial scale, one is effectively selecting the size of a circular aperture within which the gas mass and SFR are added up. It turns out that where the aperture is placed matters greatly for the ratio between gas mass and SFR within the aperture. For randomly-placed apertures, the gas mass-to-SFR ratio makes random excursions around the galactic average (which reflects the position of the galaxy on the star formation relation). However, when focusing apertures on peaks of gas emission (e.g. molecular clouds) or young stellar emission (e.g. HII regions), the gas-to-SFR ratio is biased away from the galactic average. We discovered that the magnitude of this bias and its dependence on the aperture size encodes the evolutionary timeline of molecular clouds, star formation, and feedback.

Imagine a galaxy consisting of molecular clouds (traced by the CO line) and HII regions containing young stars (traced by the Hα line). One can place apertures on peaks of CO or Hα emission, and measure how the CO-to-Hα flux ratios are elevated or suppressed, respectively, relative to the galactic average as the aperture size is changed. The shorter-lived of these two tracers will be rare compared with the longer-lived, more common one. Only a small number of apertures are required to cover the complete sample of rare, short-lived emission peaks. These will encompass a relatively small part of the galaxy and contain few of the many long-lived emission peaks. This results in a CO-to-Hα flux ratio that differs considerably from the galactic average. Conversely, covering the long-lived emission peaks requires numerous apertures that will also include many of the short-lived emission peaks, resulting in only a modest deviation from the galactic CO-to-Hα ratio. We derived a simple model describing this statistical behaviour and demonstrated that it directly probes the relative lifetimes of the CO and Hα emission, as visualised in the movie below (this is Supplementary Video 2 of our paper; follow the link to Youtube to read a detailed description).

How the (anti-)correlation between gas and young stars reflects the molecular cloud lifecycle.

This was exciting! If we could fit our model to observations of the CO-to-Hα ratio in real-Universe galaxies, this would allow us to comprehensively describe the evolutionary timeline of molecular clouds, star formation, and feedback, using just a single observational diagnostic. In many branches of astrophysics, it is extremely rare to measure timescales, because most physical processes of interest take much longer than a human lifetime. In the case of the cloud lifecycle, gaining access to the time dimension had great potential for leading to critical insights. We would not only be able to measure how long molecular clouds live, but also how quickly they are destroyed by stellar feedback. In turn, this would allow us to derive the outflow velocity of the feedback ejecta, the fraction of the gas mass eventually turned into stars, and the typical length scale on which galaxies fragment into independent clouds and star-forming regions. Constraining any of these quantities would have important implications for understanding how galaxies grow and form stars. For instance, measuring the feedback dispersal timescale would allow us to determine which feedback mechanisms (e.g. supernovae, photoionisation, stellar winds, or radiation pressure) destroy molecular clouds and halt star formation. This has been a major open question in studies of galaxy formation and evolution.

By September 2013, Steve and I realised that our initial excitement had turned into tangible results that were worth pursuing further. Out of nowhere, this simple, low-priority idea of an "uncertainty principle for star formation" jumped to the top of our priority list, decisively changing our plans for the next five years. Having published the "idea paper", we urgently needed two things. First, we needed to thoroughly demonstrate that fitting our statistical model for the change of the CO-to-Hα ratio reliably characterises the cloud lifecycle. Second, we needed observational data of nearby galaxies suitable for carrying out this measurement.

We set out to address both requirements simultaneously. By mid-2014, we had written a code that could take a pair of galaxy images in two different tracers (here taken to be CO and Hα), quantify the bias of the CO-to-Hα ratio around emission peaks in either of the maps as a function of the spatial scale, and fit our statistical model to constrain the underlying evolutionary timeline. It ran from beginning to end and returned sensible numbers, but it was still missing all kinds of detail that later turned out to be critical. For instance, our model was still describing individual regions as point sources rather than as extended structures, the error propagation was oversimplified, and the way in which our code dealt with real data was clumsy - noise was not treated correctly, the input images could only be masked with rectangular shapes, and we had no way of subtracting diffuse, background emission from the images.

The technical complexity of the problem turned out to be so great that it would take until early 2017 before all of these issues had been overcome. Critically, this finally allowed us to rigorously test our technique. We ran a set of hydrodynamical simulations of star-forming galaxies and performed hundreds of controlled numerical experiments, in which we knew the correct answer, to see if our technique got it right. We varied the evolutionary timeline of the cloud lifecycle, the cloud density profiles, the galaxy inclination, the spatial resolution of the observations, the size of the galaxy, and many other elements. These experiments did not only allow us to see if the technique worked, but also to quantify how well it did. We learned that we could characterise the cloud lifecycle with an accuracy of 30% or better, while only needing to resolve the separation between clouds rather than their internal structure. In practice, this required a spatial resolution of just under 100 pc, which we knew would be achievable for current observational facilities for hundreds of nearby galaxies. This meant a major step forward relative to previous methods for inferring the evolutionary timeline of cloud-scale star formation and feedback, which required observations at 10 times higher resolution (of about 10 pc). Given the great variety of potential applications of our technique, we decided to write up a comprehensive "method paper", detailing the procedure and the systematic tests. All we needed now were data.

In the meanwhile, Steve and I had joined forces with Andreas Schruba, who was also working in the Munich area and had published several papers on the spatially resolved star formation relation in nearby galaxies. His experience with exactly those observations that we wanted to apply our technique to was critical in making sure our code worked well with real data. Most importantly, our collaboration allowed us to simultaneously develop the code and carry out the observations needed to perform our intended measurements. We knew that the resolution at which nearby galaxies could be observed in the Hα line would be sufficient to identify individual star-forming regions. However, the bottleneck had always been to observe galaxies in CO at a resolution sufficiently high to resolve the separation between individual molecular clouds. With the arrival of the new ALMA telescope (the Atacama Large Millimeter/submillimeter Array), this was finally possible. In principle, the stars aligned perfectly: the combination of a new analysis technique with a telescope that for the first time could perform the observations needed to comprehensively characterise the molecular cloud lifecycle was too good to resist. We had no choice but to apply for ALMA time.

ALMA is still a relatively young facility (first light in late 2011), but regular observing programmes of up to 30 hours are now routinely observed, with Large Programmes clocking over 100 hours. But this was late 2013: only the second year of operations, when requesting more than 4 hours of observing time was already asking for trouble. In addition, we were a young team with an idea we believed in, but little to back it up. We carefully selected a target to satisfy the stringent observing requirements. At a distance of a mere 2 Mpc, in the neighbouring Sculptor group of galaxies, we found the flocculent spiral galaxy NGC300. It was not only the perfect target for our purposes, allowing an extremely high resolution of just 20 pc with a sensitivity high enough to detect all molecular clouds in the galaxy, but it was also the only target for which our experiment could feasibly be done at the time. We put together the observing proposal, of which Andreas was the PI, and waited.

In April 2014, we learned that our proposal had been ranked in the top 10% of proposals received during ALMA Cycle 2, meaning that the observations would be carried out. The image above (which features as part of Figure 1 in our paper; the background optical image is taken with the MPG/ESO 2.2-m telescope) shows the beautiful CO map observed by ALMA in blue. Star-forming regions traced by Hα show up in pink. As with all other star-forming spiral galaxies, NGC300 hosts a large molecular gas reservoir per unit SFR, so that the timescale for depleting the gas by star formation is about 1 Gyr. This is about 100 times longer than the typical dynamical times of molecular clouds, which can be explained in two ways. First, molecular clouds may live for many dynamical times and eventually convert all of their mass into stars. In this case, the positions of young stars should generally match those of the molecular clouds from which they formed, because star formation within clouds proceeds over long timescales. Second, stars may form very rapidly within molecular clouds and disperse the gas with their intense radiation and mechanical feedback, causing only a small fraction of the gas to be converted into stars. In this case, emission from young stars and molecular clouds should generally reside in different locations, because the short period over which star formation takes place means that young stars within molecular clouds would be a rare sight.

When we first compared the ALMA image of the CO emission with the Hα map, we immediately saw what the key result of our paper would be - the above image illustrates this very clearly: molecular clouds and star-forming regions are generally not co-spatial. This means that they must represent different phases of the underlying evolutionary timeline, and that stellar feedback from young stars rapidly destroys the molecular cloud from which they formed. In the movie below (this is Supplementary Video 1 of our paper; follow the link to Youtube to read a detailed description), this is visualised by the fact that the ratio between CO and Hα emission (bottom left panel) shows up as white on galactic scales (>1 kpc; indicating a strong correlation between gas and star formation), but changes to bright red and blue on cloud scales (<500 pc; indicating a strong anti-correlation between gas and star formation).

Anti-correlation between molecular clouds and young stars in the nearby galaxy NGC300.

By early 2018, almost all pieces of the puzzle were in place. We had thoroughly tested and validated our technique, carried out the necessary observations, and had a clear idea of what the physical result of the analysis would be. At this point, the original team had dispersed. Steve had moved to Liverpool, I had moved to Heidelberg, and only Andreas still worked in Munich. From a distance, we continued to collaborate towards our final goal of empirically characterising the physics of cloud evolution, star formation, and feedback. The final challenge was that we needed to quantify our findings. Even though we had tested our methodology on hundreds of simulated galaxies, real observational data behave subtly differently and we needed to make sure our results were correct. So this was not just a matter of simply running our code on the data once - we were facing the enormous task of varying an overwhelming variety of input parameters and understanding exactly which of the sometimes seemingly arbitrary choices we should use in observational applications.

At this point, my group in Heidelberg had been growing for 2.5 years. During that time, Mélanie Chevance had arrived from Paris and had accumulated more than a year of experience analysing a variety of real-Universe galaxies with our technique, using preliminary ALMA data that we had gathered as part of the PHANGS collaboration. While we had been daunted at first by the task of systematically assessing which experiment setup we should use for characterising the cloud lifecycle in NGC300, it turned out that Mélanie had already solved this problem for the PHANGS galaxies. She knew precisely which input parameters had a negligible effect on the results, which ones required careful calibration using independent constraints, and which ones were poorly known altogether. This allowed us to overcome the final hurdle and apply our methodology to observational data for the first time - we could now quantify how molecular clouds form stars in NGC300, and how these stars disrupt their formation sites with their intense feedback.

Mélanie and I spent months carefully analysing the observations that Andreas had prepared, and by June 2018 we were finally convinced of our measurements. No unconstrained parameter was left, all moving parts had been eliminated. The results left no doubt: star formation proceeds very rapidly and highly inefficiently in NGC300. Molecular clouds live for about 10 Myr (roughly corresponding to their dynamical time), and take only about 1.5 Myr to be destroyed, turning only 2-3% of their mass into stars. As a result, clouds are disrupted well before the most massive stars have reached the end of their lives and explode as supernovae (after >3 Myr). To interpret these results further, we compared the measured timescales to theoretical expectations, finding that 'early' feedback from (most likely) photoionisation or (possibly) stellar winds from young, massive stars is responsible for the destruction of their parent cloud. Interestingly, we also found that the mean separation length between clouds and star-forming regions is similar to the gas disc scale height, which is expected if the interstellar medium is structured by feedback-driven bubbles that depressurise when they break out of the disc. Taken together, our results strongly suggest that the molecular cloud lifecycle proceeds on a dynamical time and is truncated by stellar feedback. This shows that galaxies are highly dynamic systems, consisting of building blocks that constantly change their appearance.

Our paper represents the first application of this technique to a single galaxy, demonstrating the wealth of physical information that can be extracted from a pair of high-resolution images showing the galaxy at two different wavelengths. While it took us six years to go from a simple idea to its first application, we learned in the process how to perform this measurement routinely for large numbers of galaxies. By now, NGC300 is no longer the only galaxy for which this can be done. With ALMA in full operation and its observations of the PHANGS galaxies being ready for analysis, we are now quantifying the molecular cloud lifecycle across nearly a hundred galaxies in the local Universe. This major undertaking is led by Mélanie and addresses a critical result of our first application, namely that even within NGC300, we find that the cloud lifecycle varies with the galactic environment (e.g. as a function of galactocentric radius). Applications of our technique to nearly a hundred galaxies will provide the statistics necessary to understand this variation in terms of physical dependences, for instance on the local gas pressure or the dynamics of the host galaxy.

Finally, we expect the same measurements can be made for selected galaxies at high redshift, when the cosmic SFR peaked and the Universe was about one third of its current age. By investigating the relation between molecular clouds and star formation in galaxies across cosmic history, we are determining how the cloud-scale physics of star formation and feedback depend on the galactic environment. This represents an important step towards understanding galaxies as ensembles of building blocks that each undergo vigorous, star formation and feedback-driven lifecycles and together shape the appearance of their host galaxies. In turn, this will hopefully motivate a bottom-up theory of how galaxies grow and form stars, from high redshift to the present day.

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