The paper in Nature Astronomy is here: https://go.nature.com/2MniRBG

One of the most important questions in astronomy is how stars form across cosmic time.   Giant molecular clouds (GMCs) in interstellar space are where most stars find their birthplace, and these clouds come in a great variety of masses and stellar densities, that can include groups of only a few dozen stars all the way up to giant, massive clusters containing millions of stars.  These biggest ones are found in galactic nuclei, and as the famous globular clusters that formed in the earliest stages of galaxies 12 billion years ago or more.  For years we’ve been curious about how the very most massive star clusters formed.  Were they fundamentally different in their origin story, as several other recent studies have suggested, or is there something connecting them with their much smaller siblings that we can see around us in our own Milky Way?  

   It’s a question that two of us first addressed in a paper 24 years ago (Harris & Pudritz 1994).  We suggested that particularly big reservoirs of gas would be needed to form big star clusters:  “supergiant” molecular clouds of perhaps 10 million Solar masses of gas might be massive enough to generate star clusters at the level of globular clusters.  But at that time, no full 3D simulations were possible that could explore the physical mechanism in detail:  the GMC’s internal turbulence, its filamentary structure, its self-gravity, and the details of the feedback from young stars on the surrounding gas through ionization, heating, and radiation pressure.  

    Our new work built on breakthroughs in the past few years to compute star formation processes in full 3D hydrodynamic simulations.  An adaptive mesh code known as FLASH (Peters et al. 2010) allows us to compute the competing effects of all these processes inside GMCs (gravity, turbulence, and feedback), and we realized the time had arrived to mount a bigger project.  We needed to go beyond rough analytical arguments or low-resolution views to simulate star-cluster formation within a GMC in full detail. Corey arrived as a grad student in 2012, and with Ralph’s group expertise in FLASH simulations and Bill’s long observational experience with massive star clusters, we were in a great position to tackle this project.  

    A big question was how to handle the full dynamical range of clusters and their effects:  Massive GMCs may be a few hundred lightyears across, whereas the newly formed star clusters embedded inside them are 2 or 3 lightyears in diameter, a volume a million times smaller.  This led to our use of “cluster sink particles” which allowed us to avoid the impossible task of simulating the formation of every individual star within every cluster on a scale millions of times smaller still.   Observational data tell us that star formation needs a threshold gas density of about 10⁴  gas particles per cubic cm.  So any region inside the simulated GMC that exceeded this threshold and that obeyed some other critical constraints (sitting at a gravitational potential minimum, velocity motions focused inward, etc.) could be identified as a cluster forming region:  i.e. a “sink”.  Using some observationaly calibrated rules for the conversion efficiency of gas into stars and the initial mass function of those new stars, we could calculate the radiation fields from the new massive stars that would push on the surrounding gas; that is, the feedback of the new clusters on their host GMC.  

   Corey’s PhD thesis explored a wide range of all this input physics and a range covering the entire real GMC mass spectrum, from 10⁴ to 10⁷  solar masses.  We found that there is indeed an amazingly simple scaling of cluster mass with GMC mass.  The most massive star cluster that a GMC can produce goes as M_max ~ M_cl^0.92 for cluster formation without radiative feedback, which becomes more shallow (~M^0.78 ) when feedback is included.  Again, the message is that big star clusters need to grow within suitably big reservoirs of gas. 

  We found that massive star clusters and low-mass clusters all formed through the same universal mechanism, through the action of gas dynamics and feedback in GMCs.  But there was one important feature that depended on cluster mass:  the small ones form almost exclusively just by accreting gas out of their natal filaments, but the most massive ones grow almost equally by the combination of direct gas accretion and by merging with their smaller neighboring clusters.  Massive clusters are composite systems right from the start.  And all of this action happens within the first 5 million years or so, even before supernovae start kicking in and pushing the remaining gas around more violently.
  
   The figure below is Fig 1 from our paper showing the time of the appearance of the most massive cluster (star) and all those that will eventually merge with it at other times.  The left image is for a massive cloud at solar metalicity, the right for a low metalicity cloud in the early universe.   See also videos on the Nature Astronomy website.

     Finally, we were intrigued to find that the masses of the clusters at the end of the simulation run don’t depend much on the adopted density threshold for star formation.  Much previous work suggested that massive star clusters (like globular clusters) should form in particularly dense gas and with higher thresholds.  But even when we assumed this, the cloud just needed to wait a little long for some clumps to build up to this higher threshold, but their final masses were the same.  Maybe we can finally understand the striking  observation by Lada et al.  (2012) that star formation rates scale with cloud mass, from local clouds right up to the most actively star forming extragalactic systems.  

    Our new work is complementary to other recent computational studies that focus on the formation of entire galaxies with larger-scale simulations.  Our simulations provide crucial physical calculations about what actually happens on the sub-parsec scales where the massive star-cluster “engines” form and how they influence their surroundings.  There’s now a new, rich vein to explore in this subject.

Corey Howard, Ralph E. Pudritz, and William E. Harris