How do bound star clusters form?

Title: How do bound star clusters form?

Authors: Mark R. Krumholz and Christopher F. McKee

First author’s institute: Research School of Astronomy and Astrophysics, Australian National University & ASTRO-3D, Australia

Status: Submitted to MNRAS [open access on arXiv]

Where do stars form in galaxies? We know stars form from gas, which collapses and cools. Whilst stars will form wherever gas is dense enough, regions of high stellar densities called star clusters are observed in all galaxies. From observations, we know that only around 10% of star-forming gas clumps within a galaxy become gravitationally-bound star clusters. Moreover, we observe these star clusters to form stars at continually increasing rates. This 10% of star-forming regions that do go on to form gravitationally-bound star clusters must be special in some way.

To explore this, today’s authors propose five different models for forming star clusters and evolve them analytically in order to calculate the evolution of the gas and the stars. They then compare this with observations to see which model fits best.

Bring in the models…

Static Cloud (ST)

This is the simplest of the five models, which describes an isolated spherical cloud of gas. The cloud does not accrete any gas external from the cloud so as the cloud forms stars, it uses up its gas. Once all the gas is used up, star formation stops. Physically, this scenario would occur if a gas cloud assembles fully before it starts forming any stars.

Conveyor Belt (CB)

This model describes a spherical gas cloud that is forming stars but at the same time accreting gas external from the cloud. Remember that star formation increases with time, and so continuous accretion of gas means the cloud won’t run out of fuel for forming stars.

Conveyor Belt plus Rapid Dispersal (CBD)

Very similar to the conveyor belt model, CBD forms stars at the same time as accreting gas. But once gas accretion stops, the star formation efficiency (SFE, the percentage of star forming gas which is actually converted into stars, typically around 1%) decreases significantly, leading to a rapid dispersal of gas.

Global Hierarchical Collapse (GHC)

This model (also described in this Astrobite) is quite different from the others in the sense that it starts with a spherical cloud at a density too low to form stars. Under its own gravity the cloud collapses. As it collapses, the density increases and therefore the SFR begins to increase.

Increasing Star Formation Efficiency (IE)

IE uses a different approach to reproduce the increasing star formation rate. Instead of altering the densities by adding gas or collapsing as the previously described models do, IE keeps the densities the same and instead increases the SFE.

The authors then analytically evolve the equations for the evolution of stellar mass and gas mass for each of these models in order to see which model fits best to observations.

Fitting to observations

The Orion Nebula Cluster. Credit: ESO/G. Beccari
NGC6530 otherwise known as the Lagoon Nebula. Credit: ESO/IDA/Danish 1.5 m/ R. Gendler, U.G. Jørgensen, K. Harpsøe

The authors first observation that they choose to fit is the star formation histories (SFH) of a gas cloud, that is, the mass in stars formed over time. They use observations of the Orion Nebula Cluster (ONC) and NGC6530 (shown above), which are both young, open clusters. For each model, the authors produce a fit to the observations and vary the free parameters in order to get the best fit for each model.

Firstly, they find that the ST and CB models perform quite poorly. As mentioned earlier, the SFR within these clusters increase with time. However, in the ST and CB models, the star formation rate at early times is far too high, leading to too many old stars. In order to compensate for the fact that the model inherently forms too many stars, the best fit for these models forms hardly any stars at all, only using around 10% or less of the gas in the cloud. This is in contrast to what we actually observe, particularly in the ONC, where we see much lower gas mass fractions at the current day. The other three models fit the observations well, with the IE model performing the best. However, in order to fit the observations, the IE must adopt very low SFE at early times and a much higher SFE at later times in order to explain the observed increase in SFR that is observed. The problem is that to fit the observations, IE requires that the SFE increases extremely rapidly with time, which is likely unphysical.

So we’ve ruled out ST and CB, and potentially also IE. The other two models did relatively well. The authors then look into the young stellar objects (YSOs) within clusters in order to determine the SFE. With the SFE as a free parameter in fitting the models to observations, all models match the observations well. However, the IE model in order to match the SFE observations now requires that the SFE stays roughly constant over time, in contrast with the fitting of the SFHs. We expect a model to behave similarly for different observations, and so for this reason, the authors decide to reject the IE model.

Ok so we’ve managed to get rid of three of the five models so far! So what about the final two. To recap, we have the Global Hierarchical Collapse (GHC) model and the Conveyor Belt plus Rapid Dispersal (CBD) model, both of which have performed well on both the ONC and NGC6530 for both the SFHs and the SFE. In order to distinguish them, the authors look to the current star formation rate of the Milky Way. Both models predict very different current star formation rates. For the CBD model, a gas cloud forms stars from relatively early times. As the cluster accretes more gas the SFR increases until the gas accretion stops. For the GHC model, a gas cloud doesn’t form many stars at the beginning of its evolution because the cloud is not dense enough. As it collapses, the density increases and star formation suddenly starts, forming many stars in a short times. The GHC model would therefore require the gas clumps in the observations to produce stars at a rate much higher than the entire current star formation rate of the Milky Way. Therefore the best and most physical model is the CBD.

So how do gravitationally-bound star clusters form?

With this final piece of information, we therefore arrive at the conclusion that in order to form gravitationally-bound star clusters, we need to have a cloud that forms stars at the same time as accreting gas. When the gas surrounding the cluster runs out, the cloud stops forming stars and rapidly disperses its gas. The key dispute in the literature has been whether the observed increase in star formation rate comes from a changing star formation efficiency or from the accretion of more gas. Today’s authors strongly argue for the latter, so mayyybbbeee the debate is finally settled!

About Jessica May Hislop

Doctoral Student at the Max Planck Institute of Astrophysics in Munich, Germany. Studying the formation of nuclear star clusters and intermediate mass black holes in high resolution simulations of dwarf galaxies.

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