Harvard Astronomy 201b

ARTICLE: Why are most molecular clouds gravitationally unbound?

In Journal Club, Journal Club 2011 on February 16, 2011 at 11:37 pm

Read the paper by C.L. Dobbs, A. Burkert, and J.E. Pringle (2011)

Summary by Elisabeth Newton


The most recent observational evidence seems to indicate that giant molecular clouds are predominantly gravitationally unbound objects. In this paper we show that this is a natural consequence of a scenario in which cloud-cloud collisions and stellar feedback regulate the internal velocity dispersion of the gas, and so prevent global gravitational forces from becoming dominant. Thus, while the molecular gas is for the most part gravitationally unbound, local regions within the denser parts of the gas (within the clouds) do become bound and are able to form stars. We find that the observations, in terms of distributions of virial parameters and cloud structures, can be well modeled provided that the star formation efficiency in these bound regions is of order 5 – 10 percent. We also find that in this picture the constituent gas of individual molecular clouds changes over relatively short time scales, typically a few Myr.

I posted a short, nontechnical summary of this paper on Astrobites which is a good place to start for a general idea of what’s going on in this paper.  Here, I will present the article in more detail.


The figure above (left panel) is from Heyer et al. (2009), a recent observational study revising estimates of giant molecular cloud (GMC) masses. The solid line shows where the virial parameter (\alpha) is equal to 1; above this line a cloud is typically considered unbound. The errors indicated in the legend include a 20% uncertainty on the distance to each cloud, but the authors also believe that the true cloud mass has been underestimated by a factor of 2-3 because LTE was assumed. Thus, even though most of the data points lie above the \alpha=1 line, Heyer et al. say their data is consistent with most molecular clouds being gravitationally bound.

The right panel of the figure is from this work and shows the Heyer et al. data, but with masses increased by a factor of 2 as suggested by those authors. With this increase, most points still have \alpha>1. Even taking a more stringent definition of unbound (\alpha>2; using \alpha=1 as the dividing line is actually only valid for spherical clouds and complicated geometry can push the critical point up by a factors of a few) 50% of the clouds are unbound.

This motivates the authors to explore the properties of molecular clouds in a simulation.

Simulations of the galactic disk

Figure 2. "The gas column density is shown for Run C... at a time of 200 Myr. Dense gas, corresponding to the clouds located in the analysis presented here, predominantly lies along the arms, and spurs which extend from the arms into interarm regions."

This work uses 3D smoothed particle hydrodynamics simulations to model the galactic disk.  The idea behind SPH is calculating a density from a distribution of individual point mass by using a smoothing function (see also this paper and Nathan’s review).  The galaxy is modeled by as a fixed gravitational potential and includes the halo, the disk and 4 spiral arms.  The velocity of gas particles is set by the rotational curve, plus an extra 6 km/s in a random direction.

Dobbs uses 4 runs.  Run A was originally presented in a previous paper which looked at the formation of GMCs through agglomeration (dominant in cool, low surface density disks) and gravitational instability (dominant in warm, high surface density disks).  This run is simpler than the others and includes only a 2-phase ISM with no heating or cooling.  However, magnetic fields are included.

Runs B, C and D are aimed at exploring the effect of stellar feedback.  These include a multiphase ISM, cooling and heating (allowing gas to change phase) and stellar feedback.  Heating is from background UV and from feedback while a variety of cooling processes are included.  Stellar feedback is included by assuming that stars form whenever certain conditions are met, mostly related to the strength of the gravitational interaction; stars then form according to a Salpeter IMF with an efficiency of 1, 5 and 10% for Runs B, C and D respectively.  This inputs a set amount of energy per stellar mass into the ISM, which would include phenomena like supernovae.  It isn’t necessary to include a time-lag between the onset of star formation and a supernova because the time-steps are ~Myr.  Runs C and D are able to reach an equilibrium.

In this work, clouds are defined using an algorithm which locates regions with surface densities exceeding 100 M_\odot pc^{-2}.  Groups of adjacent, over-dense cells that are large enough are termed clouds.

General results of the simulation

In Run A, magnetic pressure prevents gravitational collapse and most clouds are unbound.  Run B does not include magnetic fields, has a slightly higher surface density and has a low SF efficiency (thus minimal feedback); a large number of the clouds are found to be gravitationally bound.  In Runs C and D, most clouds remain unbound and the cloud morphology and virial parameter distributions are in best agreement with observations.

Figure 1. "The distribution of the virial parameter (α) is plotted with mass for clouds identified in Run A (top left, with magnetic fields), in the calculations with feedback adopting efficiencies of 1, 5 and 10 %, and the Heyer et al. (2009) data (lower middle). We find a population of predominantly unbound clouds, in rough agreement with the observations, for the models where localised gravitational collapse is limited by magnetic fields (Run A), or gravitational collapse occurs but there is a realistic level of stellar feedback (Run C, top right, Run D, lower left). There are many more bound clouds for the case with a very low level of stellar feedback (Run B, top middle). In the final panel (lower right), the cumulative fraction of clouds with a given α is shown for the Heyer data (dotted) and for the clouds from Run C, with 5 per cent efficiency (solid line). The KS test confirms that the distributions of α from the observations and simulations match, giving P = 0.11 and P = 0.21 for Runs C and D respectively."

Figure 8. "The distribution of aspects ratios of the clouds is shown for the models with 1 % efficiency feedback (Run B, left), and 5 % efficiency feedback (Run C, centre). The distribution of aspect ratios for Galactic clouds is shown on the right (Koda et al. 2006). The clouds for the 5 % efficiency case (centre) reasonably match the observations,although even in this case our clouds are slightly more peaked towards low aspect ratios than the observations. The distribution does not change with time, once equilibrium has been established. With 1 % efficiency (left), the distribution evolves to a strong peak at 1, in definite contradiction to the observations."

Evolution of individual clouds

First, the authors look at the evolution of a cloud in Run A.  Stellar feedback is not included, but a collision with another cloud increases the velocity dispersion and virial parameter of the resulting cloud: the energy from the collision goes into increasing internal velocities.  Even without magnetic fields and in isolation, a collision between two clouds prevents the overall collapse of the cloud for ~10 Myr.

They also explore the evolution of a cloud in Run C.  The figure to the left (click to make it bigger) shows the history and future of a cloud selected at 200 Myr (third row).  It was formed from several smaller clouds, has a filamentary structure and eventually breaks apart.  The authors say, “Feedback plays a large role in shaping the cloud, and regulating the dynamics.”  Collisions also contribute to clouds being disrupted on time scales of a few million years.

The caption reads:
Figure 4. “The evolution of a cloud from Run C (with 5 % effi- ciency stellar feedback) is shown, at 189 (top), 198 (second), 200 (third) and 202 (fourth panel) Myr. The cloud is formed by the merger of smaller clumps. Stellar feedback events (for example the cross in the second panel) then alter the shape of the cloud and finally result in the separation of the cloud into several separate clumps. Separate clumps, (as picked out by the clumpfinding algorithm), are shown simply in different colours, but the constituent particles are not all the same at different times. For example only 2/3 of the particles in the cloud at 198 Myr are in the cloud shown at 200 Myr…”

On the other hand, more massive clouds are not as easily disrupted.  Looking at the evolution of another cloud in Run C (not shown), we can see that feedback and collisions do not fragment the cloud although feedback does keep the velocity dispersion from dropping below ~6 km/s.  Throughout the simulation, the cloud gains mass and becomes more gravitationally bound and the authors believe such a cloud would eventually form a bound stellar cluster.


The authors present a picture in which most molecular clouds are not gravitationally bound and back it up with simulations and analysis of recent observations; the run with a star formation efficiency of 5% provides the best match to observations.  In this scenario, GMCs change their identity on timescales of a million years; most have virial coefficients >1 and are irregularly shaped.  Some parts of the clouds are self-gravitating and form stars.  On relatively short timescales, collisions and stellar feedback tear most clouds apart, although the largest maintain their identities for longer.

Comments and questions

The galaxy in this simulation has 4 spiral arms, but it is believed the Milky Way has only two.  This does not significantly effect the results–in fact, the outcome is similar even with no spiral structure (A.B., personal communication).

It’s not easy to define a cloud and different definitions can lead to different results.  The authors note that “the properties and lifetimes of clouds depend somewhat on the size scales considered.”  For example, if you set the threshold density high enough, only dense cores would be selected as clouds and as a result all clouds would be gravitationally bound.

Does pressure confinement play a role?  This will necessitate a discussion of what the surface of a cloud means.

In this work, the authors look at the true virial parameter; but, the virial parameter as observed by observations is necessarily somewhat different.  How do their results of the virial parameter distribution look when projected from 6 coordinates to 3?

  1. […] more?  I recently posted about this article in more depth on the website for my interstellar medium (ISM) […]

  2. […] Molecular gas. “Bound” according to Draine (though maybe not). . Sites of star […]

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