Simulating Star Formation on a Galactic Scale

Clare Dobbs. American Scientist. Volume 102, Issue 2. Mar/Apr 2014.

Spiral galaxies are continuously evolving. They rotate, their pinwheel arms winding and stretching and splitting apart. Their constituent stars change as well, forming, growing old, and dyingsometimes simply fading away, sometimes with a supernova bang. These two types of change are tightly interconnected, yet it has been difficult to link the large-scale dynamics of galaxies with the small-scale processes regulating the birth of their stars. That is changing. Using powerful new supercomputers, astronomers can make detailed models of star formation in a galactic context. The result is an unprecedented understanding of the life of spiral galaxies-the dominant bright structures in the universe.

Galaxies are classified by their shapes; in addition to spiral (or disc) galaxies, there are ellipticals and irregulars. Spiral galaxies are further divided into “grand design” ones, with typically two symmetric arms, or “flocculent” spirals, with many transient, short arms. Spiral galaxies are of particular interest not just because of their prevalence. Our own galaxy, the Milky Way, is a spiral. More important, unlike elliptical galaxies, spirals are home to ongoing star formation. Spirals foster a cycle: As gas condenses into clouds, those clouds collapse to form stars, and through supernovae and winds some gas is ejected from stars back into the galactic disc. Spiral galaxies are the cosmic hubs of stellar rejuvenation.

Until recently, studying how galaxies form new stars was largely limited to carrying, out and analyzing telescopic observations. Such data left big gaps in our knowledge. For example, how many stars form in our galaxy per year, and why? Over the past decade, numerical simulations of galaxies have begun providing answers, but this approach is challenging. A meaningful computer model must account for all of the physical processes that govern the gas and stars in galaxies. It also needs to simulate those processes accurately across the vast range in scale between galaxies and stars.

One way to simplify the problem is to break it into two parts: first look at the formation of the clouds where stars are bom, and then zoom in on star formation within the clouds. Although spiral galaxies are full of diffuse gas, stars arise specifically in regions where the gas is relatively cold and dense. Typically that dense gas is located in clouds, the most massive of which are called giant molecular clouds because they contain molecules (mostly hydrogen, or H2), whereas other parts of the interstellar medium are mostly ionized gas. Giant molecular clouds contain young stars and ongoing star formation, and thus are often bright and colorful. Giant molecular clouds are the defining piece in the whole process of star formation in galaxies. Figure them out, and you begin to figure out the bigger question of how galaxies light up.

Galaxy in a Computer

Modeling the structure of giant molecular clouds and linking them with galactic evolution is a major focus of my recent work. In one recent simulation (page 133), my colleagues and I produced a symmetric two-arm spiral galaxy, highlighting dense gas that indicates the presence of molecular clouds. The computer code we used, called Smoothed Particle Hydrodynamics, is able to model flows and mimic the effects of gravity, but it is Lagrangian, meaning the coordinates aren’t static in space but move with the fluid. This program treats gas as a fluid, and then divides the fluid into a set of discrete elements or particles. The properties of a particle are dependent on its neighbors, and the length of each particle’s spatial distance (also called its smoothing length) can vary by local conditions, such as how densely the particles are packed together. This method is adaptable to simulating phenomena over many orders of magnitude.

Our simulation models only the gas in the galaxy, which significantly decreases the computational time required. Of course, real galaxies also include stars and invisible dark matter components. The bright stars and dark matter account for most of the galaxy’s mass (and therefore the gravitational component), and these are included implicitly in the models by using a prescribed potential. In other words, we build in the deviations in the gravitational field that would be created by these massive objects.

The virtual galaxy clearly shows considerable structure, with the gas organized into dense clouds that closely match real giant molecular clouds. If we consider hypothetical test particles that are not subject to any forces except the gravity of the galaxy, we would expect a much smoother distribution, simply with an increased density at the spiral arms. The dense clouds in our model illustrate that processes beyond gravity are at work.

Gas pressure allows shock waves to occur, and gas dissipation enables gas parcels to lose momentum as they collide or interact with other gas parcels. Collisions between regions of gas, or between small clouds, have long been proposed as a means of producing giant molecular clouds. The smaller clouds may themselves be molecular or could be composed of neutral atomic hydro- gen. Cooling instabilities in the gas also promote the formation of denser clouds, which can merge to form the giant clouds. (Gas cools more efficiently when it is dense because collisions between atoms and molecules are predominantly responsibly for cooling.) Self-gravity, the effect from the mass of the gas itself on the structure, also allows gravitational instabilities in the gas.

My colleagues and I performed simulations demonstrating that gravitational instabilities significantly influence the structure of the gas for surface densities greater than 10 solar masses per square parsec (1 parsec equals 3.26 light-years), whereas cloud collisional processes dominate for lower surface densities. The surface density in this particular virtual galaxy is 8 solar masses per square parsec, hence most of the structure is a result of cloud collisions, but the largest clouds (shown in yellow on page 133) are also formed by self-gravity. The other main process determining the gas distribution in the simulated galaxy is stellar feedback: Young stars emit winds and ionizing radiation, and supemovae explosions return mass and energy back into the interstellar medium. Magnetic fields may also be relevant to the evolution of the interstellar medium and star formation, but they are not included here.

As a reality check, we placed our simulation next to an image of the Whirlpool Galaxy, taken by the Hubble Space Telescope. In this image, dark regions indicate the location of dense gas, including molecular clouds, whereas the red parts are regions of star formation. Overall, the Whirlpool appears remarkably similar to the simulated galaxy. In both the molecular clouds and star formation are strongly concentrated to the spiral arms, and there are many long, thin interarm spokes, or spurs. Because of the underlying gravity from the stellar spiral arms, the number of clouds increases in the spiral arms, compared to other galactic components. My colleagues and I have shown that this increase promotes the formation of giant molecular clouds in the arms. We also have found that cloud collisions in the interarm regions or in galaxies without spiral arms are relatively infrequent. Gravitational instabilities are also heightened in the spiral arms because of the higher gas densities there.

In grand design galaxies, such as our simulated galaxy and the Whirlpool Galaxy, the speed of the rotation of the spiral arms is generally slower than that of the stars in the galaxy because of density differences. This nonhomogeneous setup creates gravitational attraction toward the dense material, and more material clumps there, setting up a density wave that causes gas to flow through the spiral arms. As the giant molecular clouds move away from the spiral arms, differential rotation subjects them to shear and stretching, creating new interarm spurs.

A Star Is Bom, But How Often?

Most stars in our galaxy are old, having formed when, or soon after, the galaxy itself collapsed more than 12 billion years ago. At these early epochs, the star formation rate would have been much higher than it is today. In fact it is surprising that our Milky Way galaxy and others are still forming stars at all. Some impediments evidently prevented all of the gas in spiral galaxies like ours from collapsing into stars. By the latest estimates, the Milky Way forms on the order of 100 new stars like the Sun over the course of an average human lifetime. But this total is a small fraction of the number of stars that would form if giant molecular clouds all turned into stars with 100 percent efficiency.

My research group and others have recently shown that feedback mechanisms are important in regulating star formation. Stellar feedback includes supernovae, stellar winds, ionizing feedback, and radiation pressure; with the exception of Supernovae, these processes occur throughout the lifetime of a massive star. They modulate star formation by injecting energy, and in some cases mass, into the interstellar medium, which pushes back against the forces of gravity and makes it harder for the clouds to cool and collapse into stars. Simulations of the galactic star formation rate with different levels of stellar feedback are shown in the figure on the top of page 134. The amount of energy is determined from the number of stars expected to form, which in turn is calculated from the mass of molecular gas above a given density multiplied by an efficiency parameter. Also shown are the star formation rates and surface densities of observed galaxies.

If the star formation efficiency parameter is doubled, twice as many stars form at each event, but the amount of energy added to the interstellar medium is also twice as large. In our model, the global star formation rate increases less than twofold, indicating that fewer star formation events are occurring due to stellar feedback. If the star formation rate decreases, there is less feedback, less energy is deposited in the interstellar medium, the gas becomes more strongly gravitationally bound (held together and even collapsing under its own gravity), and then more star formation occurs. The converse happens if the star formation rate increases. Hence, star formation tends toward an equilibrium rate. That rate is one or two orders of magnitude lower than it would be without the feedback effects. That is why spiral galaxies are still producing bright, young stars.

A Cloud’s Life

In early models of the interstellar me dium, molecular clouds were often presumed to be long-lived entities that could survive for tens of millions of years. In this picture, giant molecular clouds were assumed to be gravitationally bound but prevented from collapsing in on themselves by some combination of turbulence, rotation, and magnetic fields. Better observations have shown that clouds typically exhibit elongated structures, which is not typical of objects in equilibrium. Furthermore, several recent studies argue that the lifetimes of clouds may be quite short, countering the idea that star formation might be delayed by magnetic fields. Instead, it seems that stars form spontaneously and then fairly quickly disrupt their birth clouds through the processes of stellar feedback.

These new discoveries present important tests of the accuracy of our simulations. Determining the lifetime of clouds in numerical simulations is difficult. First clouds need to be identified. This part is done by dividing the galaxy into grid cells and requiring that the grid cells covering a cloud must have a surface density above a given threshold. The constituent gas of the clouds changes over time, so to follow the evolution of clouds it is necessary to recalculate their locations at different time steps and further identify which steps correspond to the evolution of a single cloud. In this way, estimates of cloud lifetimes can be obtained (see the bottom of page 134). Our calculations show that the lifetimes of clouds are only several million years-much briefer than the rotation period of a spiral galaxy, which is about 200 million years. This result supports the idea that clouds are dynamic aspects of the evolution of a galaxy.

The lifetimes of the clouds can also be compared to the time it takes for matter to cross through them, which is given by the length scale of the cloud divided by the velocity dispersion of the gas. The estimated cloud lifetimes are similar to the crossing times, indicating that the lifetimes of the clouds are driven by large-scale dynamics and are not supported against gravitational collapse. The clouds are disrupted by a combination of shear (due to differential rotation) and stellar feedback. A few of the giant molecular clouds, particularly more massive ones, have longer lifetimes-these clouds are closest to being in equilibrium, although they still undergo significant changes of their constituent gas over their lifetimes.

More detail of the evolution of an individual cloud is shown in the figure on page 135, over a period of 40 million years. The cloud has a mass of 2 million solar masses, and it is situated at a galactic radius (the distance from the center of the galaxy) of 3 kiloparsecs, or about 10,000 light-years. The cloud was selected at a time of 250 million years after the start of the simulation, as shown in the center frame; the preceding and subsequent frames show the evolution before and after. The cloud forms from a mixture of smaller clouds (shown as solid blocks of color) and ambient interstellar medium and similarly disperses back into those constituent elements. The effect of shear can be seen in the figure, with the cloud becoming more elongated and breaking up, but with the smaller clouds still situated along a spur. Shear tends to act over larger scales, whereas stellar feedback tends to act over smaller scales and is important for breaking up individual gravitationally bound clouds or gravitationally bound clumps within clouds. The timescale over which there is an obvious, single, massive cloud is around 25 million years (from about 240 to 265 million years), which is in agreement with the time calculated for the previous figure (in that case the lifetime was about 20 million years).

Another indication of the dynamic state of the clouds is whether they are gravitationally bound. Traditionally, clouds have been supposed to be in virial equilibrium, meaning that their gravitational energy is balanced by kinetic energy (usually associated with turbulent motions). The virial parameter, expressing the ratio of kinetic to gravitational energy, is about 1 for clouds in equilibrium, less than 1 for bound clouds, and greater than about 2 for unbound clouds. The figure on the top of page 136 shows the virial parameters for clouds found from the simulation in the first figure. Our data indicate that most of the clouds are unbound. Hence, the dynamics of the gas are sufficient that such clouds are not in a state of global gravitational collapse. Local regions of the clouds can be gravitationally unstable, and the collapse of these regions leads to local star clusters, but the whole cloud is not collapsing.

The unbound state of most clouds helps explain the low star formation rate in galaxies. Also, if large clouds or complexes are unbound, they can readily expand after leaving the arms and form the interarm spurs that we see in many galaxies, Bound clouds, in, contrast, tend to retain roughly spherical shapes. In our simulations, we find that stellar feedback is important for maintaining a population of unbound clouds. In the absence of feedback, the clouds are mostly bound, and they form far too many stars. Stellar feedback drives motions in the interstellar medium, blowing clouds apart and increasing their velocity dispersion. Some giant molecular clouds in our simulation are bound, but their short lifetimes suggest that most of the dense, bound clouds rapidly collapse, form stars, and disappear.

We can also use our model to study the formation of clouds in more detail. My research group considered the constituent material that goes into forming molecular clouds. The interstellar medium in galaxies is mostly composed of atomic and molecular hydrogen, the former typically making up lower density, diffuse regions, and the latter denser, colder clouds. One question is whether giant molecular clouds predominantly form from atomic or molecular hydrogen. (They are called “molecular” because they are large enough to encourage molecular hydrogen formation, but the clouds may not all have this uniform composition.) We showed that the composition of the material that forms the clouds simply reflects the average composition of the galaxy. Most galaxies contain a mixture of atomic and molecular hydrogenalthough some galaxies are predominantly either atomic or molecularand their clouds look similar.

Getting from Galaxies to Stars

Galactic scale simulations are useful for modeling the formation and evolution of giant molecular clouds, but on such a large scale we cannot resolve individual stars or even stellar clusters; we can resolve only on the order of 100 solar masses of stars forming at any moment of time. One way to investigate star formation explicitly is to perform a zoom operation in simulations of a region of a galaxy. In this approach, we select a region and trace the gas there back to an earlier time. Our simulation code, Smoothed Particle Hydrodynamics, allows us to repopulate that region with more particles, and thus increase the resolution.

In the figure on the bottom of pages 136-137, my colleagues and I produced three different simulations demonstrating a zoom-in. The first one is a global galaxy simulation, modeling just a torus of the galaxy to maximize resolution. A section of this simulation is then resimulated for a shorter time scale at a higher resolution. Then a third resimulation is carried out, zooming in on a region of the second simulation. By resimulating progressively smaller scales, the resolution of the third simulation reaches a particle mass of 0.156 solar masses. That level of detail is still not quite sufficient to follow the formation of individual, Sun-like stars. The minimum mass that can be resolved in the third simulation is 11 solar masses. To follow star formation, we typically insert “sink particles,” which replace 50 to 100 standard particles, to denote places where stars have formed. These insertions represent either massive stars or a small group of stars.

These high-resolution simulations give us a better handle on what determines the relationship between the formation rate of stars and the surface density of the galaxy (known as the Schmidt-Kennicutt relation) in individual clouds, and on the nature of star formation within a cloud. In particular, my team found that cooling and shocks have a strong role governing the amount of cold, dense gas, which is largely associated with the largerscale dynamics of the interstellar medium and in turn drives the Schmidt-Kennicutt relation. A nonlinear relationship exists between the amount of cold gas and the total amount of gas, but the relationship between cold gas and star formation rate is linear. Without any stellar feedback or magnetic fields in these simulations, the star formation rates are found to be too high compared to those observed. Stellar feedback and possibly magnetic fields are probably required to obtain the correct values.

Another means of linking between stars on smaller scales and giant clouds in the global simulations is examining the ages of stars in the clouds. Using a simulation similar to that shown in the first figure, my colleagues and I determined the ages of star particles (each star particle represents about 160 solar masses of star formation in the simulations) for giant molecular clouds in different environments. Stellar ages have already been theorized as a possible means of distinguishing largerscale molecular cloud formation. For instance, Lee Hartmann of the University of Michigan and his colleagues have shown that a predominance of young stars is an indicator of local converging flows-from stellar feedback and local gravitational instabilities, for instancebringing gas together over a short time and inducing star formation. But that work considered only small clouds of approximately 10 solar masses. The global simulations of galactic discs allow stellar age distributions to be computed for larger clouds. The figure on page 138 shows the stellar age distributions summed up over all giant molecular clouds (those that are over 100,000 solar masses) in the arms, interarm, and outer galaxy regions.

Statistical tests confirm that the age distributions for the clouds in the arms are different compared to those in the interarm regions. The reason is that the interarm clouds were formed in the spiral arms and have stars that date back to this time. Therefore, they have a broader stellar age distribution and comparatively more older stars, with ages around 20 million years. Spiral arm clouds are comparatively younger, preferentially containing a youthful stellar population. So a young star population indicates clouds that formed recently, in the environment where they are found, whereas an older age distribution is indicative of clouds that were formed in a different environment (the spiral arms) and have now moved into the interarm region.

Across the Scales

Astronomers’ physical understanding of star formation has been greatly advanced by computer simulations that can explore the evolution of gas and stars in galaxies. With them, we are starting to show how giant molecular clouds form and evolve, and how star formation evolves within them. But this field remains a work in progress.

Calculations take months to complete on supercomputers, so the simulations thus far have been necessarily simplified. One of the main pieces of physics that has not been included is magnetic fields, an important topic of future research. We would also like to add large-scale processes, such as Supernovae and galactic rotation, into our models. Another limiting simplification is that the galaxy simulations here consider isolated grand design spiral galaxies, whereas most (if not all) such galaxies are interacting with other galaxies, a process that influences the dynamics and formation of the spiral arms.

Star formation is a central result of the interplay of gravity, electromagnetism, and nuclear physics: Diffuse matter gets clumped together and condensed into stars, which then produce energy and heavier elements. Without star formation and the surrounding disks of material they accrete, there would be no planets. So understanding the basic physics of the universe can lead to a better comprehension not just of stars but also extrasolar planets and other objects in outer space. By connecting these processes across scales-from individual stars to giant molecular clouds to whole galaxiesour picture of the universe becomes clearer and more comprehensive.