High-Mass Star Formation

The formation of high-mass stars remains one of the most significant unsolved problems in astrophysics. These stars, with masses from 10 to 100 times the mass of our sun, eventually explode as supernovae and produce most of the heavy elements in the Universe. They also have a major influence on the structure and evolution of galaxies. But observing the formation of massive stars is difficult, because they are born in distant, dense, and dusty regions of space, and they swallow up much of their birth environment as they are born.

Massive star formation also poses major theoretical challenges. Massive stars begin burning their nuclear fuel and radiating prodigious amounts of energy while still accreting mass from the dense clouds of mostly hydrogen gas surrounding them. But this radiation exerts a repellent effect on molecules in the accreting material that could theoretically exceed the attractive force of gravity. This paradox poses a question: How can a massive protostellar core sustain a high-mass accretion rate despite its repellent radiation pressure on the surrounding matter?

That is only one of the questions that Richard Klein and his collaborators, Christopher McKee and Mark Krumholz, are determined to answer. Klein is an adjunct professor of astronomy at UC Berkeley and a researcher at the Lawrence Livermore National Laboratory; McKee is a physics and astronomy professor at UC Berkeley; and Krumholz is now a post-doc at Princeton University. Together they are working toward a comprehensive theory of star formation, and they have already made major progress.

For a long time, scientists have understood that stars form when interstellar matter inside giant clouds of molecular hydrogen undergoes gravitational collapse, but the puzzle remained of how the protostars could grow to become high-mass stars in spite of the strong radiation and stellar winds that they generate. That question led to two competing theories on how massive stars come into being.

In the competitive accretion theory, the cloud gravitationally collapses to produce clumps containing small protostellar cores. These cores are the seeds which undergo growth by gravitationally pulling in matter from around them, competing with other cores in the process, and sometimes colliding and merging with other cores, eventually accreting many times their original mass.

The rival direct gravitational collapse theory, which Klein and his collaborators subscribe to, contends that the protostellar cores are already large soon after the star-forming clouds have fragmented into clumps (Figure 1). These cores subsequently collapse to make individual high-mass stars or small multiple systems, in either case continuing to accrete some matter from the parent clump, but not enough to change their mass substantially.

Figure 1. Column density of a simulated protostellar core 20,000 years after the beginning of gravitational collapse. (Click image for larger view)

Krumholz, McKee, and Klein gave a major boost to the direct gravitational collapse theory in the November 17, 2005 issue of Nature,[1] where they reported the results of star formation simulations carried out at NERSC and the San Diego Supercomputer Center. “Our work was the first attempt with fully three-dimensional simulations to show how high-mass stars are formed, and it dealt a serious blow to the competitive accretion theory,” said Klein.

The 3D simulations determined the conditions in which competitive accretion can occur: low turbulence (the ratio of turbulent kinetic energy to gravitational potential energy) in the gas clumps in which the cores are formed, and low-mass clumps (a few solar masses). Earlier three-dimensional simulations with particle-based codes that appeared to support competitive accretion were based on these assumptions, and also had the turbulence taper out quickly in the star-forming process.

But do these two conditions necessary for competitive accretion actually exist? After reviewing observations of a broad sample of star-forming regions, Klein and his team found no evidence to support these two assumptions. On the contrary, star-forming regions show significant turbulence, and the clumps tend to have several thousand solar masses. “Every observation of these large clouds indicates that a mechanism, perhaps protostellar winds, must be present that keeps stirring the clouds to keep the turbulence around,” Klein said.

The researchers have also demonstrated that radiation pressure is a much less significant barrier to massive star formation than has previously been thought. In proof-of-principal calculations of the recently observed gas outflows from massive protostars, they found that an outflow can substantially change the radiation field and radiation pressure around the protostar. The outflow cavity in the surrounding gaseous envelope provides a thin channel through which radiation can escape, significantly reducing the radiation pressure and allowing accretion to continue. “Surprisingly,” they concluded, “outflows that drive gas out of a collapsing envelope may increase rather than decrease the size of the final massive star.”[2]

Another issue for the direct gravitational collapse theory to resolve is fragmentation: why wouldn’t a massive core collapse into many fragmented, low-mass protostars rather than one or a few high-mass stars? In three-dimensional simulations with a wide range of initial conditions, the researchers found that radiation feedback from accreting protostars inhibits the formation of fragments, so that the vast majority of the gas collapses into a handful of objects, with the majority of the mass accreting onto one primary object (see "A Star Is Born" below).[3] The emerging picture, then, is that massive cores are the direct progenitors of massive stars, without an intermediate phase of competitive accretion or stellar collisions.

Klein’s team created these simulations using a code called Orion, which employs adaptive mesh refinement (AMR) to create three-dimensional simulations over an enormous range of spatial scales. “AMR enabled us for the first time to cover the full dynamic range with numerical simulations on a large scale, not just in star formation but in cosmology,” Klein said. “We want to solve the entire problem of the formation of high-mass stars.”

Figure 2. Column density as a function of time in one of a series of star formation simulations. From top to bottom, the rows show the cloud state over time. From left to right, each column “zooms out” to show 4 times more area. In the left column, the image is always centered on the point of origin, and the region shown in the second column is indicated by the black box. In the other columns, the image is centered on the location of the primary star at that time. Stars are indicated by red plus signs. (Click image for larger view)

A Star Is Born

Figure 2 shows a time sequence of the evolution of one simulation run, starting from the initial state shown in the top row. Turbulence delays the gravitational collapse for a while, but as the turbulence decays, gas starts to collapse. The primary star appears 5,300 years after the start of the simulation. It forms in a shocked filament, which continues to accrete mass and by 6,000 years is beginning to form a flattened protostellar disk (second row).

As the evolution continues, several more dense condensations appear, but most of these are sheared apart in the primary protostellar disk before they can collapse and form a protostar. After 12,200 years, a second protostar forms, but it falls into the primary star and merges with it at 12,700 years, before it has accreted one-tenth of a solar mass of gas. The primary star is already 2.1 solar masses, so the mass it gains in the merger is negligible. The third row shows the state of the simulation at 12,500 years, about halfway between when the second protostar appears and when it merges with the primary.

Only after 14,400 years does one of the condensations collapse to form a second protostar that is not immediately accreted, as shown in the fourth row of Figure 2. At this point the primary star is 3.2 solar masses and has a well-defined massive disk. The condensation from which the new protostar forms is already visible in the third row. Unlike several others, it is able to collapse and form a protostar because it is fairly distant from the primary protostar, which reduces the amount of radiative heating to which it is subjected.

The next significant change in the system occurs when one of the arms of the disk becomes unstable and fragments to form a third protostar at 17,400 years, as shown in the fifth row. At this point the central star mass is 4.3 solar masses; the fragment is very small in comparison.

The configuration after 20,000 years of evolution, shown in the sixth row, is substantially similar. Two more small disk fragments form, but they both collide with the primary star almost immediately after formation. At the end of 20,000 years, the primary star is 5.4 solar masses, the second star is 0.34 solar masses, and the third star, which formed in the disk of the first, is 0.2 solar masses. The disk itself is 3.4 solar masses. The system is well on its way to forming a massive star, and thus far the vast majority of the collapsed mass has concentrated into a single object. A larger plot of the full core at this point is shown in Figure 1.

Thus far the researchers have carried out 3D simulations, not yet complete, that show stars greater then 35 solar masses forming and still accreting gas from the surrounding turbulent core.