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. 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.

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 sidebar 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.”

From soundwaves to supernovae

Once every 30 to 50 years in our galaxy—and then just for a few milliseconds—an exploding star known as a core-collapse (Type II) supernova emits as much energy in neutrinos as is emitted in photons by all the other stars in the Universe combined.

Supernovae have been documented for 1,000 years, and astrophysicists know a lot about how they form, what happens during the explosion and what’s left afterward. But for the past 40 years, one problem has dogged astrophysicists—what is the mechanism that actually triggers the massive explosion? Hydrodynamic, neutrino, convec- tive, viscous, and magnetic mechanisms for driving core-collapse supernova explosions have all been proposed and investigated.

One thing that is known is that Type II supernovae produce neutrinos, particles with very little mass which travel through space and everything in their path. Neutrinos carry energy from the deep interior of the star, which is being shaken around like a jar of supersonic salad dressing, and deposit the energy on the outer region. One theory holds that if the neutrinos deposit enough energy throughout the star, this may trigger the explosion.

To study this, a group led by Adam Burrows, professor of astronomy at the University of Arizona and a member of the SciDAC Computational Astrophysics Consortium, developed codes for simulating the behavior of a supernova core in two dimensions. While a 3D version of the code would be optimum, it would take at least five more years to develop and would require up to 300 times as much computing time. As it was, the group ran 1.5 million hours of calculations at NERSC.

But the two-dimensional model is suitable for Burrows’ work, and the instabilities his group is interested in studying can be seen in 2D. What they found was that there is a big overturning motion in the core, which leads to wobbling, which in turn creates sound waves. These waves then carry energy away from the core, depositing it farther out near the mantle.

According to Burrows, these oscillations could provide the power that puts the star over the edge and causes it to explode. To imagine what such a scenario would look like, think of a pond into which rocks are thrown, causing waves to ripple out. Now think of the pond as a sphere, with the waves moving throughout the sphere. As the waves move from the denser core to the less dense mantle, they speed up. According to the model, they begin to crack like a bullwhip, which creates shockwaves. It is these shockwaves, Burrows believes, which could trigger the explosion (Figures 3 and 4).

Figure 3. A 2D rendition of the entropy field of the early blast in the inner 500 km of an exploding supernova. Velocity vectors depict the direction and magnitude of the local flow. The bunching of the arrows indicates the crests of the sound waves that are escalating into shock waves. These waves are propagating outward, carrying energy from the core to the mantle and helping it to explode. The purple dot is the protoneutron star, and the purple streams crashing in on it are the accretion funnels. (Click on images to enlarge.)

So, what led the team to this new model of an acoustic triggering mechanism? They came up with the idea by following the pulsar—the neutron star which is the remains of a supernova. They wanted to explore the origin of the high speed which pulsars seem to be born with, and this led them to create a code that allowed the core to move. However, when they implemented this code, the core not only recoiled, but oscillated and generated sound waves.

The possible explosive effect of the oscillations had not been considered before

because previous simulations of the conditions inside the core used smaller time steps, which consumed more computing resources. With this limitation, the simulations ran their course before the onset of oscillations. With SciDAC support, however, Burrows’ team was able to develop new codes with larger time steps, allowing them to model the oscillations for the first time.

Figure 4. This shell of isodensity contours, colored according to entropy values, shows simultaneous accretion on the top and explosion on the bottom. The inner green region is the blast, and the outer orange region is the unshocked material that is falling in. The purple dot is the newly formed neutron star, which is accumulating mass through the accretion funnels (in orange).

In the paper resulting from this research,⁴ neutrino transfer is included as a central theme in a 2D multi-group, multi-neutrino, flux-limited transport scheme—the first truly 2D neutrino code with results published in the archival literature. The results are approximate but include all the important components.

Calling the simulation a “real numerical challenge,” Burrows said the resulting approach “liberated the inner core to allow it to execute its natural multidimensional motion.” This motion led to the excitation of the core, causing the oscillations at a distinct frequency.

The results look promising, but as is often the case, more research is needed before a definitive mechanism for triggering a Type II supernova is determined. For example, if a simulation with better numerics or three dimensions produces a neutrino triggering mechanism that explodes the star earlier, then the acoustic mechanism would be aborted. Whether this happens remains to be seen and is the subject of intense research at NERSC and elsewhere.

“The problem isn’t solved,” Burrows said. “In fact, it’s just beginning.”

Calibrating cosmology

Type Ia supernovae are extraordinarily bright, remarkably uniform exploding stars which make excellent “standard candles” for measuring the expansion rate of the Universe at different times in its history. Researchers use supernovae’s distance and the redshift of their home galaxies to calculate the speed at which they are moving away from us as the Universe expands. In 1998, by comparing the redshifts of dozens of supernovae, scientists discovered that, contrary to expectations, the expansion of the Universe is speeding up, and they coined the term dark energy to designate the unknown force behind this acceleration. Subsequent observations and calcu- lations have determined that dark energy makes up about 70 percent of the Universe.

The nature of dark energy has been called the deepest mystery in physics, and its resolution may revolutionize our understanding of matter, space, and time. “This discovery has revolutionized cosmology,” said Greg Aldering, head of the Nearby Supernova Factory (SNfactory) at Lawrence Berkeley National Laboratory. “Now astrophysicists want to understand the physical cause for the dark energy. This requires more precise measurements, and with large numbers of accurately measured Type Ia supernovae this should be possible.”

The SNfactory is an international collaboration between astrophysicists at Berkeley Lab, at several institutions in France, and at Yale University. The aim of the collaboration is to discover as many nearby (low-redshift) supernovae as possible and to study them in detail in order to reduce the statistical uncertainties in previous data. Supernovae can then be used more effectively as cosmological distance indicators to measure the expansion history of the Universe and explore the nature of dark energy.

“The ingredients which go into a supernova explosion are fairly well known,” Aldering continued, “and although computer modelers are not yet able to accurately predict the properties of supernovae in great detail, they do know something about how supernova properties change when the input ingredients are changed. Since measuring the change in the expansion rate of the Universe requires only relative distances, astrophysicists simply need to understand how supernovae will change in brightness when their input ingredients are changed by small amounts. This question can be explored empirically using nearby supernovae, which have a wide range of values for these input ingredients. Such exploration—and comparison with computational studies—is the basic goal of the Nearby Supernova Factory.”

Of course, the first step in studying nearby supernovae is to find them. “For the studies needed, we would like to discover the supernovae as soon as possible after they explode,” Aldering explained. “This requires imaging the night sky repeatedly, returning to the same fields every few nights, and then quickly processing the data.”

To that end, the SNfactory collaboration has built an automated system consisting of custom-built hardware and software that systematically searches the sky for new super- novae, screens potential candidates, then performs multiple spectral and photometric observations on each supernova. The imaging is done by a powerful CCD (charge-coupled device) camera built by the QUEST group that delivers 300 MB of imaging data every 100 seconds, amounting to 50–100 GB per night. These data are transferred via the High Performance Research and Education Network and ESnet to NERSC, where digital image subtraction software, running on the PDSF cluster, compares the new images to images of the same field archived on NERSC’s HPSS system to find the light of any new supernovae.

“The processing and storage of these images requires resources on a scale only available at NERSC,” Aldering said. “Near-line storage is critical for this project since archival images must be rapidly recalled so they can be compared with new images.”

Figure 5. A small sample of the hundreds of supernovae discovered by the Nearby Supernova Factory. (Click on image to enlarge.)

In 2006 the SNfactory processed 4,172,340 images, which corresponds to 11 TB of raw data and 356,185 square degrees worth of images (Figure 5). These images covered approximately half the sky, 20 times over, at a resolution of 0.7 microradians (or one-fourth of a millidegree). This data resulted in 603,518 subtractions processed (one PDSF job per subtraction), more than 16 million output files, and a total of 17 TB of output data. The database of supernova spectra obtained by the SNfactory is now the most extensive in the world, and it soon will be available to researchers worldwide.

From this data, 249 supernovae were discovered and confirmed photometrically in 2006. In addition, using the SNfactory’s SuperNova Integral Field Spectrograph (SNIFS), remotely operated on the University of Hawaii’s 2.2-meter telescope on Mauna Kea, Aldering’s team spectroscopically confirmed 136 supernovae: 89 Type Ia, 41 Type II, and 6 Type Ib/c. They also have used their trove of images to eliminate some objects as variable stars or quasars—as opposed to supernovae—based on their brightness behavior over the past six years in which the SNfactory has been archiving images.

During the past year, the SNfactory has implemented machine learning techniques that decreased the time required for human verification by a factor of 10, allowing the researchers to focus their attention on the best candidates immediately. This improved efficiency has resulted in a one-day turnaround—a supernova imaged at Palomar Observatory on one night is discovered by the SNfactory the next day and confirmed as a supernova the following night by SNIFS in Hawaii.

One example of the importance of early spectroscopy is a supernova designated SN 2006D. The SNfactory obtained SNIFS spectra of SN 2006D only three days after it was discovered by the Brazilian Supernova Search team and one week before it reached maximum brightness. The SN 2006D spectra provided the most definitive evidence to date of unburned carbon in a Type Ia supernova.⁵ The white dwarf stars that explode as Type Ia supernovae are composed primarily of carbon and oxygen, most of which is burned into heavier elements by nuclear fusion during the explosion; and as expected, SN 2006D’s carbon signature dissipated as the supernova approached peak brightness. But the presence of detectable unburned carbon in the early light of SN 2006D provides valuable data for researchers seeking to understand variations in supernova progenitors as well as explosion mechanisms.

To make their archived data even more useful, the SNfactory is now in the process of coadding (calculating average measurements for) the millions of distinct images of the night sky they have obtained over the past six years. Typically each sky location has been visited 40 times in the past six years, so the resulting coadded sky images should be very robust. Each set of 40 images covering one square degree of sky will be combined to construct a 4000-by-4000-pixel image, for a total of roughly 80,000 overlapping images. These images cover two-thirds of the entire sky and will constitute the greatest combination of depth and sky coverage of any sky atlas ever generated.

This article written by: John Hules, Jon Bashor, and Ucilia Wang, Berkeley Lab.

1 Mark R. Krumholz, Christopher F. McKee, and Richard I. Klein, “The formation of stars by gravitational collapse rather than competitive accretion,” Nature 438, 332 (2005).

2 Mark R. Krumholz, Christopher F. McKee, and Richard I. Klein, “How protostellar outflows help massive stars form,” Astrophysical Journal 618, L33 (2005).

3 Mark R. Krumholz, Richard I. Klein, and Christopher F. McKee, “Radiation-hydrodynamic simulations of collapse and fragmentation in massive protostellar cores,” Astrophysical Journal 656, 959 (2007).

4 A. Burrows, E. Livne, L. Dessart, C. D. Ott, and J. Murphy, “A new mechanism for core-collapse supernova explosions,” Astrophysical Journal 640, 878 (2006).

5 R. C. Thomas et al. (The Nearby Supernova Factory), “Nearby Supernova Factory Observations of SN 2006D: On Sporadic Carbon Signatures in Early Type Ia Supernova Spectra,” Astrophysical Journal 654, L53 (2007).