A new model of massive star formation by astrophysicists at the University of California, Berkeley, finally resolves the issue. By extending the widely accepted theory of low-mass star formation, they have calculated that stars about 100 times the mass of the sun would form in about 100,000 years.

For comparison, our sun is thought to have formed in a much less dense molecular cloud in about several hundred thousand years.

The model also suggests that protostars most likely grow big by the infall of gas from the surrounding molecular cloud, rather than by the collision of a number of smaller stars, as some astronomers have proposed.

"These massive stars are very important because they produce most of the heavy elements from which we are made," said Christopher McKee, professor of astronomy and physics and chair of physics at UC Berkeley and one of two co-authors of a paper describing the model that appears this week in the British journal Nature. "But previous theories have been mostly phenomenological and suggested formation times ranging from thousands of years to millions of years. Some of these theories were saying that it would take the entire lifetime of the star for it to form.

"We were able to show, by proper extension of the theory (former UC Berkeley astronomer) Frank Shu had developed many years ago, that you could predict how long it would take a massive star to form. We put the theory of massive star formation on a firmer footing."

One of the problems in modeling the formation of massive stars, said co-author Jonathan C. Tan, a former graduate student at UC Berkeley who now is a postdoctoral fellow at Princeton University Observatory, is that protostars are so hot that the radiation pressure pushes the infalling gas and dust away. Because they burn their nuclear fuel so fast, they have relatively short life spans: as short as 3 million years, compared to 10 billion years for our sun.

As a result, some have concluded that massive stars would never be able to grow big enough by accretion. They proposed, instead, that massive stars form from the collision of several smaller stars, even though the density of protostars in star clusters would seem to make this a rare event.

What McKee and Tan found, however, is that the pressure of the infalling gas is more than sufficient to overcome the radiation pressure from the protostar.

"The very high pressures of the star-forming regions need to be considered," Tan said. "The densities and ram pressures associated with the infall of gas are strong enough to overcome the radiation pressure and boost the accretion rate onto the star."

Interestingly, the actual formation time doesn't depend very strongly on the mass of the star. While a 100-solar-mass star forms in about 100,000 years, a star the mass of the sun - 100 times smaller - would form only three times faster - in about 30,000 years.

"This helps us understand how clusters form, because there is no direct evidence, for example in the Orion Nebula, one of the nearest clusters, that massive stars formed at a different time from the low-mass stars," Tan said.

The accepted theory of low-mass star formation was laid out some 30 years ago by Frank Hsia-San Shu, a UC Berkeley astronomer who early this year left to become president of National Tsing Hua University in Taiwan. He calculated that interstellar clouds of atomic and molecular hydrogen gas, helium and dust would begin to collapse under their own weight, swirling and flattening into a disk. As material fell inward, the pressure and temperature would rise as the gravitational energy is converted to heat.

A protostar eventually would form at the center of the collapsing accretion disk, heated by its own gravitational energy, and continue to draw more matter onto it until it was large enough to trigger nuclear fusion at the core.

McKee and Tan applied this theory to the much more extreme conditions observed in the densest regions of giant molecular clouds, where massive stars are observed to form. The model will help them understand other processes in massive star formation, such as the production of high-powered jets as matter accretes onto a star, and the protostar mass at which nuclear burning in the core produces enough radiation to outshine the glowing accretion disk.

"This is certainly going to be important in understanding star clusters," said Tan.

McKee agreed, noting that massive stars are hard to study because their early stages are hidden behind a veil of gas and dust.

"Massive star research is way behind research on low-mass stars," he said. "It's definitely going to be a very active area of research during the coming decade."