How large were the first stars in the universe?

Since it is currently, and for the foreseeable future, not possible to actually observe what the first stars in the universe were like when they formed, the only way to answer this question is by detailed calculations from first principles. In other words, by computer simulations. Until very recently, such simulations couldn’t be very conclusive, since they simply couldn’t handle the amount of detail required. But they indicated that the first stars may typically have been very massive – perhaps often 100 solar masses each.

However, the very latest simulations, which can take advantage of the most powerful supercomputers now available in order to do more detailed calculations, indicate that a typical first generation star may have been less than half as massive as previously indicated.

It’s much harder than one might suppose to simulate, in detail, the formation of stars in the very early universe. Ten years ago the best that could be done was to simulate the process just up to the point where a single clump of dense, hot gas only about 1% as massive as the Sun has formed. That’s really only the first part of the process, and what happens after that is crucial in order to figure out what the typical size of one of the first stars in the universe was.

This is even though the very early universe about 100 million years after the big bang was a lot less complex than the universe is at present, so that star formation now is an even more complicated process. Almost all of the ordinary matter in the universe (i. e., except for the dark matter) was in the form of very diffuse atomic hydrogen and helium gas. There were only the smallest traces of heavier elements (lithium and beryllium), so there were no dust particles. There were no strong magnetic fields. And there were definitely no regions of turbulent gas, existing stars, stellar winds, or galaxies to complicate those initial conditions.

All there was were regions where the dark matter was slightly more dense than average, due to density fluctuations that had existed since the big bang itself. But because the total mass of dark matter was about 5 times as large as that of ordinary matter, the distribution of ordinary matter – out of which stars can form – closely followed the distribution of dark matter. However, dark matter interacts with itself mostly (if not entirely) only through gravity. So after a certain point, contracting clouds of dark matter cannot lose their internal kinetic energy as quickly as the ordinary matter can, and the ordinary matter begins to collapse increasingly quickly – until eventually stars are formed.

True simulation of star formation requires following the fate of every particle of ordinary matter over large volumes of space, initially on the scale of hundreds of thousands of light-years. On the other hand, the density was very low, much less than a few particles per cubic centimeter (cm³), so that the particles hardly interacted at all with each other. However, once a simulation reaches the stage of that small clump of hot matter the density reaches 10²⁰ particles per cm³ at the very center of a region with a radius of about 10 times the radius of the Sun.

That’s a lot of particles even for a supercomputer to handle. On the other hand, supercomputers today are 1000 times as fast as they were 10 years ago. About 4 years ago it was possible to run the simulation up to the point where the highest density was 10²⁰ cm^-3 when that very small clump of hot gas – the “protostar” – formed. But no further, without resorting to approximations that used bulk properties of gas to continue, instead of following every individual particle. About the most that could be determined from such simulations was that the final masses of stars in the very early universe might be in the range of 60 to 300 M_⊙. Although a very few stars in the present universe can reach that size range, it’s obvious that most stars are far more like the Sun, at 1 M_⊙ or less.

The main reason that the very early stars were generally so massive is that the matter out of which they formed was almost entirely hydrogen and helium, with insignificant amounts of heavier elements. The consequence is that it was much harder for such gas to cool off as it contracted. Therefore, thermal pressure in the gas was higher, so more mass was required for gravity to overcome thermal pressure.

The reason it is harder for a gas consisting only of hydrogen and helium to cool off lies in the way heat energy is released. The mechanism involved gas particles colliding with each other and converting some of their kinetic energy into excited states of the atoms or molecules of gas. These excited states eventually return to lower energy states, releasing photons of the appropriate energy, and the photons carry the energy out of the gas. Heavier elements have more electrons in their atoms, so there are more available energy levels spaced more closely together, hence many more low-energy photons to drain energy from the gas.

So, was it normal for a star in the very first generation of stars in the universe to have a mass around 100 M_⊙? It wasn’t possible to tell from earlier simulations, since there are important additional factors to consider after the protostar forms. In particular, the geometry becomes more complicated. The gas in the central region is no longer in roughly spherical form. Instead, it develops into a flattened disk, and eventually even develops several “arms” much like a spiral galaxy. This is a consequence of even small amounts of angular momentum in the gas cloud, because it is easier for gas to move parallel to the axis of spin instead of in towards the axis, which would require loss of angular momentum by the gas particles. So the gas tends to collapse naturally into a disk configuration.

Furthermore, temperatures rise so high in the centermost region that intense radiation is emitted, especially after thermonuclear reactions begin. This has a very significant feedback effect on the accreting gas. In particular, much of the gas above the disk becomes completely ionized, and therefore much less able to lose its internal heat. Eventually it may be expelled from the cloud instead of collapsing inward.

In order for simulations to proceed beyond the protostar stage they must deal with this more complicated geometry, as well as the much larger number of particles as gas continues to accrete into the densest regions of the cloud. Now simulations are being done that can handle this higher complexity. And one recent example, which was published last November in Science, has found that in fact the first stars to form in the universe may have typically had masses of “only” 30 to 40 M_⊙.

The simulation proceeded past the point where thermonuclear reactions had begun in the protostar. By the time the growing star reached 43 M_⊙ even the matter in the accretion disk around the star had evaporated from the intense ultraviolet radiation, so growth stopped entirely.

The simulation started from cosmological conditions of matter distribution. Individual particles were tracked up to a density of 10⁶ cm^-3 within a gravitationally bound sphere of 1 light-year radius. This sphere contained a gas mass of 300 M_⊙ and a protostar had formed. Under the assumed initial conditions, this occurred about 300 million years after the big bang (z∼14).

At that point, the 3-dimensional simulation was simplified to 2-dimensions by assuming a symmetric distribution around the rotation axis, i. e. the same radial profile at all angles around the axis, but different profiles at different heights above or below the equatorial plane.

The system was further evolved up to a central density of 10¹² cm^-3. A “sink cell” with a radius of 10 astronomical units (AU, 1.5 billion km) then replaced individual particles in the center and was assumed to behave somewhat like a “normal” star. The luminosity of the star, which determines the radiative feedback, was calculated based on the accretion rate of gas onto its surface.

By the time the stellar mass had reached 10 M_⊙, the accretion disk had grown to a radius of 400 AU of gas that was cool enough to still be mostly molecular hydrogen. At that point the star was gaining mass at about 1.6 M_⊙ per thousand years – very fast on a cosmological scale.

The star grew at a rate that balances inward gravitational force with outward radiation pressure. The intensity of the radiation was the sum of intensity due to thermal emission due to high temperature and emission due to rapid accretion of matter (from conversion of gravitational potential energy). These processes are modeled analytically instead of in terms of individual particles.

At first the luminosity due to accretion was much greater than that due to thermal emission. But when the stellar mass reached 8 M_⊙ the two sources of luminosity were about equal. Up to that point the contraction was roughly “adiabatic“, meaning that the total energy in the system remained about the same. But after that point, energy was radiated away. The internal temperature rose rapidly along with the ultraviolet luminosity from thermal emission.

The intense ultraviolet flux ionized gas in a cone of increasing opening angle above and below the accretion disk, as the star passed 20 M_⊙ in mass. At 25 M_⊙ the ionized region extended more than .3 light-years along the axis, outside the envelope of accreting gas, so that gas in that region was expelled from the neighborhood. This also stopped infall of gas onto the disk.

Thermonuclear burning of hydrogen began at a stellar mass of 35 M_⊙. At first this didn’t generate enough energy to prevent further contraction, but at even higher temperatures the helium also began to participate in thermonuclear reactions. This combines 3 He nuclei to produce carbon, which then also participates, and reactions involving carbon became the dominant source of energy. At this point, the star was much like a modern main sequence star, although somewhat hotter and more compact than modern stars of the same mass.

At a mass of about 43 M_⊙ all gas in the region was ionized and accretion stopped completely. This entire process took only about 100,000 years from initial protostar formation until completion.

Variations in some of the assumptions of the model could produce somewhat different results. For instance, if the initial angular momentum of the gas cloud were less the disk shape would be less flattened and gas densities above and below the disk would be higher. The net result is that accretion could continue somewhat longer and yield a higher eventual mass.

Even so, there should be very few stars more massive than 140 M_⊙. This number is important, because stars more massive than that quickly experience a type of supernova event rather different from an “ordinary” core-collapse supernova, namely a “pair-instability” (PI) supernova event. A PI supernova produces meaningfully different proportions of heavy elements.

However, some of the earliest stars in the universe after the first generation still exist (almost 13.7 billion years in age). These stars are much smaller than the very first ones (having been able to form out of gas containing heavy elements). But studies of such stars have not found evidence of the proportions of heavy elements that would result from a significant number of PI supernovae. The simulation results are thus consistent with this implication that PI supernovae and extremely massive stars must have been, at best, very rare.

An interesting question that remains unresolved is whether the accretion disks around the first stars might have often been unstable and therefor subject to fragmentation, which would result in an even higher proportion of stars with mass under 40 M_⊙. The authors of the research described here found that the accretion disks were marginally stable.

Fully 3-dimensional simulations being performed by other groups might find otherwise. Indeed, older simulations have found structures resembling galactic spiral arms in their accretion disks, violating full axial symmetry. On the other hand, “galactic paleontology” studies of very old stars in our own galaxy have not identified any 0-metallicity stars initially formed from only hydrogen and helium that have masses under 1 M_⊙, which is the norm of stars formed well after the first generation. So apparently if much fragmentation did occur, it didn’t result in an appreciable part of the first stellar population.

Hosokawa, T., Omukai, K., Yoshida, N., & Yorke, H. (2011). Protostellar Feedback Halts the Growth of the First Stars in the Universe Science, 334 (6060), 1250-1253 DOI: 10.1126/science.1207433

Further reading:

New Study Shows Very First Stars Not Monstrous

First stars ten times smaller

Universe’s first stars not so big after all

Universe’s first stars were more suns than supergiants

Protostellar Feedback Halts the Growth of the First Stars in the Universe – arXiv.org