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Once upon a time there was a star. It was big, hot, luminous, and very proud of itself. It was the First Star. It had already devoured all the gas around, so no other stars could be born nearby. No neighbor stars were visible in vicinity either. It was lonely. The First Star spent its life in grief burning H and He and died shortly in pair-instability supernova. Or maybe it died quietly in a black hole. Or maybe I should tell another story……

Why do we think that Population III stars exist?

The term “Population III” could be assigned to two types of stars: “1) the ones which form out of the pristine gas left over after cosmological nucleosynthesis and generated the first metals; and 2) the ones which have been hypothesized to provide the dark matter in galactic halos” – Carr (CarrCaltechWeb 2012).

The first type definitely exists, since we have metals in our disposal, and we know that elements heavier than H and He could only be generated through stellar nucleosynthesis. The second type, however, not necessarily exist, because first galactic halos could also be made of some ancient pre-atomic particles. I am going to discuss the first type of Population III stars.
Note that both types of Population III stars might have formed during the first phase of galaxy formation or even before first galaxies were formed.

What kind of information do we have about early ages of the Universe?

WMAP provides us with the information of state of the Universe up to 400 000 years after the Big Bang by measuring the temperature anisotropies in the cosmic microwave background (CMB). By observing the Universe in all different wavelengths (radio, infrared, µv, visible, x-ray, gamma-ray, etc.) we can get even information about the early Universe up to z ~ 10 .

The first stars are believed to be formed at redshifts z ~20 – 30. But how exactly they have been formed; their masses, lifetimes and luminosities are still subjects of a constant debate.

The cosmic timeline as it appears in the work of Bromm & Larson (2009)

The cosmic timeline as it appears in the work of Bromm & Larson (2009)

Lambda-CDM model

According to the Lambda-CDM model (ΛCDM), the first star-forming regions (or protogalaxies) appeared 100—250 million years after the Big Bang. They had masses of 10^3—10^6Msun and dimensions of 30—100 ly. They were made mostly of a mix of dark and baryonic matter. The segregation between those two would come later.

Computer simulations show that the early cosmic structure evolved from the density fluctuations (nodes) in primordial matter. The small density fluctuations appear first, and then they grow through two processes 1) by merging with other fluctuations, and 2) by accretion matter due to gravity. Primordial gas would gather around these nodes creating bigger and denser clouds. At a certain point, some of gas clouds started contracting under their own gravity and then collapse.

During the collapse, the temperature of baryonic matter raised due to compression heating. For a minihalo mass 10^6 Msun at z~ 20 Tvirial is estimated to be ~ 8000 K (Bromm and Larson 2004, 2009; Bromm 2012). At these temperatures some lonely hydrogen atoms meet and made hydrogen molecules (H2).

What is the probability that a certain density fluctuations would grow big enough?

Bromm (2012) presents the calculations of how density perturbations grow in time following the proportionality D(z) ~ 1/1+z, where z is a redshift and D is the growth factor. As we could see, D(z) is really small at high z, but it grows as z decreases. That means that some of density fluctuations could grow big enough over zs to become the first star forming sites. In the same paper, Bromm (2012) also introduced the important parameter (called over-density or sigma) that defines the probability that at the given redshift the density of a given region of primordial gas is above an average density of nearby Universe by a given value. The growth of a single density fluctuation becomes non-linear, when sigma approaches 1. At this point, the nearby dark matter (DM) collapses, taking baryonic matter with it. For a protogalaxy with a minihalo mass ~ 10^6 Msun to start a runaway collapse at z=20, its sigma should be ~ 1.7, which means that at z~20 the star forming spots were rare, but “not so rare that we should eliminate them from the theory” – Bromm.

Molecular hydrogen and separation of dark and baryonic matter

Cooling rate of primordial gas as a function of temperature

Cooling rate of primordial gas as a function of temperature. The solid line represents the contribution from atomic hydrogen and helium and the dashed line represents the contribution from molecular hydrogen. At temperatures below 10^4 K cooling is provided by H2, which is a poor coolant, but at T> 10^4 K more efficient atomic hydrogen line cooling comes to play. Courtesy: Bromm (2012).

The primordial gas needs to cool in order to star formation to start. The major mechanism that cools primordial gas right after Big Bang is the excitation of resonance lines of atomic hydrogen and helium. It was enough to cool the gas to the temperatures of ~ 10^3 – 10^4 K. In order to cool below Tvirial, the gas must form molecules of hydrogen, whose rotational excitation allowed it to cool to T~200 K (Abel et al. 1997).

At temperatures of T > 10^4 K atomic hydrogen line cooling is very efficient, whereas at lower temperatures, cooling mainly relies on H2, which is a less efficient coolant.

The cooling of molecular hydrogen played the major role in star formation. It allowed the baryonic matter to separate from the dark matter. It worked the following way: H2 molecules would emit radiation, lose energy and then gather together and form a proto-disk, while dark matter particles would remain scattered in the primordial gas cloud.

This happens because dark matter only reacts on gravity and does not emit or accept radiation. The best analogy that comes into my mind is a separation of oil and water. Imagine (or just do it in your kitchen) that you are putting several drops of oil into a glass of water. They would stay separated for some time, but eventually (especially if you introduce some disturbances by shaking/rotating the glass) they would gather into bigger drops and finally form a single one, which would stayed separated from water.

Over a period of time, the structure resembling a galaxy forms with a disk made of H2 and He and a dark matter halo. Inside the gaseous disk, the local inhomogeneities would grow and eventually form big clumps. Some of them grow so big that they would collapse under their own gravity. When a clump begins to collapse, its density raises. That in turn, also raises the gas temperature and therefore slows the clump contraction down, so it needs to gather more mass to star collapsing again. Bromm & Larson (2004, 2009) have shown that the masses of the star-forming gas clumps could reach masses of 500 – 1000 Msun. Some of these clumps would undergo the runaway collapse and form the first stars (Loeb 2010; Bromm 2009, Bromm, Kudritzki, Loeb 2001).

The first stars

The general notion is that Pop III stars followed the same paths as same physics in their development as Pop I and Pop II stars. The general theory of star formation considers 3 basic mechanisms – gravitational instability, proto-stellar accretion and properties of initial mass function (IMF).

Gravitational instability could be explained in terms of Jeans mass (Mj) and Jeans length (Lj). Since a primordial gas cloud contained mainly molecular H and He, “the physics of the hydrogen molecule” rather than cosmological conditions, are considered to play an essential role in primordial gas collapsing and formation of the first stars (Bromm and Larson 2004).

Therefore, the Jeans mass equation can be used to estimate a critical mass for a primordial gas cloud.
Mj describes the equilibrium between the inner pressure of the gas cloud (due its temperature) and the gravitational force. The first one makes a cloud inflate and the last one makes it collapse. The inner pressure in primordial gas was similar to the present day molecular clouds, but the temperature was ~ 200 K, which is much higher ( ~100°K in the outer layers of present day molecular clouds and 10°K in the cores of molecular clouds) (Bromm & Larson, 2004, 2009).

It defines the minimum mass that a clump of an ideal gas must have in order to collapse under its own gravity

Mj= ρ Lj ^3 ~ 500 Msun (T/200K)^ 3/2 (n/10^4) or

Jeans mass

Jeans mass

Where ρ is the density of hydrogen, n~ρ /mH is its number density, and the normalization coefficients are introduced to reflect the typical values in Pop III star forming regions (Bromm 2012).

Another condition – the Jeans length – is based on assumption that in runaway collapse the sound crossing time tsound (for a sound that moves in a media with a given density) should exceed the free fall time.

Both equations for Jeans mass and Jeans length produce the similar result of mass estimate of ~ 100 Msun.

Accretion: The current notion of star formation is that every star (Pop I, II III) grows from inside-out and a small core is formed first at the center of a gas cloud, and then it grows through accretion (Bromm 2009).

How the core is formed?

Runaway collapse due to gravitational instability could proceed as long as the gas is able to radiate away the heat due to compression. After a certain density threshold, the gas cloud becomes optically thick – or that H2 molecules start to collide with other atoms/molecules before they even have a chance to emit an infrared photon.
That makes the further cooling impossible. That is the moment when a thermal pressure stops the collapse and a protostellar core is born. After that the star grows through accretion. Current estimate for a proto-stellar core mass is ~ 10^-2 Msun (Bromm & Larson, 2004, 2009; Bromm 2012).

There are two types of accretion mechanisms that could be found in stars – spherical and disk accretion.
Spherical accretion dominates at early stages, but over time, as the proto-star gains more material with some angular momentum, a proto-stellar disk forms. Then, accretion is shifted to a disk mode.

The key assumption for the spherical accretion rate is that gravity cannot move any baryonic matter faster than its free fall speed, which is close to the speed of sound cs in a given media with given temperature and density. And cs is proportional to the square root of the temperature.

    • For Pop I stars the temperature of the interstellar media (ISM) is ~ 10K that makes the accretion rate ~10^-5 Msun per year.
    • For Pop III stars, the ISM temperature was 300K and the accretion rate was 10^-3 Msun per year. In order to cool to the present day molecular clouds temperatures, the gas must have more effective cooling agents such as metals and grains of dust, which were not available yet.

Here we see the difference in 2 magnitudes, which explains why Pop III stars were so big.

The disk accretion is proportional to the gas viscosity and mass density (Clark et al. 2011). Both mechanisms give us the accreting mass of Macc ~ 10^-3 Msun per year. Accretion of a massive stars follows the Kelvin-Helmholtz timescale, which gives us the time estimate of 10^5 years and results in an upper limit for the Pop III star mass of 100 Msun. The real masses would be smaller, due to the various negative feedbacks from the growing protostar that would stop accretion at some point (Stacy et al. 2012).

Initial Mass Function

Zero-age main sequence (ZAMS) for very massive stars, shown for Pop III (left line) and Pop I stars (right line).

Zero-age main sequence (ZAMS) for very massive stars, shown for Pop III (left line) and Pop I stars (right line). Stellar luminosity shown in Lsun is plotted vs. effective temperature (in K). Stellar masses are represented as diamonds along the sequence, from 1000 Msun (at the bottom) to 1000Msun ( at the top). In shows that the Pop III ZAMS is shifted to higher values of effective temperature, asymptotically reaching Teff ≃ 10^5 K. Figure and caption adopted from Bromm et al. (2001). Current estimates for the Pop III mass however shifted to smaller values.

Initial mass function (IMF) is an empirical function that describes the distribution of stellar masses immediately after star formation. Current estimates for an average mass for a Pop III stars are stirring down from a very high mass up to 300 Msun (Abel et al. 1997) to 100—200 Msun (Bromm and Larson 2009), to even lower values of few dozens of Msun (Bromm 2001, 2012).

How exactly massive first stars were?

The most important property of a star is its mass. If we know the mass of the star, we could estimate its temperature, luminosity, lifespan, and also effects it produces on its environment. That’s why it is so important to estimate how massive the first stars were. However, precise estimates are difficult to provide because of the various scenarios that could occur during the stages of star formation.
For example:

The initial gas could may not fragment at all and create one huge star that eventually consumes all the gas around (Abel et al. 1997). Or it might miss the star formation stage and collapse directly to a black hole (Johnson et al. 2008).

Or it could fragment and form multiple moderate stars instead of a single big one. There is still probability that the fragments would be also big (the H2 cooling keeps the Jeans mass high) and form binary system. Bromm and Larson (2004, 2009) demonstrated that Population III star formed in such binaries could accrete ~ 50Msun in first 10,000 years, making final mass of 100—200Msun.

Or the angular momentum of the collapsing cloud could produce a combination of small and bigger stars, where smaller stars move around a central massive star. Turk, Abel and O’Shea (2009) have shown that multiple fragmentations were possible in the protostellar disks resulting in that “a substantial fraction of Population III stars are forming binaries or event multiple systems”.

Stacy et al (2010) simulate the accretion mechanism of the central protostar for 5000 years after its formation. The initial core was represented as a sink particle with adding some essential detail from accretion physics, including rotation, density, and gas chemistry. The result was a small multiple system “dominated by a binary with masses of 40 and 10Msun” – Stacy et al. If the first stars were born in multiple systems, the old model depicting a fat lone Pop III star living in isolation and disappearing in SNe should be modified. This would also affect the expected feedback from the first stars and their observational signatures.
However, due to computational difficulties, none of the above groups was able to proceed with simulations to the point where the actual stars were born.

Some studies suggest that early stars were rapidly rotating with a speed up to 1000 km s−1 which is close the star’s break point (Stacy et al 2010, 2011; Chiappini et al 2011). That means that strong rotational mixing could have impacted their structure and nucleosynthesis with possible outcome in hypernova explosions and gamma ray bursts (GRBs). Well, in that case we could search for distant GRBs and signatures of early hypernovae as a proof of existence.

Two generations of Pop III stars?

There is also a possibility that two generations of Pop III stars actually existed – both made from the same metal-free gas. Very massive (1000 Msun) PopIII.1 stars formed first and less massive Pop III.2 stars (40—60Msun) formed later (Johnson et al. 2008).

How could that happen?

High massive Pop III stars were very hot and luminous. They radiate in UV, creating a large amount of energetic photons, as well as winds and shock waves. This feedback would ionize the neutral H and He around and outside their DM halos creating large H II regions. This results in formation of a large fraction of HD molecules. HD could cool the gas much more efficient that H2, down to 40– 50 K. At such low temperatures, restrictions due to Jeans mass would relax, allowing formation of less massive stars of ∼50Msun. These less massive Pop III stars formed (close to the end of life of Pop III.1s) in ionized but still metal-free primordial gas. These were named “Pop III.2” stars (Johnson et al. 2008; Ohkubo et al 2009). Note that both Pop III.1 and Pop III.2 coexisted for some period of time.

Not the end of story

So it looks like that first stars may had come in different shapes and flavors. And that is good, because if more various they were more chances we have to catch (eventually) at least some of them.


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