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3. ENDING THE COSMIC DARK AGES

Cosmic reionization involves the coupling of non-linear physics of galaxy formation with the non-local physics of gravity and radiation transport to produce a global phase transition. Reionization is completely different from the local nature of the earlier phase transitions that only depend on the thermal state of the plasma. The mixture of small- and large-scale physics makes for a complex problem. Some important questions to ask about cosmic reionization are: What are the main sources of reionization? When does reionization begin and end? What is the topology of the ionized regions? What can be learned about early galaxies from reionization and vice-versa? How does reionization affect galaxy formation?

The present-day IGM has a mean temperature around 105 K and the primordial elements of hydrogen and helium are near complete ionization (e.g. [22]). Maintaining this relatively high temperature and ionization state is an ultraviolet and X-ray radiation background, sourced by countless galaxies and their central black holes [23]. But how did the IGM become ionized and heated in the first place?

This becomes a particularly rich question when combined with the fact that galaxies were first assembling during the epoch of reionization (EoR). Depending on their mass, DM halos can support the formation of various types of galaxies during the epoch of reionization, shown in Figure 5. As halos grow with time, their gravitational potentials deepen, and their gaseous components shock to higher virial temperatures Tvir. The shocked gas undergoes various radiative processes, cooling the gas. Cold, dense gas fuels star formation and is a good tracer of its strength. Several physical processes control the amount of cold dense gas, but two key processes are the (1) efficiency of radiative cooling and (2) the ability of the halo to retain gas that is heated by radiation and supernovae. They are both directly related to the halo mass. Thus, we can categorize halos by their mass and associate different types of behavior with them.

Figure 5

Figure 5. Below 105.5 M, halos cannot host cold gas and stars. As halos grow, they can host increasingly more cold gas and fuel stronger star formation, ranging from metal-free massive stars (105.5 − 107 M) to the first generation of galaxies (107 − 109.5 M) to more massive galaxies and supermassive black holes (> 109.5 M).

These star forming halos all contribute to cosmic reionization, which can be divided into three phases [24] — pre-overlap, overlap, and post-overlap — that describe the connectivity of the cosmological H ii regions, illustrated in Figure 1. In the pre-overlap phase, each galaxy produces its own H ii region as it forms. These regions are divided by a vast neutral IGM, and their evolution can be treated independently, only requiring the escaping ionizing luminosity of the central galaxy. In the overlap phase, these regions start to combine with nearby regions [25]. Multiple galaxies can contribute to the UV emissivity that pervades the ionized region, dramatically increasing the mean free path of ionizing photons and accelerating the reionization process. Finally in the post-overlap phase, most of the IGM is ionized with some neutral patches remaining the universe. These neutral regions erode away as ionization fronts created from the UVB propagate into these vestiges of an earlier cosmic time.

3.1. The Dark Ages

The Cosmic Dark Ages began after recombination at z ∼ 1090 (380,000 years after the Big Bang) and lasted until the first stars and galaxies started to light up the universe hundreds of millions of years later. However first, it is worthwhile to discuss the supersonic relative velocities between DM and gas that arises before and during recombination. The importance of this phenomenon was overlooked until recently [26]. Before recombination, free electrons scatter off photons, strongly coupling the gas and radiation, but the collisionless DM is not affected by this coupling. These two components of the universe thus had different velocities as radiation and gas decoupled at recombination. The root-mean-square value at this time was ∼ 30 km s−1 and fluctuated on comoving scales between ∼ 3−200 Mpc. Thus on comoving scales of ∼Mpc, the gas has a uniform bulk velocity relative to DM. This so-called streaming velocity decayed as a−1, remained supersonic throughout the Dark Ages, and prevented gas from collecting in the potential wells of the smallest DM halos that would have otherwise formed stars.

The mean gas temperature of the universe after recombination is tightly coupled to the CMB temperature through Compton scattering until a redshift zt ≈ 136 at which time T = 2.73 K (1 + zt) = 374 K [27], where 2.73 K is the current CMB temperature TCMB,0. Afterwards in the absence of any heating, the IGM in an expanding universe cools adiabatically with its temperature decreasing proportionality to a−2, or equivalently (1 + z)2. Throughout this epoch, DM halos are continually assembling, but the gas cannot collapse into these halos because of this excess thermal energy and kinetic energy from streaming velocities. The Jeans mass

Equation 6

(6)

describes the required mass of an object that has enough gravity to overcome thermal pressure, inducing a collapse. Here ρ and cs = (γ kb T / µmp)1/2 are the gas density and sound speed, respectively. Using the IGM temperature Tgas and the mean gas density bar{rho}b = ρc Ωb (1 + z)3, one can calculate the cosmological Jeans mass MJ that is around 32,000 M at z = 30 (100 Myr after the Big Bang) and changes as a−3/2. It provides an estimate of the minimum halo mass that can collect baryonic overdensities [28] in the case without streaming velocities.

3.2. The first stars

Historically, astronomers have categorized stars by their metallicity 5 – Population I for stars like our Sun, which has 1.3% metals by mass [29], and Population II for stars with metallicities less than 1/10th of the solar metallicity fraction. However, the Big Bang only produced hydrogen, helium and trace amounts of lithium. So there must have been an initial population of stars composed of these light elements, whose supernovae enrich later generations of stars with metals that we observe today.

This first generation of stars, known as Population III (Pop III), is inherently different than present-day stars because they form in a neutral, pristine, untouched environment from a primordial mix of hydrogen and helium. Being metal-free reduces the cooling ability of the collapsing birth cloud, resulting in stars that are typically more massive than nearby stars (e.g. [30, 31]).

Metal-free gas loses most of its thermal energy through H2 formation in the gas-phase, using free electrons as a catalyst, in the following reactions.

Equation 7

(7)

(8)

Recombination leaves behind a residual free electron fraction on the order of 10−5. As gas falls into the halos, it shock-heats to around the virial temperature Tvir, and its electron fraction is slightly amplified.

But H2 is a fragile molecule that can be dissociated in the Lyman-Werner (LW) bands between 11.1 and 13.6 eV at soft UV wavelengths where the universe is optically thin. Furthermore, the intermediary product H can be destroyed through the photo-detachment of the extra electron that has an ionization potential of 0.76 eV in the infrared. Accordingly, the timing and host halo masses of Pop III star formation is dependent on the preceding star formation that produces the soft UV and infrared radiation backgrounds. The minimum halo mass that can support sufficient H2 formation that can induce a catastrophic collapse is around 105 M in the absence of LW radiation but steadily increases to 107 M in strong LW radiation fields [32]. Additionally, streaming velocities can suppress Pop III star formation in halos with masses M ≲ 106 M with its exact value depending on the local streaming velocity magnitude that varies on scales of tens of Mpc (e.g. [33, 34]).

Simulations of the first stars and galaxies that consider a LW background have found that Pop III stars form at a nearly constant rate of ∼ 3 × 10−5 M yr−1 Mpc−3 until the end of reionization (e.g. [35]). Each star produces a tremendous amount of ionizing radiation because they are thought to be massive with characteristic masses of tens of solar masses (e.g. [36]), some forming in binary systems and small clusters (e.g. [37, 38]). They have effective surface temperatures ∼ 105 K that is approximately mass-independent above 20 M because of the lack of typical opacities associated with metals in their photospheres. They live for 3–10 Myr and produce between 2 × 1048 and 1050 hydrogen ionizing photons per second in the mass range 15 – 100 M [39]. Most of these photons escape into the nearby IGM, and the averaged escape fraction fesc increases from 20% for a single 15 M star to nearly 90% for a single 200 M star [40]. The exact values of fesc will depend on the total Pop III stellar mass in the halo, the halo mass, and its gas fraction. After their main sequence, some explode in supernova, chemically enriching the surrounding few proper kpc, where the exact fraction depends on their uncertain their initial mass function. Because of this strong feedback, they quench their own formation, blowing out most of the gas that originally existed in their host halos. Furthermore once the medium is enriched with metals, it’s ’game over’ for Pop III stars in affected regions because by definition, they are metal-free.

3.3. The first galaxies

These heavy elements set the stage for the first galaxies that form in larger halos, in which atomic (Lyα) line cooling is efficient. Accordingly, these halos are known as atomic cooling halos and have virial temperatures above ∼ 8000 K. These pre-galactic halos are generally gas-poor (fgasMgas / Mvir ≃ 0.05−0.10) because they are recovering from the gas blowout that their halo progenitors experienced. If the halo is below the atomic cooling limit, star formation is bursty but still intense during active periods, forming between 104 and 105 M of stars before they can cool efficiently through atomic hydrogen transitions. They have star formation rates dot{M} between 10−4 and 10−3 M yr−1, doubling their stellar masses M every ∼ 30 Myr (corresponding to a specific star formation rate, sSFR ≡ dot{M} / M∼ 3 × 10−8 yr−1), and producing ∼ 3 × 1049 ionizing photons per second. After the halo crosses the atomic cooling limit, it can form stars in a continuous fashion at sSFR ∼ 3 × 10−8 yr−1, which can vary by an order of magnitude from galaxy to galaxy, depending on how it has been affected by feedback from previous star formation (e.g. [41, 42, 43]). By the time the halo mass reaches 109 M, the first generations of galaxies contain between 106 and 107 M of metal-poor (Z ≲ 0.1 Z) stars.

An important quantity in reionization calculations is the UV escape fraction fesc, which is notoriously difficult to observationally measure and to theoretically calculate. Most reionization models find that fesc = 0.05−0.2, independent of halo mass, generally produce reasonable reionization histories (e.g. [45]). In the past decade, there have been great strides in the development of radiation hydrodynamics simulations of the first galaxies in which a direct calculation of fesc is feasible. This fraction is highly variable from galaxy to galaxy, and even in a single object, it can vary from nearly zero to unity over its formation sequence (see Figure 6). Because the interstellar medium (ISM) is clumpy, the ionization fronts propagate outwards toward to the IGM at varying velocities with respect to angle. The ionizing radiation generally escapes in the directions with small neutral column densities. Once an ionized channel is opened between a star cluster and the IGM, it remains ionized as long as massive stars remain alive. Thus, the value of fesc can be thought as the solid angular fraction that the ionized channels cover. Such efforts have found that the smallest galaxies have high escape fractions. The median time-averaged value of fesc is ∼ 0.5 in halos with masses Mvir ≃ 107 M, and it decreases to 0.05–0.10 at Mvir ≃ 108 M [41, 46, 43]. When the total escaping photons are integrated over all galaxies, half of the photon budget to reionization originate from halos with Mvir ≲ 109 M.

Figure 6

Figure 6. Projections of gas density (left) and UV radiation flux (right) of a first generation galaxy with a stellar mass ∼ 105 M at redshift z ≃ 8 with the bottom panels pictured 10 Myr after the top panels. The white circle marks the virial radius. The UV escape fractions are 1% (top) and 7% (bottom). Adapted from [44].

3.4. The first black holes

Black holes grow through mergers of two black holes and the accretion of gas. The latter is the primary growth mechanism, where material falls down the deep gravitational potential well. It forms an accretion disk orbiting around the black hole because of conservation of angular momentum. Eventually, gas migrates to increasingly smaller radii and falls into the black hole. In the process, the gas is heated intensely from the strong gravity field and emits radiation. Any outward radiation interacts with the inflowing gas, which can suppress the growth rate of the black hole.

Because Pop III stars are thought to be massive, a large fraction will leave a black hole remnant. Temperatures in accretion disks around stellar-mass black holes are between 104 and 107 K and thus emits strongly in the hard UV and X-ray energies. Their UV luminosities are insignificant when compared to stellar sources, but their X-rays should have an impact on the thermal and ionization state of the IGM. These high energy photons can penetrate much deeper into the IGM, creating large partially ionized regions with xe = 0.01−0.02 out to distances of 100 kpc [47], creating a much different reionization topology than stellar sources [48].

Pop III stars leave behind some of the first black holes in the universe. These could be the “seeds” for more massive black holes that we observe in the nearby Universe. They can possibly grow to supermassive black holes that are millions and sometimes billions of times more massive than our Sun. The most extreme cases have masses over 109 M at redshifts z > 6 when the universe was younger than 800 million years old [49]. The formation and growth of black holes are still active research topics. A few pressing questions are: How did massive black holes in the distant universe grow so rapidly? Did their radiation contribute to reionization? How often did stellar-mass black holes grow into supermassive black holes? Where are these stellar remnants today? Observations from the epoch of reionization will provide us with clues in order to solve these mysteries.



5 In astronomy, any element heavier than hydrogen (usually denoted by the variable X) and helium (Y) is historically termed as a metal (Z). Back.

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