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While the first stars are for the most part well-defined objects, the definition of the first galaxies is somewhat more ambiguous (see e.g. Bromm & Yoshida 2011). Here we shall adopt the common view that a galaxy must be able to host ongoing star formation, even in the face of the radiative and mechanical feedback that accompanies the formation and evolution of stars. By this definition, the formation sites of the first stars, dark matter minihalos with masses 105 - 106 M, are unlikely candidates for the first galaxies, as the high energy radiation emitted by young stars and the supernovae that mark their end of life can rarify and expel any dense gas from which stars may form at a later time. As shown in Figure 1, it is only somewhat larger halos, with masses 107 - 108 M, which have deep enough gravitational potential wells and enough mass to prevent the expulsion of gas after an episode of star formation (e.g. Kitayama & Yoshida 2005; Read et al. 2006; Whalen et al. 2008).

Figure 1

Figure 1. The fate of host halos of the first stars, as a function of the mass Mh of the halo and the energy ESN with which the stars explode as supernovae. Less massive halos have their gas blown away when even relatively weak (e.g. ESN ∼ 1050 erg) Pop III supernovae explode within them, both along with (circles) and in the absence of (triangles) the additional radiative feedback from the progenitor stars. Halos which retain their gas are shown by crosses. From equation (1) we can see that for the suite of halos shown here at z ≃ 20, those with Tvir ≥ 104 K are able to retain their gas, in contrast to the less massive minihalos. From Kitayama & Yoshida (2005).

As can be inferred from this Figure, one of the distiguishing characteristics of halos massive enough to host ongoing star formation, and so to host the first galaxies, is the characteristic temperature Tvir that gas reaches during their virialization. This, referred to as the virial temperature of the halo, can be derived by assuming that the absolute magnitude of the gravitational potential energy of the halo is twice its kinetic energy, which yields

Equation 1


where Mh is the mass of the halo, z is the redshift at which it collapses, and µ is the mean molecular weight of the gas in the halo, here normalized to a value appropriate for neutral primordial gas. The Hubble constant H0 = 100 h km s−1 Mpc−1 also appears here through h. 1 From Figure 1 we see that the mass of halos which are large enough to host ongoing star formation, at z ∼ 20, is ∼ 107 M; this corresponds to a virial temperature of Tvir ∼ 104 K. One of the reasons for this is that 104 K is roughly the temperature to which photoionization by stars heats the gas (see e.g. Osterbrock & Ferland 2006); thus, gas that is photoheated by stars remains bound within a halo with such a virial temperature. In turn, the presence of this gas when stars explode as supernova leads to the rapid loss of the mechanical energy in the explosion to radiation, thereby limiting the amount of gas blown out of the halo, in contrast to the case of the first supernovae in less massive minihalos (see Section 3.1). Also, due to the efficient cooling of atomic hydrogen at this temperature, gas can collapse into halos with Tvir ≥ 104 K regardless of its molecular content, in contrast to the minihalos that host the first stars, into which primordial gas only collapses if it is cooled by H2 molecules (e.g. Oh & Haiman 2002); this implies that star formation can take place even under the influence of the molecule-dissociating radiation emitted by the first stars (see Section 2.2).

Figure 2 shows the properties of an atomic cooling halo 2, in which a first galaxy would form, at z ∼ 10 in a cosmological simulation (see Greif et al. 2008). As shown here, much of the primordial gas that falls from the intergalactic medium (IGM) into the potential well of the halo is shock-heated to Tvir ∼ 104 K at a physical distance of ∼ 1 kpc from the center of the halo. This distance corresponds to the virial radius rvir of the halo, defined in general terms as the radius within which the average matter density is equal to the value at which virial equilibrium is established, which is ≃ 18π2 times the mean matter density of the universe at the redshift z at which the halo forms (e.g. Barkana & Loeb 2001). For the standard ΛCDM cosmological model, this is given in physical units as

Equation 2


where we have normalized to values of halo mass and redshift that are typical for atomic cooling halos hosting the first galaxies. Near the virial radius a large fraction of the gas is hot (≥ 500 K) and rotating about the center of the halo at nearly the circular velocity vcirc of the halo (Greif et al. 2008), defined as the velocity with which a body must move in order to be centripetally supported against gravity at the virial radius:

Equation 3


However, there is also a substantial portion of the infalling gas that falls to the center of the halo in cool, dense filaments and is not shock-heated to the virial temperature. These dense filaments feed cold gas into the central ∼ 100 pc of the halo, contributing to the majority of the gas the temperature of which is < 500 K and which may collapse to form stars (Greif et al. 2008).

While the atomic cooling halo shown in Figure 2 is a prime example of the type of halo in which the first galaxies likely formed, there are numerous physical effects that were not included in the cosmological simulation from which this halo was drawn, most notably the feedback effects of Population (Pop) III stars (see e.g. Wise & Abel 2008; Johnson et al. 2008; Greif et al. 2010; Whalen et al. 2010). The high energy radiation emitted by the first stars both ionizes the primordial gas and dissociates molecules, which are critical cooling agents. Also, many of the first stars explode as violent supernovae, which inject large amounts of mechanical energy into their host minihalos and the IGM, as well as dispersing the first heavy elements, thereby altering forever the properties of the gas from which the first galaxies form.

Figure 2

Figure 2. The properties of the primordial gas collapsing into an atomic cooling dark matter halo at z ≃ 10. Shown are the hydrogen number density (left panel) and temperature (right panel), the dashed lines denoting the virial radius rvir at a distance of ≃ 1 kpc. Note that most of the gas is accreted directly from the IGM and shock-heated to the virial temperature of Tvir ≃ 104 K, although cold accretion also becomes important as soon as gas cools in filaments and flows towards the centre of the galaxy, such as through the streams coming from the left- and right-hand sides of the panels. In contrast to the minihalos in which the first stars form, a halo with a virial temperature Tvir ≥ 104 K is massive enough and has a deep enough gravitational potential well to retain its gas even when stars formed within it explode as supernovae (see Figure 1). Hence, such halos are strong candidates for the formation sites of the first galaxies. From Greif et al. (2008).

In this Chapter, we shall focus on how this feedback from the first generations of stars impacts the formation and evolution of the first galaxies. In Section 2, we briefly discuss how the cooling properties of the primordial gas, which shape the nature of Pop III star formation, are affected by the radiation emitted from the first stars and accreting black holes. In Section 3, we then turn to discuss how the first supernovae enrich the primordial gas with heavy elements, and how this process leads to the epoch of metal-enriched Pop II star formation. In Section 4, we briefly discuss the prospects for observing the first galaxies, and for finding Pop III star formation therein, using facilities such as the James Webb Space Telescope (JWST). Finally, in Section 5, we close with a summary of the results presented in this Chapter and give our concluding remarks.

1 Note that this formula is derived assuming a standard CDM cosmological model in which h ≃ 0.7 (see e.g. Barkana & Loeb 2001); as such, this formula is valid at the high redshifts (i.e. z >> 1) at which the first galaxies form, but must be modified at lower redshifts in order to account for a cosmological constant Λ. Back.

2 Because the primordial gas can cool via emission from atomic hydrogen and collapse into halos with Tvir ∼ 104 K, such halos are commonly referred to as 'atomic cooling' halos. Back.

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