4. THEORETICAL STUDIES

4.1. Overview

The formation of the first galaxies is an intrinsically more complex process, compared to the appealing simplicity of how the first stars formed. In the latter case, the initial conditions are cosmologically determined, and the relevant physical processes are virtually all known (e.g., Yoshida, Omukai & Hernquist 2008). In the standard hierarchical (CDM) structure formation model, the first generation of stars is formed before galaxies emerged. Feedback effects from these stars are thus expected to play a key role in setting the scene, i.e., the initial conditions, for first galaxy formation (see Figure 1). In turn, the nature of the first stars may be imprinted in various properties of the first galaxies.

4.1.1. FORMATION EPOCH    When did the first galaxies form? This is an intricate question, because it is directly related to the definition of `first galaxy', as discussed in Section 2. If minihalos were the hosts of the first galaxies (Ricotti, Gnedin, & Shull 2002a, 2002b, 2008), the very first galaxies would be formed at z > 40 within standard CDM cosmology (Miralda-Escudé 2003; Naoz, Noter & Barkana 2006). However, it is more plausible that continuous star-formation can be sustained in larger mass dark matter halos, where at least atomic hydrogen cooling operates efficiently. Such large halos with virial temperatures greater than ~ 10⁴ K are significantly biased objects at z > 15 (Miralda-Escudé 2003; Gao et al. 2007). The abundance of the rare density peaks sensitively depends on the assumed cosmological parameters, most notably on the fluctuation amplitude of the initial density field at the relevant mass (length) scales. Typically, such atomic cooling halos, corresponding to ~ 2-peaks in the Gaussian random field of initial density perturbations, are predicted to form at z ~ 10-15, or roughly 500 Myr after the Big Bang. Thus, the epoch of the first galaxies lies just beyond the current horizon of observability, and the JWST or the next-generation, 30-40m, ground-based telescopes will be able to detect them.

4.1.2. STELLAR FEEDBACK    A key element in the physics of first galaxy formation is the feedback from the first stars, and the complications arising from it. If the first stars were massive, they would have exerted a strong influence on the gas in the host halo by injecting significant energy either by radiation or by supernova explosions. Then the next episode of star formation was likely to be delayed for a long time, comparable to the dynamical time of the massive halo, even if the halo's virial temperature well exceeds 10^4-5 K. Specifically, delay times of a few 10⁷ yr are predicted, which corresponds to a significant fraction of the Hubble time at z ~ 15. Cosmological simulations performed so far generally support the notion (Johnson & Bromm 2007; Yoshida et al. 2007a; Alvarez, Wise & Abel 2009). The strength of the feedback effect could in principle be reflected in the very faint-end shape of the luminosity function of high-redshift (z > 7) galaxies (Haiman 2009). The characteristic mass of the first stars, ultimately driving the strength of the negative feedback, may thus be constrained.

4.1.3. CONDITIONS FOR STAR FORMATION    When we approach the assembly of the first galaxies, the degree of complexity is greatly enhanced compared to the simplicity that governed the formation of the very first stars. In particular, this emerging complexity set the stage for the second generation of star formation that occurred inside the first galaxies. The existence of heavy elements, and possibly of dust grains, the degree of turbulence, and the likely presence of dynamically significant magnetic fields all need to be taken into account. External radiation fields, either from nearby stars and galaxies, or built up globally, also regulated the formation of molecular gas clouds (Ahn & Shapiro 2007; Johnson, Greif & Bromm 2007; Susa 2008). Star formation in the first galaxies is thus as complicated as present-day star formation, and may also be qualitatively similar. Recent cosmological hydrodynamical simulations confirmed that strong turbulence develops within large, proto-galactic halos (Wise & Abel 2007; Greif et al. 2008). Turbulence is generated by supernova explosions or dynamically through dark matter halo mergers, or more generally as a result of gravity-driven virialization. The turbulence is typically supersonic, related to the cold-flow accretion streams that feed gas into the very centers of the first galaxies (see Figure 6). In the presence of rapid cooling by atomic hydrogen and by heavier atoms such as carbon, oxygen and iron, the turbulent gas might settle into rotationally supported, central disks (Wise & Abel 2007). We thus have obtained a much improved picture of the physical conditions just prior to the onset of the initial starburst inside the first galaxies.

Figure 6. Turbulent collapse into the first galaxy. Shown is the hydrogen number density (left-hand panel) and temperature (right-hand panel) in the inner 4 kpc (physical), surrounding the BH at the center of the galaxy, indicated by the filled black circle. The dashed lines denote the virial radius at a distance of 1 kpc. Hot accretion dominates where gas is accreted directly from the IGM and shock-heated to 104 K. In contrast, cold accretion becomes important as soon as gas cools in filaments and flows towards the center of the galaxy. These cold streams drive a prodigious amount of turbulence and create transitory density perturbations that could in principle become Jeans-unstable. Adopted from Greif et al. (2010).

4.1.4. SIMULATED VERSUS OBSERVED GALAXIES    Current state-of-the-art cosmological simulations followed the formation of objects with still rather low masses, typically ~ 10⁸ M. The real target of the next-generation telescopes, however, will be those with masses 10⁹ M (Mashchenko, Wadsley & Couchman 2008; Pawlik, Milosavljevic & Bromm 2011). Therefore, there still remains a large gap between the available highly-resolved, ab initio simulations and the realistic targets for the upcoming observations. For the simulation community, much work is still required in building the bridge to the observations. We already know the rough outlines of the 10⁹ M halo formation problem though. Semi-analyic models of galaxy formation combined with large-volume cosmological simulations show that such "luminous" galaxies appear as early as z ~ 15-20 (Springel et al. 2005; Lacey et al. 2010). A concerted use of both of these approaches, semi-analytical and ab-initio simulations, will be needed to address the many important questions about the formation of the first galaxies (Benson 2010; Raicevic, Theuns & Lacey 2011).

4.2. Pre-Galactic Metal Enrichment

The first galaxies are plausible sources of heavy elements that existed in the IGM at high redshifts (Songaila et al. 2001; Simcoe 2006; Ryan-Weber et al. 2009). The IGM metalicity evolution can place constraints on the prior star formation history (Maio et al. 2011). Although it has also been proposed that Pop III stars, formed in minihalos, can contribute to early chemical evolution (Yoshida et al. 2004; Tornatore, Ferrara & Schneider 2007; Greif et al. 2007), recent observations suggest that the C IV abundance declines at z > 6 (Becker, Rauch & Sargent 2009). It is therefore likely that the heavy elements were dispersed by galaxies that had formed around z ~ 6. Assuming that the first galaxies are the dominant source of the IGM enrichment and reionization, one should be able to build a consistent model for the reionization history, the galaxy luminosity function and its evolution, as well as the stellar population and chemical evolution in the first galaxies (Choudhury & Ferrara 2006).

Galactic scale outflows driven by radiation pressure from hot stars and/or by supernovae can transport heavy elements into the IGM (Madau, Ferrara & Rees 2001; Mori, Ferrara & Madau 2002; Wada & Venkatesan 2003). How exactly this happened during the reionization epoch can be inferred by comparing the metallicity evolution and the star-formation history. The currently available data seem to point to delayed enrichment via galactic outflows, rather than prompt enrichment (Kramer, Haiman & Madau 2010). Three-dimensional cosmological simulations consistently show that the IGM metal pollution is patchy, leaving a large volume of unpolluted, chemically pristine regions at z > 6 (Bertone, Stoehr & White 2005; Tornatore, Ferrara & Schneider 2007). One possible implication of such inhomogeneous enrichment is the existence of Pop III star clusters or SN explosions at lower redshifts, z < 6 (Scannapieco et al. 2005; Johnson 2010). Such objects, if they existed, would be an exciting target for direct observations with the JWST and future 30-40m ground-based telescopes.

Inside individual first galaxies, the mixing of heavy elements can occur rapidly. Hydrodynamic simulations confirmed this, showing that a large volume of the halo gas in the first galaxies is already metal-enriched before it condenses again to trigger the next episode of star formation (Greif et al. 2010; JH Wise et al., submitted). Specifically, metallicities inside the first galaxies prior the the initial starburst can reach average levels of already ~ 10^-3 Z, with maximum levels even up to an order of magnitude higher (see Figure 7). The degree of mixing and details of the chemical enrichment history can be studied by the very promising approach of stellar archaeology (Section 7). In particular, the metallicity distribution and the relative elemental abundance patterns of stars in dwarf galaxies in the Local Group may preserve the fossil record of early chemical enrichment.

Figure 7. Metal enrichment in the first galaxy. Shown is the aftermath of tens of pair-instability supernovae (PISNe) which exploded inside the progenitor minihalos. The situation here corresponds to z 17. The projection of metallicity is shown in color, and that of gas density in shades of grey, with values indicated by the insets. The box has a proper size of 8.6 kpc. Adopted from Wise & Abel (2008).

4.3. Star Formation in the First Galaxies

Outstanding questions regarding star-formation in the first galaxies are the star-formation efficiency, the stellar IMF, and the strength of stellar feedback. These three elements are indeed closely connected to each other. The star-formation efficiency is largely affected by the ability of the halo gas to cool and condense. Because the gas density is low initially, cooling by atomic heavy elements such as carbon, oxygen, and iron is effective in early phases (Bromm et al. 2001; Bromm & Loeb 2003a; Santoro & Shull 2006; Omukai et al. 2005; Maio et al. 2010). Unlike hydrogen molecules, which are fragile to soft UV radiation in the Lyman-Werner (LW) bands, cooling by metallic atoms and ions can operate even under the influence of a UV radiation field (Maio et al. 2007; Safranek-Shrader, Bromm & Milosavljevic 2010).

The stellar IMF is more difficult to address. Observationally, at least for local star-forming regions, it is well determined to peak at roughly solar masses and to exhibit a power-law extension towards higher masses: dN / dlnM M^x with x ~ -1.35 (Salpeter 1955; Zinnecker & Yorke 2007). However the mechanism that shapes the IMF is not well understood even in the local Universe. It is often thought that predicting the IMF for the first stars would be simpler in many ways, and that it would be more top-heavy, with stars more massive than a few tens of solar masses being predominant (for a review of the argument, see Bromm & Larson 2004). In the first galaxies, there are a number of physical ingredients that have been suggested to significantly affect the IMF: supersonic turbulence (Wise & Abel 2008; Greif et al. 2008; 2010), atomic cooling by heavy elements (Bromm et al. 2001; Santoro & Shull 2006; Smith, Sigurdsson & Abel 2008), cooling by dust (Schneider et al. 2006; Omukai et al. 2005), the angular momentum transfer and heating due to magnetic fields (Schleicher et al. 2010), the initial degree of ionization (Nagakura & Omukai 2005; Johnson & Bromm 2006; Yoshida, Omukai & Hernquist 2007; Cazaux & Spaans 2009), and a lower floor to the attainable gas temperature set by the CMB (Larson 1998; Schneider & Omukai 2010). All these processes acted to render star formation in the first galaxies similar again to the present-day case. In particular, the presence of supersonic turbulence likely allowed the formation of multiple stars in a molecular cloud, with a broad mass spectrum that may have resembled the local self-similar form towards high masses. This expectation, however, still needs to be tested with sophisticated simulations.

The ionization degree is important particularly for a primordial gas. The IGM can be ionized by radiation from the first stars (Kitayama et al. 2004; Whalen et al. 2004), blastwaves driven by the first supernovae (Bromm et al. 2003; Machida et al. 2005), by cosmic rays (Vasiliev & Shchekinov 2006; Jasche, Ciardi & Ensslin 2007; Stacy & Bromm 2007), by X-rays emitted from early mini-quasars (Oh 2001; Ricotti & Ostriker 2004; Kuhlen & Madau 2005), or through dark matter annihilation/decay (Ripamonti, Mappeli & Ferrara 2007; Iocco et al. 2008; Spolyar, Freese & Gondolo 2008). An initially ionized gas of primordial composition can cool to ~ 100 K, where cooling by hydrogen deuteride (HD) molecules becomes important. The abundance of additional free electrons here catalyzes a boost in H₂ formation, which in turn leads to the build-up of a critical abundance of HD, thus enabling this low-temperature cooling channel (e.g., Johnson & Bromm 2006). Primordial stars formed under this condition, the so-called Population III.2 stars (McKee & Tan 2008; Bromm et al. 2009), are thought to include ordinary massive stars (Johnson & Bromm 2006; Yoshida, Omukai & Hernquist 2007; Clark et al. 2011). However the relative importance of Pop III.2 stars remains uncertain (Trenti & Stiavelli 2009; Wolcott-Green & Haiman 2010). If Pop III.1 and Pop III.2 stars have different characteristic masses, detection of high-redshift supernovae of different types, pair-instability SNe and core collapse SNe, will provide constraints on the relative formation rates of PopIII.1 and PopIII.2 stars.

Because of the chemical feedback discussed in Section 4.2, many stars in the first galaxies are probably metal enriched. Detailed calculations on the thermal evolution of a low-metallicity gas have been carried out (Schneider et al. 2002; Jappsen et al. 2007; Omukai, Hosokawa & Yoshida 2010). The results suggest that dust thermal emission remains an efficient cooling mechanism up to very high densities where atomic line cooling is ineffective. Dust cooling allows fragment masses to reach very small, essentially opacity-limited values of 10^-2 M (see Figure 8). Three-dimensional simulations are needed to determine the ability of a low-metallicity gas to fragment, and to follow the subsequent accretion and merging history of the growing protostars. One such study has been carried out by Clark, Glover & Klessen (2008) who employed a tabulated barotropic equation of state for a low-metallicity gas. The challenge now is to extend such calculations to realistic initial conditions, and to self-consistently determine the equation of state during the dynamical collapse.

Figure 8. Thermal evolution of pre-stellar gas with various metallicities. The constant Jeans masses are indicated by the dashed lines. Characteristic temperature dips are caused by cooling due to atomic line cooling at low densities, molecular cooling at intermediate densities, and dust thermal emission at high densities. Adopted from Omukai, Hosokawa & Yoshida (2010).

4.4. Radiation from the First Galaxies

4.4.1. IONIZING PHOTON BUDGET AND THE ESCAPE FRACTION    First galaxies are promising sources of ultra-violet photons that reionized the intergalactic hydrogen. A critical quantity is the escape fraction of ionizing photons, f_esc. Recent simulations that couple the hydrodynamics of the gas in the vicinity of the central star cluster to the continuum radiative transfer of the ionizing radiation from these stars find that the escape fraction strongly evolves with time (Johnson et al. 2009). Initial values are close to zero, when gas densities are still high, and most of the ionizing radiation is bottled up inside the galaxy. With time, however, the photo-ionization heating creates a central high-pressure bubble which in turn drives a strong outflow. Densities thus decrease, until ionizing photons can freely escape into the IGM, leading to a large instantaneous escape fraction of f_esc ~ 1. Time-averaged escape fractions are typically quite large, f_esc ~ 0.1 - 0.8 (Wise & Cen 2009; Razoumov & Sommer-Larsen 2010). Extinction by a substantial amount of dust can reduce it to f_esc ~ 0.1 or less (Gnedin, Kravtsov & Chen 2008; Yajima et al. 2009). Available observations suggest f_esc < 0.01 for low-redshift galaxies (e.g., Bridge et al. 2010), whereas f_esc = 0.01 - 0.1 for z ~ 1-3 galaxies (Inoue et al. 2006; Shapley et al. 2006; Siana et al. 2007; Iwata et al. 2009). There are indirect hints from observations of high-redshift galaxies regarding the escape of ionizing radiations, and the stellar populations responsible for this emission (e.g., Jimenez & Haiman 2006).

The ionizing photon budget derived from the currently estimated UV luminosity function of z > 6 galaxies falls short of what is necessary to reionize the Universe (Ouchi et al. 2009). A possible resolution may be either that faint, low-mass galaxies host a substantially "bluer" stellar population, or that the escape fraction from the faint galaxies is actually large. This interpretation of the data agrees with the results from recent cosmological simulations, which consistently predict such large values of f_esc.

4.4.2. GLOBAL SIGNATURE    The radiation produced by the first galaxies cumulatively contributes to reionization, to the CIB, and to the redshifted 21-cm signal. Here, we only briefly discuss these global signals, as they have been extensively reviewed elsewhere: 21cm cosmology by Furlanetto, Oh & Briggs (2006), Barkana & Loeb (2007), and Morales & Wyithe (2010), the CIB by Hauser & Dwek (2001), Kashlinsky (2005), and Arendt et al. (2010), and reionization in the review papers mentioned in Section 1.

Cosmic reionization imprints distinct large angular-scale patterns in the CMB polarization maps. CMB photons are Thomson-scattered by free electrons in the reionized IGM. As a consequence, the CMB photons are polarized and the temperature fluctuations are damped. These signatures can be used to infer the approximate epoch of reionization. The seven-year WMAP data yields the CMB optical depth to Thomson scattering, 0.09 ± 0.03 (Komatsu et al. 2009), where

(3)

for the standard CDM cosmology. Here, we have assumed for simplicity that the IGM is fully ionized at z < z_reion. The WMAP measurement provides an integral constraint on the total ionizing photon production at z > 6. The contribution from z < 6 to the total optical depth amounts only to 0.04 and thus a significant volume fraction of the IGM must be ionized to z = 10 or higher. Matching the WMAP Thomson optical depth constraint provides a non-trivial test for models of early star and galaxy formation. It is unlikely that reionization is completed very early by massive Pop III stars (Cen 2003; Greif & Bromm 2006; Haiman & Bryan 2006). More accurate polarization measurements by the Planck Surveyor Satellite will further tighten the constraint on the Thomson optical depth, and in addition might even allow researchers to estimate the reionization history of the Universe (Holder et al. 2003; Mukherjee & Liddle 2008). The latter is usually expressed as the redshift-dependent free electron fraction, x_e (z), which could be much more complex than the simple step function, which is often assumed in approximate interpretations of the data (see Fan, Carilli & Keating 2006).

The first galaxies inevitably contributed to the CIB, through the redshifted Lyman- recombination line from the H II regions surrounding their stellar sources (Santos, Bromm & Kamionkowski 2002; Salvatera & Ferrara 2003). A vigorous debate has developed around the question of how important still unresolved galaxies at the highest rdshifts are, compared to more local, known sources (e.g., Kashlinsky et al. 2005; Thompson et al. 2007). If the difficult subtraction of foreground sources, such as the emission from the interplanetary dust, can be reliably accomplished, a number of key parameters of the first galaxies might be derived from the CIB. One is the typical mass of the first galaxies. In hierarchical structure formation, the mass function is dominated by the lowest mass satisfying the first galaxy criteria (see Section 2). The corresponding dark matter halos then exhibit clustering properties that are characteristic for that mass scale. Those clustering properties are subsequently reflected in the CIB fluctuation power spectrum (Fernandez et al. 2010). A second quantity is the escape fraction of hydrogen ionizing photons from the first galaxies, which could possibly be inferred from the mean intensity of the CIB. The basic idea here is that the production of rest-frame Lyman- photons is greatly enhanced if the ionizing radiation inside the first galaxies cannot escape into the IGM, where densities are very low (recombination lines are emitted at a rate n²). The measured CIB angular power spectrum can largely be attributed to galaxies at z<4, but the possibility for a contribution from z > 8 sources still remains (Cooray et al. 2007).

Redshifted 21-cm emission from neutral hydrogen directly probes the topology of reionization (Furlanetto, Oh & Briggs 2006). LOFAR has already begun to collect data and is carrying out its initial calibrations. It will provide statistical information on the distribution of neutral hydrogen at z ~ 6, and will eventually be able to map out the distribution directly. Even more powerful is the planned Square Kilometer Array (SKA), with an unprecedented sensitivity and spectral coverage. The clustering of the first galaxies can be used to study the topology of reionized regions. If the first galaxies were dominant sources of reionization, their distribution should be anti-correlated with ionized regions that appear as dark holes in 21-cm maps (Lidz et al. 2009).

These global signatures have the advantage that they do not suffer from incompleteness or selection effects of the target galaxies. Very small, faint galaxies that cannot be seen by JWST may in principle leave distinct signatures in the global quantities discussed here.