There is currently no universally agreed upon definition of what we mean by "first galaxy". Observers and theorists operate with different working hypotheses, and those hypotheses have changed with our evolving understanding. We here summarize the most common attempts to define a primordial galaxy. Intriguingly, to properly pose the question ("What is a first galaxy?"), we already need to know the answer to it. It is thus likely, that we will witness a continuing iterative process, but it is also evident that devising a proper definition must be part of the discovery process.
2.1. Theoretical Perspective
On the theory side, the discussion typically begins with an enumeration of defining properties. What are the ingredients required for a first galaxy ? For a galaxy in general, the presence of a confining dark matter halo hosting a long-lived stellar system seems inevitable. Often, there is gas present as well, but there are galaxies without any apparent gas. In addition, we may stipulate that the potential well of the DM halo is sufficiently deep to retain gas that was heated to temperatures in excess of ~ 104 K as a result of photo-ionization by stellar radiation (Mesinger & Dijkstra 2008; Mesinger, Bryan & Haiman 2009). More stringently, we may also want to demand that the halo can retain gas heated and accelerated through SN explosions. Finally, we may ask whether the system is able to support a multi-phase interstellar medium, which in turn could sustain a stable mode of self-regulated star formation.
The theorists' debate now centers on identifying the smallest, lowest-mass, DM halos that fulfill the criteria listed above. According to the tentative list of criteria for what constitutes a galaxy, DM halos that are unable to form stars and therefore remain dark would not be galaxies. This would in particular apply to the first DM halos to collapse, or virialize, at z ~ 100. Their mass scale strongly depends on the nature of the CDM particle (Diemand, Moore & Stadel 2005). For DM consisting of weakly interacting massive particles, as predicted by the theory of supersymmetry, the first DM halos comprise a mass of ~ 10-6 M, roughly the mass of Earth. For axion DM, on the other hand, the smallest halos would only contain ~ 10-13 M. Returning to the discussion of those DM halos that are able to form stars, one class of models proposes minihalos, defined in Section 1, as hosts for the first galaxies (Ricotti, Gnedin, & Shull 2002a, 2002b, 2008). In this case, the halos that host the formation of the first (Pop III) stars would coincide with the first galaxies. This Ansatz, however, makes the implicit assumption that the initial mass function (IMF) of the first stars was not very different from the locally observed one, where the distribution peaks at low masses around < 1 M. Negative feedback effects from them, in terms of star-formation efficiency, would not be so severe for a subset of minihalos, such that they could sustain star formation and effectively self-enrich.
Assuming that primordial stars were predominantly massive, as is suggested by most current theoretical models and simulations (Omukai & Palla 2003; Bromm et al. 2009), leads to a very different picture, though. After the first stars are formed inside a minihalo, vigorous negative feedback effects would effectively shut off the potential for subsequent star formation. For once, the heating due to photo-ionization drives a pressure wave that greatly suppresses the gas density inside of minihalos (Kitayama et al. 2004; Whalen, Abel & Norman 2004; Alvarez, Bromm & Shapiro 2006). If, in addition, energetic SNe occurred, the minihalo would be virtually devoid of any gas, leaving behind a sterile system as far as star formation is concerned (Bromm, Yoshida & Hernquist 2003; Greif et al. 2007). More massive systems that are able to re-assemble the high-entropy material affected by Pop III stars inside minihalos might therefore be needed. There are, however, studies of the SN feedback in primordial minihalos that suggest a different conclusion (Whalen et al. 2008). If the bulk of the minihalo were to remain substantially neutral, thus not triggering such dramatic outflows and the corresponding density suppression, the SN remnant would be highly radiative and largely confined to the minihalo, thus effectively self-enriching them. The condition of near-neutrality would be satisfied in more massive ( ~ 107 M) minihalos (Kitayama & Yoshida 2005), combined with not too massive Pop III progenitor stars. It is an open question whether these conditions are ever met in a realistic cosmological setting, where Pop III star formation first occurred in lower-mass systems.
To gauge how susceptible a given halo will be to negative stellar feedback, it is useful to introduce its virial temperature
where Vc is the circular velocity, µ is the mean molecular weight, and c gives the density contrast established through virialization as a function of redshift (Bryan & Norman 1998). Closely related is the gravitational binding energy of the halo
where rvir is the virial radius of the halo. In evaluating these expressions, we have assumed cosmological parameters as recently determined by the Wilkinson Microwave Anisotropy Probe (WMAP) (Komatsu et al. 2009), and that z >> 1.
Another series of recent simulations has suggested that DM halos containing a mass of ~ 108 M and collapsing at z ~ 10 were the hosts for the first bona fide galaxies (Wise & Abel 2007, 2008; Greif et al. 2008, 2010). These dwarf systems can indeed re-virialize the gas that was affected by previous star formation in minihalos (see Figure 1). They are special in that their associated virial temperature exceeds the threshold, ~ 104 K, for cooling due to atomic hydrogen (Oh & Haiman 2002). These so-called `atomic-cooling halos' did not rely on the presence of molecular hydrogen to enable cooling of the primordial gas. In addition, their potential wells were sufficiently deep to retain photoheated gas, in contrast to the shallow potential wells of minihalos (Dijkstra et al. 2004). Our tentative conclusion is that atomic cooling halos thus seem to fulfill the requirements for a first galaxy, but important open questions remain that need to be addressed with future simulations (see Section 4).
Figure 1. Assembly of the first galaxy. We here illustrate the scenario where the first galaxies reside in atomic cooling halos. These comprise total masses of ~ 108 M and typically collapse at z ~ 10. Note that within the scenario illustrated in this figure, minihalos are not considered galaxies, because of the strong negative feedback from the Pop III stars that form inside of them. This feedback will effectively destroy the minihalos such that neither gas nor low-mass stars will remain in them. Their assembly is affected by the feedback from the first (Pop III) stars that had formed earlier in the minihalo progenitor systems. Within this model, atomic cooling halos hosted the second generation of stars, including the first low-mass (Pop II) stars that could have survived to the present day.
A related issue is to identify the conditions that enable the formation of the first disk galaxies (Pawlik, Milosavljevic & Bromm 2011), or of central supermasive black holes (see Section 5). However, such disks and central black holes may well have emerged only at a later stage of hierarchical structure formation, after the first galaxies had already formed. In this regard, they would not be necessary ingredients for a first galaxy, although they may well have been prevalent at the highest redshifts.
2.2. Observational Perspective
From the observational side, there are two main operational definitions employed. One may simply equate "first galaxy" with the highest redshift galaxies observable at a time, given its technology is pushed to the very limit. Currently, with a combination of Hubble Space Telescope (HST) photometry and ground-based 8-10m class spectroscopy, this allows us to see galaxies at z > 7, with a record of z 8.6 (Iye et al. 2006; Bouwens et al. 2010a; Lehnert et al. 2010), or possibly even of z ~ 10 (Bouwens et al. 2011). Evidently, this is a moving target, and such a temporary definition makes it hard to provide a focus for theoretical studies. In general, a number of galaxies at different evolutionary stages will be present concurrently at a given redshift. Thus it would clearly be preferable if a definition involved some unambiguous criteria, based on the underlying physics.
A more precise definition is to search for galaxies with zero metallicity, or one that hosts predominantly Pop III stars. This popular definition of a first galaxy may however be misleading, and may render any attempts to find first galaxies futile from the very outset. This is because most first galaxies could be already metal-enriched by SNe triggered by the first stars. Recent simulations have indicated that heavy element production and dispersal was very rapid, leading to a bedrock of pre-galactic enrichment after only a few Pop III stars had formed (see Section 4). Indeed, some models predict that the first galaxies predominantly already hosted Pop II stars (Greif et al. 2010; Maio et al. 2011). In summary, we will employ the following tentative definition of "first galaxy" in this review: a galaxy comprised of the very first system of stars to be gravitationally bound in a dark matter halo, regardless of whether the stars are Pop III or Pop II.
In concluding this section, we would like to briefly comment on the concept of a "protogalaxy", which is now largely only of historical interest. The idea was that a mature galaxy like our Milky Way (MW) more or less evolved in a monolithic fashion (Eggen, Lynden-Bell & Sandage 1962; hereafter ELS), and not in the hierarchical, bottom-up way that is now widely favored within the standard CDM model. One could then go back in time, making predictions for the luminosity and color of such systems during their initial, monolithic, collapse at high z (Partridge & Peebles 1967). First galaxy then referred to this initial collapse phase. In many ways, defining, and understanding, the first galaxies in a hierarchical context is more difficult than it would have been in a simple ELS model of galaxy formation.