THE PREMATURE FORMATION OF HIGH-REDSHIFT GALAXIES

Simulations tracing the growth of initial perturbations in the expanding medium begin with a set of well-posed initial conditions, derived from the fluctuation power spectrum and elemental abundances of the plasma constrained by observations of the cosmic microwave background (CMB; Komatsu et al. 2009). These calculations show that the first stars (Population III) formed by redshift z ∼ 20 at the core of dark matter minihalos of mass M_halo ∼ 10⁶ M_☉ (Haiman et al. 1996; Tegmark et al. 1997; Abel et al. 2002; Bromm et al. 2002). In the concordance ΛCDM model with parameter values Ω_m = 0.27, Ω = 1, , and a Hubble constant H₀ ≈ 70 km s⁻¹ Mpc⁻¹, this redshift corresponds to a cosmic time t ≈ 200 Myr. Here, Ω ≡ ρ/ρ_c is the density ρ scaled to the critical (or closure) density ρ_c () in a flat universe, Ω_m is the correspondingly scaled (luminous and dark) matter density, and is the dark energy (assumed to be a cosmological constant Λ) equation-of-state parameter yielding the pressure in terms of .

It is difficult to see how Population III stars could have formed any earlier than this, since primordial gas in the early universe could not cool radiatively. Only after molecular hydrogen started to accumulate could the plasma cool and eventually condense to make stars (Galli & Palla 1998). Once the density fluctuations had condensed to a minimum temperature of about 200 K, set by the internal rovibrational transitions of H₂ (Omukai & Nishi 1998), the gas cloud could become Jeans-unstable and collapse to form a protostar at the center of the halo. These objects, which would eventually become Population III stars, attained a mass of ≳ 100 M_☉ once they reached the main sequence (Kroupa 2002; Chabrier 2003). Feedback from these first stars determined the fate of the surrounding primordial gas clouds, because the UV radiation from a single massive star could destroy all of the H₂ in the parent condensation. As such, probably only one Population III star could form in each minihalo (Yoshida et al. 2008). These early structures were not galaxies.

However, the enormous flux of ionizing radiation and H₂-dissociating Lyman–Werner radiation emitted by massive Population III stars had an impact on more than just their immediate surroundings (Bromm et al. 2001; Schaerer 2002); this radiation field apparently had a dramatic influence out to several kiloparsecs or more of the progenitor. In combination with strong outflows, which lowered the density in the mini-halos, this outpouring of radiative and mechanical energy delayed subsequent star formation considerably (Johnson et al. 2007).

The gas expelled by this first generation of Population III stars would have been too hot and diffuse to permit further star formation until it had time to cool and reach high densities again. But cooling and re-collapse take a long time. Analytic models (Yoshida et al. 2004), confirmed by detailed numerical simulations (Johnson et al. 2007), show that the gas re-incorporation time was roughly 100 Myr, essentially the dynamical time for a first-galaxy halo to assemble itself. The critical mass for hosting the formation of the first galaxies is not yet known with high precision, though it is thought that these would have probably been atomic cooling halos, i.e., condensations with mass ∼10⁸ M_☉ and virial temperatures ≳ 10⁴ K, so that atomic line cooling could have been possible (Wise & Abel 2007). This mass scale is supported by simulations of the energetics, feedback, and chemical enrichment associated with the first (Population III) supernova explosions (Greif et al. 2007). The supernova remnant propagates for a Hubble time at z ∼ 20 to a final mass-weighted mean shock radius of 2.5 kpc, sweeping up a total gas mass of 2.5 × 10⁵ M_☉ in the process. A dark matter halo of at least 10⁸ M_☉ must be assembled to recollect and mix all components of the shocked gas.

At t ∼ 300 Myr, with z → 15 toward the end of the Dark Ages, the formation of structure would have begun in earnest. But this is where a potential conflict emerges between theoretical expectations and the recent observation of high-z galaxies because, in ΛCDM, there simply was not sufficient time for these galaxies to form by z ∼ 10–12, a mere ∼200 Myr later. We will demonstrate this quantitatively in the next section, but first, let us see what the simulations predict.

The results of simulations by independent workers essentially confirm each other's conclusions, chiefly because their calculations incorporate the same set of physical principles described above. We will summarize the key features of two of these simulations, by Jaacks et al. (2012) and Salvaterra et al. (2013), who use different metrics to characterize their results, though with very similar outcomes.

Starting their simulation at z = 100, Salvaterra et al. (2013) follow the growth of structure all the way out to z = 2.5 and find that by redshift z ∼ 6–10, most of the early galaxies had a mass ∼10⁶–10⁸ M_☉, with a few percent as high as ∼10⁹ M_☉. These structures had a specific (i.e., per solar-mass) star-formation rate (sSFR) ∼3–10 Gyr⁻¹. The 10⁸–10⁹ M_☉ galaxies were therefore forming stars at a rate SFR ∼0.3–10 M_☉ yr⁻¹, in line with SFRs observed over a remarkably broad range of redshifts (z ∼ 2–7). In this redshift range, observations indicate that galaxies of this size formed 2–3 M_☉ per year per 10⁹ M_☉ of total stellar mass (Stark et al. 2009; Gonzalez et al. 2010; McLure et al. 2011). As we shall see in the next section, the recent discoveries appear to be tracing the high end of this mass and SFR distribution (see Table 1).

The key result of this work most relevant to our discussion in this paper is that the ratio between the doubling time t_db (i.e., the inverse of the sSFR) and the corresponding cosmic time seems to be universally equal to ∼0.1–0.3, independently of redshift. Let us conservatively take the smaller value, which minimizes the growth time. Then, a galaxy with mass M_* = 10⁸ M_☉ at z = 6 (corresponding to t_* ∼ 900 Myr in ΛCDM), would have started its condensation at cosmic time t_init ∼ (0.9)ⁿ t_*, where n ≡ [log (M_*/M_init)]/log 2 is the number of doublings since the galaxy started growing with a mass M_init at t_init. Conservatively putting M_init = 10⁴ M_☉, this gives t_init ≈ 230 Myr, roughly where the arguments concerning the transition from Population III to Population II stars would placed it.

In other words, these simulations appear to be consistent with the growth implied by 10⁸ M_☉ galaxies at z = 6. But let us now consider whether this same type of growth rate would allow a similar galaxy to have formed by z = 10 (i.e., t_* ≈ 550 Myr in ΛCDM). Such a galaxy would have begun its growth with M_init = 10⁴ M_☉ at t_init ∼ 140 Myr, well before even the Population III stars would have had sufficient time to develop and explode, producing the conditions necessary to initiate the subsequent growth of galactic structure. A 10⁹ M_☉ galaxy observed at z ∼ 10.7, corresponding to a cosmic time t_* ∼ 490 Myr, would have started at t_init ∼ 82 Myr, which appears to be completely untenable, given what we now believe occurred at the dawn of cosmic structure formation.

Jaacks et al. (2012) took a different approach and examined the duty cycle and history of the SFR for high-redshift galaxies at z ≳ 6, and found that, though individual galaxies have "bursty" SFRs, the averaged SFR between z ∼ 15 and z ∼ 6 can be characterized well by an exponentially increasing functional form with characteristic timescales t_c = 70–200 Myr, for galaxies with stellar mass M_* ∼ 10⁶ M_☉ to ∼10¹⁰ M_☉, respectively.

From their hydrodynamic simulations, one may therefore infer that stellar mass grew at a rate

using the definition that a galaxy has mass M_* at cosmic time t_*. In these calculations, galaxies begin with a mass M ≪ M_* at t ∼ 400 Myr and, for M_* = 10⁸ M_☉ at t_* = 900 Myr (i.e., z = 6), t_c ∼ 100 Myr. Therefore, K ≈ 1 M_☉ yr⁻¹ in Equation (1). Placing a comparable M = 10⁸ M_☉ galaxy at z ∼ 10, where t ≈ 550 Myr, would then mean that its mass at t = 300 Myr would have been ∼8 × 10⁶ M_☉, which is inconsistent with the transition from Population III to Population II stars described above.

Both of these calculations therefore suggest that, whereas 10⁸ M_☉ galaxies would have had no problem forming by redshift 6 with the timeline predicted by ΛCDM, similar galaxies at z ∼ 10 could not have grown to this mass during the short time elapsed since the emergence of Population III and II stars. We are not aware of any other simulations published thus far that produce an outcome contrary to this result.

In the next section, we will summarize the observational status of these high-z galaxies, including a discussion of the actual, measured SFR as a function of redshift. The empirically derived expression for SFR(t) for galaxies at z ≲ 8 matches the theoretical predictions quite well. Therefore, when we use these relations to trace comparably massive galaxies at larger redshifts, the results reinforce the view that ∼10⁸–10⁹ M_☉ galaxies probably could not have had sufficient time to form by z ∼ 10–12 in ΛCDM.

Observations by Spitzer of the assembled stellar mass at z ∼ 5–6 suggest that star formation must have started well beyond z ∼ 8 (Stark et al. 2007; Gonzalez et al. 2010), though only recently have attempts succeeded in finding the earliest galaxies. Various groups have utilized an assortment of techniques, some based on gravitational lensing by foreground clusters of galaxies, others relying on spectral energy distribution fitting techniques on objects selected from a deep multi-band near-infrared stack. The Cluster Lensing and Supernova survey with Hubble (CLASH; Postman et al. 2012) has discovered several z > 8.5 candidates, three at z ∼ 9–10 (Zheng et al. 2012; Bouwens et al. 2012) and a multiply-imaged source at z = 10.7 (Coe et al. 2013).

The deepest search to date for star-forming galaxies beyond a redshift z ∼ 8.5 utilizing a new sequence of the WFC3/IR images of the Hubble Ultra Deep Field (UDF12) was just completed in 2012 September (Ellis et al. 2013). This search has thus far yielded 7 promising z > 8.5 candidates, including the recovery of UDFj-39546284 (previously proposed at z = 10.3, though now suspected of lying at z = 11.8). It is not entirely clear whether this object is really a young galaxy at such a high redshift, or is perhaps an intense emission line galaxy at z ≈ 2.4. Both interpretations are problematic (see Bouwens et al. 2011, 2013; Brammer et al. 2013).

The highest redshift galaxies discovered so far are shown in Table 1, together with best estimates of their SFRs and current masses. Galaxies observed with deep-exposure imaging are too faint to yield masses directly. In these cases, their mass is inferred by comparing their SFR with the specific star formation rate (sSFR ∼2–3 Gyr⁻¹) observed on average for galaxies over a broad range of redshifts (z ∼ 2–7; see, e.g., Stark et al. 2009; Gonzalez et al. 2010; McLure et al. 2011).

Other than the candidate UDFj-39546284 which may not even be a high-z galaxy, the most distant galaxy reliably known to date, with a photometric redshift of z ≈ 10.7, is MACS0647-JD (Coe et al. 2013). Estimates of its mass are based on the aforementioned sSFR measured at lower redshifts, but also on the fact that the average stellar mass (∼10⁹ M_☉) of galaxies at z ∼ 7–8 rose to a few times 10¹⁰ M_☉ by z ∼ 2 (Gonzalez et al. 2010). Based on this trend, one might expect the average stellar mass of galaxies at z ∼ 11 to be ≲ 10⁹ M_☉. If this holds true for MACS0647-JD, its stellar mass would be on the order of 10⁸–10⁹ M_☉. In ΛCDM, this redshift corresponds to a cosmic time t ∼ 427 Myr. Therefore, almost a billion solar masses had to assemble inside this galaxy in only ∼130 Myr.

However, the high-z galaxy with the best measured properties appears to be MACS1149-JD, a gravitationally lensed source at redshift z ∼ 9.7 (Zheng et al. 2012). The availability of both Hubble and Spitzer data has made it possible to produce a broad spectrum in the object's rest frame which, when combined with state-of-the-art models of synthetic stellar populations, yields reliable estimates for several key parameters. This analysis suggests a stellar mass of ∼1.5 × 10⁸ M_☉ and an SFR of ∼1.2 M_☉ yr⁻¹. It is comforting to note that the estimates of M and SFR for the other high-z galaxies in Table 1 are consistent with these measurements.

The comparison between theory and observations shows that the calculations can account quite well for the empirically derived average SFR based on a comprehensive analysis of z ≲ 8 galaxies using the ultra-deep WFC3/IR data (Oesch et al. 2013). These data sets exploit all of the WFC3/IR observations from HUDF09, HUDF12, as well as wider area WFC3/IR imaging over GOODS-South. (This compilation also produced three samples centered around z ∼ 9, z ∼ 10, and z ∼ 11, with seven z ∼ 9 galaxy candidates, and one each at z ∼ 10 and z ∼ 11.)

At least in this redshift range, the simulations thus appear to be handling the galaxy evolution rather well. It is therefore problematic that none of the calculations completed thus far have shown the possibility of forming 10⁸–10⁹ M_☉ galaxies prior to redshift ∼10. To better understand why the basic physical principles summarized in Section 2.1 produce this outcome, we will take the following approach. We will assume that a galaxy of mass M ∼ 10⁹ M_☉ at z ∼ 10 would have followed a growth history similar to a comparably massive galaxy at z ≲ 8, though with an appropriate translation in cosmic time t. This seems reasonable because t also functions as the proper time in the local co-moving frame, so that locally (at least) the growth rate would not be overly affected by the universal expansion rate, i.e., by the functional form of z(t). (This cannot be completely true, however, since the expansion history does affect the rate at which a local condensation of mass–energy can accrete from larger volumes. Our analysis here should therefore be viewed as preliminary, with the need of a more comprehensive simulation to follow before our conclusions can be made definitive.)

Let us now consider the evolutionary growth of the galaxies in Table 1 as a function of cosmic time. Figure 1 shows the history of three representative members of this set, calculated using the analytic (exponential) form of the time-dependent SFR from Jaacks et al. (2012), though with the time t_* shifted to coincide with the measured redshift. We include the candidate UDFj-39546284, though there are concerns about whether this source is truly a galaxy at redshift z ∼ 11.8, rather than an interloper at z ∼ 2.4. However, our conclusions are not affected either way, though if this is indeed a high-z galaxy, the conflict with ΛCDM is even worse than that implied by the other galaxies on this list.

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Figure 1 also shows several critical periods in the early universe. These include (1) the Dark Ages at t ∼ 0.4–400 Myr, (2) the epoch of reionization at t ∼ 400–900 Myr, (3) the time at which Population III stars created the necessary conditions for the subsequent formation of Population II stars (at t ∼ 300 Myr), and (4) the time during which 5–10 M_☉ black-hole seeds would have had to form in ΛCDM in order for them to grow via Eddington-limited accretion into the ∼10⁹ M_☉ quasars seen at z ∼ 6–7 (Melia 2013a, 2014b).

Our earlier conclusion that ΛCDM would not have allowed the universe sufficient time to form high-z quasars consistent with our current understanding of how structure evolved during the first ∼900 Myr is strongly reinforced by very similar, and compatible, issues regarding the premature formation of high-z galaxies. In some ways, the conflict between theory and observations is worse for the latter because the physics of Population II star formation, and their subsequent assembly into primordial galaxies, does not allow enough flexibility for ∼10⁹ M_☉ structures to appear in only ∼200 Myr. As this figure shows, some of the high-z galaxies would have had to start forming right after the big bang; several would have had to start with a mass M ≳ 10⁵–10⁶ M_☉ right at the big bang. Clearly, there simply was not enough time in ΛCDM for the first galaxies to form by redshift z ∼ 10–11.

The tension between theory and observations disappears in the R_h = ct universe. The R_h = ct universe is an FRW cosmology whose basic principles follow directly from a strict adherence to the Cosmological Principle and Weyl's postulate (Melia 2007; Melia & Shevchuk 2012; see also Melia 2012a for a pedagogical treatment). Over the past several years, the predictions of R_h = ct have been compared with those of ΛCDM and with the available observations, both at low and high redshifts. These include cosmic chronometer data, which appear to favor the expansion history in the former (Melia & Maier 2013), and the gamma-ray burst Hubble diagram, which confirms that R_h = ct is more likely to be correct than ΛCDM (Wei et al. 2013). A short summary of the current status of this cosmology appears in Melia (2012b, 2013b, 2014a).

Insofar as accounting for the high-z quasars and galaxies is concerned, the essential feature of the R_h = ct universe that distinguishes it from ΛCDM is its expansion factor, a(t)∝t. In this cosmology, the redshift is given as

where t₀ is the current age of the universe and t is the cosmic time at which the light with redshift z was emitted. In addition, the gravitational horizon R_h is equivalent to the Hubble radius c/H(t), and therefore one has t₀ = 1/H₀. With these equations, we can produce a diagram like that shown in Figure 1, except this time for the R_h = ct universe, and this is illustrated in Figure 2. The EoR redshift range z ∼ 6–15 here corresponds to the cosmic time t ∼ 830–1, 890 Myr, so the Dark Ages did not end until ∼830 Myr after the big bang. Note also that in this cosmology, 5–20 M_☉ black-hole seeds formed during the period t ∼ 830–1, 200 Myr, at the beginning of the EoR, would have grown via Eddington-limited accretion into the ∼10⁹ M_☉ quasars seen at z ∼ 6–7.

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Our examination of the evolutionary history of high-z galaxies confirms and reinforces the view that R_h = ct may be better than ΛCDM in accounting for the timing and duration of various important epochs in the early universe. From Figure 2, we see that in R_h = ct, not only did all the high-z galaxies have time to grow into ∼10⁹ M_☉ structures by redshift z ∼ 10–11, but all of them (including UDFj-39546284) would have done so after the transition from Population III to Population II star formation at t ∼ 300 Myr. This would appear to be a minimal requirement in any successful cosmological theory, given that the assembly of primordial galaxies could not have started until after the clouds that would make Population II stars had begun their condensation.

But how accurately do we know the masses of these galaxies, and is it possible that our current estimates of M are simply greatly overestimated? To gauge the possibility that the timing problem in ΛCDM may be due to such uncertainties, we show in Figure 3 the impact of changing M by a factor 10 in two representative galaxies from the sample listed in Table 1. These two objects span the range of redshifts covered in this group, other than UDFj-39546284 which, as we have already noted, may simply be a mis-identification. The shaded regions in this figure show the possible evolutionary trajectories of these galaxies in both ΛCDM and R_h = ct, when we allow for an order-of-magnitude uncertainty in the mass. It is quite straightforward to see that the problem still persists. In order to alleviate the negative impact of the time compression in the standard model, the inferred masses for these objects would have to be wrong by at least 4 or 5 orders of magnitude. Even with the range of masses used in this figure, none of the galaxies in this sample could have grown to their observed size following the transition from Population III to Population II stars, and at least one member of this set would have had to start growing before the big bang.

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Finally, one of our stated goals at the beginning of this discussion was to see if the creation of 5–20 M_☉ black-hole seeds could be made compatible with the evolutionary growth of structure in the early universe. Figure 2 suggests that the answer is yes. If the high-z quasars grew at an Eddington-limited accretion rate, they would have started as black holes created in Population III (and possibly Population II) stars near the beginning of the EoR. In fact, this diagram even allows for the possibility that their growth was slower than the standard Eddington rate, since Population III stellar explosions could have occurred up to ∼500 Myr earlier. According to this figure, most of the primordial galaxy growth also took place within a period of roughly 600 Myr, starting near the end of the Dark Ages, and extending into the middle of the EoR. Quite tellingly, most of this growth also would have coincided with the formation of the 5–20 M_☉ black-hole seeds.

However, it is still too early to tell whether the black hole seeds formed during Population III supernovae, or later, from the explosions of Population II stars. Perhaps the answer is both. Even if a Population III supernova would have produced the seed, the fact that the explosion expelled most of the material, forcing a delay by another ∼100 Myr before gravitational collapse could have replenished the gaseous medium surrounding the black hole, would have significantly slowed down the rate at which the quasar could have grown initially. It is likely that regardless of whether the black hole seeds formed at ∼300–400 Myr, or later within primordial galaxies (at t ∼ 1 Gyr), their rapid growth into ∼10⁹ M_☉ supermassive black holes would have been delayed until t ∼ 1–1.9 Gyr. However, this kind of timing flexibility is only available in R_h = ct. It is not possible in ΛCDM.