THE SPECTRAL EVOLUTION OF THE FIRST GALAXIES. I. JAMES WEBB SPACE TELESCOPE DETECTION LIMITS AND COLOR CRITERIA FOR POPULATION III GALAXIES

Due to the lack of efficient coolants in metal-free, primordial gas, the first stars to form in our universe were likely very massive (≳ 10 M_☉ and possibly even up to 1000 M_☉; e.g., Bromm et al. 1999; Nakamura & Umemura 2002; Tan & McKee 2004; Greif & Bromm 2006; Ohkubo et al. 2009). Some of these Population III stars probably exploded as supernovae (Heger et al. 2002) and initiated the chemical enrichment that allowed less massive and more metal-rich stars to form (the Population I and II stars known from the local universe, with characteristic masses below 1 M_☉). The highly energetic radiation emitted from Population III stars may have played an important role in the cosmic reionization at redshifts z > 6 (e.g., Sokasian et al. 2004; Trenti & Stiavelli 2009), and the remnants left behind by these objects may also have acted as seeds for the supermassive black holes (e.g., Trenti & Stiavelli 2007) known to exist already at z ≈ 6 (e.g., Willott et al. 2007).

Current predictions for the initial mass function (IMF) of Population III stars are, however, still shaky. The most recent simulations suggest that the typical Population III masses may be lower than previously believed (e.g., Stacy et al. 2008; Clark et al. 2011; Greif et al. 2011a, 2011b), and the chemical abundance patterns of extremely metal-poor stars in the Milky Way halo also point toward early supernovae with progenitor masses closer to ∼10 M_☉ than ∼100 M_☉ (for reviews, see Beers & Christlieb 2005; Karlsson et al. 2011). At the same time, it is not clear that the chemical signatures of the most massive Population III supernovae would be detectable in current halo samples. The stars bearing the mark of such supernovae may be too scarce (e.g., Salvadori et al. 2007; Trenti & Shull 2010), hiding at too high metallicities (Karlsson et al. 2008) or in the inner regions of the Galaxy (e.g., Tumlinson 2010). Direct observations of massive Population III stars in the high-redshift universe would help settle the issue, but this is beyond the capabilities of current telescopes.

The very first Population III stars are expected to form in isolation or in small numbers within ∼10⁵–10⁶M_☉ dark matter halos at redshifts z ≈ 20–50 (e.g., Tegmark et al. 1997; Yoshida et al. 2003), but the prospects of detecting such stars on an individual basis appear bleak (e.g., Gardner et al. 2006; Greif et al. 2009; Rydberg et al. 2011), at least before they become supernovae (Weinmann & Lilly 2005; Whalen & Fryer 2010). However, Population III stars may continue to form within the more massive halos (≳ 10⁷–10⁸ M_☉) hosting the first galaxies⁵ at z ≲ 15 (Scannapieco et al. 2003; Tornatore et al. 2007; Johnson et al. 2008, 2009; Stiavelli & Trenti 2010; Johnson 2010; Schneider et al. 2006b), and this could in principle allow their integrated signatures to be detected with the upcoming James Webb Space Telescope⁶ (JWST; Bromm et al. 2001; Johnson et al. 2009; Johnson 2010).

Since the first generation of galaxies is predicted to form in high-density regions that have been pre-enriched by Population III stars in minihalos, these galaxies are not expected to be metal-free, and are most likely dominated by chemically enriched stars (e.g., Greif et al. 2010). It is true that Population III galaxies may, however, form at slightly later epochs, in low-density environments which have remained chemically pristine (e.g., Scannapieco et al. 2003; Trenti et al. 2009; Stiavelli & Trenti 2010).

Due to the exceedingly high temperatures of massive Population III stars (T_eff ∼ 10⁵ K), such objects may contribute substantially to the photoionization of the interstellar medium and alter the overall spectra of their host galaxies. A number of authors have pointed out that Population III-dominated galaxies could be identified based on the strengths of the Lyα line, the He ii λ1640, λ4686 lines, or the Lyman "bump" (e.g., Tumlinson & Shull 2000; Tumlinson et al. 2001; Oh et al. 2001; Malhotra & Rhoads 2002; Schaerer 2002, 2003; Inoue 2010) and several searches have since tried to apply these techniques (e.g., Dawson et al. 2004; Nagao et al. 2005, 2008; Dijkstra & Wyithe 2007; Ouchi et al. 2008; Cai et al. 2011). While a few potential Population III candidates have indeed been reported (Fosbury et al. 2003; Raiter et al. 2010a; di Serego Alighieri et al. 2008; Inoue et al. 2011), their exact nature remains unclear. So far, essentially all searches for Population III galaxies have relied on spectroscopy or narrowband photometry. If Population III galaxy candidates could instead be singled out from large samples based solely on their broadband colors (as recently attempted by Bouwens et al. 2010), this would allow for substantial gains in terms of observing time.

Here, we present Yggdrasil, a new spectral synthesis model for the first generations of galaxies, and use it to explore the spectral signatures of pure Population III galaxies in JWST photometric surveys. The technical details of the model are described in Section 2. In Section 3, we define three different classes of first galaxies, which differ by the relative amount that nebular emission is expected to contribute to their integrated spectra. The resulting JWST mass detection limits for both Population III and more chemically evolved galaxies in photometric surveys are presented in Section 4. Potential strategies for searching for Population III galaxies (dominated either by nebular emission or direct starlight) in deep JWST images are presented in Sections 5 and 6. A number of potential caveats with the proposed approaches are discussed in Section 7. Section 8 summarizes our findings.

While the properties of galaxies at z ≳ 10 remain an uncharted territory observationally, theory and simulations provide a number of clues as to what one might expect from such objects. In the models of Stiavelli & Trenti (2010), the very first galaxies are predicted to form in high-density regions that have been pre-enriched by Population III stars that exploded as supernovae in minihalos at even higher redshifts. True Population III galaxies start to form somewhat later, in low-density environments which have remained chemically pristine. Since pockets of primordial gas may survive in galaxies that have already experienced some chemical enrichment, hybrid galaxies in which Population III, Population II (representative of the metallicity in the Milky Way halo; Z < Z_☉/10), and Population I (representative of the metallicity in the Milky Way disk; Z ≳ Z_☉/10) stars continue to form in parallel can also be expected (e.g., Salvaterra et al. 2011), and signatures of this may already have been detected (Jimenez & Haiman 2006). Even more exotic galaxies may be envisioned if the dark matter of the universe has the properties required for the formation of long-lived Population III stars fueled by weakly interacting massive particle annihilations in minihalos (e.g., Spolyar et al. 2008). Many such "dark stars" may then end up within the first galaxies during their hierarchical assembly, and possibly imprint detectable signatures in their spectra (Zackrisson et al. 2010). In this paper, however, we focus on pure Population III galaxies.

Here, we present Yggdrasil,⁷ a new population synthesis code custom-designed for modeling the spectral energy distributions (SEDs) of high-redshift galaxies. To reflect the significant variance in terms of stellar content that these objects may display, Yggdrasil is equipped to handle mixtures of conventional Population I, II, and III stars (hereafter Pop I, II, and III, respectively) as well as dark stars. This code also allows the treatment of nebular emission from the photoionized gas and extinction due to dust. A number of Yggdrasil model grids are publicly available from the lead author's homepage.⁸

The SEDs of single stellar populations (SSPs⁹) from various other population synthesis models can be used as inputs to Yggdrasil, which will then reweight the SSP time steps to accommodate arbitrary star formation histories. Currently, the SSP models of Zackrisson et al. (2001), Starburst99 (Leitherer et al. 1999; Vázquez & Leitherer 2005), and Maraston (2005) are implemented as options for Pop I and II stars. For the duration of this paper, we will adopt Starburst99 SSPs generated with Padova stellar evolutionary tracks with asymptotic giant branch stars (Vázquez & Leitherer 2005) and the Kroupa (2001) universal stellar IMF throughout the mass range 0.1–100 M_☉ for Pop II (assumed metallicity Z = 0.0004) and Pop I (assumed metallicity Z = 0.020) galaxies.

While both theoretical arguments and numerical simulations give strong support to the notion that Pop III stars must have been more massive than the Pop II and I stars forming later on (for a review, see Bromm & Larson 2004), the exact IMF of Pop III stars remains unknown. It has been argued that the universe may have produced two classes of Pop III stars—Pop III.1 stars which formed first, with characteristic masses of about ∼100 M_☉, and Pop III.2 stars which formed somewhat later and had lower characteristic masses of ∼10 M_☉ due to HD cooling promoted by the Lyman–Werner feedback provided by the Pop III.1 stars (e.g., Mackey et al. 2003; Greif & Bromm 2006). Naively, one would expect the Pop III.1 IMF to be appropriate for the stars forming in isolation (or in small numbers) within ∼10⁵–10⁶ M_☉ minihalos capable of H₂ cooling at z ≈ 20–40, whereas the Pop III.2 IMF may be more relevant for the first Pop III galaxies forming in ≳ 10⁷–10⁸ M_☉ halos capable of H i cooling at z ⩽ 15 (e.g., Johnson et al. 2008). However, this Pop III.1 (∼100 M_☉) versus Pop III.2 (∼10 M_☉) picture is looking increasingly uncertain, as the latest simulations indicate more fragmentation than before, with lower Pop III masses as a result (e.g., Stacy et al. 2008; Clark et al. 2011; Greif et al. 2011a). It has recently also been recognized that supersonic streaming velocities of baryons with respect to the dark matter (e.g., Tseliakhovich & Hirata 2010; Maio et al. 2011) could have increased the turbulence within minihalos and assisted in reducing the masses of Pop III.1 stars (Greif et al. 2011b). For simplicity, we have chosen to stick to the traditional Pop III.1 (∼100 M_☉) and III.2 (∼10 M_☉) convention throughout this paper. To cover all the bases, we adopt both of these top-heavy IMFs as viable options for our primordial galaxies, but also consider Pop III galaxies with the same Kroupa (2001) IMF as that used for Pop II/I galaxies.

For Pop III.1 galaxies, we will adopt the Schaerer (2002) stellar SSP with a power-law IMF (dN/dM∝M^−α) of slope α = 2.35 throughout the mass range 50–500 M_☉. For Pop III.2 galaxies, we will adopt the Raiter et al. (2010b) TA model, which has a log-normal IMF with characteristic mass M_c = 10 M_☉ and dispersion σ = 1 M_☉, but with wings extending from 1 to 500 M_☉.

The contribution to the SED from photoionized gas is computed using the procedure outlined in Zackrisson et al. (2001). In this machinery, the stellar population SED is, at every age step (once the star formation history has been taken into account), used as an input to the photoionization code Cloudy (Ferland et al. 1998). This results in a self-consistent prediction for the nebular continuum and emission line fluxes, which reflects the temporal changes in the ionizing radiation field. Other approaches in the literature include calculating the nebular continuum based on tabulated emissivities assuming a fixed electron temperature (e.g., Leitherer et al. 1999, see Raiter et al. 2010b for a description of the shortcomings of this technique), or using emission-line ratios fixed by empirical calibrations (e.g., Anders & Fritze-v. Alvensleben 2003). While the latter technique may be useful for certain classes of objects, it will be of little use for objects with properties that differ significantly from the empirical templates, since the emission-line ratios are expected to vary as a function of age, IMF, metallicity, and the physical conditions in the nebula. Throughout this paper, we will assume the nebula to be spherical, ionization-bounded and to have a constant, non-evolving hydrogen density n(H). These assumptions concerning the properties of the nebular gas, and their impact on our conclusions, are further discussed in Section 3. Additional Cloudy parameters include the gas filling factor f_fill (which describes the porosity of the gas), the gas covering factor f_cov (which regulates the amount of Lyman-continuum leakage into intergalactic space), and the gas metallicity Z_gas.

In the case of plane-parallel nebulae, there is a homology relation between photoionization models with the same ionization parameter U:

$$\begin{equation} U=\frac{Q(\mathrm{H})}{4\pi c R^2 n(\mathrm{H})}, \end{equation} \tag{ 1 }$$

where Q(H) is the number of ionizing photons per unit time and R is the distance to the ionization source. The situation becomes more complicated for spherical nebulae (as assumed here), due to the dilution of the radiation as it propagates through the nebula (giving high U close to the center and low U further out). Instead of specifying U directly, the inner radius of the cloud, R_in, and the mass available for star formation, M_tot, are instead used as inputs to Yggdrasil. The latter is defined as the gas mass converted into stars during a star formation episode of duration τ:

$$\begin{equation} M_\mathrm{tot}=\int _0^\tau \mathrm{SFR}(t)\; dt. \end{equation} \tag{ 2 }$$

While the shape of the stellar SED is set by the stellar SSP, the age, and the star formation history, M_tot determines the overall scaling, and hence luminosity and Q(H). Please note that M_tot does not represent the mass of the resulting nebula, which may be either higher or lower than M_tot, depending on Q(H) and the gas parameters (n(H), f_fill, f_cov, and to smaller extent Z_gas).

As in the Zackrisson et al. (2001) model, the inner radius of the ionizing cloud is set to

$$\begin{equation} R_\mathrm{in} = 100\ R_\odot \left(\frac{L}{L_\odot }\right)^{1/2}, \end{equation} \tag{ 3 }$$

where L represents the bolometric luminosity of the model galaxy. This gives an effective mean ionization parameter in the same range as observed in local H ii regions (Kewley & Dopita 2002), if f_fill = 0.01 and n(H) = 100 cm⁻³. Throughout this paper, we adopt M_tot = 10⁶ M_☉ to reflect the likely stellar population masses of the faintest galaxies detectable with JWST (see Section 4). However, we have verified that the resulting JWST colors remain practically unchanged for objects that are up to a factor of ∼10³ more massive.

While dust extinction is not expected to be present during the very first star formation episode of Pop III galaxies, it may well become important after a few Myr, when pair-instability supernovae from 140–260 M_☉ stars or Type II supernovae with M < 50 M_☉ (mass limits valid in the absence of stellar rotation; Heger et al. 2002) release their nucleosynthesis yields into the surroundings. In Pop II/I galaxies, extinction is likely to be relevant at all ages. To allow for the treatment of dust extinction, Yggdrasil allows a choice of four different dust-correction recipes: the Milky Way, Large Magellanic Cloud, Small Magellanic Cloud (Pei 1992), and Calzetti (1997) attenuation models. In the latter case, corrections are applied separately to the nebular and stellar contributions to the SED, so that the nebular emission experiences a higher extinction. All dust extinction corrections are applied after the nebular SED has been generated. This is equivalent to assuming that the dust is located outside the H ii region, and hence does not affect the Lyman-continuum flux prior to gas absorption. This is a reasonable assumption, at least for young Pop III galaxies experiencing a brief star formation episode, since no current models predict dust formation in the immediate vicinities of Pop III stars.

Nebular emission typically has a strong impact on the SEDs of young or star-forming galaxies, and the relative contribution from nebular gas is expected to become stronger if the metallicity becomes very low or if the IMF turns more top-heavy (Schaerer 2002, 2003; Raiter et al. 2010b). This is demonstrated in Figure 1, where we compare the rest-frame SEDs of 1 Myr old SSP models for a Pop I galaxy (Z = 0.020; Kroupa 2001 IMF) and a Pop III.1 galaxy. In both cases, the blue line represents the purely stellar SEDs whereas the red line describes the total SED, i.e., the SED including both stellar and nebular contributions. The nebular component completely transforms the appearance of the SED for both types of galaxies, but the relative contribution of nebular emission becomes much stronger for the zero-metallicity, top-heavy IMF object (Pop III.1).

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As we have argued in several previous papers (e.g., Zackrisson et al. 2008; Schaerer & de Barros 2009, 2010), the flux boost due to photoionized gas can also have a notable impact on the broadband fluxes of high-redshift galaxies. In Figure 2(a), we demonstrate this by plotting the ratio of nebular to stellar flux, f_neb/f_stars, in the JWST/NIRCam F444W filter (at 4.44 μm) as a function of redshift (within the range z = 0–20) for newborn (age 1 Myr), galaxies with SEDs representative of Pop I (Z = 0.020), Pop II (Z = 0.0004), Pop III with Kroupa (2001) IMF, Pop III.2, and Pop III.1 SEDs, assuming an instantaneous burst. Nebular emission is seen to dominate the flux in this filter at all redshifts considered for the Pop III models. As expected, the highest f_neb/f_stars ratios are produced by the Pop III.1 IMF (cyan line), followed by the Pop III.2 IMF (blue line) and Pop III with a Kroupa (2001) IMF (green line). The Pop II (red line) and Pop I models (black line) produce significantly lower ionizing fluxes per unit mass.

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The bumps and wiggles along the lines in Figure 2(a) are produced when various emission lines and continuum features redshift in and out of the filter. The bump at z ≈ 5–7 is due to the Hα line at 6563 Å, and the extension of this bump to z ≈ 9 in the case of the Pop II galaxy is primarily due to the [O iii] line at 5007 Å, which is strong at low to intermediate metallicities, weak in high-metallicity objects, and completely missing from Pop III spectra due to lack of metals in these objects, as further discussed in Section 5. The overall increase in f_neb/f_stars toward very low redshifts is due to the very different spectral slopes of the stellar and nebular continuum at rest-frame wavelengths above 10⁴ Å (see Figure 1).

In Figure 2(b), we plot the f_neb/f_stars ratio at z = 10 as a function of age for the same instantaneous-burst models as in Figure 2(a). At an age of 1 Myr, going from a Kroupa (2001) IMF Pop I (black line) to a Pop II (red line) increases the f_neb/f_stars ratio by a factor of ≈2.5, and going from a Pop II to a Pop III galaxy (green line) boosts f_neb/f_stars by an additional factor of ≈4. Shifting to more top-heavy IMFs (blue for Pop III.2 and cyan for Pop III.1) raises f_neb/f_stars even further. These overall ratios between the models are approximately stable as a function of age, except for the Pop III.1 model, which evolves much faster than the others due to the lack of stars with masses below 50 M_☉, fading from sight after just 3 Myr. In the case of the Pop III.2 and Pop III, Kroupa (2001) IMF models, it takes ≈12–16 Myr before direct starlight starts to dominate over nebular emission (thin horizontal dashed line), and ≈40–50 Myr until nebular emission gives a negligible contribution (10%, as indicated by the thick horizontal dashed line) to the flux.

Even though Lyman-continuum leakage from high-redshift galaxies may well reduce the relative contribution from nebular emission (as further discussed below), it is clear from Figure 2 that it would take a very large amount of leakage to break the dominance of nebular light in the SEDs of young Pop III galaxies. For a 1 Myr Pop III.1 galaxy, f_neb/f_stars ≈ 20 at z = 10, whereas the corresponding values for Pop III.2 and Pop III galaxies with a Kroupa (2001) IMF are f_neb/f_stars ≈ 15 and ≈10, respectively. After 10 Myr, Pop III galaxies with a Pop III.2 or a Kroupa (2001) IMF have f_neb/f_stars ≈ 5 and ≈3, respectively. To bring nebular emission down to a level where it no longer affects the broadband fluxes of ⩽10 Myr old Pop III objects in any significant way (f_neb/f_stars ∼ 0.1), the ionizing escape fraction would have to be f_esc ≳ 0.95.

It is doubtful whether Pop III galaxies can be identified based on color criteria for much longer than ∼10⁷ yr. The lifetimes of massive Pop III stars are very short (≈2–3 × 10⁶ yr for ≈50–500 M_☉ stars; Schaerer 2002), and as soon as the first supernovae explode, metals will be dispersed into the surrounding medium. While the ejecta from the first Pop III supernovae may take ∼10⁸ yr to cool sufficiently to be used in the subsequent formation of Pop II and I stars (Greif et al. 2007), the time it takes before metal emission lines start to emerge from the surrounding nebula may be much shorter, perhaps no more than a few Myr. At that point, the broadband signatures of metal-free nebulae discussed in Section 5 would be jeopardized. If feedback from the first supernovae clears the galaxy of photoionized gas, the SED would be dominated by direct starlight from Pop III stars until Pop II/I star formation sets in (after ∼10⁸ yr), but even then, the unique spectral characteristics of Pop III stars are only retained for ∼10⁷ yr (see Section 6).

3.1. Types A, B, and C

While Figures 1 and 2 would suggest that the SEDs of Pop III galaxies are almost completely nebular in nature, there are a number of mechanisms that could diminish the impact of nebular emission. As shown in the simulations by Johnson et al. (2009), stellar feedback can drive the photoionized gas present in these systems outward, eventually pushing it beyond the virial radius of the dark matter halo. Once the H ii region breaks out of its host halo, the gas density will be extremely low, resulting in a huge intergalactic nebula with very long recombination timescales. This nebula, while very important for cosmic reionization, is probably of little importance for JWST observations of individual galaxies. When attempting aperture photometry of galaxies surrounded by such large, low-surface-brightness nebulae, the nebular contribution (appearing in both the object and sky annulus) may be almost completely subtracted away, effectively leading to the detection of an SED dominated by the more concentrated stellar component. Whether or how quickly the gas gets expelled depends on the star formation efficiency within a given halo, and also the form of the IMF. Having a very low ratio of stellar to dark matter mass, and/or an IMF without too many high-mass stars, would likely result in a situation in which the H ii region stays completely confined within the cold dark matter halo (for the limiting case of just one Pop III star in halos with different masses, see, e.g., Kitayama et al. 2004).

In Figure 3, we have schematically defined three classes of objects in different stages of gas expulsion. For type A, the ionization-bounded H ii region (gray region) remains compact and confined well inside the virial radius (dashed line). This implies a Lyman-continuum escape fraction f_esc ≈ 0 and a maximal contribution from nebular emission to the overall SED of the galaxy. In the case of type B, stellar feedback has pushed the H ii region partly outside the virial radius (∼1 kpc for a 10⁸ M_☉ halo at z ≈ 7–13), giving rise to the partial leakage of ionizing radiation into the intergalactic medium (IGM): 0 < f_esc < 1. For type C galaxies, the ionizing gas has been expelled outside the dark matter halo, resulting in an SED with minimal nebular contribution and a Lyman-continuum escape fraction f_esc ≈ 1. While this simple picture admittedly neglects the anisotropic outflow of gas and the irregularities within the photoionized medium evident from actual simulation (Johnson et al. 2009), it still captures the salient points when it comes to modeling the nebular contribution to the galaxy SED.

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In this paper, we will only treat galaxies that belong to categories A (full nebular contribution) and C (no nebular contribution). The intermediate type B would be far more challenging to model in detail—the gas density profile is highly time-dependent at this stage, the long recombination timescales introduce a time lag between the evolution of the stellar and nebular SEDs, and commonly used sky subtraction strategies may interfere with the predicted contribution from the nebula to the observed SED. While the relative flux contribution of the nebula—and therefore the overall luminosity—does depend on these effects, the colors of type A and type B galaxies are nonetheless likely to be similar as long as the system is young and nebular emission is dominant. The youth criterion comes in because the mismatch between the momentary stellar SED and the prior ionizing field to which the nebula responds becomes more severe once the high-mass stars of the stellar population have died and many intermediate-mass stars have evolved off the main sequence.

The nebular contribution from type A galaxies is modeled assuming a constant-density H ii region with hydrogen density n(H) = 100 cm⁻³ and filling factor f_fill = 0.01. In the case of Pop III galaxies, the gaseous metallicity is set to Z_gas = 10⁻⁷ (whereas Z_stars = 0), whereas Pop II (Z = 0.0004) and Pop I (Z = 0.020) galaxies have Z_gas = Z_stars. Scaled solar abundances are used in all cases. The default value for the gas covering factor of type A galaxies is f_cov = 1 (implying a Lyman-continuum escape fraction f_esc = 0). However, in the case of a compact H ii region, anisotropic feedback, supernova chimneys, and irregularities in the gas density may result in large holes in the nebula, through which ionizing radiation can escape into the IGM. Simulations predict that the amount of Lyman-continuum escape may be a function of dark halo mass (Gnedin et al. 2008; Razoumov & Sommer-Larsen 2010; Yajima et al. 2011), but the likely escape fraction and its exact mass dependence remain controversial. In our model, the possibility of Lyman-continuum escape through holes is treated by allowing the gas covering factor f_cov to take on values 0 < f_cov < 1. While having a very low but non-zero f_cov does not capture all the complexities of a type B galaxy, it still gives some indication of what to expect from such an object.

Type C objects are treated by setting f_cov = 0, which implies a Lyman-continuum escape fraction of unity and an SED composed of stars only. Since no nebula is produced, a photoionization code like Cloudy is not required to model this case.

In Figure 4, we use Yggdrasil to predict the population masses of the faintest star-forming galaxies detectable through JWST broadband imaging when taking extremely long exposures of a small patch of the sky, i.e., a so-called ultra deep field (UDF). The mass limits presented are based on the requirement that galaxies are detected at 10σ in at least one JWST broadband filter (spectral resolution R = 4) after a 100 hr exposure (per filter). While the detailed specifications of JWST UDFs have not yet been fixed, 100 hr represents a reasonable estimate of the longest exposure times that are likely to be relevant. The resulting mass limits can easily be rescaled to other exposure times t_exp using

$$\begin{equation} M_\mathrm{min}\propto \left(\frac{t_\mathrm{exp}}{100\; \mathrm{h}\rm{r}} \right)^{1/2}. \end{equation} \tag{ 4 }$$

Our derived mass limits take all of the 17 JWST broadband (R = 4) filters into account, and are based on the actual JWST transmission curves of these filters¹⁰ and the estimated AB-magnitude limits listed in Table 1. These 10σ, t_exp = 100 hr detection limits $m_\mathrm{AB,\; 100 \,\rm{hr}}$ can be rescaled to other exposure times using

$$\begin{equation} m_\mathrm{AB}=2.5\log _{10}\left[\left(\frac{t_\mathrm{exp}}{100\; \mathrm{h}\rm{r}}\right)^{1/2}\right] + m_\mathrm{AB,\; 100\, \rm{hr}}. \end{equation} \tag{ 5 }$$

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To avoid predictions hinging on the highly uncertain luminosity of the Lyα emission line at high redshifts (e.g., Fontana et al. 2010; Hayes et al. 2011), we assume the Lyα escape fraction to be zero—i.e., the Lyα line does not contribute to the predicted fluxes at all. When computing the JWST broadband fluxes, we furthermore set all SED fluxes short of Lyα to zero for model galaxies at z > 6, to reflect the high level of absorption in the neutral IGM at these epochs.

The mass limits in Figure 4 are presented for Pop I, II, and III galaxies of both type A (maximal contribution from the nebula) and type C (no contribution from the nebula) with constant star formation rates as a function of age (up to 30 Myr) and redshift (up to z = 20). As discussed in Section 3, galaxies starting from zero metallicity are not likely to retain their Pop III characteristics for much longer than this. While Pop I and II galaxies may well have higher ages at these epochs, such objects would need to be even more massive than suggested by the limits at 30 Myr in Figure 4 to be detectable with JWST. Hence, Figure 4 places hard limits on what can realistically be observed with this telescope through ultra deep imaging in the absence of gravitational lensing.

The mass used to define these limits is the mass of gas converted into stars since the beginning of a star formation episode:

$$\begin{equation} M(t)=\int _0^t \mathrm{SFR}(t^{\prime })\; dt^{\prime }. \end{equation} \tag{ 6 }$$

This is equivalent to the population mass often discussed in the context of simulations, where the overall gas mass is multiplied by the star formation efficiency of the first starburst episode to compute the gas converted into stars. The mass in luminous stars (stars that have not yet exploded as supernovae or turned into compact remnants) at these ages can be considerably lower at ages ≳ 3 Myr (especially in the case of top-heavy IMFs), since many of the stars forming at t = 0 yr have then already faded away. For instance, the mass in luminous stars in a Pop III.1 galaxy with constant star formation is lower than the plotted limits by a factor of ≈5 after 10 Myr, and by a factor of ≈14 at 30 Myr. On the other hand, the mass in luminous stars within Kroupa (2001) IMF populations is reduced by only ≈20% (Pop III) and ≈10% (Pop II and I) after 30 Myr of constant star formation. In the case of star formation episodes with finite duration τ, M(t) equals M_tot defined in Equation (2) if evaluated at a time after the end of the starburst (t ⩾ τ).

As seen in Figure 4, M ∼ 10⁶ M_☉ star-forming Pop I and II galaxies (black and red lines) can be detected at z ≈ 10, whereas Pop III.1 galaxies (cyan lines) can be detected even if the mass is as low as M ∼ 10⁵ M_☉. Pop III.2 galaxies (blue lines) lie between Pop I/II and Pop III.1 galaxies in this diagram. On the other hand, Pop III galaxies with a Kroupa (2001) IMF (green lines) tend to require a mass at least as high as Pop I/II galaxies (and sometimes significantly higher) to be detected because of their lower stellar mass-to-light ratios in these passbands.

For galaxies with a given IMF and metallicity, type A objects (maximal nebular flux contribution) are always brighter than type C objects (no nebular flux contribution) and can therefore be detected at lower masses. However, the difference is much smaller for Pop I and II galaxies (less than a factor of two at z = 10) than for Pop IIIs, due to the higher relative ionizing fluxes of the latter objects. For instance, nebular emission allows young (≈3 Myr old) Pop III.1 galaxies at z = 10 to be detected at masses a factor of ≈4 lower than in the case where all the ionizing radiation is escaping into the IGM. The mass detection limits presented for Pop III and II galaxies in Figure 4 are similar (within a factor of two, once differences in exposure times are considered) to those derived by Pawlik et al. (2011), who considered the JWST detectability of lines and continuum radiation separately.

The detection limits in Figure 4 indicate the masses of galaxies that JWST would be able to detect at a single wavelength, but to derive the properties of the objects observed, photometry in several filters is always required. Since the JWST sensitivity varies greatly as a function of wavelength, the detection limits are sensitive to the filters used. In Figure 5, we plot the lowest stellar population masses of 3, 10, and 30 Myr old type A galaxies (maximal nebular emission) detectable in a JWST UDF (10σ detections after 100 hr exposures) as a function of central filter wavelength at z = 6, 8, 10, and 12. The mass limits stay approximately constant within the wavelength range of the JWST/NIRCam instrument (operating at 0.7–4.4 μm), but then rise by an order of magnitude as one switches to JWST/MIRI observations at ⩾5.5 μm and continue to deteriorate almost monotonically all the way up to the 25 μm limit of MIRI. Hence, detections of high-redshift galaxies in the MIRI filters will be very expensive in terms of observing time compared to those in NIRCam filters. On average, the relative contribution from nebular continuum grows with increasing rest-frame wavelength, and this compensates for some of the sensitivity loss in the MIRI bands. For galaxies without nebular emission (type C), the decline in mass sensitivity with increasing JWST passband wavelength is even more dramatic than plotted here.

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As discussed in Section 1, all searches for Pop III galaxies with largely nebular SEDs (our type A) have so far focused on the fluxes of the Lyα line, the He ii λ1640, λ4686 lines, or the Lyman "bump" (e.g., Tumlinson & Shull 2000; Tumlinson et al. 2001; Oh et al. 2001; Malhotra & Rhoads 2002; Schaerer 2002, 2003; Inoue 2010). However, none of these spectral features is likely to produce a robust and detectable signature in broadband filters for objects at z > 6. He ii is too weak, the Lyman "bump" is absorbed by the IGM, and the escape fraction of Lyα photons is notoriously difficult to predict.

Here, we propose a different strategy, based on the fact that such galaxies are likely to have strong hydrogen and helium emission lines, but—due to the lack of metals—no lines due to heavier elements. Certain rest-frame UV and optical metal emission lines, most notably [O ii]λ3727, [O iii]λ5007, and [S iii]λ9069, are sufficiently strong to influence the broadband fluxes of galaxies (e.g., Anders & Fritze-v. Alvensleben 2003; Zackrisson et al. 2008; Schaerer & de Barros 2009), and removing these lines will therefore alter the broadband colors of type A objects. Recently, Inoue (2011) argued that the lack of [O iii]λ5007 emission would be one of the best ways to single out Pop III galaxies. Our analysis agrees with this conclusion.

5.1. NIRCam Color Criteria

Inoue (2011) suggests that imaging in the two JWST/NIRCam filters F277W and F444W could be useful to single out Pop III galaxies at z ≈ 8, since the lack of [O iii] emission in the F444W filter would render the colors of such objects very blue. However, the m₂₇₇ − m₄₄₄ ⩽ 0 criterion proposed by Inoue for Pop III objects is not unique, as demonstrated using instantaneous-burst models in Figure 6—both Pop II and I galaxies of type A can at certain ages venture blueward of this limit. In the case of our Pop II model (red line), this happens because of a short-lived evolutionary phase at ages of ≈10–20 Myr, where the ionizing flux has dropped sufficiently to make the nebular contribution irrelevant, yet the UV continuum of the stars remains very blue. In the case of our Pop I model (Z = 0.020; black solid line), this happens because very young (≲ 5 Myr) populations with high metallicities also display very weak [O iii] emission lines (e.g., Panagia 2003; Nagao et al. 2006). In an instantaneous-burst scenario, the timescales over which Pop I/II systems display these very blue colors are shorter than the corresponding timescales for Pop III systems, which may limit the risk of Pop I/II interlopers in surveys for Pop III galaxies. On the other hand, the typical star formation histories may be different in the two cases, and adopting a more extended star formation history for Pop I/II could make these objects display Pop III-like colors for a longer period of time. Dust extinction, which is likely to be associated with star formation in high-metallicity environments, may of course render the colors of young Pop I/II systems redder and possibly prevent metal-enriched galaxies from entering color-selected Pop III samples.

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While the details of the IMF determine the longevity of Pop III galaxies, the m₂₇₇ − m₄₄₄ colors predicted for type A Pop III objects of age ≲ 10 Myr are not sensitive to the exact Pop III IMF, as illustrated by the largely overlapping cyan, blue, and green lines in Figure 6.

5.2. Combined NIRCam and MIRI Color Criteria

In Figure 7, we demonstrate that cleaner selection criteria for type A Pop III galaxy candidates at z ≈ 8 can in principle be derived by combining JWST/NIRCam data in the F444W filter with observations in two JWST/MIRI filters: F560W and F770W. The lack of [O iii]λ5007 in F444W and the presence of Hα in F560W make young Pop III galaxies redder in m₄₄₄ − m₅₆₀ (Figure 7(a)), yet bluer in m₅₆₀ − m₇₇₀ (Figure 7(b)) than other types of galaxies. Due to the [O iii] degeneracy between Pop III and I galaxies, both can attain similar m₄₄₄ − m₅₆₀ colors. However, since there is no similar degeneracy in m₅₆₀ − m₇₇₀, Pop III objects appear in a corner of the m₅₆₀ − m₇₇₀ versus m₄₄₄ − m₅₆₀ diagram (Figure 8) where no other galaxies should appear. Pop III objects remain in the upper left corner (gray region) up to ≈15 Myr after formation in the case of an instantaneous burst, and longer in the case of more extended star formation histories (in principle up to ∼100 Myr in the case of a constant star formation rate, although such high ages are unlikely to apply, as discussed in Section 3). The colors of Pop III galaxies with different IMFs are almost identical at young ages. We have verified that these criteria hold for objects up to an age of ≈15 Myr as long as the Lyman-continuum escape fraction is f_esc ≲ 0.5, irrespective of the Pop III IMF (but higher f_esc are allowed in the case of younger ages or more top-heavy IMFs). Figure 8 also illustrates the effect of dust reddening on these color criteria. Even though substantial dust reddening (if at all possible in Pop III galaxies) could conceal Pop III galaxies by making them appear as newborn, high-metallicity objects, there is no risk of false positives—i.e., no other type of galaxies in our model grid can spuriously appear as Pop III objects at this redshift.

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5.3. The Redshift Evolution of Type A Galaxy Colors

One major obstacle for any color criteria applied to SEDs dominated by nebular emission is that they evolve very quickly as a function of redshift. In Figure 9, we plot the redshift dependence of the m₂₇₇ − m₄₄₄ and m₅₆₀ − m₇₇₀ colors for young (1 Myr old) Pop III, II, and I galaxies of type A. As seen, both colors evolve dramatically as a function of redshift. By contrast, the colors of equally young type C galaxies (i.e., with SEDs dominated by direct starlight; dashed lines) hardly evolve at all. Even though the m₂₇₇ − m₄₄₄ < 0 criterion picks up on Pop III galaxies at z ≈ 6.7–8.5, it also selects young Pop I and II galaxies of both type A and C at z < 5 and at z ⩾ 6.5. The risk of confusion can be limited, but not completely removed, by adding photometry in other NIRCam filters and applying dropout criteria. For instance, additional observations in the F090W and F115W filters should effectively limit the redshift range of the sample to z ≈ 6.5–9.0 since objects in this redshift range are expected to appear as dropouts in F090W, but not in F115W, due to IGM absorption shortward of Lyα.

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A MIRI-based Pop III criterion like m₅₆₀ − m₇₇₀ ⩽ −1.3 (shaded region in Figure 7) is not likely to generate nearly as many interlopers. This color is useful as a Pop III diagnostic over the limited range z ≈ 7–8 (shaded region in Figure 9) only, but within that range, Pop III galaxies produce bluer colors than all other kinds of Z ⩽ 0.020, z > 1 galaxies in our model grid. Even though we have here only plotted the colors of very young galaxies (1 Myr old), this holds for all interloper ages (up to the age of the universe at each redshift considered). While there is some room for confusion with z < 1 galaxies—which due to dust emission in the F560W filter (not taken into account in our models) may potentially produce similar colors in this diagram—such objects are not likely to display apparent magnitudes in the same range as high-redshift Pop III galaxies. Hence, objects that end up in the upper left corner of Figure 8, and have apparent magnitudes in the range expected for high-redshift galaxies, are likely to be z ≈ 7–8 Pop III galaxies even in the absence of additional redshift constraints.

5.4. Sensitivity Issues

If Pop III galaxies can experience sufficient Lyman-continuum leakage to render the nebular contributions to their SEDs negligible, such type C objects would stand out in JWST surveys because of their very blue rest-frame UV continuum slopes. This is demonstrated in Figure 10, where we compare the SEDs of 1 Myr old, instantaneous-burst Pop III, II, and I galaxies at rest-frame wavelengths from 1250 Å to 4600 Å (the range accessible for the NIRCam instrument for a z = 10 target). The stellar continuum is seen to become progressively steeper when going toward lower metallicities and more top-heavy IMFs—a fact previously noted by, e.g., Bromm et al. (2001), Schaerer (2003), Tumlinson et al. (2003), Schaerer & Pelló (2005), Bouwens et al. (2010), Taniguchi et al. (2010), and Raiter et al. (2010b). However, the difference between the Pop III.2 and III.1 galaxies appears to be undetectably small. As seen in Figure 1, inclusion of nebular emission would make the observed continua substantially redder, thus potentially allowing type C galaxies to be identified by their very blue broadband colors. The filters would, however, need to be carefully selected for the redshift range of interest to prevent small amounts of lingering nebular emission from interfering with this spectral signature.

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Basically, a photometric measurement of the rest-frame UV continuum should ideally use filters with as large wavelength separation as possible. However, since IGM absorption short of Lyα likely precludes the use of certain NIRCam filters at z > 6, we have here selected m₂₀₀ − m₄₄₄, as a trade-off between redshift range and UV slope sensitivity. In Figure 11, we demonstrate that m₂₀₀ − m₄₄₄ should be able do distinguish type C, Pop III galaxies from all kinds of Pop I and II galaxies throughout the redshift range z ≈ 7.5–13.

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In Figure 11(a), we demonstrate that any type C galaxies at z = 8 (solid lines) that display m₂₀₀ − m₄₄₄ ⩽ −1.2 is bound to be a type C Pop III system. Nebular emission in type A galaxies would only drive the color redward. For instance, all newborn (≈1 Myr old) type A galaxies start off with m₂₀₀ − m₄₄₄ ⩾ −0.4 mag at this redshift. The σ(m₂₀₀ − m₄₄₄) ≈ 0.15 mag photometric error resulting from demanding a 10σ detection (the detection threshold assumed in Figure 4) in both filters should be sufficient to separate Pop III.1 and III.2 galaxies from Pop II and I, but would make it difficult to distinguish Pop III galaxies with a Kroupa (2001) IMF from Pop I or Pop II galaxies. The m₂₇₇ − m₄₄₄ color suggested by Inoue (2011) as a diagnostic is not as suitable, since the predicted difference between Pop III and Pop II/I galaxies is smaller.

In the instantaneous-burst models used in Figure 11(a), Pop III.1 systems only last for ≈3 Myr before fading away and Pop III.2 systems will eventually (at ages ≳ 10⁷ yr) attain colors redder than the m₂₀₀ − m₄₄₄ ⩽ −1.2 criterion. Pop III galaxies with a Kroupa (2001) IMF evolve redward of this limit after about 4 Myr. More extended star formation scenarios would in principle allow Pop III galaxies to retain their m₂₀₀ − m₄₄₄ ⩽ −1.2 colors for longer periods of time. In the case of a constant star formation rate, type C Pop III galaxies with a Kroupa (2001) IMF would display m₂₀₀ − m₄₄₄ ⩽ −1.2 for about 6 Myr, and Pop III.2 and III.1 would meet the same color criteria as long as star formation remains active. Of course, a type C object requires that much of the gas of the system has been vacated, and this is likely to prevent Pop III star formation from progressing efficiently. Hence, it seems unlikely that type A galaxies can retain their unique UV-slope signatures for much longer than ∼10 Myr.

For reference, we have in Table 2 included the UV slope β (f_λ∝λ^β) predicted for our different Pop III, II, and I models, derived the way this is currently done for galaxies at z ≈ 7 (e.g., Bouwens et al. 2010; Dunlop et al. 2011). Here, β is based on the Hubble Space Telescope WFC3 J₁₂₅ − H₁₆₀ color, using the Bouwens et al. (2010) calibration. At z = 7, these filters sample the rest-frame UV at wavelengths of ≈1370–1750 Å and ≈1760–2110 Å, respectively. We caution, however, that the β parameter does depend on the exact wavelength range sampled (e.g., Raiter et al. 2010b), especially for models involving nebular emission. Additional UV slope predictions for some of the Pop III SEDs used in this work are available in electronic format, along with numerous other quantities, from Raiter et al. (2010b).

6.1. The Redshift Evolution of Type C Galaxy Colors

6.2. Lingering Nebular Emission

7.1. Caveats Related to the [O iii] Method

7.2. Narrowband Imaging

7.3. How Much Do the Details of the Pop III IMF Matter?

Yggdrasil is a new spectral synthesis model that includes Pop I, II, and III stars, dark stars, nebular emission, and dust extinction. Using this model, we derive the stellar population masses of the faintest galaxies detectable by JWST through broadband imaging in UDFs. Assuming 100 hr exposures per filter, we find that JWST may be able to detect Pop III galaxies with stellar masses as low as ∼10⁵ M_☉ at z = 10, whereas the corresponding limit for Pop II/I galaxies is ∼10⁶M_☉. We also argue that the broadband fluxes of young (age ≲ 10 Myr) Pop III galaxies are likely to be significantly affected by nebular emission, unless the fraction of ionizing radiation escaping directly into the IGM is extremely high (f_esc ≳ 0.95).

We also discuss different strategies for selecting Pop III galaxy candidates based on their JWST broadband colors, both in the limiting cases of having dominant (low f_esc) and negligible (very high f_esc) nebular emission. In the former case, we particularly highlight the possibility of adding imaging in two MIRI filters (F560W and F770W) to the NIRCam filter sets usually discussed in the context of JWST UDFs, since this should allow for a clean selection of Pop III galaxies at z ≈ 7–8. Selecting targets for spectroscopic follow-up using color criteria based solely on NIRCam filters would be more economical in terms of exposure time, but also increases the risk of interlopers. In the case of Pop III galaxies dominated by direct starlight (very high f_esc), we argue that imaging in the NIRCam F200W and F444W filters should allow Pop III candidates to be selected throughout the redshift range z ≈ 6.5–13.

E.Z., C.-E.R., and G.Ö. acknowledge a grant from the Swedish National Space Board and the Swedish Research Council. D.S. is supported by the Swiss National Science Foundation. The authors are indebted to Marcia J. Rieke and Kay Justtanont for giving us access to the NIRCam and MIRI broadband filter profiles prior to public release. The anonymous referee is thanked for useful comments which helped to improve the quality of the paper.