UV-to-optical spectrum of primordial galaxies

Rest-frame ultraviolet-to-optical spectral characteristics of extremely metal-poor and metal-free galaxies

Akio K. Inoue
College of General Education, Osaka Sangyo University, 3-1-1, Nakagaito, Daito, Osaka 574-8530, Japan
E-mail: akinoue@las.osaka-sandai.ac.jp
Abstract

Finding the first generation of galaxies in the early Universe is the greatest step forward for understanding galaxy formation and evolution. For strategic survey of such galaxies and interpretation of the obtained data, this paper presents an ultraviolet-to-optical spectral model of galaxies with a great care of the nebular emission. In particular, we present a machine-readable table of intensities of 119 nebular emission lines from Ly to the rest-frame 1 m as a function of metallicity from zero to the Solar one. Based on the spectral model, we present criteria of equivalent widths of Ly, He ii , H, H, [O iii] to select extremely metal-poor and metal-free galaxies although these criteria have uncertainty caused by the Lyman continuum escape fraction and the star formation duration. We also present criteria of broad-band colours which will be useful to select candidates for spectroscopic follow-up from drop-out galaxies. We propose the line intensity ratio of [O iii] to H as the most robust criterion for of the Solar metallicity. This ratio of a galaxy with a few yr at is detectable by spectroscopy with the James Webb Space Telescope within a reasonable exposure time.

keywords:
cosmology: observations — galaxies: evolution — galaxies: formation — galaxies: high-redshift
pagerange: Rest-frame ultraviolet-to-optical spectral characteristics of extremely metal-poor and metal-free galaxiesAppendixpubyear: 2009

1 Introduction

Understanding galaxy formation and evolution is one of the most important issues in the modern astronomy. Finding the first generation of galaxies is the largest step to solve the question, while it is also an open question what the first generation of galaxies is. Galaxies in the very early Universe should be metal-poor or may be even metal-free. Therefore, the most metal-poor galaxies would be the first generation.

The galaxy with the lowest known metallicity is I Zw 18, a blue compact dwarf galaxy in the local Universe. The measured gas metallicity (to be precisely oxygen abundance) is about 1/50 of the Sun (Izotov et al., 1997). If we adopt the classical Solar metallicity (Anders & Grevesse, 1989), it corresponds to . At –3, Lyman break galaxies (LBGs) selected by the so-called drop-out technique have –0.01 (–1/2 ) (e.g., Pettini et al., 2001; Erb et al., 2006; Mannucci et al., 2009; Erb et al., 2010). The metallicity measurements for galaxies selected by the strong Ly emission line, Ly emitters (LAEs), are still very rare because of the difficulty of spectroscopy for these faint galaxies. Finkelstein et al. (2011) report ( ) at . These measurements are made by some strong nebular emission lines, so that the measured metallicity is that in the ionized gas not in the stellar atmosphere.

There are hundreds of stars whose metallicity in the atmosphere is found to be extremely low in the halo of the Galaxy (e.g., Beers & Christlieb, 2005). The mass of such extremely metal-poor (EMP) stars in the present epoch is small ( ), while their high-mass counter part should exist in the past (Komiya et al., 2007). Indeed, there are some possible signatures suggesting that LBGs and LAEs at contain massive EMP stars or even metal-free stars, the so-called Population III (Pop III) stars, of a non-negligible fraction in their stellar mass (Malhotra & Rhoads, 2002; Jimenez & Haiman, 2006; Bouwens et al., 2010a; Inoue et al., 2011).

To find the first generation of galaxies, we are pushing out the redshift frontier. The current record of redshift measured by spectroscopy is of UDFy-38135539 (Lehnert et al., 2010). Like this object, the brand-new Hubble Space Telescope/Wide Field Camera 3 (HST/WFC3) imaging enabled us to select LBGs at and even at (e.g., Bouwens et al., 2010b, 2011). These highest- galaxies may contain more EMP or Pop III stars than lower- LBGs. The very blue ultraviolet (UV) colours of the HST/WFC3 LBGs suggest such a possibility (Bouwens et al., 2010a) (but see Dunlop et al., 2011). Future telescopes such as 30-m class extremely large telescopes and James Webb Space Telescope (JWST) will further push out the redshift frontier by imaging observations.

Spectroscopy is finally required to measure metallicity of galaxies as well as the precise redshift of them. However, it is time-consuming because of the faintness of the target galaxies. Thus, any pre-selections for spectroscopy will be useful. We will start from a sample selected by the standard drop-out technique first. Then, it may be useful if we can select EMP or even metal-free candidates only with imaging data, in particular, broad-band photometric colours. This paper presents such a method.

In this paper, we will present a spectral model of EMP or even metal-free galaxies with a great care of the nebular emission (both lines and continuum). Young starburst galaxies emit strong Lyman continuum (i.e. hydrogen ionizing continuum with wavelength less than 912 Å; hereafter LyC). Thus, the nebular emission is a very important spectral component (Zackrisson, Bergvall, & Leitet, 2008; Schaerer & de Barros, 2009, 2010; Inoue, 2010; Ono et al., 2010; Raiter, Schaerer, & Fosbury, 2010). This model will be useful to discuss the physical nature of very high- LBGs with broad-band data (i.e. so-called spectral energy distribution [SED] fit) as well as to select EMP or metal-free galaxies for follow-up spectroscopy.

In section 2, we will describe the modelling of nebular emission and SED of galaxies. In section 3, we will present the resultant spectra from UV to optical in the rest-frame for various metallicities and present equivalent widths of emission lines as a function of metallicity and star formation duration. In section 4, we compare our model with the observed broad-band colours of –8 galaxies and discuss how we find EMP and Pop III galaxies in the future. In the final section, we will present a summary of this paper.

This paper follows a standard CDM cosmology with , , and . All the magnitude is described in the AB system.

2 Model

2.1 Stellar spectra

The SED of pure stellar populations depends on metallicity , initial mass function (IMF), star formation history, and age. Here, we assume a Salpeter IMF (Salpeter, 1955) with 1–100 and a constant star formation with a duration of 1, 10, 100, or 500 Myr. The metallicities considered are (), 0.008, 0.004, 0.0004, (EMP), , and 0 (Pop III). SEDs of the former 4 cases are generated by the population synthesis code starburst99 version 5.1 (Leitherer et al., 1999). Those for the latter 3 cases are taken from Schaerer (2002, 2003).

2.2 Nebular emission

2.2.1 Lines

Emission lines of hydrogen, helium, and some other major elements are taken into account. Based on a large grid of photo-ionization models by using cloudy 08.00 (Ferland et al., 1998), we have obtained emissivities of emission lines relative to H. Table 1 shows the parameter space of nebulae explored by the cloudy calculations in this paper: 7 metallicities , 5 ionization parameters , and 5 hydrogen number densities . The set of is the same as that of the stellar spectra adopted (§2.1). For each case of , we input the corresponding stellar spectrum into the code. Since there are 4 cases of the duration of star formation for each , the total number of the model calculated is 700 (). The considered and are typical ranges of Galactic and extra-galactic H ii regions (e.g., Osterbrock & Ferland, 2006) and the validity of the values will be confirmed by a comparison with observations for some strong lines later (Fig. 1). We assume the plane-parallel geometry for all the calculations and assume the abundance of elements to be the Solar one as the default in the code. We consider two cases with and without dust in ionized nebulae (see §2.2.3 for details). The electron temperatures in the nebulae are calculated in the code with energy balance between heating and cooling rates. Table 2 shows average temperatures for each cases which are used to calculate H luminosity by equations (1) and (2) later and nebular continuum emission in §2.2.2. The higher temperatures in dusty cases are probably due to photoelectric heating by dust.

Parameter Values , , , , , , 0.0 , , , , 0.0, 0.5, 1.0, 1.5, 2.0
Table 1: Nebular parameters explored in this paper.
no dust dusty (kK) (kK) 20 20 20 20 20 18 18 12 13 9.5 10 0.0 5.4 6.3
Table 2: Average electron temperatures in the nebulae for various metallicities.
Figure 1: Emissivities relative to H of six strongest metal emission lines as a function of metallicity. The circles are results calculated with the code cloudy 08.00 (Ferland 1998) in this work: no dust model (filled) and dusty model (open). The squares are empirical results by Anders & Fritze-v. Alvensleben (2003). The triangles are the observations of I Zw 18 (northwest and southeast components) measured by Izotov et al. (1999). The diamonds are observations of a galaxy measured by Erb et al. (2010). The dashed lines are empirical results by Nagao et al. (2006) and updated by Maiolino et al. (2008).

We select 119 emission lines between Ly and 1 µm in the rest-frame: H Ly, Balmer and Paschen series, and He and other elements’ lines which have an emissivity more than about 1% of H in at least one case calculated (except for H lines, for which we adopt all the lines output from the cloudy: up to ). The list of the lines is presented in Appendix.

For each stellar spectrum (i.e. each and star formation duration), we calculated 25 set of (, ). Among the 25 cases, line emissivities relative to H vary within about an order of magnitude for metal lines but the standard deviation relative to the average is about 5–25%. The variations of H and He lines are much smaller and the relative standard deviations are typically %. For calculations in later sections, we adopt average line emissivities obtained for each set of and star formation duration. We have also found that the line emissivities are very stable against the change of star formation duration if it is larger than 10 Myr. This is probably because the saturation of the LyC luminosity and spectrum after Myr star formation. In Appendix, we present machine-readable tables of line emissivities relative to H as a function of only (i.e. averaged over 3 star formation durations of 10, 100, and 500 Myr) which may be useful for future calculations by readers. On the other hand, in this paper, we adopt the line emissivities depending each star formation duration.

Figure 1 shows the relative emissivities of 6 strongest metal emission lines as a function of metallicity (ones presented in Appendix, i.e. averaged over the star formation durations). The circles are theoretical results of this paper by cloudy 08.00: no dust case (filled) and dusty case (open). The squares and dashed lines are empirical relations compiled by Anders & Fritze-v. Alvensleben (2003) and Maiolino et al. (2008) (see also Nagao et al. 2006), respectively. The triangles and diamonds are observations of a local galaxy, I Zw 18, (Izotov et al., 1999) and a galaxy (Erb et al., 2010). We find a good overall agreement between ours and theirs but an order of magnitude difference is found for some cases. This indicates a large uncertainty of the line emissivities which depend on the nebular physical parameters such as and . Indeed, Nagao et al. (2006) suggest dependence of to explain their empirical relations. Despite such uncertainties and difficulties, our emissivity of the strongest line, [O iii] , excellently agrees with that of Nagao et al. (2006) who compiled the largest sample of galaxies distributed over the widest range of and updated by Maiolino et al. (2008). As pointed out by literature (Zackrisson, Bergvall, & Leitet, 2008; Schaerer & de Barros, 2009, 2010) and also seen in later sections, this [O iii] emission line has the largest effect on broad-band colours and other metal lines do not affect the colours significantly. Therefore, we consider that using our theoretical line emissivities (or our choice of and ) is justified and a large uncertainty of line emissivities does not degrade our conclusions based on the [O iii] line.

To obtain the luminosity of the emission lines based on the relative emissivities, we need the luminosity of H. We assume the following expression:

(1)

where is the H emission coefficient, is the stellar production rate of LyC photons, is the escape fraction of the photons, is the fraction of the photons absorbed by dust within the ionized gas, is the Case B recombination rate, and is the recombination rate to the ground state. The denominator is usually described as just . However, our expression is correct when the nebular LyC escapes from the nebulae and is absorbed by dust with the same probability of and as the stellar LyC and the ionization equilibrium is established in the nebulae (Inoue, 2010). The fractions of and is assumed to be independent of wavelength, which is valid for clumpy nebulae as discussed in Inoue (2010). The LyC escape should be taken into account especially for because a significant escape was detected at (Shapley et al., 2006; Iwata et al., 2009) and such galactic ionizing radiation probably caused the cosmic reionization. On the other hand, we omit the LyC absorption in this paper (i.e. ) because the effect is very small for low-metallicity cases, according to a discussion in §2.2.3.

In , we have omit the density dependence because we only consider densities smaller than 10 cm which is well below a criterion for the small density limit ( cm; Osterbrock & Ferland 2006). The electron temperature dependence of can be approximated to

(2)

which is obtained from Table B.5 in Dopita & Sutherland (2003) for the density of cm. The uncertainty is less than 4% between 5,000 K and 30,000 K. This emission coefficient is obtained with the Case B assumption (Dopita & Sutherland, 2003). Recently Raiter, Schaerer, & Fosbury (2010) have shown that H luminosity is excellently predicted by the Case B even for extremely metal-poor cases. However, they also show that the Case B prediction underestimates Ly luminosity. On the other hand, our prediction of Ly is based on the ratio of Ly to H obtained from the cloudy, in which the effect discussed by Raiter, Schaerer, & Fosbury (2010) is already taken into account.

Figure 2: H luminosity per unit star formation rate as a function of metallicity. The diamonds, triangles, and squares are the cases of the LyC escape fraction and the constant star formation duration of 10, 100, and 500 Myr. The crosses are the case of and 100 Myr. The small triangles are the same case but obtained by the scaling of equation (3). The arrows at the left edge of the panel are the metal-free cases. The LyC absorption in nebulae is neglected (i.e. ).

Figure 2 shows H luminosity as a function of metallicity of the stellar population. The luminosity is normalized by the star formation rate. The H luminosity increases when metallicity decreases because the ionizing photon production rate is larger when metallicity is lower. The dependence of star formation duration is weak or absent when the duration is longer than 10–100 Myr depending on the metallicity. The dependence of the escape fraction found in equation (1) can be approximated to

(3)

where the factor 0.6 in the denominator comes from for K. Note that the scaling is not just as usually assumed when the nebular LyC can escape. This scaling is very nice as shown by the comparison of the crosses with the triangles in Figure 2.

2.2.2 Continuum

As the nebular continuum, we consider bound-free, free-free, and two photon emissions of hydrogen. Any helium continuum emission is not taken into account in this paper. While this simplification underestimates the nebular continuum emission, the helium continuum is not important very much because it is weak and negligible in fact (see e.g., Inoue, 2010). Continua of metal elements are not taken into account, either. The luminosity density of hydrogen nebular continuum at the frequency is given by the very similar form to equation (1) as

(4)

where is the emission coefficient of the continuum. The volume emissivity and the recombination rates and are calculated as described in Inoue (2010). Raiter, Schaerer, & Fosbury (2010) have shown that the Case B assumption, which is adopted in Inoue (2010), underestimates the nebular two-photon emission for the stellar effective temperature of K and the density of cm. This point causes an underestimation of the nebular continuum for m, while the effect is negligible for m where the nebular continuum is dominated by the bound-free emission.

Figure 3: Rest-frame model spectra of (a) Pop III () galaxies and (b) moderate sub-solar metallicity (: ) galaxies. In each panel, the lines correspond to 10, 100, and 500 Myr of constant star formation (bottom to top). LyC escape fractions and 0 are assumed for the solid and the dotted lines, respectively. The emission line width is assumed to be 300 km s as an example. No attenuation by dust and IGM is not included.

2.2.3 Dust

There are two effects of dust; one is attenuation (or extinction) of radiation by dust in the interstellar medium (mainly in the outside of ionized nebulae). This effect is often described with the Calzetti law (Calzetti et al., 2000), and we do so in §4, although some studies have suggested a different attenuation law in high- (e.g., Siana et al., 2009; Gallerani et al., 2010).

The other effect is LyC absorption by dust within ionized nebulae (i.e. in eqs. [1] and [3]). Dust competes with hydrogen to absorb LyC in nebulae. Indeed, a half of LyC is directly absorbed by dust in H ii regions in the Milky Way and some local group galaxies (Inoue et al., 2001; Inoue, 2001). The amount of LyC absorption depends metallicity and dust-to-gas ratio (Inoue, 2001). To see this effect, we ran cloudy with the interstellar dust of the code (i.e. Milky Way dust). The amount of dust was simply assumed to be scaled by metallicity. We also assumed that dust was well mixed with gas, while a central dustless cavity is likely to exist in nebulae (Inoue, 2002). The uniform dust distribution may overestimate the effect of LyC absorption. As found from Figure 1, the dust effect on emission lines results in larger emissivities relative to H in most cases, because LyC absorption reduces H emissivity. However, this effect is not very large, especially for low-metallicity cases. Therefore, we omit LyC absorption (i.e. ) and adopt only no dust cases in the following sections.

3 Result

3.1 Rest-frame UV-to-optical spectrum

Figure 3 shows resultant model spectra in the rest-frame for two cases of : (a) (Pop III) and (b) (). A constant star formation rate is assumed and the duration of star formation is 10, 100, or 500 Myr (bottom to top in each panel). The LyC escape fraction is assumed to be 0.5 (solid) or 0 (dotted) for both stellar and nebular continua. We do not consider any attenuation by dust and IGM in this figure. Note that the vertical axis is normalized by a unit star formation rate.

In both cases of , many H recombination lines such as Ly, H, H are highly visible. In addition, some He lines such as He ii and He i are also remarkable in the Pop III case. In the case, many metal emission lines appear. Especially, metal emission lines shown in Figure 1 such as [O iii] lines are very strong. These lines affect even the broad-band colours as found later.111A spectral dip just longward of the Paschen limit (8204 Å) is not real but an artifact caused by the lack of Paschen series lines higher than .

Figure 4: Rest-frame spectra of luminosity density ratio of nebular emission to stellar emission: (a) Pop III and (b) moderate sub-solar metallicity (: ). In each panel, the solid lines correspond to the LyC escape fraction and the dotted lines correspond to . For each type of the lines, the top to bottom correspond to 10, 100, and 500 Myr of constant star formation. The dashed horizontal lines indicate the ratio to be unity (i.e. equal contribution from stellar and nebular emissions).

The nebular contribution to the continuum is more significant in the case than in the case. The Balmer jump in the bound-free continuum is easily recognised in the and the duration of 10 Myr case. This point is shown more clearly in Figure 4 which shows spectra of luminosity density ratio of nebular to stellar emissions. The lines top to bottom correspond to the duration of 10, 100, and 500 Myr. As the duration of star formation increases, the ratio decreases. In addition, we see a stronger nebular contribution for a longer wavelength.

There are three spectral jump in the nebular continuum within the wavelength range shown: Lyman, Balmer, and Paschen jump of the bound-free continuum. In particular, the Balmer jump at 3646 Å is strong and can be found in the total (stellar+nebular) spectra shown in Figure 3. For example, the Pop III case with 10 Myr duration in Figure 3 shows a factor of Balmer jump. Note that the ‘Balmer jump’ is a sudden decrease of the continuum level towards longer wavelength. This is opposite to the ‘Balmer break’ which is a sudden increase of the continuum towards longer wavelength found in spectra of older stellar populations. For example, the 100 and 500 Myr cases in Figure 3 (b) show a prominent Balmer break.

Figure 5: Luminosity density ratio of nebular to stellar emissions at 3640 Å, very close to the Balmer limit (3646 Å), as a function of the duration of star formation. There are 7 metallicity cases: (plus), (asterisk), (circle), (diamond), (triangle), (square), and 0.0 (cross). No escape of the LyC is assumed ().

The strength of the Balmer jump depends on the duration of star formation and metallicity. This point is shown in Figure 5 more clearly: the nebular-to-stellar ratio at just shortward of the Balmer limit as a function of the duration. The LyC escape fraction of is assumed in Figure 5, and thus, the ratio shown is the maximum. The dependence of the nebular-to-stellar ratio is simply the same as equation (3). For all the 7 cases of metallicity, the nebular contribution, or the strength of the Balmer jump, monotonically decreases as the duration increases. The nebular contribution also decreases for higher metallicity. For Myr duration, only EMP () or metal-free cases exceed the ratio of unity, i.e. stronger nebular emission. Thus, a prominent Balmer jump appears only for these cases, while normally sub-solar metallicity (i.e. ) cases expect a weaker Balmer jump. Therefore, the strong Balmer jump can be a signature of EMP or Pop III stellar populations.

In Figure 4, we can find another strong jump at the Lyman limit. This feature is also caused by H bound-free emission and appears only when . As proposed by Inoue (2010), this Lyman jump (or ‘bump’) can be also useful as a signature of EMP or Pop III stellar populations because the jump becomes strong enough only when EMP or metal-free (Inoue, 2010). Inoue et al. (2011) showed that strong LyC emission detected by Iwata et al. (2009) from LAEs can be attributed to the Lyman jump by EMP or Pop III stars. However, this feature is easily obscured by IGM attenuation at (Inoue, 2010) and we cannot use it to find EMP or Pop III galaxies at very high-.

3.2 Equivalent width of emission lines

The equivalent width (EW) of an emission line is defined as

(5)

where is the line luminosity, is the stellar luminosity density at the line wavelength , and is the nebular continuum luminosity density at . As explicitly expressed in the equation, and depend on the LyC escape fraction . The dependence of these two terms is the same as equation (3). Thus, the dependence of EW has two extreme cases: (a) the same form as equation (3) when and (b) independent of when . Therefore, the dependence of EW is not very simple when the nebular continuum is relatively strong. Such cases happen at the rest-frame optical when the star formation duration is very short ( Myr) or when metallicity is extremely low () as shown in the previous subsection.

3.2.1 Ly

Figure 6: Rest-frame equivalent width of Ly emission line as a function of the duration of star formation. The symbols correspond to 7 metallicities same as Fig. 5. No escape of the LyC is assumed ().

Figure 6 shows the rest-frame EW of Ly as a function of the duration of star formation. The LyC escape fraction is assumed. We can scale the EW for other by the dependence same as equation (3) excellently well because the nebular continuum at 1216 Å is weak enough. We see that the EW decreases monotonically as the duration becomes longer. We also see that the EW is smaller as metallicity is higher. These are already reported in literature (e.g., Schaerer, 2002, 2003; Raiter, Schaerer, & Fosbury, 2010). Note that our EWs are quantitatively very consistent with those with the same IMF and a similar duration in Raiter, Schaerer, & Fosbury (2010).

We expect the maximum EW for galaxies with () to be 460 Å, or to be 230 Å if we consider only the age larger than 10 Myr (Note that the probability to observe a galaxy as young as 1 Myr is generally small because of its short time). Therefore, we may conclude that galaxies with an EW Å (or Å for more conservative) are EMP or Pop III (see also Malhotra & Rhoads, 2002). However, Ly transfer in the interstellar medium (ISM) is complex, and sometimes, it enhances the EW (Neufeld, 1991). Thus, a galaxy with higher metallicity may have a boosted EW which exceeds the criterion, and then, may be identified as an EMP/Pop III galaxy. On the other hand, it is worth noting that the EW becomes smaller than the criterion even for EMP/Pop III galaxies if . For example, we find that the EW is 65 Å for and 10 Myr constant star formation when . Therefore, Ly EW is intriguing but we need other signatures simultaneously to conclude a galaxy to be EMP/Pop III.

3.2.2 He ii

Figure 7: Same as Fig. 6, but for He ii 1640.

Figure 7 shows the rest-frame EW of He ii 1640. We see that the EW Å is realized only when metallicity is zero (i.e. Pop III). Therefore, this emission line is proposed as the signature of Pop III stars (e.g., Schaerer, 2002, 2003). However, this line may be too weak to be detected, and what is worse, the EW becomes even smaller than those in Figure 7 if . The scaling of in equation (3) is good for Myr cases because the nebular continuum contribution is not very large at the wavelength of the line for the cases. Even if we detect the He ii line, there is another issue that the line becomes observable from Wolf-Rayet stars with normal metallicity. In fact, the line has been detected from –3 LBGs but its origin is attributed to the stellar winds of these stars (Shapley et al., 2006; Erb et al., 2010). Therefore, using the He ii line needs more careful considerations, for example, about the line width (Erb et al., 2010).

3.2.3 H and H

Figure 8: Same as Fig. 6, but for H.
Figure 9: Same as Fig. 6, but for H.

Figures 8 and 9 show the rest-frame EWs of H and H, respectively. These two cases show qualitatively similar results: the EW becomes smaller as metallicity is higher or the duration is longer. For –100 Myr durations, we can separate EMP and Pop III cases from other higher metallicity cases by criteria, for example, EW(H) Å and EW(H) Å. If we wish to remove very young galaxies with higher metallicities, the criteria should be EW(H) Å and EW(H) Å. Unlike Ly, H and H photons do not undergo resonant scattering. Therefore, there are any contaminants of galaxies with higher metallicities in the sample selected by these criteria, except for AGNs. In this sense, the H and H EWs are promising tool to find primordial galaxies in the near future.

Note that we will miss EMP and Pop III galaxies with by these criteria. The dependence of the EWs is not simple because the nebular continuum significantly contributes to the total continuum at H and H, especially for the EMP and Pop III cases. The scaling of equation (3) overestimates the EWs by a factor of 2 or more, unfortunately. We need full calculations in order to obtain the EWs for other with higher accuracy.

3.2.4 [O iii]

Figure 10: Same as Fig. 6, but for [O iii] 5007.

Figure 10 shows the rest-frame EW of [O iii] 5007 which is the strongest metal emission line in our expected spectra. As shown in Figure 1, the metallicity dependence of this line is not monotonous. The line strength becomes maximum at around . For higher or lower than the metallicity, the EW becomes lower. We expect that EMP and Pop III galaxies have the EW Å. If we consider , the EW becomes even lower. Thus, all EMP and Pop III galaxies satisfy this criterion. On the other hand, the EW for a higher metallicity will also satisfy the criterion if . This will be contaminant. In addition, very old quiescent galaxies with higher metallicities, if they exist at high-, are also contaminant.

4 Discussion

Figure 11: HST/WFC3 colours of galaxies for seven metallicities. Each metallicity, there are four cases of the star formation duration: 1 Myr (circle), 10 Myr (triangle), 100 Myr (square), and 500 Myr (diamond). The metal-free case are indicated by arrows at the left edge of the panel. The four models of each metallicity are horizontally shifted each other for the display purpose. Each model has three cases of the LyC escape fraction : the upper open symbols for , the middle filled symbols for , and the lower open symbols for . The vertical arrow is the dust reddening vector based on Calzetti et al. (2000), which is likely to be applied for higher metallicity cases. At the right edge of the panel, the UV slope based on the conversion by equation (1) in Bouwens et al. (2010a) is shown. The two shaded regions are the observed ranges of for luminous and less luminous galaxies at reported by Bouwens et al. (2010a); the thick and thin shades indicate the ranges within 1- and 2- uncertainties, respectively.
Figure 12: Same as Fig. 11, but for galaxies. Note the much wider range of the colours than Fig. 11. The crosses with vertical error-bars near the right edge of the panel are the eight robust sample of galaxies compiled by Taniguchi et al. (2010). Their positions along the horizontal axis are meaningless and just for the sake of showing.

4.1 Rest-UV colours of high- galaxies with HST/WFC3

4.1.1

Bouwens et al. (2010a) have reported very blue UV colours of less luminous LBGs found in the ultra-deep survey with HST/WFC3, while Dunlop et al. (2011) recently challenged their finding. The argument by Bouwens et al. (2010a) is that the UV slope found in the LBGs with to AB indicates extremely low metallicity as and large escape fraction of the LyC as . Let us examine this argument with our model spectra.

Figure 11 shows a comparison of our model with the observed UV slope (or colour) by Bouwens et al. (2010a). For each metallicity, we consider four cases of the star formation duration (1, 10, 100, and 500 Myr) and three cases of the LyC escape fraction (0, 0.5, and 1). We find that almost all the EMP and Pop III cases with reside within a 2- range of the observed of the less luminous LBGs. The most plausible duration and among the EMP and Pop III cases are the duration of Myr and –1. For the metallicity , the observed is reproduced only when the duration is Myr, while the 10 Myr cases of and still remain within the upper 2- range if . It is unlikely to observe galaxies with Myr age because of the short time to observe them. Furthermore, the higher metallicity cases are probably reddened by dust, which makes more difficult to reproduce the observed with such higher metallicities. Therefore, we agree with the Bouwens et al. (2010a)’s argument if their very blue is real.

On the other hand, Bouwens et al. (2010a) have reported the UV slope for luminous LBGs ( to AB) at . Without dust reddening, we need the Solar metallicity and the star formation duration of Myr to reach the . If we apply a small amount (e.g., ) of the dust reddening to the model, lower metallicity cases can reach the . However, the EMP and Pop III cases are unlikely to have dust enough and to reach the observed . Therefore, the luminous LBGs at probably have metallicity larger than .

4.1.2

Taniguchi et al. (2010) have presented a robust sample of galaxies at detected with HST/WFC3 (Bouwens et al., 2010b; Bunker et al., 2010; McLure et al., 2010; Yan et al., 2010; Finkelstein et al., 2010). Let us compare the UV colours of the galaxies with our model. Figure 12 shows the comparison. However, a large uncertainty and variance on the observed colour make it difficult for us to derive any implication from the comparison. Thus, we comment just one thing about the bluest two objects which are much bluer than our bluest model (i.e. EMP and Pop III cases with ). This may indicate the presence of a strong Ly emission line in the band of the two objects (Taniguchi et al., 2010). Indeed, the line enters into the band if the object is located at . Note that the colour at shown in Figure 12 does not include the effect of the line.

4.2 Rest-optical colours of high- galaxies with JWST/NIRCAM

Figure 13: JWST/NIRCAM F277WF444W colours of galaxies as a function of redshift: (a) Pop III () galaxies with 10 Myr constant star formation, (b) () galaxies with 10 Myr star formation, (c) Pop III case but 100 Myr star formation, and (d) case but 100 Myr star formation. Four LyC escape fractions are assumed: for the filled circles, for the triangles, for the squares, and (i.e. pure stellar spectrum) for the diamonds. The open circles are the case with but no emission lines (i.e. stellar+nebular continua).

As discussed in section 3.1, there are the Balmer jump and some strong emission lines in the rest-frame optical. The observed wavelength of these features from high- becomes near- and mid-infrared where ground-based observations are difficult. The forthcoming JWST will cover the wavelength from the space. Let us examine the effect of the optical features on broad-band colours observed with the Near Infrared Camera (NIRCAM) on the JWST. In particular, we focus on F244WF444W colour because the Balmer jump at comes between the two bands.222The wavelength coverages of the two broad-bands taken from http://ircamera.as.arizona.edu/nircam/.

Figure 13 shows the redshift dependence of the colour. Although we show only four combinations of metallicity and star formation duration as indicated in the panels, the trend of other cases is similar to these cases. We find that the nebular emission makes the colour redder than the pure stellar one. The degree of the reddening increases as the LyC escape fraction decreases. This reddening is mainly caused by the emission lines like H, H, and [O iii] as found by the comparison between the cases with and without emission lines which are indicated by the filled and open circles, respectively. In fact, the nebular continuum makes the colour bluer than the stellar one for galaxies because of the Balmer jump. However, the reddening by strong H and [O iii] emission lines in the F444W band overcomes the bluing by the Balmer jump. We also find that for a longer star formation duration, the reddening by the nebular emission is smaller. In the same time, the stellar colour is redder because of the Balmer break of older stars. As a result, the colour with the nebular emission (with the both of lines and continuum) does not depend on the duration strongly.

The difference of metallicity appears in the colour. At , H is in the F444W band, and then, F277WF444W for the Pop III cases with but the cases are almost always F277WF444W . At , the cases show F277WF444W due to [O iii] in the F444W band, but the Pop III cases show F277WF444W thanks to the lack of the [O iii] line. Figure 14 shows the metallicity dependence of the colour for galaxies more in detail. As found from the figure, the EMP and Pop III cases with expect F277WF444W . On the other hand, the higher metallicity cases expect F277WF444W , except for the cases of very young ( Myr) and . Note that the colour of the higher metallicity cases is the lower limit. These galaxies probably have dust which reddens the colour as indicated by the upper arrow in the panel. Therefore, a colour criterion of F277WF444W may be useful to select EMP and Pop III candidates from galaxies at .

Figure 14: JWST/NIRCAM F277WF444W colours of galaxies as a function of metallicity. The meaning of the symbols are the same as Fig. 11. The horizontal dashed line is a criterion to separate the EMP cases from other higher metallicity cases.

4.3 Signatures of primordial galaxies

We discuss what signatures of EMP and Pop III galaxies we can detect in the near future. First, we present the selection criteria for EMP/Pop III candidates with broad-band colours. Then, we present more robust signatures to be searched by follow-up spectroscopy. Table 3 is a summary of the criteria.

Broad-band colours HST/WFC3 for –8 JWST/NIRCAM F277WF444W for F277WF444W for Rest-frame EW (Å) Ly H H He ii O iii Metal/hydrogen ratio O iii /H
Table 3: Proposed criteria to find extremely metal-poor and metal-free galaxies.

4.3.1 Broad-band colours

As discussed with Figure 11, the rest-frame UV colours can be used as the signature for EMP and Pop III galaxies (see also Bouwens et al., 2010a). However, the colour difference between EMP/Pop III and higher metallicity cases is relatively small, –0.2 mag. Thus, the observational uncertainty for individual objects prevents us from distinguishing them, e.g., Figure 12. If future facilities suppress the uncertainty of the colour, the UV colours will be useful as the signature for EMP/Pop III stars in individual galaxies. A proposed criterion is for –8.

The discussion with Figure 14 suggests the possibility to use the rest-frame optical colours as a signature of EMP and Pop III galaxies. The colour difference between EMP/Pop III and higher metallicities is larger than those of the UV colours: –0.4 mag. In this respect, the optical colours is better than the UV colours. However, we need space telescopes in order to measure the optical colours of very high- galaxies. The JWST and a Japanese project, Wide-field Imaging Surveyor for High-redshift (WISH)333http://www.wishmission.org/en/index.html will be useful. Proposed criteria are F277WF444W for and F277WF444W for .

4.3.2 EW of emission lines

If emission lines characterising EMP and Pop III galaxies are strong enough to be detected, the lines are very useful as the signature of these primordial galaxies. The He ii is the most discussed feature for Pop III stars (e.g., Schaerer, 2002, 2003). As shown in Figure 7, this line is indeed special feature for the metal-free case. However, there are two problems to use the line. One is that the strength of the line is not very strong. The expected EW is about 1–3 Å in the rest-frame for the star formation duration longer than 10 Myr. This corresponds to the observed EW of Å for . The other is that the strength becomes even weaker if the LyC escape fraction . In addition, there is contamination of the He ii line from Wolf-Rayet stars with normal metallicity (Shapley et al., 2006; Erb et al., 2010). Therefore, we need other signatures to confirm the galaxies selected by the line to be truly Pop III. In any case, we can use the line to select the candidates. A proposed criterion is EW(He ii) Å in the rest-frame.

As discussed in section 3.2, EWs of Ly, H, and H can be used as a signature of EMP and Pop III galaxies. However, if we adopt a lower limit on the EWs to select the primordial galaxies based on the estimations with , we will miss some of them which have . In addition, Ly photons undergoes resonant scattering in the ISM, and sometimes, the EW with higher metallicities is boosted by dust (Neufeld, 1991), and may exceed the criterion and become contaminant. There is no such case with H and H. Thus, these lines are more reliable signatures. Proposed criteria are EW(Ly) Å, EW(H) Å, and EW(H) Å in the rest-frame, or to avoid very young ( Myr) galaxies with higher metallicities, EW(Ly) Å, EW(H) Å, and EW(H) Å in the rest-frame.

With the EW of [O iii] 5007, we can select all the primordial galaxies by an upper limit on the EW. However, in this case, we will have contaminants of galaxies with higher metallicities and . A proposed criterion is EW(O iii) Å in the rest-frame.

4.3.3 [O iii]/H line ratio

Metal-to-hydrogen line ratio is free from the uncertainty of , unlike the EWs. As found from Figure 1, the ratio of [O iii] /H if . Although the ratio also becomes if based on the empirical relation reported by Nagao et al. (2006), such very high metallicity galaxies would not exist at very high-, or if they exist, itself is very interesting. Therefore, searching a galaxy with the ratio is very attractive.

Based on Figure 2, the H luminosity per a unit star formation rate of EMP/Pop III galaxies is erg s ( yr) if the star formation duration is longer than 10 Myr and . Thus, the expected upper limit on the [O iii] luminosity of EMP/Pop III galaxies is erg s ( yr). This corresponds to the [O iii] line flux erg s cm ( yr) for a source. The expected line sensitivity of the Near Infrared Spectrograph (NIRSpec) on the JWST is erg s cm at 4.5 m at S/N=10 with R=1000 mode in 100,000 s exposure time.444http://www.stsci.edu/jwst/instruments/nirspec/sensitivity/R1000_line.pdf Therefore, we can reach [O iii]/H at 3- for a 10 (or 3) yr galaxy at in 10,000 (100,000) s with the JWST/NIRSpec.

4.3.4 Balmer jump

As discussed in previous sections, we expect a significant Balmer jump in spectra of EMP/Pop III galaxies. Let us examine if we detect this feature with spectroscopy. Based on Figure 3 (a), we expect the continuum level around the Balmer jump (3646 Å in the rest-frame) to be (2–10) erg s Hz ( yr), depending on and the star formation duration. Thus, we expect an observed flux density of (2–10) nJy ( yr) for galaxies. On the other hand, the expected sensitivity of the JWST/NIRSpec is about 200 nJy at 3–4 m at S/N with R100 mode in 10,000 s exposure time.555http://www.stsci.edu/jwst/instruments/nirspec/sensitivity/R100_cont.pdf Therefore, we can detect continuum of a 10 yr galaxy at in 100,000 s exposure with very high significance of S/N –15. Namely, we can detect the Balmer jump of primordial galaxies at with the JWST/NIRSpec.

5 Summary

This paper presents a spectral model from UV to optical in the rest-frame of galaxies with various metallicities. A special feature of the model is the nebular emission of lines and continuum. We have calculated intensities of 119 emission lines from H Ly to 1 m in the rest-frame with the public photo-ionization code cloudy 08.00 (Ferland et al., 1998). The stellar spectra input into the code are generated by starburst99 (Leitherer et al., 1999) for metallicity or taken from Schaerer (2002, 2003) for EMP and metal-free cases. We input the stellar spectrum with the same metallicity as that in the nebular gas into the photo-ionization code. After exploring a wide range of nebular parameters (Table 1) which are appropriate to real H ii regions, we have derived average intensities of 119 emission lines relative to H (Figure 1 for the 6 strongest metal lines) and temperatures of the nebular gas (Table 2) as a function of metallicity. The emission line intensities are presented in Appendix as a machine-readable form.

The resultant spectra of galaxies show some interesting features in the rest-frame optical (Figure 3). In the EMP and metal-free cases, we find a strong Balmer jump, which is a spectral plummet towards longer wavelength, by the nebular bound-free continuum (Figures 4 and 5). As a result, broad-band colours straddling the Balmer jump becomes bluer than the stellar one (see Figure 13). However, strong Balmer emission lines can fill in the jump and can make the colours even redder than the stellar one (Figure 13). In higher metallicity cases, some emission lines of oxygen like [O iii] are so strong that they redden the broad-band colours (Figure 13; see also e.g., Schaerer & de Barros, 2009).

We have extensively discussed the signatures of EMP and metal-free galaxies expected from the model. In current and future observational data, we can obtain a sample of galaxies at high- by the standard drop-out technique. If we can select EMP and metal-free candidates from it by broad-band data, it is very useful to select the target for follow-up spectroscopy. The bluest galaxies in rest-frame UV are a good target (Figures 11 and 12). An example criterion in the colour with the HST/WFC3 is for –8. The blue galaxies with the UV spectral slope reported by Bouwens et al. (2010a) are likely to be EMP or metal-free although we cannot deny the possibility that these galaxies have normal metallicity if they are very young ( Myr) and have a large LyC escape fraction () (Figure 11). Rest-frame optical colours are also useful because there are some metallicity indicators such as the strong Balmer jump, Balmer series lines, and oxygen lines (Figures 13 and 14). For example, the criteria with the JWST/NIRCAM colour are F277WF444W for and F277WF444W for .

After selected the candidates, we will perform follow-up spectroscopy for them, and then, measure the metallicity. At this point, equivalent widths (EWs) of emission lines become useful as an indicator. We have examined EWs of Ly, He ii , H, H, and [O iii] as a function of metallicity, star formation duration, and LyC escape fraction (Figures 6–10). For the duration Myr and , the EMP and metal-free criteria of the rest-frame EW are as follows: EW(Ly) Å, EW(He ii) Å, EW(H) Å, EW(H) Å, and EW(O iii) Å. Note that the Ly and He ii criteria have a further uncertainty due to the resonant scattering in the ISM and IGM and due to the contribution of Wolf-Rayet stars, respectively. A criterion independent of the star formation duration and is the metal-to-hydrogen line ratio. The most easily detectable ratio is [O iii] /H. If we find the ratio from a galaxy, it is EMP or metal-free. This ratio at can be detectable by spectroscopy with the JWST/NIRSpec within a reasonable exposure time. In addition, we find that the Balmer jump can be also detected with the JWST/NIRSpec spectroscopy.

Acknowledgments

The author thanks to Roberto Maiolino, reviewer, for understanding this paper well and giving some useful comments. The author also thanks to Ikuru Iwata, Toru Yamada, and Koji Ohta for discussions and suggestions which let him initiate this work. The author is supported by the Institute for Industrial Research, Osaka Sangyo University and by KAKENHI (the Grant-in-Aid for Young Scientists B: 19740108) by The Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

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Appendix

A machine-readable tables of emission line intensities relative to H; Table A1 is the no dust model and Table A2 is the dusty model.

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