Clustering and lifetime of Lyman Alpha Emitters in the Epoch of Reionization

Abstract

1 INTRODUCTION

The Epoch of Reionization (EoR) marks a major phase change in the ionization state of the Universe. While the intergalactic medium (IGM) is predominantly composed of neutral Hydrogen (H i) at the beginning of this epoch, it is completely ionized by the end, as a result of H i ionizing photons produced by both stars and quasars. However, the progress of reionization has been hard to pin down since it depends on a number of parameters including the initial mass function (IMF) of reionization sources, their star formation rates (SFR), their stellar metallicity and age, the escape fraction of H i ionizing photons produced by each source and the clumping of the intergalactic medium (IGM), to name a few. A further complication is introduced by supernova feedback and (to a lesser extent) the ultraviolet background (UVB) built up during reionization in suppressing the gas content (and hence star formation) in low-mass galaxies which are the main sources of H i ionizing photons (see e.g. Barkana & Loeb 2001; Ciardi & Ferrara 2005; Maio et al. 2011; Sobacchi & Mesinger 2013; Wyithe & Loeb 2013; Dayal et al. 2015, and references therein).

Given these uncertainties, we require an alternative measurement to constrain the ionization state using LAEs. One such strong measure is provided by the two-point angular correlation function (ACF) of LAEs that describes their spatial clustering. Indeed, McQuinn et al. (2007) have shown that the spatial clustering can hardly be attributed to anything other than the large-scale (∼ Mpc scale) ionization regions created during reionization. This result is similar to that obtained by Jensen et al. (2014) who find that upcoming large-field LAE surveys should be able to detect the clustering boost for sufficiently high global IGM neutral fractions (20 per cent at z = 6.5), although Jensen et al. (2013) point out that a sample of several thousand objects is needed to obtain a significant clustering signal. Furthermore, Zheng et al. (2010) have shown that Lyα radiative transfer (RT) modifies the ratio of observed and intrinsic Lyα luminosities depending on the density and velocity structure of the environment, i.e. lines of sight (LOS) (transverse) density fluctuations are suppressed (enhanced), leading to a change in the amplitude of the two-point correlation function compared to the case without the environmental selection effect. However, while Behrens & Niemeyer (2013) have confirmed a correlation between the observed Lyα luminosity and the underlying density and velocity field, they do not find a significant deformation of the two-point correlation function by post-processing hydrodynamical simulations with an Lyα RT code.

A second probe is presented by the fraction of Lyman Break Galaxies (LBGs) that show Lyα emission: given that the physical properties of LBGs do not evolve in the 150 Myr between z ≃ 6 and 7, a sudden change in the fraction of LBGs showing Lyα emission could be attributed to reionization (e.g. Fontana et al. 2010; Stark et al. 2010; Stark, Ellis & Ouchi 2011; Pentericci et al. 2011; Caruana et al. 2014; Faisst et al. 2014; Schenker et al. 2014; Tilvi et al. 2014). However, this interpretation is complicated by caveats including the redshift dependence of the relative effects of dust on Lyα and ultraviolet (UV) continuum photons (Dayal & Ferrara 2012) and the fact that simple cuts in equivalent width (EW) and UV luminosity may lead to uncertainties in the LAE number densities (Dijkstra & Wyithe 2012).

Coupling a cosmological smoothed particle hydrodynamics (SPH) simulation snapshot at z ≃ 6.6 with a RT code (pcrash) and a dust model, Hutter et al. (2014) have shown that the effects of f_esc , f_α and T_α are degenerate on the LAE visibility; reproducing the observed Lyα LFs cannot differentiate between a Universe which is either completely ionized or half neutral (⁠|$\langle \chi _{\rm H\,\small {I}} \rangle$| ≃ 0.5–10⁻⁴), or has an f_esc ranging between 5–50 per cent, or has dust that it either clumped or homogeneously distributed in the interstellar medium (ISM) with f_α/f_c = 0.6–1.8; here f_c represents the fraction of UV photons that emerge out of the ISM unattenuated by dust. In this work, we extend our calculations to use the two-point LAE ACF to narrow down the three-dimensional parameter space of |$\langle \chi _{\rm H\,\small {I}} \rangle$|⁠, f_esc and f_α/f_c. Further, we study the time evolution of both the Lyα and UV luminosities to show the fraction of time during the past 100 Myr prior to z = 6.6 that a galaxy is visible as an LBG or as an LBG with Lyα emission, both considering the intrinsic and observed (dust and IGM-attenuated) luminosities. In principle, the ratio of these fractions could be measured by relating the number of observed LBGs with Lyα emission to the number of observed LBGs at z = 6.6–7.3.

The cosmological model corresponds to the Λ cold dark matter Universe with dark matter (DM), dark energy and baryonic density parameter values of (Ω_Λ, Ω_m, Ω_b) = (0.73, 0.27, 0.047), a Hubble constant H₀ = 100 h = 70 km s⁻¹ Mpc⁻¹, and a normalization σ₈ = 0.82, consistent with the results from WMAP5 (Komatsu et al. 2009).

2 THE MODEL

In this section, we briefly describe our physical model for high-redshift LAEs that couples cosmological SPH simulations run using gadget-2 with an RT code (pcrash; Partl et al. 2011) and a dust model, and interested readers are referred to Hutter et al. (2014) for a detailed description.

The hydrodynamical simulation analysed in this work was carried out with the treepm-SPH code gadget-2 and has a box size of 80 h⁻¹ comoving Mpc (cMpc) and contains 1024³ DM particles, and initially the same number of gas particles; the mass of a DM and gas particle is 3.6 × 10⁷ and 6.3 × 10⁶ h⁻¹ M_⊙, respectively. The simulation includes all the standard processes of star formation and its associated metal production and feedback using the prescription of Springel & Hernquist (2003), assuming a Salpeter (Salpeter 1955) IMF between 0.1–100 M_⊙. Bound structures of more than 20 total (DM, gas and star) particles are recognized as galaxies using the Amiga Halo Finder (AHF; Knollmann & Knebe 2009). Of all these galaxies, we only use ‘resolved’ galaxies that are complete in the halo mass function in all our calculations – these consist of at least 160 (10) gas (star) particles and have a halo mass M_h ≳ 10^9.2 M_⊙. Assuming each star particle to have formed in a burst, we calculate its spectra, and rest-frame intrinsic Lyα (⁠|$L_\alpha ^{{\rm int}}$|⁠) and UV continuum (⁠|$L_{\lambda ,{\rm c}}^{{\rm int}}$|⁠; 1505 Å) luminosities depending on the stellar mass, age and metallicity using the population synthesis code starburst99 (Leitherer et al. 1999). For each galaxy, the dust mass and its corresponding UV attenuation are calculated using the dust model described in Dayal et al. (2011). The observed UV specific luminosity is then calculated as |$L_{\lambda ,{\rm c}}^{{\rm obs}}=f_{\rm c}\times L_{\lambda ,{\rm c}}^{{\rm int}}$| where f_c is the fraction of UV photons that emerge out of the ISM unattenuated by dust which is fixed by matching to the observed evolving UV LF at z ≃ 6–8; galaxies with an absolute UV magnitude M_UV ≲ −17 are then identified as LBGs. The observed Lyα luminosity (⁠|$L_\alpha ^{{\rm obs}}$|⁠) is then calculated as |$L_{\alpha }^{{\rm obs}} = f_{\alpha } T_{\alpha } L_{\alpha }^{{\rm int}}$|⁠, where f_α and T_α account for dust attenuation in the ISM and by H i in the IGM, respectively. Galaxies with |$L_\alpha ^{{\rm obs}} \ge 10^{42}$| erg s⁻¹ and |${\rm EW} = L_\alpha ^{{\rm obs}}/L_{\lambda ,{\rm c}}^{{\rm obs}} \ge 20$| Å are identified as LAEs.

Given that both |$L_\alpha ^{{\rm int}}$| and |$\langle \chi _{\rm H\,\small {I}} \rangle$| depend on the fraction of H i ionizing photons that can escape out of the ISM (f_esc), we use five values of f_esc = 0.05, 0.25, 0.5, 0.75, 0.95 to post-process the z ≃ 6.6 snapshot of the hydrodynamical simulation with the 3D RT (pcrash). To explore the full range of |$\langle \chi _{\rm H\,\small {I}} \rangle$| (that determines T_α), we run pcrash starting from a completely neutral to a completely ionized state and obtain ionization fields for different values of the mean fraction of neutral hydrogen |$\langle \chi _{\rm H\,\small {I}} \rangle$|⁠; for each galaxy, we assume the initial line profile to be Gaussian and compute the average Lyα transmissions along 48 different LOS. For each combination of f_esc and |$\langle \chi _{\rm H\,\small {I}} \rangle$|⁠, the transmission T_α is then fixed and the only free parameter that can be adjusted to match Lyα luminosities to observations is the relative escape fraction of Lyα and UV photons from the ISM, p = f_α/f_c.

From the Lyα LFs, we find the following trends: the amplitude of the LAE Lyα LF decreases with increasing f_esc due to a decrease in |$L_\alpha ^{{\rm int}}$|⁠. However, this decline can be compensated by an increase in either f_α/f_c or T_α (in an increasingly ionized IGM). Comparing our model Lyα LFs to observations (Kashikawa et al. 2011), we found that allowing for clumped dust (p ≳ 0.7), the observations can be reproduced for |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≃ 0.5–10⁻⁴, f_esc ≃ 0.05–0.5 and f_α/f_c = 0.6–1.8 within a 1σ error.

3 CONSTRAINTS FROM LAE CLUSTERING

We start by calculating the LBG ACF (over the entire box) to get an estimate of the underlying galaxy population. As seen from Fig. 1, LBGs are almost homogeneously distributed and the ACF is consistent with essentially no clustering on scales ≲ 30 h⁻¹ Mpc. On the other hand, the LAE ACF is affected both by ISM dust, as well as the large-scale topology of reionization. It might be expected that in the early stages of reionization, only those galaxies that are clustered and hence capable of building large H ii regions would be visible as LAEs (leading to a large amplitude of the ACF), with the amplitude of the ACF decreasing as reionization progresses and faint objects are able to transmit enough flux through the IGM to be visible as LAEs. Indeed, as shown in Fig. 1, LAEs exhibit precisely this behaviour. For a given f_esc value (we remind the reader this corresponds to a fixed |$L_\alpha ^{{\rm int}}$|⁠), as the IGM becomes more ionized (going down the vertical columns in the Fig. 1), smaller galaxies are able to transmit more of their flux through the IGM, requiring lowering f_α/f_c values to fit the Lyα LF. While for a half neutral IGM (panel a), only strongly clustered galaxies are visible as LAEs (w(r) ≃ 4.5) at scales of ≃ 2 h⁻¹ Mpc, T_α increases for a completely ionized IGM at the same scale, leading to a more homogeneous LAE distribution resulting in a lower amplitude of the ACF (panel m; w(r) ≃ 1.5).

Figure 1.

ACF for simulated LAEs. The mean ACF is calculated from 36 mock catalogues (12 along each of x, y, z directions) assuming volumes with a depth of 30 h⁻¹ Mpc and an FoV of ∼3 × 10³ h⁻² Mpc². In each panel, the solid line shows the ACF of the best-fitting (f_α/f_c, f_esc , |$\langle \chi _{\rm H\,\small {I}} \rangle )$| combinations for which the simulated LAE Lyα LFs are within the 1σ limit of the observations by Kashikawa et al. (2011) with shaded regions showing the variance across the mock catalogues. In each panel, the grey dashed line shows the ACF for LBGs from the whole box, corresponding errors on the ACF for LBGs are comparable with the line width, and black points represent the observational results by Kashikawa et al. (2006). Columns show the results for f_esc = 0.05, 0.25 and 0.5, as marked. The values of |$\langle \chi _{\rm H\,\small {I}} \rangle$| are marked at the end of each row, with the f_α/f_c value marked in each panel, along with the χ² error.

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At a given value of |$\langle \chi _{\rm H\,\small {I}} \rangle$|⁠, |$L_\alpha ^{{\rm int}}$| decreases with increasing f_esc (horizontal rows in the same figure) which must be compensated by an increase in f_α/f_c. However, this compensation results in very similar ACFs at a given |$\langle \chi _{\rm H\,\small {I}} \rangle$| value. Our results therefore show that the ACF is driven by the reionization topology (as determined by |$\langle \chi _{\rm H\,\small {I}} \rangle$|⁠), with f_esc and the local f_α/f_c having a marginal effect (a factor of about 1.5) on its amplitude.

We then calculate the χ² errors between our simulated ACFs and observations, and find that observations constrain |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≲ 0.01 for f_esc = 0.05, 0.5 and |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≲ 10⁻⁴ for f_esc = 0.25 (to within a 3σ error). Further, while the f_α/f_c ratio is compatible with homogeneously distributed dust for f_esc = 0.05, the decrease in |$L_\alpha ^{{\rm int}}$| requires clumped dust (f_α/f_c ≥ 0.7) for f_esc = 0.25 and 0.5.

To highlight the importance of the spatial clustering of LAEs, we show the (1–5)σ constraints allowed by matching the Lyα LFs to observations in Fig. 2. As seen, these encompass a region such that |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≃ 10⁻⁴–0.5, f_esc = 0.05–0.5 and f_α/f_c = 0.6–1.8. However, building ACFs for each of these allowed combinations, we find that theory and observations yield much tighter constraints of |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≃ 0.01–10⁻⁴, f_esc = 0.05–0.5 and f_α/f_c = 0.6–1.2 to within a 3σ error.

Figure 2.

The grey shaded regions show the (1σ–5σ)σ (dark grey to white, respectively) regions for the combinations of f_esc, |$\langle \chi _{\rm H\,\small {I}} \rangle$| and f_α/f_c that best fit the observed Lyα LF data from Hutter et al. (2014). We overplot black contours for 3σ (stars), 5σ (dots), >5σ (hatching) by comparing model results to observed ACF data (Kashikawa et al. 2006). As shown, LAE clustering observations (3σ) require an IGM that has |$\chi _{\rm H\,\small {I}} \lesssim 0.01$|⁠, f_α/f_c ≤ 1.2 and f_esc ≤ 0.5. See Section 3 for details.

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Finally, our results show that it is the reionization topology (as parametrized by |$\langle \chi _{\rm H\,\small {I}} \rangle$|⁠) that drives the ACF, supporting the results obtained by McQuinn et al. (2007) and Jensen et al. (2013, 2014). Although Jensen et al. (2014) have assumed a simple scaling down of the L_α luminosity of all galaxies by a fixed amount due to galaxy evolution, they also find that galaxies are more likely to be observed as LAEs if they reside in ionized regions for |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≳ 20 per cent. We note that the number of galaxies we identify as LAEs is similar to within 10 per cent for the different f_esc, |$\langle \chi _{\rm H\,\small {I}} \rangle$|and f_α/f_c combinations, demonstrating that the enhanced LAE clustering in our model can be attributed to an increasing neutral IGM.

We note that the average number of LAEs in our mock catalogues (∼300) exceeds the number of identified objects in Kashikawa et al. (2006). In order to compare to a complete sample, we have considered all galaxies with |$L_{\alpha }^{{\rm obs}}\ge 10^{42}$| erg s⁻¹ and EW ≥ 20 Å as LAEs. Since this luminosity cut may include fainter galaxies than observed, the obtained ACFs represent a lower limit, as the clustering increases for higher luminosity cuts (Jensen et al. 2014). According to Jensen et al. (2013), our galaxy sample size of ∼300 is sufficient to distinguish a half-ionized from an ionized IGM, but does not provide the necessary sample size of ∼500 to distinguish |$\langle \chi _{\rm H\,\small {I}} \rangle$| = 0.25 from |$\langle \chi _{\rm H\,\small {I}} \rangle$| =1. However, we have modelled the luminosity of each galaxy according to its stellar population obtained from the hydrodynamical simulation. This makes our results more sensitive to the ionization state of the IGM than Jensen et al. (2013); their clustering signal was reduced by the random scatter they added to the imposed fixed mass-to-light ratio. Hence, in agreement with McQuinn et al. (2007), we find our sample size sufficient to distinguish |$\langle \chi _{\rm H\,\small {I}} \rangle$| = 0.25 from |$\langle \chi _{\rm H\,\small {I}} \rangle$| = 10⁻⁴.

4 THE RELATION BETWEEN LAES AND LBGS

In this section, we show how simulated z ≃ 6.6 galaxies build up their stellar mass (M_*), and the time evolution of their UV and Lyα luminosities, and Lyα EWs. We then present the fraction of time during the last 100 Myr prior to z = 6.6 for which galaxies of different UV magnitudes are visible as LBGs or as LBGs with detectable Lyα emission, both considering intrinsic and observed luminosities for each combination of f_esc, |$\langle \chi _{\rm H\,\small {I}} \rangle$| and f_α/f_c that reproduces the Lyα LF and LAE ACF within 1σ and 3σ, respectively. In order to consider a time span independent of resolution effects, we have chosen a period of time of 100 Myr as an interval. We discuss the limiting case, i.e. considering the total lifetime of each galaxy in our simulation as the corresponding period of time, in the Appendix A.

4.1 Time evolution of stellar mass, Lyα and UV luminosities

We use the ages of each star particle to trace the growth of M_*, and the metallicity and time dependent values of the intrinsic UV and Lyα luminosities (⁠|$L_{\lambda ,{\rm c}}^{{\rm int}}$| and |$L_\alpha ^{{\rm int}}$|⁠, respectively) and the intrinsic Lyα EW (⁠|$= L_{\alpha }^{{\rm int}}/L_{\lambda ,{\rm c}}^{{\rm int}}$|⁠) for galaxies in three bins of M_* ≃ 10^{8, 9, 10} M_⊙. We assume that all ionizing photons emitted within galaxies are absorbed in the ISM and produce Lyα radiation, i.e. f_esc = 0, to investigate the most extreme case.

As seen from the upper three panels of Fig. 3, both |$L_{\lambda ,{\rm c}}^{{\rm int}}$| and |$L_\alpha ^{{\rm int}}$| (averaged over the galaxies in the given M_* bin) rise as galaxies steadily build up in (stellar) mass, albeit with a large scatter reflecting the assembly history of different galaxies. As expected for normal star forming galaxies, the average intrinsic Lyα EW for all the three M_* bins considered here has a value between 30 and 300 Å (lower three panels of the same figure) that is larger than the minimum value of 20 Å used to identify LAEs. Indeed, we find that once a galaxy exceeds a critical mass of roughly 10^8.5(10^7.5) M_⊙, it can produce enough luminosity to intrinsically be an LAE (LBG), it has also met the LBG criterion.

Figure 3.

Time evolution of M_*, Lyα and UV luminosities and EWs across three M_* bins of 10⁸, 10⁹ and 10¹⁰ M_⊙ as marked above each column. The upper three panels show the intrinsic quantities [M_* in black; |$L_\alpha ^{{\rm int}}$| in red (upper line); |$L_{\lambda ,c}^{{\rm int}}$| in blue (lower line)]; we use f_esc = 0 for the Lyα luminosity. The middle three panels show the observed quantities [M_* in black; |$L_\alpha ^{{\rm obs}}$| in red (upper line); |$L_{\lambda ,{\rm c}}^{{\rm obs}}$| in blue (lower line)] where we assume T_α = 0.45, f_α = 0.68f_c and an individual f_c depending on the dust mass of each galaxy. The dashed lines in the top two panels show the current observational limits corresponding to the Lyα (10⁴² erg s⁻¹) and UV (10^39.6 erg s⁻¹Å⁻¹) luminosities. The lower three panels show the intrinsic (yellow, upper line) and observed (green, lower line) Lyα EWs with the dashed line showing the minimum limit of 20 Å. In each panel, shaded regions show the variance in the given M_* bin.

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As for observed luminosities, we remind the reader that we compute |$L_\alpha ^{{\rm obs}}$| using the fraction of UV photons that escape out of the galaxy (f_c); |$L_\alpha ^{{\rm obs}}$| is computed assuming homogeneously distributed dust (f_α/f_c = 0.68) and an IGM transmission value of T_α = 0.45 (Hutter et al. 2014). As expected, including the effects of dust and the IGM reduces both the Lyα and UV luminosities, as shown in the middle panels of the same figure so that the critical M_* at which a galaxy has the minimum luminosity to be an LAE (LBG) increases to 10^9.5(10^8.5) M_⊙, although in most cases the observed EW is still larger than the minimum required value of 20 Å (bottom most panels).

As expected from our discussion above, the time a galaxy spends as an LBG or LAE increases with increasing M_*. However, in our model a galaxy becomes an LBG before it also turns into a LAE because of the more stringent (luminosity + EW) constraints imposed on identifying a galaxy as an LAE, as expected from the critical M_* values quoted above. To quantify, while galaxies with stellar masses of |${\sim }10^8\,{\rm \,{\rm M}_{\odot }}$| are visible as LBGs for roughly the last 80 Myr, they do not meet the selection criterion to be visible as LAEs: although their intrinsic EW are larger than the minimum value of 20 Å required by observations (bottom panel of same figure), |$L_\alpha ^{{\rm int}}$| does not meet the required Lyα luminosity of 10⁴² erg s⁻¹. Galaxies with M_* ≳ 10⁹ M_⊙ are massive enough to sustain star formation and maintain |$L_{\lambda ,{\rm c}}^{{\rm int}}$| and |$L_\alpha ^{{\rm int}}$| values above the required limits. Again, the lifetime spent as an LAE is driven by |$L_\alpha ^{{\rm int}}$|⁠, with the intrinsic EW always exceeding 20 Å (bottom panel of Fig. 3).

When considering observed luminosities, the time a galaxy is visible as an LBG decreases; the decrease is more pronounced for LAEs that are additionally affected by IGM transmission. From panels (d)–(f) of Fig. 3, we see that in addition to galaxies with 10⁸ M_⊙, galaxies with M_* ≃ 10⁹ M_⊙ are also no longer visible as LAEs as a result of the Lyα luminosity dropping below visible limits.

4.2 The fraction of time spent as LBG and as LBG with Lyα emission

We now calculate the fraction of time during the last 100 Myr prior to z = 6.6 that galaxies in different UV magnitude bins spend as an LBG (f_LBG) and as an LBG with Lyα emission (f_LBGα, i.e. as an LAE), and discuss the resulting fractions (f_LBGα and f_LBG) for galaxies of varying UV magnitudes M_UV = −18 to −25 in more detail. We start with intrinsic UV luminosities as shown in Fig. 4: first, as galaxies become more massive, they are able to sustain large rates of star formation, leading to M_UV values that scale with M_*. Secondly, we find that both f_LBG and f_LBGα increase with an increase in the UV magnitude (or M_*), as explained in Section 4.1 above: f_LBG increases from 65 to 100 per cent as M_* increases from 10⁸–10^10.5 M_⊙. As a result of the stricter luminosity and EW criterion imposed to identify galaxies as LAEs, f_LBGα < f_LBG and declines more rapidly than f_LBG towards fainter UV luminosities, decreasing from 100 to 10–30 per cent as M_* decreases from 10^10.5–10⁸ M_⊙. Further, the decrease in |$L_\alpha ^{{\rm int}}$| with increasing f_esc results in a (linear) decrease in f_LAE as shown from panels (a)–(c) of the same figure: while f_LAE is comparable for f_esc = 0.05, 0.25, it decreases by about 0.15 for f_esc = 0.5, where half of the ionizing photons do not contribute to the Lyα luminosity thereby reducing the fraction of time it shows Lyα emission.

Figure 4.

Fraction of time during the last 100 Myr prior to z = 6.6 that galaxies spend as LBGs (f_LBG, circles) and as LBGs with a Lyα line (f_LBGα, squares), as a function of the intrinsic UV luminosity for intrinsic values of Lyα and UV luminosities. The panels show the fractions for the indicated values of f_esc = 0.05, 0.25, 0.5. The mean stellar mass in each M_UV bin is encoded in the shown colour scale. The fractions are computed as the mean of the galaxies within M_UV bins k ranging from k − 0.25 to k + 0.25 for k = −25,...,−18 in steps of 0.5. Error bars show the standard deviations of the mean values. The dotted black line in each panel represents f_LBGα for f_esc = 0.05; as clearly seen, increasing f_esc to 0.5, leads to a decrease in f_LBGα.

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We then calculate f_LBG and f_LBGα including the effects of dust and IGM attenuation for each of the best-fitting parameter combinations that match both the observed Lyα LF and ACF as shown in Section 3. We use the f_c value for each galaxy according to its final dust mass at z ≃ 6.6, the Lyα transmission T_α of each galaxy was obtained from the ionization field and the ratio of the escape fractions of Lyα and UV continuum photons (f_α/f_c) was set according to Table 1. As can be seen from Fig. 5 (since f_LBGα is nearly identical for all best-fitting cases, we show only one best-fitting case) the additional attenuation by dust in the ISM and neutral hydrogen in the IGM leads to a rise of the mean stellar mass in each M_UV bin, as well as to lower values for f_LBGα (compared to the intrinsic case) but not for f_LBG. Nevertheless, we find the same trends as when considering intrinsic luminosities: f_LBG always exceeds f_LBGα, and f_LBG and f_LBGα decrease towards fainter UV luminosities with f_LBGα declining more rapidly. However, the relative difference between f_LBG and f_LBGα is larger and the decline of f_LBGα is more rapid; while f_LBG decreases from 100 to 65 per cent as M_UV increases from −23.5 to −18.5, f_LBGα drops from 100 per cent to essentially 0 for the same magnitude range. The stronger decline in f_LBGα is not only due to the additional dust- and IGM attenuation of the Lyα luminosities, but also due to the additional selection criterion in Lyα EW which becomes more important towards UV fainter galaxies.

Figure 5.

Fraction of time during the last 100 Myr prior to z = 6.6 that galaxies spend as LBGs (f_LBG, circles) and as LBGs with an Lyα line (f_LBGα, squares) as a function of the UV luminosity for our best-fitting models. The mean stellar mass in each M_UV bin is encoded in the shown colour scale. This panel shows the best-fitting case for f_esc = 0.05, |$\langle \chi _{\rm H\,\small {I}} \rangle$| =10⁻⁴ and f_α/f_c = 0.60. The fractions are computed as the mean of the galaxies within M_UV bins k ranging from k − 0.25 to k + 0.25 for k = −25...−18 in steps of 0.5. Error bars show the standard deviations of the mean values. The independence of f_LBGα on the chosen best-fitting model clearly shows that the effects of f_esc, |$\langle \chi _{\rm H\,\small {I}} \rangle$| and f_α/f_c are degenerate on f_LBGα.

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We also find that the decrease in f_esc is compensated by the increase in f_α/f_c, leading to very similar f_{LBG, α} ratios for all the models ; note that the IGM is almost ionized in most cases, leading to similar T_α values. This clearly shows that |$\langle \chi _{\rm H\,\small {I}} \rangle$|⁠, f_esc and f_α/f_c compensate each other (as shown in Hutter et al. 2014), as a result of which f_LBGα only depends on the combination of the parameters but not on their individual values.

Thus in our model, the most luminous (massive) LBGs most often show Lyα emission, irrespective of whether intrinsic or observed luminosities are considered.

5 DISCUSSION AND CONCLUSIONS

We couple a cosmological hydrodynamical simulation (gadget-2) with a dust model and an RT code (pcrash) to model high-z LAEs. Starting from a neutral IGM, we run pcrash until the IGM is completely ionized, for f_esc values ranging from 0.05 to 0.95. In Hutter et al. (2014), we showed that comparing model results to Lyα LF observations simultaneously constrains the escape fraction of ionizing photons f_esc, the mean amount of neutral hydrogen |$\langle \chi _{\rm H\,\small {I}} \rangle$| and the ratio of the escape fractions of Lyα photons and UV continuum photons f_α/f_c to |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≃ 10⁻⁴–0.5, f_esc = 0.05–0.5 and f_α/f_c = 0.6–1.8. In this paper, we calculate the ACFs for these different combinations and find that comparing these to observations significantly narrows the allowed 3D parameter space (within a 3σ error) to |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≃ 0.01–10⁻⁴, f_esc = 0.05–0.5 and f_α/f_c = 0.6–1.2. While the effects of these three parameters are degenerate on the Lyα LFs, the ACF is most sensitive to large-scale ionization topologies and reionization leaves clearly distinguishable ACF imprints (boosting up the strength of the ACF) that cannot be compensated by varying f_esc or f_α/f_c. Further, the ACF allows us to constrain |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≤0.01, independent of the other two parameters, and we also constrain f_esc �� 0.5 and f_α/f_c ≤ 1.2.

We then analyse the average time evolution of UV and Lyα luminosities of simulated galaxies at z ≃ 6.6 in three bins of M_* = 10^{8, 9, 10} M_⊙, finding the following: as soon as a galaxy exceeds a critical stellar mass of M_* ≃ 10^8.5(10^7.5) M_⊙, its intrinsic Lyα (UV) luminosity is large enough for it to be identified as an LAE (LBG). Including the effects of dust and IGM attenuation naturally results in an increase in this critical mass to 10^9.5 and 10^8.5 M_⊙ for LAEs and LBGs, respectively.

Considering the fraction of time during the last 100 Myr (prior to z = 6.6), a galaxy spends as an LBG with Lyα emission (f_LBGα) or as an LBG (f_LBG), we find that the former is always smaller due to the more stringent luminosity and EW constraints imposed on identifying galaxies as LAEs. We find that both the intrinsic and dust-attenuated fraction f_LBGα and f_LBG rise with increasing UV luminosity (and hence M_*): intrinsically, f_LBG (f_LBGα) increases from 65 to 100 per cent (10–30–100 per cent) as M_* increases from 10⁸–10^10.5 M_⊙. As expected, including the effects of dust and IGM transmission reduces the values for f_LBGα such that f_LBGα decreases from 100 per cent to essentially 0 as M_* decreases from 10^10.5–10⁸ M_⊙. Finally, we find that the fraction f_LBGα of all our models that reproduce the observed Lyα LF and LAE ACFs are independent of the chosen set of parameters; a larger f_α/f_c compensates a decrease in T_α, or an increase in f_esc. As a result, f_LBGα only depends on the combination of these three parameters but not on their individual values. Thus, it is most often the most luminous LBGs that are visible in the Lyα.

Finally, we summarize the major caveats involved in this study. First, given the cosmological volumes probed by the simulation, we are unable to resolve Lyman Limit systems (LLS) which could lead to a further decrease in the transmission T_α along LOS intercepted by such systems (Bolton & Haehnelt 2013). However, whether LLS are preferentially located in clustered regions, leading to an increasing suppression of T_α for massive galaxies remains an open question.

Secondly, as a natural consequence of simulating cosmological volumes we are unable to resolve the ISM of individual galaxies, for which reason we assume a Gaussian profile (with a width set by the rotation velocity of the galaxy) for the Lyα line that emerges out of any galaxy which is probably an unrealistic scenario (see e.g. Verhamme et al. 2008). We note that our constraint on the ionization state of the IGM is model dependent, since the IGM Lyα transmission is sensitive to the assumed line profile (Jensen et al. 2013).

Thirdly, we assume dust attenuation and IGM transmission to be equal to the values at z ≃ 6.6 in order to calculate both f_LBGα and f_LBG. While the dust mass (and hence attenuation) would be expected to be lower at earlier times, tracing this build-up would require tracking the dust growth in the progenitors of our simulated galaxies. This is beyond the scope of this paper and we defer to this analysis to a work that is in preparation. Fourthly, f_LBGα would be expected to decrease with increasing z as a result of an increase in |$\langle \chi _{\rm H\,\small {I}} \rangle$| (leading to a decrease in T_α). However, properly accounting for the latter effect requires modelling the entire history of reionization.

While we have explored the full range of possible values for f_esc, its mass and z-dependence remain poorly understood, which is also one of the main caveats involved in modelling the time-evolution of reionization. An increase in f_esc with decreasing mass (e.g. Ferrara & Loeb 2013) would suppress the visibility of low-mass objects, and strongly impact the reionization fields we generate, emphasizing the strong clustering of high-mass haloes (Kaiser 1984; Bardeen et al. 1986; Mo & White 1996), whilst depressing the LF at the faint end. Bringing these values into agreement with observations would then require an f_α/f_c ratio that decreases with increasing mass. With its observations of the ionization topology, instruments such as the Low Frequency Array (LOFAR) will be invaluable in answering some of these outstanding questions.

Finally, we calculate the fraction of LBGs that would be identified as LAEs, X_LAE. Imposing an LAE selection criterion of L_α ≥ 10⁴² erg s⁻¹ and EW ≥ 20 Å we find that it is the faintest LBGs that do not show Lyα emission (cf. Dayal & Ferrara 2012), while all LBGs brighter than M_UV ∼ −20 are identified as LAEs at z ≃ 6.6 (see Fig. 6). Even if the Lyα selection criterion is made more stringent, i.e. EW > 55 Å, X_LAE does not show the behaviour observed by Stark et al. (2010), increasing instead of decreasing with UV magnitude. This mismatch is probably due to a combination of the following effects: first, the Lyα IGM transmission (T_α) is subject to a large variance along different LOS (see Hutter et al. 2014) due to the patchy nature of reionization; while we use T_α values averaged over 48 LOS, using values along a specific LOS would lead to an over- or underestimate of T_α. Secondly, as mentioned before, it is possible that the inclusion of LLS could decrease T_α of massive galaxies, leading to lower Lyα EW values, respectively. Thirdly, the results by Stark et al. (2010) are based on a post-reionization sample of galaxies (4.5 < z < 6.0), while our simulation samples the end of reionization era. The evolution of the UV (and Lyα ) LFs of LAEs and LBGs suggest that the emitted observable Lyα radiation varies with cosmic epoch, depending predominantly on the evolution of dust and gas at z < 6 and on the IGM neutral hydrogen fraction at z > 6. Thus, the probe of LBGs with/without Lyα emission in Stark et al. (2010, dusty, ionized IGM) may differ to the LBG and LAE population at the end of reionization (less dusty, partly neutral IGM). Indeed, a remarkable high fraction of strong LAEs among 6.0 < z < 6.5 luminous LBGs (−21.75 < M_UV < −20.25; Curtis-Lake et al. 2012) indicates that most LBGs are also identified as LAEs, which is in agreement with our findings. However, their sample suffers from low statistics, which will be overcome by upcoming Subaru/HST/UltraVISTA data. Finally, as an observational caveat, Verhamme et al. (2012) have shown that detailed Lyα RT calculations of simulated galaxies suggest stronger inclination effects for Lyα photons than for UV continuum photons, introducing biases in the selection function of narrow-band LAE surveys that could lead to a significant fraction of LBGs galaxies being missed as LAEs. We aim at investigating these effects in detail in future works and shedding light on the tantalizing connection between LBGs visible/invisible as LAEs.

Figure 6.

Fraction of LBGs detected also as LAE (X_LAE) as a function of UV luminosity. The fractions are shown for fiducial best-fitting models of f_esc = 0.05: |$\langle \chi _{\rm H\,\small {I}} \rangle$| =0.01, f_α/f_c = 0.68 (red dashed) and |$\langle \chi _{\rm H\,\small {I}} \rangle$| =10⁻⁴, f_α/f_c = 0.60 (blue solid). Error bars are derived from the Poissonian errors of the LAE and LBG numbers. The upper panel (a) shows the fraction X_LAE for an LAE selection criterion of L_α > 10⁴² erg s⁻¹ and EW > 20 Å, and the lower panel (b) adopts an selection criterion of EW > 55 Å, which is in agreement with the observations by Stark et al. (2010). Black points represent the observational constraints of Stark et al. (2010) at 4.5 < z < 6.0.

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The authors thank the anonymous referee for their insightful comments and suggestions that helped to improve the paper, as well as M. Dijkstra, N. Kashikawa, D. Schaerer and P. Creasey for useful discussions. PD acknowledges the support of the Addison Wheeler Fellowship awarded by the Institute of Advanced Study at Durham University.

REFERENCES

APPENDIX A: THE FRACTION OF LIFETIME SPENT AS LBG WITH AND WITHOUT LYα EMISSION

We also show results for the limiting case where the age is the time since the onset of star formation, showing how the fractions of lifetime change when the time span is increased. We take the total age of a galaxy as the time between the formation of the first star and z = 6.6, and calculate the corresponding fractions of lifetime that galaxies in different M_UV bins spend as an LBG and as an LBG with Lyα emission (f_LBG and f_LBGα, respectively). As described in Section 4.2, we compute the fractions of lifetime for our best-fitting models (see Table 1) and show the fractions for the f_esc = 0.5, |$\langle \chi _{\rm H\,\small {I}} \rangle$| ≃ 0.01 and f_α/f_c best-fitting case in Fig. A1. We note that the fractions f_LBGα of all other best-fitting cases are nearly identical to the shown one. Compared to the fractions derived for a time span of 100 Myr, the fractions of the total lifetime decrease for all UV luminosities. Galaxies that have been identified as LBGs or LBGs with Lyα emission within 100 Myr prior to z = 6.6 have been fainter at earlier times where they have not met the selection criteria. The decrease in f_LBG and f_LBGα illustrates the growth of stellar mass in galaxies with time and the existence of a critical stellar mass above which a galaxy produces enough luminosity to be identified as an LBG or as an LBG with Lyα emission. However, we like to note that the point in time when the first star forms depends on the resolution of the simulation, making our fractions of lifetime resolution-dependent but showing their trends as the time span is increased.

Figure A1.

Fraction of lifetime that galaxies spend as LBGs (f_LBG, circles) or as LBGs and LAEs (f_LBGα, squares) as a function of the UV luminosity for our best-fitting models. The mean stellar mass in each M_UV bin is encoded in the shown colour scale. This panel shows the best-fitting case for f_esc = 0.05, |$\langle \chi _{\rm H\,\small {I}} \rangle$| =10⁻⁴ and f_α/f_c = 0.60. We omit to show the other best-fitting cases, since they are nearly identical to the shown one. For each best-fitting model, we assume individual f_c values for each galaxy according to its final dust mass at z ≃ 6.6; the Lyα transmission T_α of each galaxy was obtained from the respective ionization field and the ratio of the escape fractions of Lyα and UV continuum photons was set according to Table 1. The fractions are computed as the mean of the galaxies within M_UV bins k ranging from k − 0.25 to k + 0.25 for k = −25,...,−18 in steps of 0.5. Error bars show the standard deviations of the mean values.

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