Redshift wavelength

Figure 4.7. A schematic representation of a star-forming galaxy situated beyond the reionization redshift (here indicated at zr ~ 6.5), its surrounding cosmological HII region, the neutral IGM down to zr and the transparent (ionized) IGM towards observer. Redshift and observed Lya wavelength increase to the right.

galactic Lya profile plus a reduction of the Lya flux if neutral H is present close in velocity/redshift space to the source. The first is well known observationally as the Lya forest, leading even to complete absorption (the so-called Gunn-Peterson trough) in distant (z ~ 6) quasars; see the review by Fan et al. (2006). The appearance of a complete Gunn-Peterson trough in high-z quasars implies a quantitative change of the ionization of the IGM, possibly tracing the end of the epoch of cosmic reionization (Fan et al. 2006). The second effect leads e.g. to the alteration of the Lya profile and to a strong reduction of the Lya flux in high-z quasars, due to absorption by the red damping wing of Lya by nearby HI (Miralda-Escude 1998; Fan et al. 2003).

The two effects just discussed have the following immediate implications.

• The SED of high-z galaxies is altered by Lyman-forest attenuation at wavelengths shorter than Lya (<1216 A). A statistical description of this attenuation is given by Madau (1995).

• For z > 4-5 the Lyman forest attenuation is so strong that it effectively leads to a spectral break at Lya, replacing therefore the "classical" Lyman break (at 912 A) due to photoelectric absorption by H I. The Lya break becomes then the determining feature for photometric redshift estimates.

• The reduction of the Lya flux implies that (a) determinations of the SFR from this line will underestimate the true SFR, (b) the observed Lya-luminosity function (LF) does not correspond to the true (intrinsic) one, and (c) the detectability of high-z Lya emitters (hereafter LAEs) is reduced.

• The Lya profile, Lya transmission and Lya LF contain information on the ionization fraction of hydrogen and can hence in principle constrain cosmic reionization.

We will now discuss how/whether it is still possible to observe LAEs beyond the reionization redshift.

How is it possible to observe Lya emission from sources "beyond the end of reionization", i.e. at very high redshift where the IGM contains a significant fraction of neutral hydrogen, which absorbs the Lya emission? The way to achieve this is in principle quite simple and sketched in Figure 4.7. It suffices to create around the Lya source a "cosmological" H II region big enough that no or very little H I is present at velocities - i.e. redshifts -close to the source. In this way attenuation close to the Lya emission is avoided and the line flux from this distant source can propagate freely to the observer, since it comes from the most-redshifted part along the line of sight.

So, how are these cosmological H II regions created? Obviously this requires one or several sources (galaxies or quasars) producing ionizing photons that are able to escape

4.3.7 Lya from sources prior to reionization

Figure 4.8. Predicted Lya line profile, Lya transmission and other properties from the model of a ^ = 6.56 lensed galaxy taking IGM absorption into account. Adapted from Haiman (2002). Left: intrinsic and resulting line profiles (top), opacities leading to the Lya attenuation. Right: parameters, such as asymmetry, peak position and total transmission (bottom right) of the predicted Lya line as a function of the SFR.

Figure 4.8. Predicted Lya line profile, Lya transmission and other properties from the model of a ^ = 6.56 lensed galaxy taking IGM absorption into account. Adapted from Haiman (2002). Left: intrinsic and resulting line profiles (top), opacities leading to the Lya attenuation. Right: parameters, such as asymmetry, peak position and total transmission (bottom right) of the predicted Lya line as a function of the SFR.

the galaxy and can then progressively ionize the surrounding IGM. This is referred to as the "proximity effect". The properties and the evolution of cosmological HII regions have been studied and described analytically in several papers; see e.g. Shapiro & Giroux (1987), Cen & Haiman (2000), and the review by Barkana & Loeb (2001). For example, neglecting recombinations in the IGM (since for the low IGM densities the recombination timescale is much longer than the Hubble time) and assuming that the ionizing source is "turned on" and constant during the time tQ the Stromgren radius (size) of the HII region becomes

where Nph = fescQH is the escaping ionizing flux and (nH) the mean IGM density, taking possibly a non-uniform density distribution into account. The residual HI fraction inside the HII region is given by photoionization equilibrium and can also be computed. Then the resulting attenuation e~T can be computed by integrating the optical depth along the line of sight:

T(Aobs,zs) = J dz c — nH(z)aa(Aobs/(1 + z)). (4.3)

Here zs is the source redshift, zr a limiting redshift (the redshift of reionization in Figure 4.7) below which the IGM is supposed to be transparent and aa the Lya absorption cross section.

For example, the observability of Lya from a z = 6.56 galaxy observed by Hu et al. (2002) has been examined with such a model by Haiman (2002). The results are illustrated in Figure 4.8. For a source with SFR 9M0 yr_1, an age of ~100Myr and an escape fraction fesc = 25% the proper (comoving) radius of the HII region is approximately 0.45(3) Mpc. Assuming an intrinsic Lya profile of FWHM width 300kms-1 Haiman obtains a transmission of ^16% of the Lya flux and an asymmetrical line profile, as observed. A wider range of transmission encompassing also this value is found from an independent estimate based on stellar-population modelling (Schaerer & Pello 2005).

In the picture described above, the Lya transmission is expected to increase with increasing SFR, escape fraction, source lifetime and intrinsic line width, as also shown in Figure 4.8 (right). The first three increase the size of the cosmological HII region; with the latter a higher fraction of the line flux is emitted far from line centre, thus reducing the absorption by the red damping wing in the H I. Other factors also affect the Lya transmission and the resulting line profile: IGM infall, outflows (galactic winds), peculiar velocities of the emitting gas within halo, the halo mass etc.; see Haiman (2002) and Santos (2004).

In a more-realistic setting, this simple model can be subject to several "complications" (e.g. Gnedin & Prada 2004; Furlanetto et al. 2004; Wyithe & Loeb 2004).

• Clustering of sources helps to create a larger HII region. Since the probability of clustering increases with z and for fainter galaxies, this could play an important role in determining the detectability of high-redshift Lya sources.

• In a non-homogeneous structure around the source the HII regions are expected to deviate from spherical symmetry, since the ionization fronts will propagate more rapidly into directions with lower IGM density.

From this it is clear that strong variations depending on the object, its surroundings and the viewing direction are expected and the simple scaling properties of the spherical models described before might not apply. A statistical approach using hydrodynamic simulations will be needed.

In short, the answer to the question "Is Lya emission from sources prior to reioniza-tion detectable?" is affirmative from the theoretical point of view, but the transmission depends on many factors! In any case, searches for such objects are going on (Section 4.4.2) and will provide the definitive answer.

4.3.8 The Lya luminosity function and reionization As a last illustration of the use of Lya in distant, primeval galaxies, we shall now briefly discuss the statistics of LAEs, in particular the Lya luminosity function LF(Lya), how it may be used to infer the ionization fraction of the IGM at various redshifts, and difficulties affecting such approaches.

Since, as discussed above, the presence of neutral hydrogen in the IGM can reduce the Lya flux of galaxies, it is clear that the Lya LF is sensitive to the ionization fraction xH I. If we knew the intrinsic LF(z) of galaxies at each redshift, a deviation of the observed LF from this intrinsic distribution could be attributed to attenuation by H I, and hence be used to infer xH I (see Figure 4.9). In practice the approach is of course to proceed to a differential comparison of LF(Lya) with redshift. Indeed, from simple Lya-attenuation models like the ones described in the previous section, a rapid decline of the LF is expected on approaching the end of reionization.

Haiman & Spaans (1999) were among the first to advocate the use of LF(Lya) and to make model predictions. Since then, and after the detection of numerous LAEs allowing the measurement of the Lya LF out to redshift z = 6.5 (see Section 4.4.2), several groups have made new predictions of the Lya LF and have used it to constrain cosmic reionization. Some prominent examples are Malhotra & Rhoads (2004), Le Delliou et al. (2005, 2006) and Furlanetto et al. (2006).

One of the most recent of such attempts is presented by Dijkstra et al. (2006c), who predict the Lya LF using a modified Press-Schechter formalism and introducing two main free parameters, a SF duty-cycle eDc and another parameter depending on the SF efficiency, the escape fraction and the Lya transmission of the IGM. They find a typical

<*HI>=0 <*„,>= 0.1 <*„,>= 1.0

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