In this Section, we summarise various sets of observational data which shape our current understanding of reionization (for a detailed review on recent developments, see ). These observational probes can be broadly divided into two types: the first set probes the extent and nature of the reionization through observations of the IGM while the second is mostly concerned with direct observations of the sources responsible for reionization.
2.1. Observations related to the state of the IGM
As far as the IGM is concerned, the observational constraints on its ionization and thermal state can be divided broadly into three classes, which are discussed in the next three subsections.
2.1.1. QSO absorption lines
We have discussed in the previous Section that the primary evidence for the IGM to be ionized at z < 6 comes from the measurements of GP optical depth in the spectra of QSOs. Under the assumptions of photoionization equilibrium and a power-law relation between temperature and density, the Ly optical depth GP arising from a region of overdensity at a redshift z can be written as
where Y denotes the helium mass fraction, and HI is the neutral hydrogen fraction (defined as the ratio between neutral hydrogen density and total hydrogen density) at the mean density = 1. The exponent of is determined by the photoionization equilibrium and is given by = 2.7 - 0.7 , where is the slope of the pressure-density relation. For a isothermal medium = 1 and hence GP 2. All other symbols in the above expression have standard meanings. This expression clearly shows that for a uniform medium ( = 1) at z 6, the presence of a neutral hydrogen fraction HI 10-5 would produce an optical depth of the order unity and hence would show clear GP absorption trough in the spectra. Since such absorption is not observed for QSOs at z < 6, the constraint on the average neutral fraction is HI < 10-5, which is a robust indication of the fact that the universe is highly ionized at z < 6.
The observational situation changes for the observed QSOs at z > 6. The ongoing Sloan Digital Sky Survey (SDSS) 1 has discovered quite a few QSOs at z 6, the spectra of which are markedly different from their low-redshift counterparts. Very long absorption troughs, which are of the size ~ 80-100 comoving Mpc, have been seen along tens of lines of sight at z > 6 [83, 84, 85, 86, 87, 88]. This implies that the GP optical depth at z 6 is larger than a few. Unfortunately, such a constraint does not necessarily imply that the universe is neutral at such redshifts. For example, a neutral hydrogen fraction HI ~ 10-3 would produce an optical depth GP ~ 100, more than what is required to produce the absorption troughs. This is the typical level of constraint one can obtain through such model-independent simplistic arguments based on an uniform medium. Such arguments, though quite effective in giving robust conclusions at low redshifts, do not yield any strong constraint on the neutral hydrogen fraction at z 6.
The next line of argument for the approach to the final stages of reionization at z 6 is based on the change in the slope of the optical depth [86, 89, 88] around z ~ 5.5 - 6, which indicates that some qualitative change in the physics of IGM occurs at these redshifts. To understand this in simple terms, let us write the neutral hydrogen fraction HI in terms of more physically meaningful quantities:
where T0 is the temperature of the medium at the mean density ( = 1) and PI is the photoionization rate of neutral hydrogen (assumed to be homogeneous). Combining the above equation with (1), one can see that GP(z) (1 + z)1.5 T0-0.7 (z) / PI(z). Thus when T0 and PI are not changing substantially with redshift, we expect GP(z) (1 + z) with 4.5. This is indeed seen in the observations at z< 5.5 . However, at higher redshifts, the observations show that GP evolves much faster combined with a rapid deviation from a power-law evolution, thus implying that the properties of IGM (like T0 and PI) are evolving considerably. This argument points towards a possible phase change in the IGM and thus suggesting that we are approaching the final stages of reionization at z 6. However, one should keep in mind that this argument does not conclusively prove that the IGM is neutral at z 6 - it simply indicates for a rapid change in properties. Furthermore, the above defined GP is not a directly measured quantity; one instead measures the mean transmitted flux which is computed by integrating the optical depth over all possible overdensities:
The quantity P() denotes the density distribution of the IGM. It is thus clear from the above expression that any robust conclusion based on the observed evolution of would require a good knowledge of P().
Hence, the next step for calculating the ionization properties of the IGM from QSO spectra is to include the density inhomogeneities in the analysis. From this point on, the conclusions become extremely model-dependent as we do not have a clear understanding of the density distribution of the IGM. One approach would be to use numerical simulations for obtaining the IGM density distribution and then compute the absorption spectra of high-redshift quasars in the Ly region . Using this approach, a rapid evolution of the volume-averaged neutral fraction of hydrogen has been found at z 6 (HI ~ 10-5 at z = 3 to HI ~ 10-3 at z = 6). On the other hand, a different set of analyses [91, 92] from nearly similar data set conclude that the transmitted fractions have a relatively smooth evolution over the entire range of redshifts, which can be modeled with a smoothly decreasing ionization rate; hence no evidence of a rapid transition could be established.
In addition to the global statistics discussed above, there are some results based on the transmission observed in the spectra of individual sources. For example, the analyses of the spectrum of the most distant known quasar (SDSS J1148+5251) at an emission redshift of 6.37 show some residual flux both in the Ly and Ly troughs, which when combined with Ly region , imply that this flux is consistent with pure transmission. The presence of unabsorbed regions in the spectrum corresponds to a highly ionized IGM along that particular line of sight. However, a complete GP trough was detected in the spectrum of SDSS J1030+0524 (z = 6.28) , where no transmitted flux is detected over a large region (300 Å) immediately blueward of the Ly emission line. Such differences in the ionization state of the IGM along different lines of sight have been interpreted as a possible signature of the pre-overlap phase of reionization.
There have been other different approaches to investigate the neutral hydrogen fraction. For example, one can estimate the sizes of the ionized regions around the QSOs from the spectra [94, 95]. Then the neutral gas surrounding the QSO can be modelled as a function of different parameters: the Strömgren sphere size RS, the production rate of ionizing photons ph from the QSO, the clumping factor of the gas C and the age of the QSO tage. Considering 7 QSOs at z 6 (which included the above cited QSOs), it has been argued that the small sizes of the ionized regions (~ 10 physical Mpc) imply that the typical neutral hydrogen fraction of the IGM beyond z ~ 6 is in the range 0.1 - 1. However, this approach is weighted down by several uncertainties. For example, one of the uncertainties is the quasar's production rate of ionizing photons ph as it depends on the shape of the spectral template used. Moreover it is implicitly assumed in the modelling of clumping factor that the formation of quasars and galaxies were simultaneous. This in turn implies that quasars ionize only low density regions and hence the clumping factor, which regulates the evolution of the ionized regions, is low. If, instead, stars appears much earlier than QSOs, the quasars have to ionize high density regions, which means that one should use a higher value of clumping factor in the calculations .
There has been a different approach based on the damping wings of the neutral hydrogen . Using density and velocity fields obtained by hydrodynamical simulation, the Ly absorption spectrum was computed. In this case the neutral hydrogen fraction, ph and RS are treated as free parameters, constrained by matching the optical depth observed in the QSO SDSS J1030+0524. Also in this case, the conclusion is that the neutral hydrogen fraction is larger than 10 per cent, i.e., the IGM is significantly more neutral at z ~ 6 than the lower limit directly obtainable from the GP trough of the QSO spectrum (HI 10-3). However this result is based only on one quasar. Moreover, the observational constraints on the optical depth are very uncertain and can introduce errors in the estimates of HI.
To summarise the QSO absorption line observations - there is still no robust and model-independent constraint on the neutral hydrogen fraction from the data. The spectroscopy of the Ly forest for QSOs at z 6 discovered by the SDSS [84, 87] strongly suggest that the IGM is highly ionized along some lines of sight. On the other hand, there are a few (maybe a couple) lines of sight which seems to indicate that the IGM is neutral, though the conclusion is still not robust. In case we find transmission along some lines of sight while the medium seems quite neutral along others could possibly be interpreted that the IGM ionization properties are different along different lines of sight at z 6, thus suggesting that we might be observing the end of the reionization process. However, it is also possible that such dispersion in the IGM properties along different lines of sight can be accommodated by simply the dispersion in the density inhomogeneities. As discoveries of more such objects are expected in future, spectroscopy of high-redshift QSOs remains one of the principal empirical approaches to understand the final stages of reionization.
Before completing our discussion on the QSO absorption lines, it is worth mentioning a set of indirect constraints on reionization based on the temperature of the IGM at z 2 - 4. 2 Using various techniques like, the lower envelope of the neutral hydrogen column density and velocity width scatter plot [98, 99] or wavelet transforms , one can infer the temperature of the IGM from absorption lines. These analyses suggest that T0 ~ 1-2 × 104 K at z 3, which in turn imply that hydrogen reionization must occur at z < 9 or else the temperature would be too low to match the observations. However, one should keep in mind that the analyses has large uncertainties, like, for example, the dust photoheating of the IGM could give rise to high temperatures at z 3 [101, 102, 103, 104]. Furthermore, a complex ionization history of helium could relax considerably the constraints obtained from T0 on the reionization epoch.
2.1.2. Cosmic microwave background radiation
The second most important analysis regarding the reionization history comes from the observations of temperature and polarization anisotropies in the cosmic microwave background (CMB) radiation. As far as the temperature anisotropies are concerned, reionization can damp the fluctuations on small scales due to photon diffusion in the ionized plasma. The scattering of photons suppresses the anisotropies on angular scales below the horizon at the rescattering epoch by a damping factor e-el, where
is the optical depth (measured at the present epoch) of CMB photons due to Thomson scattering with free electrons. In the above expression, ne is the average value of the comoving electron density and T is the Thomson scattering cross section. However, measuring this damping is not easy as it can be compensated by a larger strength of dark matter density fluctuations which are measured by the corresponding power spectrum, usually parametrised by the two quantities: the primordial spectral index ns and the fluctuation amplitude at cluster scales 8. Hence, it is found that el is only mildly constrained by the temperature fluctuations because of strong degeneracies with ns and 8 . For this reason, temperature anisotropy data prior to Wilkinson Microwave Anisotropy Probe (WMAP) 3 could only constrain el 0.5 . For sudden reionization models, this only implies that the redshift of reionization zre 40. To put in perspective with the discussion of QSO absorption line observations, reionization at z ~ 6 would imply el ~ 0.05.
A major breakthrough in our understanding of reionization came after the release of first year WMAP results of polarization measurements. A fundamental prediction of the gravitational instability paradigm is that CMB anisotropies are polarized, i.e., if the temperature anisotropies are produced by primordial fluctuations, their presence at the last scattering surface would polarize the CMB. The generation of polarization requires two conditions to be satisfied: (i) photons need to undergo Thomson scattering off free electrons (the corresponding cross section is polarization-dependent) and (ii) the angular distribution of the photon temperature must have a non zero quadrupole moment. Tight coupling between photons and electrons prior to recombination makes the photon temperature almost isotropic and the generated quadrupole anisotropy, and hence the polarization, is very small. Because the temperature anisotropies are of the order 10-5, the polarization is about 10-6 or less.
To generate a quadrupole, it is necessary to produce velocity gradients in the photon-baryon fluid across the photon mean free path; hence only those perturbations which have length scales smaller than the mean free path can produce polarization. At larger scales, multiple scattering will make the plasma quite homogeneous and thus no significant quadrupole can be generated, while at much lower scales polarization is suppressed due to "Silk damping". In fact, the polarization generated at the last scattering surface would be significant at scales comparable to the horizon size at that epoch (which corresponds to a multipole number ~ 100), and no polarization signal is expected at larger scales < 100. Detection of polarization signal at < 100 is a clear signature of secondary processes such as reionization.
Following the completion of recombination the quadrupole moment of temperature anisotropies grows due to the photons free streaming. In case these photons are able to scatter off free electrons at a later stage, the anisotropy can be transformed into substantial polarization. This is an ideal effect to probe reionization as it is the only process which can provide considerable number of free electrons at post-recombination epochs. For models with sudden reionization, it can be shown that the effect dominates on the angular scale of the horizon at the epoch of reionization. The polarization signal will peak at a position zre1/2 with an amplitude proportional to the total optical depth el. Thus the polarization spectrum at low is a sensitive probe of the reionization process.
The polarization measurements by the WMAP satellite  found a significant signal in the temperature-polarization cross correlation spectrum at < 10. The position and the amplitude of this excess is consistent with an optical depth el = 0.17 ± 0.04, implying a (sudden) reionization redshift 11 < zre < 30. While this result has possibly complicated the picture of reionization and thus generated tremendous amount of activity within the community, a few subtleties should be kept in mind while using the reionization constraints: (i) The result is based on a few points at low and it is necessary that such an important result is confirmed by future data. One should also note that the likelihood function for el obtained from WMAP data is heavily skewed, probably indicating some sort of a "tension" within the data. (ii) The constraints on el depend on the priors and analysis technique used. For example, fitting the temperature - E-mode polarization cross power spectrum (TE) to CDM models in which all parameters except el assume their best fit values based on the temperature power spectrum (TT), the 68% confidence range obtained is 0.13 < el < 0.21 . Fitting all parameters simultaneously to the TT and the TE data, the corresponding range changes to obtain 0095 < el < 0.24 . Including additional data external to WMAP, these authors were able to shrink their confidence interval to 0.11 < el < 0.23. Finally, by assuming that the observed TT power spectrum is scattered to produce the observed TE cross-power spectrum, the inferred range is 0.12 < el < 0.20 . (iii) The constraints of 0.17 and zre 15 usually quoted in the literature assume a sudden reionization. The constraints can change drastically when this assumption is relaxed.
In case the result is confirmed by future data sets, we note that it is not necessarily contradictory to the QSO results; the history of the luminous sources and their effect on the IGM was probably highly complex, and there was a finite time interval (maybe somewhere around a few hundred million years) from the appearance of the first sources of UV photons and the completion of the reionization.
2.1.3. Ly emitters at high redshifts
In parallel, a number of groups have studied star-forming galaxies at z ~ 6 - 7, and measurements of the Ly emission line luminosity function evolution provide another useful observational constraint [109, 110]. While the QSO absorption spectra probe the neutral hydrogen fraction regime xHI 0.01, this method is sensitive to the range xHI ~ 0.1 - 1.0. Ly emission from galaxies is expected to be suppressed at redshifts beyond reionization because of the absorption due to neutral hydrogen, which clearly affects the evolution of the luminosity function of such Ly emitters at high redshifts [111, 109, 112]. Thus a comparison of the luminosity functions at different redshifts could be used for constraining the reionization. Through a simple analysis, it was found that the luminosity functions at z = 5.7 and z = 6.5 are statistically consistent with one another, thus implying that reionization was largely complete at z 6.5. More sophisticated calculations on the evolution of the luminosity function of Ly emitters [109, 113, 111] suggest that the neutral fraction of hydrogen at z = 6.5 should be less than 50 per cent .
The analysis of the Ly emitters at high redshifts is complicated by various factors. (i) Firstly, this suppression of the Ly emission line depends on the size of the ionized region surrounding the source as larger ionized volumes allow more photons to escape. On the other hand, the sizes of the ionized regions themselves depend on the clustering properties of the sources. There is thus a strong coupling between the clustering of the sources, sizes of the ionized regions and the luminosity function of the Ly emitters at high redshifts. (ii) The ionized hydrogen regions are typically highly asymmetric because the the ionization-fronts propagate much faster across underdense voids then across dense filaments. Thus one needs to know the details of the density distribution around the sources to model the ionized regions. (iii) It is well known that bright galaxies are biased, so it is likely that more than one galaxy is located inside a single ionized region; Ly-emitters can also be located inside ionized regions of luminous quasars, which are often many times larger than the ionized regions of galaxies. It is thus clear that the modelling of the ionized regions of Ly-emitters is not straightforward, and hence the reionization constraints could be severely model-dependent.
2.2. Observations related to the sources of reionization
As we discussed in the Introduction, a major challenge in our understanding of reionization depends on our knowledge of the sources, particularly at high redshifts. In this sense, reionization is closely related to formation of early baryonic structures and thus any observation related to the detection of very distant sources can be important for constraining reionization. In the following, we shall discuss a few most important of such observational probes.
2.2.1. Direct observations of sources at high redshifts
As we understand at present, neither the bright z 6 QSOs discovered by the SDSS group  nor the faint AGN detected in X-ray observations  produce enough photons to reionize the IGM. The discovery of star-forming galaxies at z > 6.5 [117, 118, 119] has resulted in speculation that early galaxies produce bulk of the ionizing photons for reionization. However, the spectroscopic studies of I-band dropouts in the Hubble ultra-deep Field with confirmed redshifts at z 6, indicate that the measured star formation rate at z = 6 is lower by factor of 6 from the z = 3 star formation rate. If the estimate is correct, the I-dropouts do not emit enough ionizing photons to reionize the universe at z 6 . The short-fall in ionizing photons might be alleviated by a steep faint-end slope of the luminosity function of galaxies or a different stellar initial mass function (IMF); alternatively, the bulk of reionization might have occurred at z 6 through rapid star formation in galaxies at much higher redshifts.
There are estimates of a somewhat higher UV luminosity at z = 6 - 10. This is obtained by constructing a luminosity function from ~ 500 galaxies collected from all the deepest wide-area HST data . The luminosity function thus obtained extends 3 magnitudes fainter than the characteristic luminosity L*. This analysis predicts a significant evolution in L* - a doubling from z = 3 to z = 6, thus implying a luminosity density that is only a factor of 1.5 less than the luminosity density at z = 3. The observed evolution is suggestive of that expected from popular hierarchical models, and would seem to indicate that we are literally witnessing the buildup of galaxies in the reionization era.
To summarise, there are somewhat conflicting reports regarding the star formation rate at z 6 - however, it is safe to conclude that we have not yet observed enough number of sources which could ionize the bulk of the IGM at z 6. Whether the reionization was actually completed by galaxies at a much higher redshifts is still an open issue.
2.2.2. Cosmic infrared background radiation
Numerous arguments favour an excess contribution to the extragalactic background light between 1 µm and a few µm [122, 123, 124, 125] when compared to the expectation based on galaxy counts and Milky Way faint star counts (for a review see ). While these measurements are likely to be affected by certain systematics and issues related to the exact contribution from zodiacal light within the Solar System, one explanation is that a contribution to the cosmic infrared background (CIRB) radiation originates from high redshift sources. The redshifted line emission from Ly emitting galaxies at z > 9 would produce an integrated background in the near-infrared wavelengths observed today. In case this interpretation of the CIRB is correct, it would directly constrain the number of ionizing sources at high redshifts and thus would have direct implications on reionization.
However, if the entire CIRB is due to the high redshift galaxies, the explanation requires the presence of metal-free PopIII stars with a top-heavy IMF and possibly a high star-forming efficiency [127, 128, 129, 130, 131]. In fact, the number of sources required to explain the CIRB is much higher than that needed to explain the early reionization constraints. The most serious difficulty in explaining the CIRB through PopIII stars comes from the observations of the number of J-dropouts and Ly emitters in ultra deep field searches as the models severely overpredict the number of sources . At present, the origin of CIRB remains to be puzzling (as one can discard other possible sources like miniquasars and decaying neutrinos, see the next subsection), and it is not clear whether it could have any significant implications on reionization.
We end this section by briefly reviewing the constraints we have on other kind of sources, namely the Intermediate Mass Black Holes and decaying (exotic) particles.
A large population of intermediate mass black holes (IMBHs) might be produced at early cosmic times as a left over of the evolution of very massive first stars. These black holes at high redshifts (z 6) can, in principle, contribute to the ionization of the IGM; however they would be accompanied by the copious production of hard X-ray photons (with energies above 10 keV). The resulting hard X-ray background would redshift and be observed as a present-day soft X-ray background. One can show that the observed residual soft X-ray background intensity can put stringent constraints on the the baryon mass fraction locked into IMBHs and their growth [133, 134]. Thus, unless they are extremely X-ray quiet, these black holes, or miniquasars, must be quite rare and/or have a short shining phase. As a byproduct, it implies that miniquasars cannot be the only source of reionization.
The other sources which are popularly invoked to explain reionization are the exotic particles like decaying neutrinos [74, 75, 76, 77, 78, 79]. However, in most cases these particles decay radiatively (producing photons) and hence are severely constrained by Big Bang Nucleosynthesis, diffuse soft X-ray and gamma-ray backgrounds and the deviation of the CMB spectrum from Planckian shape. For example, the constraints from soft X-ray background limits the radiatively decaying sterile neutrino mass to m < 14 keV and hence the optical depth to Thomson scattering is el ~ 10-2, negligible compared to what is required for explaining observations . Similar constraints exist for other particles, including those which have decay channels into electrons instead of photons . The point what comes out from most these analyses is that different observational constraints leave out a very small parameter space accessible to the decaying particles and hence their contribution to reionization may not be that significant.
1 http://www.sdss.org/ Back
2 This determination of temperature puts constraints on the reionization of helium too; however, the helium reionization is beyond the scope of this review. Back
3 http://map.gsfc.nasa.gov/ Back