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In the final Section, we review certain observations which will shape our understanding of reionization in near future, and also discuss the theoretical predictions concerning future data sets.

The spectroscopic studies of QSOs at z gtapprox 6 hold promising prospects for determining the neutrality of the IGM. As we have discussed in Section 2, regions with high transmission in the Lyalpha forest become rare at high redshifts. Therefore the standard methods of analyzing the Lyalpha forest (like the probability distribution function and power spectrum) are not very effective. An alternative method to analyze the statistical properties of the transmitted flux is the distribution of dark gaps [160, 91], defined as contiguous regions of the spectrum having an optical depth above a threshold value (say 2.5 [91] or 3.5 [90]). The frequency and the width of the gaps are expected to increase with redshift, which is verified in different analyses of observational data [91, 90]. However, it is more interesting to check whether the dark gap width distribution (DGWD) is at all sensitive to the reionization history of the IGM, and whether one can constrain reionization through DGWD. This is indeed possible as it is found by semi-analytical models and simulations of Lyalpha forest at z gtapprox 6 [161]. In particular, about 30 per cent of the lines of sight (accounting for statistical and systematic uncertainties) in the range z = 5.7 - 6.3 are expected to have dark gaps of widths larger than 60 Å (in the QSO rest frame) if the IGM is in the pre-overlap stage at z gtapprox 6, while no lines of sight should have such large gaps if the IGM is already ionized. The constraints become more stringent at higher redshifts. Furthermore, 10 lines of sight should be sufficient for the DGWD to give statistically robust results and discriminate between early and late reionization scenarios. It is expected that the SDSS and Palomar-Quest survey [162] would detect ~ 30 QSOs at these redshifts within the next few years and hence we expect robust conclusions from DGWD in very near future.

As we have discussed already, the first evidence for an early reionization epoch came from the CMB polarization data. This data is going to be much more precise in future with experiments like PLANCK, 6 and is expected to improve the constraints on tauel. With improved statistical errors, it might be possible to distinguish between different evolutions of the ionized fraction, particularly with E-mode polarization auto-correlation, as is found from theoretical calculations [163]. An alternative option to probe reionization through CMB is through the small scale observations of temperature anisotropies. It has been well known that the scattering of the CMB photons by the bulk motion of the electrons in clusters gives rise to a signal at large ell, known as the kinetic Sunyaev-Zeldovich (SZ) effect:

Equation 13 (13)

where eta = integ dt / a is the conformal time, v is the peculiar velocity field and ne is the number density of electrons. In principle, a signal should arise from the fluctuations in the distribution of free electrons arising from cosmic reionization. Now, if the reionization is uniform, the only fluctuations in ne can arise from the baryonic density fluctuations Delta, and hence the power spectrum of temperature anisotropies Cell would be mostly determined by correlation terms like < v Delta v >. Though this can give considerable signal (an effect known as the Ostriker-Vishniac effect), particularly for the non-linear densities, it turns out that for reionization the signal is dominated by the patchiness in the ne distribution. In other words, if Deltaxe denotes the fluctuations in the ionization fraction of the IGM, the correlation term < Deltaxe v Deltaxe v > (i.e., correlations of the ionization fraction fluctuations and the large-scale bulk flow) gives the dominant contribution to the temperature anisotropies Cell. Now, in most scenarios of reionization, it is expected that the distribution of neutral hydrogen would be quite patchy in the pre-overlap era, with the ionized hydrogen mostly contained within isolated bubbles. The amplitude of this signal is significant around ell ~ 1000 and is usually comparable to or greater than the signal arising from standard kinetic SZ effect (which, as mentioned earlier, is related to the scattering of the CMB photons by the bulk motion of the electrons in clusters). Theoretical estimates of the signal have been performed for various reionization scenarios, and it has been predicted that the experiment can be used for constraining reionization history [164, 165]. Also, it is possible to have an idea about the nature of reionization sources, as the signal from UV sources, X-ray sources and decaying particles are quite different. With multi-frequency experiments like Atacama Cosmology Telescope (ACT) 7 and South Pole Telescope (SPT) 8 coming up in near future, this promises to put strong constraints on the reionization scenarios.

Another interesting prospect for constraining reionization is through high redshift energetic sources like gamma ray bursts (GRBs) and supernovae. There are different ways of using these sources for studying reionization. The first is to study the spectra of individual sources and estimate the neutral fraction of hydrogen through its damping wing effects. This is similar to what is done in the case of Lyalpha emitters as discussed in Section 2. The damping wing of the surrounding neutral medium, if strong enough, would suppress the spectrum at wavelengths redward of the Lyman break. In fact, analyses have been already performed on the GRB with highest detected redshift (zem = 6.3), and the wing shape is well-fit by a neutral fraction xHI = 0.00 ± 0.17 [166]. In order to obtain more stringent limits on reionization, it is important to increase the sample size of z gtapprox 6 GRBs. Given a reionization model, one can actually calculate the number of GRB afterglows in the pre-reionization era which would be highly absorbed by the neutral hydrogen. These GRBs would then be categorised as "dark" GRBs (i.e., GRBs without afterglows), and the redshift distribution of such objects can give us a good handle on the evolution of the neutral hydrogen in the universe [167, 168].

The second way in which GRBs could be used is to constrain the star formation history, and hence get indirect constraints on reionization. In most popular models of GRBs, it is assumed that they are related to collapse of massive stars (just like supernovae), and hence could be nice tracers of star formation. In fact, one can write the number of GRBs (or supernovae) per unit redshift range observed over a time Delta tobs as [167, 169]

Equation 14 (14)

where the factor (1 + z) is due to the time dilation between z and the present epoch, dV(z) is the comoving volume element, d Omega / 4 pi is the mean beaming factor and Phi (z) is the weight factor due to the limited sensitivity of the detector, because of which, only brightest bursts will be observed at higher redshifts. The quantity f is an efficiency factor which links the formation of stars dot{rho}SF (z) to that of GRBs (or supernovae); it corresponds to the number of GRBs (supernovae) per unit mass of forming stars, hence it depends on the fraction of mass contained in (high mass) stars which are potential progenitors of the GRBs (supernovae). Clearly, the value of f might depend on some details of GRB formation and is expected to be quite sensitive to the stellar IMF. Though such details still need to be worked out, it seems promising that data on the redshift distribution of GRBs and supernovae could give a handle on the star formation rate, which in turn could give us insights on quantities like efficiency of molecular cooling or the relative contribution of minihaloes to radiation. In general, the GRB rates at high redshifts should be able to tell us how efficient stars were in ionizing the IGM.

Perhaps the most promising prospect of detecting the fluctuations in the neutral hydrogen density during the (pre-)reionization era is through the future 21 cm emission experiments [170] like LOFAR 9. The basic principle which is central to these experiments is the neutral hydrogen hyperfine transition line at a rest wavelength of 21 cm. This line, when redshifted, is observable in radio frequencies (~ 150 MHz for z ~ 10) as a brightness temperature:

Equation 15 (15)

where TS is the spin temperature of the gas, TCMB = 2.76 (1 + z) K is the CMB temperature, A10 is the Einstein coefficient and nu0 = 1420 MHz is the rest frequency of the hyperfine line. The expression can be simplified to

Equation 16 (16)


Equation 17 (17)

The observability of this brightness temperature against the CMB background will depend on the relative values of TS and TCMB. Depending on which processes dominate at different epochs, TS will couple either to radiation (TCMB) or to matter (determined by the kinetic temperature Tk). There are four broad eras characterising the spin temperature [171, 172]: (i) At z gtapprox 30, the density of matter is high enough to make collisional coupling dominant, hence TS is coupled to Tk. However, at z gtapprox 100, the gas temperature is coupled strongly to TCMB, thus making TS appeq Tk appeq TCMB. At these epochs, the 21 cm radiation is not observable. (ii) At 30 ltapprox z ltapprox 100, the kinetic temperature falls off adiabatically and hence is lower than TCMB, while TS is still collisionally coupled to Tk. This would imply that the 21 cm radiation will be observed in absorption against CMB. (iii) Subsequently the radiative coupling would take over and make TS = TCMB, thus making the brightness temperature vanish. This continues till the sources turn up and a Lyalpha background is established. (iv) Once there is background of Lyalpha photons, that will couple TS again to Tk through the Wouthuysen-Field mechanism. From this point on, the 21 cm radiation will be observed either in emission or in absorption depending on whether Tk is higher or lower than TCMB, which turns out be highly model-dependent.

Almost in all models of reionization, the most interesting phase for observing the 21 cm radiation is 6 ltapprox z ltapprox 20. This is the phase where the IGM is suitably heated to temperatures much higher than CMB (mostly due to X-ray heating [141]) thus making it observable in emission. Furthermore, this is the era when the bubble-overlapping phase is most active, and there is substantial neutral hydrogen to generate a strong enough signal. At low redshifts, after the IGM is reionized, nHI falls by orders of magnitude and the 21 cm signal vanishes.

Most theoretical studies are concerned with studying the angular power spectrum of the brightness temperature fluctuations, which is essentially determined by the correlation terms < delta Tb delta Tb >. It is clear from equation (16) that the temperature power spectrum is directly related to the power spectrum of neutral hydrogen, i.e., < nHI nHI >. This then turns out to be a direct probe of the neutral hydrogen distribution, and potentially can track the evolution of the patchiness in the distribution over redshift. In fact, one expects a peak in the signal on angular scales corresponding to the characteristic size of the ionized bubbles. While there are some significant systematics which have to be controlled (say, for example, the foregrounds), the experiments do promise a revolution in our understanding of reionization.

There are interesting ways in which one can combine signals from different experiments too. For example, an obvious step would be to calculate the correlation between CMB signal from kinetic SZ effect and the 21 cm brightness temperatures < DeltaT deltaTb >. This will essentially be determined by the correlations < ne nHI v > [173]. It is expected, that the ionized number density ne will be highly anti-correlated with the neutral number density nHI. In fact, the simulations do show a clear signal for this anti-correlation. Depending on the angular scales of anti-correlation, one can actually re-construct the sizes of the bubbles as a function of redshift and thus compute the reionization history [174].

We hope to have convinced the reader that we are about to enter the most exciting phase in the study of reionization as new observations with LOFAR, ALMA and NGWST will soon settle the long-standing question on when and how the Universe was reionized. From the theoretical point of view, it is thereby important to develop detailed analytical and numerical models to extract the maximum information about the physical processes relevant for reionization out of the expected large and complex data sets.

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