Measurements of the HI 21-cm power spectra from the reionization epoch will be influenced by the evolution of the signal along the line-of-sight direction of any observed volume. We use numerical as well as semi-numerical simulations of reionization
in a cubic volume of 607 Mpc across to study this so-called light cone effect on the HI 21-cm power spectrum. We find that the light cone effect has the largest impact at two different stages of reionization: one when reionization is $sim 20%$ and other when it is $sim 80%$ completed. We find a factor of $sim 4$ amplification of the power spectrum at the largest scale available in our simulations. We do not find any significant anisotropy in the 21-cm power spectrum due to the light cone effect. We argue that for the power spectrum to become anisotropic, the light cone effect would have to make the ionized bubbles significantly elongated or compressed along the line-of-sight, which would require extreme reionization scenarios. We also calculate the two-point correlation functions parallel and perpendicular to the line-of-sight and find them to differ. Finally, we calculate an optimum frequency bandwidth below which the light cone effect can be neglected when extracting power spectra from observations. We find that if one is willing to accept a $10 %$ error due to the light cone effect, the optimum frequency bandwidth for $k= 0.056 , rm{Mpc}^{-1}$ is $sim 7.5$ MHz. For $k = 0.15$ and $0.41 , rm{Mpc}^{-1}$ the optimum bandwidth is $sim 11$ and $sim 16$ MHz respectively.
Observations of redshifted 21-cm radiation from neutral hydrogen during the epoch of reionization (EoR) are considered to constitute the most promising tool to probe that epoch. One of the major goals of the first generation of low frequency radio te
lescopes is to measure the 3D 21-cm power spectrum. However, the 21-cm signal could evolve substantially along the line of sight (LOS) direction of an observed 3D volume, since the received signal from different planes transverse to the LOS originated from different look-back times and could therefore be statistically different. Using numerical simulations we investigate this so-called light cone effect on the spherically averaged 3D 21-cm power spectrum. For this version of the power spectrum, we find that the effect mostly `averages out and observe a smaller change in the power spectrum compared to the amount of evolution in the mean 21-cm signal and its rms variations along the LOS direction. Nevertheless, changes up to 50% at large scales are possible. In general the power is enhanced/suppressed at large/small scales when the effect is included. The cross-over mode below/above which the power is enhanced/suppressed moves toward larger scales as reionization proceeds. When considering the 3D power spectrum we find it to be anisotropic at the late stages of reionization and on large scales. The effect is dominated by the evolution of the ionized fraction of hydrogen during reionization and including peculiar velocities hardly changes these conclusions. We present simple analytical models which explain qualitatively all the features we see in the simulations.
The epoch of reionization is one of the least known chapters in the evolutionary history of the Universe. This thesis investigates two major approaches to unveil the reionization history of the Universe using HI 21-cm maps.The most discussed approach
has been to study the global statistical properties of the reionization HI 21-cm. We develop the formalism to calculate the Multi-frequency Angular Power Spectrum (MAPS) and quantify the statistics of the HI signal as a joint function of the angular multipole l and frequency separation Delta u. We adopt a simple model for the HI distribution which incorporates patchy reionization and use it to study the signatures of ionized bubbles on MAPS. We also study the implications of the foreground subtraction. A major part of the thesis investigates the possibility of detecting ionized bubbles around individual sources in 21-cm maps. We present a visibility based matched filter technique to optimally combine the signal from an ionized bubble and minimize the noise and foreground contributions. The formalism makes definite predictions on the ability to detect an ionized bubble or conclusively rule out its presence within a radio map. Results are presented for the GMRT and the MWA. Using simulated HI maps we analyzed the impact of HI fluctuations outside the bubble on its detectability. Various other issues such as (i) bubble size determination (ii) blind search for bubbles, (iii) optimum redshift for bubble detection are also discussed.
Extending the formalism of Datta, Bharadwaj & Choudhury (2007) for detecting ionized bubbles in redshifted 21 cm maps using a matched-filtering technique, we use different simulations to analyze the impact of HI fluctuations outside the bubble on the
detectability of the bubble. In the first three kinds of simulations there is a spherical bubble of comoving radius R_b, the one that we are trying to detect, located at the center, and the neutral hydrogen (HI) outside the bubble traces the underlying dark matter distribution. We consider three different possible scenarios of reionization, i.e., (i) there is a single bubble (SB) in the field of view (FoV) and the hydrogen neutral fraction is constant outside this bubble (ii) patchy reionization with many small ionized bubbles in the FoV (PR1) and (iii) many spherical ionized bubbles of the same radius $R_b$ (PR2). The fourth kind of simulation uses more realistic maps based on semi-numeric modelling (SM) of ionized regions. We find that for both the SB and PR1 scenarios the fluctuating IGM restricts bubble detection to size R_b<= 6 Mpc and R_b<= 12 Mpc for the GMRT and the MWA respectively, however large be the integration time. These results are well explained by analytical predictions. Large uncertainty due to the HI fluctuations restricts bubble detection in the PR2 scenario for neutral fraction x_HI<0.6. The matched-filter technique works well even when the targeted ionized bubble is non-spherical due to surrounding bubbles and inhomogeneous recombination (SM). We find that determining the size and positions of the bubbles is not limited by the HI fluctuations in the SB and PR1 scenario but limited by the instruments angular resolution instead, and this can be done more precisely for larger bubble (abridged).
