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Register a new userAn Analytic Formulation of 21-cm Signal from Early Phase of Epoch of Reionization
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We present an analytic formulation to model the fluctuating component of the HI signal from the epoch of reionization during the phase of partial heating. During this phase, we assume self-ionized regions, whose size distribution can be computed using excursion set formalism, to be surrounded by heated regions. We model the evolution of heating profile around these regions (near zone) and their merger into the time-dependent background (far zone). We develop a formalism to compute the two-point correlation function for this topology, taking into account the heating auto-correlation and heating-ionization cross-correlation. We model the ionization and X-ray heating using four parameters: efficiency of ionization, $zeta$, number of X-ray photons per stellar baryon, $N_{rm heat}$, the spectral index of X-ray photons, $alpha$, and the minimum frequency of X-ray photons, $ u_{rm min}$. We compute the HI signal in the redshift range $10 < z < 20$ for the $Lambda$CDM model for a set of these parameters. We show that the HI signal for a range of scales $1hbox{-}8 , rm Mpc$ show a peak strength $100hbox{-}1000 , rm (mK)^2$ during the partially heated era. The redshift at which the signal makes a transition to uniformly heated universe depends on modelling parameters, e.g. if $ u_{rm min}$ is changed from $100 , rm eV$ to $1 , rm keV$, this transition moves from $z simeq 15$ to $z simeq 12$. This result, along with the dependence of the HI signal on modelling parameters, is in reasonable agreement with existing results from N-body simulations.
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The motion of the solar system with respect to the cosmic rest frame modulates the monopole of the Epoch of Reionization 21-cm signal into a dipole. This dipole has a characteristic frequency dependence that is dominated by the frequency derivative of the monopole signal. We argue that although the signal is weaker by a factor of $sim100$, there are significant benefits in measuring the dipole. Most importantly, the direction of the cosmic velocity vector is known exquisitely well from the cosmic microwave background and is not aligned with the galaxy velocity vector that modulates the foreground monopole. Moreover, an experiment designed to measure a dipole can rely on differencing patches of the sky rather than making an absolute signal measurement, which helps with some systematic effects.
Using a suite of detailed numerical simulations we estimate the level of anisotropy generated by the time evolution along the light cone of the 21cm signal from the epoch of reionization. Our simulations include the physics necessary to model the signal during both the late emission regime and the early absorption regime, namely X-ray and Lyman-band 3D radiative transfer in addition to the usual dynamics and ionizing UV transfer. The signal is analysed using correlation functions perpendicular and parallel to the line of sight (LOS). We reproduce general findings from previous theoretical studies: the overall amplitude of the correlations and the fact that the light cone anisotropy is visible only on large scales (100 cMpc). However, the detailed behaviour is different. At 3 different epochs, the amplitude of the correlations along and perpendicular to the LOS differ from each other, indicating anisotropy. These 3 epochs are associated with 3 events of the global reionization history: the overlap of ionized bubbles, the onset of mild heating by X-rays in regions around the sources, and the onset of efficient Lyman-alpha coupling in regions around the sources. A 20x20 deg^2 survey area may be necessary to mitigate sample variance when we use the directional correlation functions. On a 100 cMpc scale the light cone anisotropy dominates over the anisotropy generated by peculiar velocity gradients computed in the linear regime. By modelling instrumental noise and limited resolution, we find that the anisotropy should be easily detectable by the SKA, assuming perfect foreground removal, the limiting factor being a large enough survey size. In the case of the LOFAR, it is likely that only first anisotropy episode will fall in the observing frequency range and will be detectable only if sample variance is much reduced (i.e. a larger than 20x20 deg^2 survey, which is not presently planned).
We present an analytic formalism to compute the fluctuating component of the ion{H}{1} signal and extend it to take into account the effects of partial Lyman-$alpha$ coupling during the era of cosmic dawn. We use excursion set formalism to calculate the size distribution of randomly distributed self-ionized regions. These ionization bubbles are surrounded by partially heated and Lyman-$alpha$ coupled regions, which create spin temperature $T_S$ fluctuations. We use the ratio of number of Lyman-$alpha$ to ionizing photon ($f_L$) and number of X-ray photons emitted per stellar baryons ($N_{rm heat}$) as modeling parameters. Using our formalism, we compute the global ion{H}{1} signal, its auto-correlation and power spectrum in the redshift range $10 le z le 30$ for the $Lambda$CDM model. We check the validity of this formalism for various limits and simplified cases. Our results agree reasonably well with existing results from N-body simulations, in spite of following a different approach and requiring orders of magnitude less computation power and time. We further apply our formalism to study the fluctuating component corresponding to the recent EDGES observation that shows an unexpectedly deep absorption trough in global ion{H}{1} signal in the redshift range $15 <z< 19$. We show that, generically, the EDGES observation predicts larger signal in this redshift range but smaller signal at higher redshifts. We also explore the possibility of negative real-space auto-correlation of spin temperature and show it can be achieved for partial Lyman-$alpha$ coupling in many cases corresponding to simplified models and complete model without density perturbations.
Studying the cosmic dawn and the epoch of reionization through the redshifted 21 cm line are among the major science goals of the SKA1. Their significance lies in the fact that they are closely related to the very first stars in the universe. Interpreting the upcoming data would require detailed modelling of the relevant physical processes. In this article, we focus on the theoretical models of reionization that have been worked out by various groups working in India with the upcoming SKA in mind. These models include purely analytical and semi-numerical calculations as well as fully numerical radiative transfer simulations. The predictions of the 21 cm signal from these models would be useful in constraining the properties of the early galaxies using the SKA data.
It is predicted that sources emitting UV radiation in the Lyman band during the epoch of reionization (EoR) showed a series of discontinuities in their Ly-alpha flux radial profile as a consequence of the thickness of the Lyman line series in the primeval intergalactic medium. Through unsaturated Wouthuysen-Field coupling, these spherical discontinuities are also present in the 21 cm emission of the neutral IGM. In this article, we study the effects these discontinuities have on the differential brightness temperature of the 21 cm signal of neutral hydrogen in a realistic setting including all other sources of fluctuations. We focus on the early phases of the EoR, and we address the question of the detectability by the planned Square Kilometre Array. Such a detection would be of great interest, because these structures could provide an unambiguous diagnostic for the cosmological origin of the signal remaining after the foreground cleaning procedure. Also, they could be used as a new type of standard rulers. We determine the differential brightness temperature of the 21 cm signal in the presence of inhomogeneous Wouthuysen-Field effect using simulations which include (hydro)dynamics and both ionizing and Lyman lines 3D radiative transfer with the code LICORICE. We find that the Lyman horizons are clearly visible on the maps and radial profiles around the first sources of our simulations, but for a limited time interval, typically Delta z approx 2 at z sim 13. Stacking the profiles of the different sources of the simulation at a given redshift results in extending this interval to Delta z approx 4. When we take into account the implementation and design planned for the SKA (collecting area, sensitivity, resolution), we find that detection will be challenging. It may be possible with a 10 km diameter for the core, but will be difficult with the currently favored design of a 5 km core.
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