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Register a new userThe Difference PDF of 21-cm Fluctuations: A Powerful Statistical Tool for Probing Cosmic Reionization
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Authors
Rennan Barkana
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A new generation of radio telescopes are currently being built with the goal of tracing the cosmic distribution of atomic hydrogen at redshifts 6-15 through its 21-cm line. The observations will probe the large-scale brightness fluctuations sourced by ionization fluctuations during cosmic reionization. Since detailed maps will be difficult to extract due to noise and foreground emission, efforts have focused on a statistical detection of the 21-cm fluctuations. During cosmic reionization, these fluctuations are highly non-Gaussian and thus more information can be extracted than just the one-dimensional function that is usually considered, i.e., the correlation function. We calculate a two-dimensional function that if measured observationally would allow a more thorough investigation of the properties of the underlying ionizing sources. This function is the probability distribution function (PDF) of the difference in the 21-cm brightness temperature between two points, as a function of the separation between the points. While the standard correlation function is determined by a complicated mixture of contributions from density and ionization fluctuations, we show that the difference PDF holds the key to separately measuring the statistical properties of the ionized regions.
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The 21-cm PDF (i.e., distribution of pixel brightness temperatures) is expected to be highly non-Gaussian during reionization and to provide important information on the distribution of density and ionization. We measure the 21-cm PDF as a function of redshift in a large simulation of cosmic reionization and propose a simple empirical fit. Guided by the simulated PDF, we then carry out a maximum likelihood analysis of the ability of upcoming experiments to measure the shape of the 21-cm PDF and derive from it the cosmic reionization history. Under the strongest assumptions, we find that upcoming experiments can measure the reionization history in the mid to late stages of reionization to 1-10% accuracy. Under a more flexible approach that allows for four free parameters at each redshift, a similar accuracy requires the lower noise levels of second-generation 21-cm experiments.
Analytical approaches to galaxy formation and reionization are based on the mathematical problem of random walks with barriers. The statistics of a single random walk can be used to calculate one-point distributions ranging from the mass function of virialized halos to the distribution of ionized bubble sizes during reionization. However, an analytical calculation of two-point correlation functions or of spatially-dependent feedback processes requires the joint statistics of random walks at two different points. An accurate analytical expression for the statistics of two correlated random walks has been previously found only for the case of a constant barrier height. However, calculating bubble sizes or accurate statistics for halo formation involves more general barriers that can often be approximated as linear barriers. We generalize the two-point solution with constant barriers to linear barriers, and apply it as an illustration to calculate the correlation function of cosmological 21-cm fluctuations during reionization.
Measurement of the spatial distribution of neutral hydrogen via the redshifted 21 cm line promises to revolutionize our knowledge of the epoch of reionization and the first galaxies, and may provide a powerful new tool for observational cosmology from redshifts 1<z<4 . In this review we discuss recent advances in our theoretical understanding of the epoch of reionization (EoR), the application of 21 cm tomography to cosmology and measurements of the dark energy equation of state after reionization, and the instrumentation and observational techniques shared by 21 cm EoR and post reionization cosmology machines. We place particular emphasis on the expected signal and observational capabilities of first generation 21 cm fluctuation instruments.
The cross-correlation between high redshift galaxies and 21 cm emission from the high redshift intergalactic medium (IGM) promises to be an excellent probe of the Epoch of Reionization (EoR). On large scales, the 21 cm and galaxy fields are anti-correlated during most of the reionization epoch. However, on scales smaller than the size of the H II regions around detectable galaxies, the two fields become roughly uncorrelated. Consequently, the 21 cm-galaxy cross power spectrum provides a tracer of bubble growth during reionization, with the signal turning over on progressively larger scales as reionization proceeds. The precise turnover scale depends on the minimum host mass of the detectable galaxies, and the galaxy selection technique. Measuring the turnover scale as a function of galaxy luminosity constrains the characteristic bubble size around galaxies of different luminosities. The cross spectrum becomes positive on small scales if ionizing photons fail to escape from low mass galaxies, and these galaxies are detectable longward of the hydrogen ionization edge, because in this case some identifiable galaxies lie outside of ionized regions. LOFAR can potentially measure the 21 cm-galaxy cross spectrum in conjunction with mild extensions to the existing Subaru survey for $z=6.6$ Lyman-alpha emitters, while the MWA is slightly less sensitive for detecting the cross spectrum. A futuristic galaxy survey covering a sizable fraction of the MWA field of view ($sim 800$ deg$^2$) can probe the scale dependence of the cross spectrum, constraining the filling factor of H II regions at different redshifts during reionization, and providing other valuable constraints on reionization models.
We present detailed predictions for the redshifted 21cm signal from the epoch of reionization. These predictions are obtained from radiative transfer calculations on the results of large scale (100/h Mpc), high dynamic range, cosmological simulations. We consider several scenarios for the reionization history, of both early and extended reionization. From the simulations we construct and analyze a range of observational characteristics, from the global signal, via detailed images and spectra, to statistical representations of rms fluctuations, angular power spectra, and probability distribution functions to characterize the non-gaussianity of the 21cm signal. (abbreviated abstract)
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