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Register a new userA practical theorem on using interferometry to measure the global 21-cm signal
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The sky-averaged, or global, background of redshifted $21$ cm radiation is expected to be a rich source of information on cosmological reheating and reionizaton. However, measuring the signal is technically challenging: one must extract a small, frequency-dependent signal from under much brighter spectrally smooth foregrounds. Traditional approaches to study the global signal have used single antennas, which require one to calibrate out the frequency-dependent structure in the overall system gain (due to internal reflections, for example) as well as remove the noise bias from auto-correlating a single amplifier output. This has motivated proposals to measure the signal using cross-correlations in interferometric setups, where additional calibration techniques are available. In this paper we focus on the general principles driving the sensitivity of the interferometric setups to the global signal. We prove that this sensitivity is directly related to two characteristics of the setup: the cross-talk between readout channels (i.e. the signal picked up at one antenna when the other one is driven) and the correlated noise due to thermal fluctuations of lossy elements (e.g. absorbers or the ground) radiating into both channels. Thus in an interferometric setup, one cannot suppress cross-talk and correlated thermal noise without reducing sensitivity to the global signal by the same factor -- instead, the challenge is to characterize these effects and their frequency dependence. We illustrate our general theorem by explicit calculations within toy setups consisting of two short dipole antennas in free space and above a perfectly reflecting ground surface, as well as two well-separated identical lossless antennas arranged to achieve zero cross-talk.
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The redshifted 21-cm signal of neutral Hydrogen is a promising probe into the period of evolution of our Universe when the first stars were formed (Cosmic Dawn), to the period where the entire Universe changed its state from being completely neutral to completely ionized (Reionization). The most striking feature of this line of neutral Hydrogen is that it can be observed across an entire frequency range as a sky-averaged continuous signature, or its fluctuations can be measured using an interferometer. However, the 21-cm signal is very faint and is dominated by a much brighter Galactic and extra-galactic foregrounds, making it an observational challenge. We have used different physical models to simulate various realizations of the 21-cm Global signals, including an excess radio background to match the amplitude of the EDGES 21-cm signal. First, we have used an artificial neural network (ANN) to extract the astrophysical parameters from these simulated datasets. Then, mock observations were generated by adding a physically motivated foreground model and an ANN was used to extract the astrophysical parameters from such data. The $R^2$ score of our predictions from the mock-observations is in the range of 0.65-0.89. We have used this ANN to predict the signal parameters giving the EDGES data as the input. We find that the reconstructed signal closely mimics the amplitude of the reported detection. The recovered parameters can be used to infer the physical state of the gas at high redshifts.
The 21-cm signal in the vicinity of the first stars is expected to reflect properties of the first stars. In this study we pay special attention to tracing the time evolution of the ionizing photons escape fraction, which affects the distribution of neutral hydrogen, by performing radiation hydrodynamics (RHD) simulations resolving dense gas in a halo. We find that the radial profile of 21-cm differential brightness temperature is quite sensitive to the stellar and halo masses, which reflects the time evolution of the escape fraction. In the case of a less massive star, ionizing photons hardly escape from its host halo due to the absorption by dense halo gas, thus an deep 21-cm absorption feature at just outside the halo lasts a long time. Whereas photons from a massive star well working to heat the ambient intergalactic medium turn out to cause a spatially extended 21-cm emission signature. Although individual signals are found to be undetectable with the Square Kilometre Array, our analysis using the results from the RHD simulations indicates that the properties of the first stars are imprinted on the 21-cm global signal: its amplitude depends not only on the cosmic star formation rate density, but also on the typical mass of the first stars due to the stellar-mass-dependent heating rate. Thus, we suggest that the initial mass function of the first stars is an essential factor in understanding the global signal.
The global 21 cm signal from Cosmic Dawn (CD) and the Epoch of Reionization (EoR), at redshifts $z sim 6-30$, probes the nature of first sources of radiation as well as physics of the Inter-Galactic Medium (IGM). Given that the signal is predicted to be extremely weak, of wide fractional bandwidth, and lies in a frequency range that is dominated by Galactic and Extragalactic foregrounds as well as Radio Frequency Interference, detection of the signal is a daunting task. Critical to the experiment is the manner in which the sky signal is represented through the instrument. It is of utmost importance to design a system whose spectral bandpass and additive spurious can be well calibrated and any calibration residual does not mimic the signal. SARAS is an ongoing experiment that aims to detect the global 21 cm signal. Here we present the design philosophy of the SARAS 2 system and discuss its performance and limitations based on laboratory and field measurements. Laboratory tests with the antenna replaced with a variety of terminations, including a network model for the antenna impedance, show that the gain calibration and modeling of internal additives leave no residuals with Fourier amplitudes exceeding 2~mK, or residual Gaussians of 25 MHz width with amplitudes exceeding 2~mK. Thus, even accounting for reflection and radiation efficiency losses in the antenna, the SARAS~2 system is capable of detection of complex 21-cm profiles at the level predicted by currently favoured models for thermal baryon evolution.
The Epoch of Reionization (EoR) is an uncharted era in our Universes history during which the birth of the first stars and galaxies led to the ionization of neutral hydrogen in the intergalactic medium. There are many experiments investigating the EoR by tracing the 21cm line of neutral hydrogen. Because this signal is very faint and difficult to isolate, it is crucial to develop analysis techniques that maximize sensitivity and suppress contaminants in data. It is also imperative to understand the trade-offs between different analysis methods and their effects on power spectrum estimates. Specifically, with a statistical power spectrum detection in HERAs foreseeable future, it has become increasingly important to understand how certain analysis choices can lead to the loss of the EoR signal. In this paper, we focus on signal loss associated with power spectrum estimation. We describe the origin of this loss using both toy models and data taken by the 64-element configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER). In particular, we highlight how detailed investigations of signal loss have led to a revised, higher 21cm power spectrum upper limit from PAPER-64. Additionally, we summarize errors associated with power spectrum error estimation that were previously unaccounted for. We focus on a subset of PAPER-64 data in this paper; revised power spectrum limits from the PAPER experiment are presented in a forthcoming paper by Kolopanis et al. (in prep.) and supersede results from previously published PAPER analyses.
The early star-forming Universe is still poorly constrained, with the properties of high-redshift stars, the first heating sources, and reionization highly uncertain. This leaves observers planning 21-cm experiments with little theoretical guidance. In this work we explore the possible range of high-redshift parameters including the star formation efficiency and the minimal mass of star-forming halos; the efficiency, spectral energy distribution, and redshift evolution of the first X-ray sources; and the history of reionization. These parameters are only weakly constrained by available observations, mainly the optical depth to the cosmic microwave background. We use realistic semi-numerical simulations to produce the global 21-cm signal over the redshift range $z = 6-40$ for each of 193 different combinations of the astrophysical parameters spanning the allowed range. We show that the expected signal fills a large parameter space, but with a fixed general shape for the global 21-cm curve. Even with our wide selection of models we still find clear correlations between the key features of the global 21-cm signal and underlying astrophysical properties of the high redshift Universe, namely the Ly$alpha$ intensity, the X-ray heating rate, and the production rate of ionizing photons. These correlations can be used to directly link future measurements of the global 21-cm signal to astrophysical quantities in a mostly model-independent way. We identify additional correlations that can be used as consistency checks.
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