Epoch of reionization window. I. Mathematical formalism

Abstract

The 21 cm line provides a powerful probe of astrophysics and cosmology at high redshifts, but unlocking the potential of this probe requires the robust mitigation of foreground contaminants that are typically several orders of magnitude brighter than the cosmological signal. Recent simulations and observations have shown that the smooth spectral structure of foregrounds combines with instrument chromaticity to contaminate a "wedge"-shaped region in cylindrical Fourier space. While previous efforts have explored the suppression of foregrounds within this wedge, as well as the avoidance of this highly contaminated region, all such efforts have neglected a rigorous examination of the error statistics associated with the wedge. Using a quadratic estimator formalism applied to the interferometric measurement equation, we provide a framework for such a rigorous analysis (incorporating a fully covariant treatment of errors). Additionally, we find that there are strong error correlations at high spatial wave numbers that have so far been neglected in sensitivity derivations. These error correlations substantially degrade the sensitivity of arrays relying on contributions from long baselines, compared to what one would estimate assuming uncorrelated errors.

PAPER-64 CONSTRAINTS ON REIONIZATION: THE 21 cm POWER SPECTRUM ATz= 8.4

“…This relationship, known colloquially as "the wedge," was derived analytically (P12b; Vedantham et al 2012;Thyagarajan et al 2013;Liu et al 2014aLiu et al , 2014b, and has been confirmed in simulations (Datta et al 2010;Hazelton et al 2013) and observationally Dillon et al 2014). As described in P12b, the wedge is the result of the delay between when a wavefront originating from foreground emission arrives at the two antennas in a baseline.…”

“…We take the conservative approach and do not correct for this effect, noting that the leakage of Q in to I will result in positive power, increasing our limits. Foreground removal techniques discussed in the literature include spectral polynomial fitting (Wang et al 2006;Bowman et al 2009a;Liu et al 2009a), principal component analysis (Liu & Tegmark 2011;Paciga et al 2011;Masui et al 2013;Paciga et al 2013), non-parametric subtractions (Harker et al 2009;Chapman et al 2013), and inverse covariance weighting (Liu & Tegmark 2011;Dillon et al 2013Dillon et al , 2014Liu et al 2014aLiu et al , 2014b, Fourier-mode filtering Petrovic & Oh (2011), and per-baseline delay filtering described in P12b. This delay-spectrum filtering technique is well-suited to the maximum redundancy PAPER configuration, which is not optimized for the other approaches where high fidelity imaging is a prerequisite.…”

“…We use the OQE method to estimate our power spectrum as done in Liu & Tegmark (2011), Dillon et al (2013), Liu et al (2014a), Liu et al (2014b), and Trott et al (2012). Here we briefly review the OQE formalism with an emphasis on our application to data, which draws strongly from the aforementioned works, but also relies on empirical techniques similar to Color scale indicates the number of samples falling in an LST/flux-density bin.…”

Interpreting the Unresolved Intensity of Cosmologically Redshifted Line Radiation

“…As the sidelobes expand over the spatially varying continuum foreground structure, they can produce spectral structure. This is analogous to the wedge phenomenon in interferometers (see, e.g., Liu et al 2014). In a single-dish setting with approximately uniform map coverage, we can convolve all maps to a common resolution using the beam model.…”

Cross-correlation of the cosmic 21-cm signal and Lyman α emitters during reionization

“…Liu et al 2014;Chapman et al 2014). Credible observations will rely on a constant reevaluation of our data analysis, adaptively improving our ability to deal with systematics in a slow march towards increasing signal to noise (S/N).…”