Upper Limits on the 21 cm Power Spectrum at z = 5.9 from Quasar Absorption Line Spectroscopy

We present upper limits on the 21 cm power spectrum at $z = 5.9$ calculated from the model-independent limit on the neutral fraction of the intergalactic medium of $x_{\rm H{\small I }} < 0.06 + 0.05\ (1\sigma)$ derived from dark pixel statistics of quasar absorption spectra. Using 21CMMC, a Markov chain Monte Carlo Epoch of Reionization analysis code, we explore the probability distribution of 21 cm power spectra consistent with this constraint on the neutral fraction. We present 99 per cent confidence upper limits of $\Delta^2(k) < 10$ to $20\ {\rm mK}^2$ over a range of $k$ from 0.5 to $2.0\ h{\rm Mpc}^{-1}$, with the exact limit dependent on the sampled$k$mode. This limit can be used as a null test for 21 cm experiments: a detection of power at$z=5.9$ in excess of this value is highly suggestive of residual foreground contamination or other systematic errors affecting the analysis.Comment: 5 pages, 1 figure, accepted to MNRAS letter

Constraints on the temperature of the intergalactic medium at z=8.4 with 21-cm observations

We compute robust lower limits on the spin temperature, $T_{\rm S}$, of the $z=8.4$ intergalactic medium (IGM), implied by the upper limits on the 21-cm power spectrum recently measured by PAPER-64. Unlike previous studies which used a single epoch of reionization (EoR) model, our approach samples a large parameter space of EoR models: the dominant uncertainty when estimating constraints on $T_{\rm S}$. Allowing $T_{\rm S}$ to be a free parameter and marginalizing over EoR parameters in our Markov Chain Monte Carlo code 21CMMC, we infer $T_{\rm S}\ge3 {\rm K}$ (corresponding approximately to $1\sigma$) for a mean IGM neutral fraction of $\bar{x}_{\rm H{\scriptsize I}}\gtrsim0.1$. We further improve on these limits by folding-in additional EoR constraints based on: (i) the dark fraction in QSO spectra, which implies a strict upper limit of $\bar{x}_{\rm H{\scriptsize I}}[z=5.9]\leq 0.06+0.05 \,(1\sigma)$; and (ii) the electron scattering optical depth, $\tau_{\rm e}=0.066\pm0.016\,(1\sigma)$ measured by the Planck satellite. By restricting the allowed EoR models, these additional observations tighten the approximate $1\sigma$ lower limits on the spin temperature to $T_{\rm S} \ge 6$ K. Thus, even such preliminary 21-cm observations begin to rule out extreme scenarios such as `cold reionization', implying at least some prior heating of the IGM. The analysis framework developed here can be applied to upcoming 21-cm observations, thereby providing unique insights into the sources which heated and subsequently reionized the very early Universe.Comment: 7 pages, 1 figure, accepted to MNRAS (matches online version

A Bayesian approach to high fidelity interferometric calibration II: demonstration with simulated data

In a companion paper, we presented BayesCal, a mathematical formalism for mitigating sky-model incompleteness in interferometric calibration. In this paper, we demonstrate the use of BayesCal to calibrate the degenerate gain parameters of full-Stokes simulated observations with a HERA-like hexagonal close-packed redundant array, for three assumed levels of completeness of the a priori known component of the calibration sky model. We compare the BayesCal calibration solutions to those recovered by calibrating the degenerate gain parameters with only the a priori known component of the calibration sky model both with and without imposing physically motivated priors on the gain amplitude solutions and for two choices of baseline length range over which to calibrate. We find that BayesCal provides calibration solutions with up to four orders of magnitude lower power in spurious gain amplitude fluctuations than the calibration solutions derived for the same data set with the alternate approaches, and between $\sim10^7$ and $\sim10^{10}$ times smaller than in the mean degenerate gain amplitude on the full range of spectral scales accessible in the data. Additionally, we find that in the scenarios modelled only BayesCal has sufficiently high fidelity calibration solutions for unbiased recovery of the 21 cm power spectrum on large spectral scales ($k_\parallel \lesssim 0.15~h\mathrm{Mpc}^{-1}$). In all other cases, in the completeness regimes studied, those scales are contaminated

Polarized Redundant-Baseline Calibration for 21 cm Cosmology Without Adding Spectral Structure

21 cm cosmology is a promising new probe of the evolution of visible matter in our universe, especially during the poorly-constrained Cosmic Dawn and Epoch of Reionization. However, in order to separate the 21 cm signal from bright astrophysical foregrounds, we need an exquisite understanding of our telescopes so as to avoid adding spectral structure to spectrally-smooth foregrounds. One powerful calibration method relies on repeated simultaneous measurements of the same interferometric baseline to solve for the sky signal and for instrumental parameters simultaneously. However, certain degrees of freedom are not constrained by asserting internal consistency between redundant measurements. In this paper, we review the origin of these "degeneracies" of redundant-baseline calibration and demonstrate how they can source unwanted spectral structure in our measurement and show how to eliminate that additional, artificial structure. We also generalize redundant calibration to dual-polarization instruments, derive the degeneracy structure, and explore the unique challenges to calibration and preserving spectral smoothness presented by a polarized measurement.Comment: 12 pages, 3 figures, updated to match the published MNRAS versio