PAPER-64 Constraints On Reionization II: The Temperature Of The z=8.4 Intergalactic Medium

We present constraints on both the kinetic temperature of the intergalactic medium (IGM) at z=8.4, and on models for heating the IGM at high-redshift with X-ray emission from the first collapsed objects. These constraints are derived using a semi-analytic method to explore the new measurements of the 21 cm power spectrum from the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER), which were presented in a companion paper, Ali et al. (2015). Twenty-one cm power spectra with amplitudes of hundreds of mK^2 can be generically produced if the kinetic temperature of the IGM is significantly below the temperature of the Cosmic Microwave Background (CMB); as such, the new results from PAPER place lower limits on the IGM temperature at z=8.4. Allowing for the unknown ionization state of the IGM, our measurements find the IGM temperature to be above ~5 K for neutral fractions between 10% and 85%, above ~7 K for neutral fractions between 15% and 80%, or above ~10 K for neutral fractions between 30% and 70%. We also calculate the heating of the IGM that would be provided by the observed high redshift galaxy population, and find that for most models, these galaxies are sufficient to bring the IGM temperature above our lower limits. However, there are significant ranges of parameter space that could produce a signal ruled out by the PAPER measurements; models with a steep drop-off in the star formation rate density at high redshifts or with relatively low values for the X-ray to star formation rate efficiency of high redshift galaxies are generally disfavored. The PAPER measurements are consistent with (but do not constrain) a hydrogen spin temperature above the CMB temperature, a situation which we find to be generally predicted if galaxies fainter than the current detection limits of optical/NIR surveys are included in calculations of X-ray heating.Comment: companion paper to Ali et al. (2015), ApJ 809, 61; matches version accepted to ApJ; 11 pages, 7 figure

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

In this paper, we report new limits on 21 cm emission from cosmic reionization based on a 135 day observing campaign with a 64-element deployment of the Donald C. Backer Precision Array for Probing the Epoch of Reionization in South Africa. This work extends the work presented in Parsons et al. with more collecting area, a longer observing period, improved redundancy-based calibration, improved fringe-rate filtering, and updated power-spectral analysis using optimal quadratic estimators. The result is a new 2σ upper limit on Δ[superscript 2](k) of (22.4 mK)[superscript 2] in the range 0.15 < k < 0.5h Mpc[superscript -1] at z = 8.4. This represents a three-fold improvement over the previous best upper limit. As we discuss in more depth in a forthcoming paper, this upper limit supports and extends previous evidence against extremely cold reionization scenarios. We conclude with a discussion of implications for future 21 cm reionization experiments, including the newly funded Hydrogen Epoch of Reionization Array

Erratum: “PAPER-64 Constraints on Reionization: The 21 cm Power Spectrum at z = 8.4” (2015, ApJ, 809, 61)

In this erratum, we retract the upper limits on the 21 cm power spectrum presented in the published article. The published article reported an upper limit on δ 212(k ) of (22.4 mK)2 at z= 8.4 in the range 0.15 &lt; k &lt; 0.5h Mpc-1. This analysis underestimated the level of signal loss, or attenuation of the target cosmological 21 cm signal associated with the chosen power spectrum estimator, and also underestimated the statistical error on those estimates. A revised result, with a new analysis, is presented in M. K. Kolopanis et al. (2018, in preparation). Below, we briefly summarize the errors in the original analysis and how they are corrected. For an indepth analysis and discussion of the errors, we refer the reader to Cheng et al. (2018). Signal loss was expected in the original analysis because the covariance matrices, C, used to weight the un-normalized bandpower estimates, qa, in (Formula Presented) were empirically estimated from a time-averaged finite ensemble of the data, x, such that (Formula Presented). While the true covariance C leads to an inherently unbiased lossless estimator of the power spectrum, using an empirically estimated Ĉ can lead to signal loss. Specifically, weighting data by an empirically estimated covariance carries the risk of overfitting and downweighting EoR fluctuations that are coupled to the data. In Cheng et al. (2018), it is shown that these couplings are especially strong in the fringe-rate filtered PAPER-64 data set. The first and most impactful error relates to the method by which signal loss was estimated. To assess signal loss from the empirically estimated covariance matrix, different realizations of mock cosmological signals e of known amplitudes are added to the original data to form a new data vector, (Formula Presented). New covariance matrices, (Formula Presented) are used to estimate un-normalized bandpowers (Formula Presented), which can be written as (Formula Presented). The normalized power estimate can then be compared to the known injected power in e to estimate signal loss. The key error in the previous analysis was to assume that, since e was statistically independent of x, that the two middle crossterms in Equation (2) would average to zero in an ensemble. However, as shown in Cheng et al. (2018) and Switzer et al. (2015), these cross-terms can contain significant negative power because Ĉr contains information that correlates the two vectors. Ignoring these cross-terms leads to a significant underestimate of signal loss. As a result, we presented negligible signal loss in our original analysis, when in fact approximately 99.99% of the signal was removed (Cheng et al. 2018). Correcting for the actual signal loss is the biggest factor revising the upper limit on 21 D2 . The second mistake made in the original analysis was to underestimate the statistical errors in the reported power spectrum estimates. The original analysis used a bootstrap resampling technique on power spectral measurements over the baseline and time axes. However, fringe-rate filtering introduces significant correlations in the data along the time axis. As is discussed in Cheng et al. (2018), bootstrapping across correlated samples can result in a significant underestimate of the variation in the data if the number of resamplings is not equal to the number of independent samples in the data, as in the case of the original analysis. The error bars associated with this oversampling were underestimated by approximately a factor of 2 (in mK). The revised analysis in M. K. Kolopanis et al. (2018, in preparation) only applies bootstrap resampling across the baseline axis to avoid this problem. The mistake in estimating the statistical errors should have become apparent when comparing results to our theoretical thermal noise sensitivity. Unfortunately, a third miscalculation was made in estimating the thermal noise sensitivity. As detailed in Cheng et al. (2018), this miscalculation stemmed from numerous small mismatches between the idealized analysis pipeline used to estimate sensitivity and the actual analysis applied to the data. As a result, our estimated thermal noise sensitivity was approximately a factor of 3 low (in mK), leading to the mistaken impression that our error bars were consistent with the level of thermal noise. In summary, we retract the power spectrum results shown in Figures 18 and 20 in the published article. Results that relied on the original limits, including those presented in Figure 21, are retracted. Additionally, the companion paper to the original manuscript, Pober et al. (2015), used the original limits to place constraints on the spin temperature of the intergalactic medium (IGM) at z=8.4. Our revised limits do not place significant constraints on the IGM temperature, and the results of Figure 4 from Pober et al. (2015) should be disregarded. However, we note that their analysis would still be relevant should a future experiment place constraints on the 21 cm signal similar to those claimed in the published article. An updated analysis of this same data set is presented in M. K. Kolopanis et al. (2018, in preparation), where these revised results are put into context with measurements at other redshifts

Range-doppler synthetic aperture radar processing at VHF frequencies

Bibliography (pages 144-150).This thesis focuses on the application of range-Doppler processing at VHF frequencies for wide azimuth beam, airborne, stripmap SAR systems with zero Doppler centroid and modest pulse bandwidths relative to the carrier frequency (simulations less than 30 percent). Such a system is the South African SAR (SASAR) VHF sensor. The theory of such SAR operation is addressed. In general, closed form analytical expressions for range compressed, range-Doppler domain signals do not exist. Thus, in this work, extensive use is made of simulation. Using simulated SAR signals with severe range curvature, the regions of applicability of standard range-Doppler processing, when applied without Doppler frequency dependent secondary range compression, are investigated for a range of processing parameters in the frequency range of 100 MHz to 200 MHz. The effects on the range impulse response of centre frequency, target closest approach range and nominal range resolution are investigated, each for a range of processed azimuth resolutions. Information is presented in the form of plots showing the degradation in the range resolution and in the form of tabular results which also include the range peak- and integrated side lobe levels and the non-linear phase error in the Fourier domain. An extension to range-Doppler processing, suggested to the candidate by Michael Jin, is demonstrated to provide significantly improved performance over the standard range-Doppler processor for signals with severe range curvature. The basic idea of the extended algorithm, first published by Raney and Vachon in 1989 and applied in the context of a narrow beam, squinted SAR, is to make an initial correction to a reference range through a multiplication with a reference function in the 2-D frequency domain. This is followed by a residual range curvature and azimuth focusing operation in the range-Doppler domain. Airborne motion compensation strategies for flight path reconstruction are discussed. In addition, an ERIM-developed approach for efficiently including an azimuth dependence for wide beam motion compensation is discussed in the context of the SASAR system. An overview of the SASAR VHF project, the experience gained, and the encouraging results from the processing of the data from the first radiating flights, is presented. A full Statement of Originality is given

Big Science: SKA and the next phase of astronomy in Africa

In 2012 the country celebrated the news that South Africa had won a substantial part of the bid to build the most ambitious radio astronomy array in the world - the Square Kilometer Array. This audio lecture explains the purpose and function of this massive investment in international astronomy, and its implications for the future of astronomy in South Africa. This resource is useful for anyone interested in the Square Kilometer Array and astronomy in general