Delay Spectrum with Phase-Tracking Arrays: Extracting the HI power spectrum from the Epoch of Reionization

Oct 22, 2016
16 pages
Published in:
  • Astrophys.J. 833 (2016) 2, 213
  • Published: Dec 19, 2016
e-Print:

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Abstract: (IOP)
The detection of redshifted 21 cm emission from the epoch of reionization (EoR) is a challenging task owing to strong foregrounds that dominate the signal. In this paper, we propose a general method, based on the delay spectrum approach, to extract H i power spectra that are applicable to tracking observations using an imaging radio interferometer ('Delay Spectrum with Imaging Arrays'). Our method is based on modeling the H i signal taking into account the impact of wide field effects such as the w-term, which are then used as appropriate weights in cross-correlating the measured visibilities. Our method is applicable to any radio interferometer that tracks a phase center and could be utilized for arrays such as the Murchison Widefield Array (MWA), Low Frequency Array (LOFAR), Giant Meterwave Radio Telescope (GMRT), Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER), and HERA. In the literature the delay spectrum approach has been implemented for near-redundant baselines using drift scan observations. In this paper we explore the scheme for non-redundant tracking arrays. This is the first application of delay spectrum methodology to such data to extract the H i signal. We analyze 3 hr of MWA tracking data on the EoR1 field. We present both two-dimensional (k,k{k}_{\parallel },{k}_{\perp }) and one-dimensional (k) power spectra from the analysis. Our results are in agreement with the findings of other pipelines developed to analyze the MWA EoR data.
Note:
  • 17 pages, 10 figures, accepted for publication in The Astrophysical Journal
  • cosmology: observations
  • cosmology: theory
  • dark ages, reionization, first stars
  • techniques: interferometric
  • [1]
    CASA is used for initial processing of the data to calibrate raw visibility measurements. This is followed by the creation of a model sky image from clean components. This model is then subtracted in the visibility domain to obtain residual visibilities. We use both the calibrated and residual visibilities for computing the power spectrum
    • McMullin
  • [2]
    Each visibility is then Fourier transformed in frequency space (Eq. (31)). This process is needed for isolation of foregrounds in the k⊥-k plane. We note the our method utilizes both the subtraction of foregrounds and their isolation. But it does not employ an external point source catalog
    • [3]
      The procedure outlined above yields complex visibilities as a function of five variables: Vτ (u, v, w, t). For computing the power spectrum we crosscorrelate these visibilities for t = t to remove the noise bias. To weigh each cross-correlation we assume that there exist regions in k⊥-k plane which are dominated by only noise and the HI signal. This allows us to compute a weight for each crosscorrelation based on the expected HI signal. For computing these weights we take into account the impact of w-term and the distortion of intensity pattern in a tracking scan. The relevant method is elaborated in detail in sections 2, 2.1, 2.2, and 2.3 and summarized in section
      • [4]
        4. In section 4.1, we describe the power spectrum estimator, taking into account weights given by the expected HI signal, in 3-, 2- and 1-dimension. We also discuss our method to compute the errors on the estimated power spectrum. 3.1. CASA processing MWA data were collected at 2-minute intervals with a time resolution of 0.5 seconds and frequency resolution of 40 kHz. The central frequency of these observations is 154.24 MHz. For preprocessing we have used the Cotter pipeline to average to 10 seconds of integration
        • Offringa
      • [4]
        we have not performed any averaging over the frequency channels. Cotter also uses the in-built AOFlagger to flag and remove radio frequency interference. The edge channels of each coarse band are flagged with Cotter due to aliasing effects. After this preprocessing the Cotter pipeline delivers the data in the CASA readable ‘Measurement set (ms)’ format for further processing. Once the ‘ms’ files are produced for each 2-minute data set, we process each of these 2-minute data in CASA to produce an image source is used to calculate the bandpass solutions which are applied to the uncalibrated data. We next construct a sky model from
        • The Hydra A
        • [5]
          In Figure 6, we present a sample image of 2 minute deconvolution. As noted above we process the data for only 2 minutes to ensure the primary beam doesn’t substantially change during the run. For a 2-minute scan we obtain an RMS of nearly 40 mJy/beam. The residual visibility Vν(uν, vν, wν, t) is a function of five variables. We compute the discrete Fourier transform of the residual visibilities in the frequency space weighted by the Blackman-Nuttall (Nuttall (1981)) window Bν to suppress leakage into the EoR window (2013, 2016)): Vτ (u, v, w, t) = ∆ exp(i2πντ)Vν(uν, vν, wν, t)Bν (31) Notice that in Eq. (31) the frequency dependence of the baseline vector bν = {uν, vν, wν} is integrated over. Therefore, the labels {u, v, w} on the LHS of Eq. (31) need further explanation. As noted above (the discussion following Eq. (11)) they can be chosen to denote a given baseline vector at a fixed frequency, ν0. We choose this frequency to be the central frequency of the band ν0 = 154 MHz. Parsons et al (a,b) provide detail implications of the frequency dependence of the baseline vector. Here ∆ = 40 kHz and 256 channels are used for our study, which correspond to total band-
          • Thyagarajan