Fundamental Limitations on the Calibration of Redundant 21 cm Cosmology Instruments and Implications for HERA and the SKA

Precise instrument calibration is critical to the success of 21 cm Cosmology experiments. Unmitigated errors in calibration contaminate the Epoch of Reionization (EoR) signal, precluding a detection. Barry et al. 2016 characterizes one class of inherent errors that emerge from calibrating to an incomplete sky model, however it has been unclear if errors in the sky model affect the calibration of redundant arrays. In this paper, we show that redundant calibration is vulnerable to errors from sky model incompleteness even in the limit of perfect antenna positioning and identical beams. These errors are at a level that can overwhelm the EoR signal and prevent a detection. Finally, we suggest error mitigation strategies with implications for the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA).

[1]  Mervyn J. Lynch,et al.  THE PRECISION ARRAY FOR PROBING THE EPOCH OF RE-IONIZATION: EIGHT STATION RESULTS , 2009, 0904.2334.

[2]  C. Trott,et al.  Spectral performance of Square Kilometre Array Antennas - II. Calibration performance , 2017, 1705.03116.

[3]  M. Morales,et al.  Calibration requirements for detecting the 21 cm epoch of reionization power spectrum and implications for the SKA , 2016, 1603.00607.

[4]  Max Tegmark,et al.  FOREGROUNDS IN WIDE-FIELD REDSHIFTED 21 cm POWER SPECTRA , 2015, 1502.07596.

[5]  Cathryn M. Trott,et al.  Spectral performance of SKA Log-periodic Antennas I: mitigating spectral artefacts in SKA1-LOW 21 cm cosmology experiments , 2017, 1702.05126.

[6]  Cathryn M. Trott,et al.  THE IMPACT OF POINT-SOURCE SUBTRACTION RESIDUALS ON 21 cm EPOCH OF REIONIZATION ESTIMATION , 2012, 1208.0646.

[7]  Cathryn M. Trott,et al.  The Phase II Murchison Widefield Array: Design overview , 2018, Publications of the Astronomical Society of Australia.

[8]  Graeme Smecher,et al.  Calibrating CHIME: a new radio interferometer to probe dark energy , 2014, Astronomical Telescopes and Instrumentation.

[9]  M. Morales,et al.  THE FUNDAMENTAL MULTI-BASELINE MODE-MIXING FOREGROUND IN 21 cm EPOCH OF REIONIZATION OBSERVATIONS , 2013, 1301.3126.

[10]  C. Trott,et al.  The Bias and Uncertainty of Redundant and Sky-based Calibration Under Realistic Sky and Telescope Conditions , 2018, The Astronomical Journal.

[11]  N. Barry,et al.  Comparing Redundant and Sky-model-based Interferometric Calibration: A First Look with Phase II of the MWA , 2018, The Astrophysical Journal.

[12]  Donald Wiebe,et al.  Holographic beam mapping of the CHIME pathfinder array , 2016, Astronomical Telescopes + Instrumentation.

[13]  A. H. Patil,et al.  Systematic biases in low-frequency radio interferometric data due to calibration: the LOFAR-EoR case , 2016, 1605.07619.

[14]  M. Morales,et al.  Reionization and Cosmology with 21-cm Fluctuations , 2009, 0910.3010.

[15]  Bryna Hazelton,et al.  FOUR FUNDAMENTAL FOREGROUND POWER SPECTRUM SHAPES FOR 21 cm COSMOLOGY OBSERVATIONS , 2012, 1202.3830.

[16]  T. J. Dijkema,et al.  LOFAR FACET CALIBRATION , 2016, 1601.05422.

[17]  R. Sault,et al.  Understanding radio polarimetry. I. Mathematical foundations , 1996 .

[18]  Judd D. Bowman,et al.  First Demonstration of ECHO: an External Calibrator for Hydrogen Observatories , 2017 .

[19]  Steven Furlanetto,et al.  Cosmology at low frequencies: The 21 cm transition and the high-redshift Universe , 2006 .

[20]  T. L. Grobler,et al.  Calibration artefacts in radio interferometry – I. Ghost sources in Westerbork Synthesis Radio Telescope data , 2014 .

[21]  A. R. Whitney,et al.  THE MURCHISON WIDEFIELD ARRAY 21 cm POWER SPECTRUM ANALYSIS METHODOLOGY , 2016, 1605.06978.

[22]  David R. DeBoer,et al.  THE HYDROGEN EPOCH OF REIONIZATION ARRAY DISH. I. BEAM PATTERN MEASUREMENTS AND SCIENCE IMPLICATIONS , 2016, 1602.03887.

[23]  Christopher L. Williams,et al.  A STUDY OF FUNDAMENTAL LIMITATIONS TO STATISTICAL DETECTION OF REDSHIFTED H i FROM THE EPOCH OF REIONIZATION , 2013, 1308.0565.

[24]  David F. Moore,et al.  A PER-BASELINE, DELAY-SPECTRUM TECHNIQUE FOR ACCESSING THE 21 cm COSMIC REIONIZATION SIGNATURE , 2012, 1204.4749.

[25]  Aaron R. Parsons,et al.  REDUNDANT ARRAY CONFIGURATIONS FOR 21 cm COSMOLOGY , 2016, 1602.06259.

[26]  J. Hewitt,et al.  The impact of modelling errors on interferometer calibration for 21 cm power spectra , 2016, 1610.02689.

[27]  N. Udaya Shankar,et al.  IMAGING THE EPOCH OF REIONIZATION: LIMITATIONS FROM FOREGROUND CONFUSION AND IMAGING ALGORITHMS , 2011, 1106.1297.

[28]  Matias Zaldarriaga,et al.  Precision calibration of radio interferometers using redundant baselines , 2010, 1001.5268.

[29]  Cathryn M. Trott,et al.  Spectral Calibration Requirements of Radio Interferometers for Epoch of Reionisation Science with the SKA , 2016, Publications of the Astronomical Society of Australia.

[30]  O. Smirnov,et al.  Redundant interferometric calibration as a complex optimization problem , 2018, 1801.03249.

[31]  Miguel F. Morales,et al.  Toward Epoch of Reionization Measurements with Wide-Field Radio Observations , 2003 .

[32]  Ue-Li Pen,et al.  The GMRT EoR Experiment: Limits on Polarized Sky Brightness at 150 MHz , 2008, 0807.1056.

[33]  Stefan J. Wijnholds,et al.  Calibration artefacts in radio interferometry – II. Ghost patterns for irregular arrays , 2016 .

[34]  C. Carilli,et al.  BRIGHT SOURCE SUBTRACTION REQUIREMENTS FOR REDSHIFTED 21 cm MEASUREMENTS , 2010, 1005.4071.

[35]  Max Tegmark,et al.  A high reliability survey of discrete Epoch of Reionization foreground sources in the MWA EoR0 field , 2016, 1607.03861.

[36]  A. A. Deshpande,et al.  FAST HOLOGRAPHIC DECONVOLUTION: A NEW TECHNIQUE FOR PRECISION RADIO INTERFEROMETRY , 2012, 1209.1653.

[37]  T. L. Grobler,et al.  Calibration artefacts in radio interferometry – III. Phase-only calibration and primary beam correction , 2016, 1606.06320.

[38]  Christopher L. Williams,et al.  GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) survey - I. A low-frequency extragalactic catalogue , 2016, 1610.08318.

[39]  James E. Aguirre,et al.  Polarized redundant-baseline calibration for 21 cm cosmology without adding spectral structure , 2017, 1712.07212.