THE MURCHISON WIDEFIELD ARRAY 21 cm POWER SPECTRUM ANALYSIS METHODOLOGY

We present the 21 cm power spectrum analysis approach of the Murchison Widefield Array Epoch of Reionization project. In this paper, we compare the outputs of multiple pipelines for the purpose of validating statistical limits cosmological hydrogen at redshifts between 6 and 12. Multiple, independent, data calibration and reduction pipelines are used to make power spectrum limits on a fiducial night of data. Comparing the outputs of imaging and power spectrum stages highlights differences in calibration, foreground subtraction and power spectrum calculation. The power spectra found using these different methods span a space defined by the various tradeoffs between speed, accuracy, and systematic control. Lessons learned from comparing the pipelines range from the algorithmic to the prosaically mundane; all demonstrate the many pitfalls of neglecting reproducibility. We briefly discuss the way these different methods attempt to handle the question of evaluating a significant detection in the presence of foregrounds.

A. R. Whitney | S. J. Tingay | G. Bernardi | D. A. Mitchell | S. M. Ord | L. J. Greenhill | B. Pindor | R. B. Wayth | M. Johnston-Hollitt | N. Udaya Shankar | N. Hurley-Walker | J. C. Pober | M. Tegmark | C. M. Trott | Judd D. Bowman | A. E. E. Rogers | P. Carroll | E. Lenc | K. S. Srivani | A. R. Offringa | P. Procopio | J. C. Kasper | B. J. Hazelton | M. F. Morales | A. P. Beardsley | F. Briggs | D. Emrich | A. Ewall-Wice | J. N. Hewitt | J. Line | N. Thyagarajan | Daniel C. Jacobs | E. Morgan | A. Roshi | B. M. Gaensler | R. L. Webster | B. McKinley | D. L. Kaplan | J. S. B. Wyithe | Joshua S. Dillon | T. Prabu | Max Tegmark | E. Lenc | D. Kaplan | J. Hewitt | B. Pindor | R. Webster | S. Tingay | M. Morales | C. Trott | E. Morgan | A. D. Oliveira-Costa | A. Loeb | D. Oberoi | P. Carroll | A. Rogers | B. Corey | R. Cappallo | A. Whitney | I. Sullivan | R. Wayth | P. Procopio | J. Kasper | A. Offringa | J. Pober | A. Beardsley | G. Bernardi | J. Bowman | J. Dillon | A. Ewall-Wice | B. Hazelton | D. Jacobs | A. Neben | N. Thyagarajan | J. Wyithe | R. Goeke | R. Subrahmanyan | M. Johnston-Hollitt | F. Briggs | B. Gaensler | D. Mitchell | L. Greenhill | S. Ord | C. Lonsdale | S. McWhirter | M. Lynch | M. Waterson | A. Williams | S. Sethi | D. Emrich | N. Hurley-Walker | N. Shankar | K. Srivani | B. McKinley | C. Wu | E. Kratzenberg | T. Prabu | A. Roshi | C. Williams | L. Feng | J. Riding | J. Line | N. Barry | A. Williams | N. Barry | R. J. Cappallo | B. E. Corey | A. de Oliveira-Costa | L. Feng | R. Goeke | E. Kratzenberg | A. Loeb | C. J. Lonsdale | M. J. Lynch | S. R. McWhirter | A. R. Neben | D. Oberoi | J. Riding | R. Subrahmanyan | I. S. Sullivan | M. Waterson | C. L. Williams | C. Wu | H. S. Kim | S. Paul | Shiv K. Sethi | S. Paul | H. Kim

[1]  Daniel A. Mitchell,et al.  CHIPS: THE COSMOLOGICAL H i POWER SPECTRUM ESTIMATOR , 2016, 1601.02073.

[2]  Saleem Zaroubi,et al.  Non-parametric foreground subtraction for 21-cm epoch of reionization experiments , 2009 .

[3]  Matias Zaldarriaga,et al.  Will point sources spoil 21-cm tomography? , 2008, 0807.3952.

[4]  S. Markoff,et al.  The LOFAR Multifrequency Snapshot Sky Survey (MSSS) - I. Survey description and first results , 2015 .

[5]  J. Starck,et al.  The scale of the problem: Recovering images of reionization with Generalized Morphological Component Analysis , 2012, 1209.4769.

[6]  G. Bernardi,et al.  Subtraction of point sources from interferometric radio images through an algebraic forward modelling scheme , 2010, 1012.3719.

[7]  Alan E. E. Rogers,et al.  Science with the Murchison Widefield Array , 2012, Publications of the Astronomical Society of Australia.

[8]  Asantha Cooray,et al.  Cosmological and Astrophysical Parameter Measurements with 21-cm Anisotropies During the Era of Reionization , 2006, astro-ph/0605677.

[9]  Stephanie Thalberg,et al.  Interferometry And Synthesis In Radio Astronomy , 2016 .

[10]  Philip J. Bones,et al.  Image Reconstruction from Incomplete Data V , 2006 .

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

[12]  A. R. Rao Annual Review of Astronomy and Astrophysics , 2015 .

[13]  S. J. Tingay,et al.  The Low-Frequency Environment of the Murchison Widefield Array: Radio-Frequency Interference Analysis and Mitigation , 2015, Publications of the Astronomical Society of Australia.

[14]  Judd D. Bowman,et al.  IMPROVING FOREGROUND SUBTRACTION IN STATISTICAL OBSERVATIONS OF 21 cm EMISSION FROM THE EPOCH OF REIONIZATION , 2006 .

[15]  W. A. Coles,et al.  Interferometric Imaging with the 32 Element Murchison Wide-Field Array , 2010, 1010.1733.

[16]  Max Tegmark,et al.  A model of diffuse Galactic radio emission from 10 MHz to 100 GHz , 2008, 0802.1525.

[17]  Edward J. Wollack,et al.  NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: COSMOLOGICAL PARAMETER RESULTS , 2012, 1212.5226.

[18]  M. A. Voronkov,et al.  Wide field imaging for the square kilometre array , 2012, Other Conferences.

[19]  David F. Moore,et al.  New Limits on 21cm EoR From PAPER-32 Consistent with an X-Ray Heated IGM at z=7.7 , 2013, 1304.4991.

[20]  S. Velzen,et al.  The Very Large Array Low-frequency Sky Survey Redux (VLSSr) , 2014, 1404.0694.

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

[22]  S. Zaroubi,et al.  Foreground simulations for the LOFAR-epoch of reionization experiment , 2008, 0804.1130.

[23]  A. A. Deshpande,et al.  Empirical covariance modeling for 21 cm power spectrum estimation: A method demonstration and new limits from early Murchison Widefield Array 128-tile data , 2015, 1506.01026.

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

[25]  J. Curran,et al.  SUMSS: a wide-field radio imaging survey of the southern sky – II. The source catalogue , 2003, astro-ph/0303188.

[26]  Lu Feng,et al.  The Murchison Widefield Array Correlator , 2015, Publications of the Astronomical Society of Australia.

[27]  Saleem Zaroubi,et al.  The Scale of the Problem : Recovering Images of Reionization with GMCA , 2012, 1209.4769.

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

[29]  D. A. Rafferty,et al.  LOFAR calibration and wide-field imaging , 2012 .

[30]  Max Tegmark,et al.  Mapmaking for precision 21 cm cosmology , 2014, Physical Review D.

[31]  Max Tegmark,et al.  CONFIRMATION OF WIDE-FIELD SIGNATURES IN REDSHIFTED 21 cm POWER SPECTRA , 2015, 1506.06150.

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

[33]  Jason Manley,et al.  OPENING THE 21 cm EPOCH OF REIONIZATION WINDOW: MEASUREMENTS OF FOREGROUND ISOLATION WITH PAPER , 2013, 1301.7099.

[34]  D. Kaplan,et al.  The EoR sensitivity of the Murchison Widefield Array , 2012, 1204.3111.

[35]  David F. Moore,et al.  NEW 145 MHz SOURCE MEASUREMENTS BY PAPER IN THE SOUTHERN SKY , 2011, 1105.1367.

[36]  Stefan J. Wijnholds,et al.  Fast gain calibration in radio astronomy using alternating direction implicit methods: Analysis and applications , 2014, 1410.2101.

[37]  B. Pindor,et al.  Subtraction of Bright Point Sources from Synthesis Images of the Epoch of Reionization , 2010, Publications of the Astronomical Society of Australia.

[38]  Rachel L. Webster,et al.  Overcoming real-world obstacles in 21 cm power spectrum estimation: A method demonstration and results from early Murchison Widefield Array data , 2013, 1304.4229.

[39]  K. Gorski,et al.  HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere , 2004, astro-ph/0409513.

[40]  David R. DeBoer,et al.  WHAT NEXT-GENERATION 21 cm POWER SPECTRUM MEASUREMENTS CAN TEACH US ABOUT THE EPOCH OF REIONIZATION , 2013, 1310.7031.

[41]  David F. Moore,et al.  A FLUX SCALE FOR SOUTHERN HEMISPHERE 21 cm EPOCH OF REIONIZATION EXPERIMENTS , 2013, 1307.7716.

[42]  David F. Moore,et al.  PAPER-64 CONSTRAINTS ON REIONIZATION: THE 21 cm POWER SPECTRUM AT z = 8.4 , 2015, 1502.06016.

[43]  Cathryn M. Trott,et al.  Epoch of reionization window. I. Mathematical formalism , 2014, 1404.2596.

[44]  Max Tegmark How to Make Maps from Cosmic Microwave Background Data without Losing Information , 1996, astro-ph/9611130.

[45]  Max Tegmark,et al.  A method for 21 cm power spectrum estimation in the presence of foregrounds , 2011, Physical Review D.

[46]  A. R. Whitney,et al.  THE IMPORTANCE OF WIDE-FIELD FOREGROUND REMOVAL FOR 21 cm COSMOLOGY: A DEMONSTRATION WITH EARLY MWA EPOCH OF REIONIZATION OBSERVATIONS , 2016, 1601.06177.

[47]  J. Hewitt,et al.  Statistical EOR detection and the Mileura Widefield Array , 2006 .

[48]  Alan E. E. Rogers,et al.  The Murchison Widefield Array: Design Overview , 2009, Proceedings of the IEEE.

[49]  Michael Biehl,et al.  Post‐correlation radio frequency interference classification methods , 2010, 1002.1957.

[50]  E. Lenc,et al.  Understanding instrumental Stokes leakage in Murchison Widefield Array polarimetry , 2014, 1412.4466.

[51]  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.

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

[53]  T. Murphy,et al.  wsclean: an implementation of a fast, generic wide-field imager for radio astronomy , 2014, 1407.1943.

[54]  Abhirup Datta,et al.  BRIGHT SOURCE SUBTRACTION REQUIREMENTS FOR REDSHIFTED 21 cm MEASUREMENTS , 2010 .

[55]  J. M. Oschmann,et al.  Ground-based Telescopes , 2004 .

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

[57]  E. Lenc,et al.  GLEAM: The GaLactic and Extragalactic All-Sky MWA Survey , 2015, Publications of the Astronomical Society of Australia.

[58]  Roger Cappallo,et al.  The Murchison Widefield Array Commissioning Survey: A Low-Frequency Catalogue of 14 110 Compact Radio Sources over 6 100 Square Degrees , 2014, Publications of the Astronomical Society of Australia.

[59]  A. R. Whitney,et al.  The Murchison Widefield Array: The Square Kilometre Array Precursor at Low Radio Frequencies , 2012, Publications of the Astronomical Society of Australia.

[60]  Jan E. Noordam,et al.  LOFAR calibration challenges , 2004, SPIE Astronomical Telescopes + Instrumentation.

[61]  Judd D. Bowman,et al.  FOREGROUND CONTAMINATION IN INTERFEROMETRIC MEASUREMENTS OF THE REDSHIFTED 21 cm POWER SPECTRUM , 2008, 0807.3956.

[62]  E. Greisen,et al.  The NRAO VLA Sky Survey , 1996 .

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

[64]  S. J. Tingay,et al.  Measuring phased‐array antenna beampatterns with high dynamic range for the Murchison Widefield Array using 137 MHz ORBCOMM satellites , 2015, 1505.07114.

[65]  Michael I. Large,et al.  A machine-readable release of the Molonglo Reference Catalogue of Radio Sources , 1991 .

[66]  David R. DeBoer,et al.  MULTIREDSHIFT LIMITS ON THE 21 cm POWER SPECTRUM FROM PAPER , 2014, 1408.3389.

[67]  Max Tegmark,et al.  A fast method for power spectrum and foreground analysis for 21 cm cosmology , 2013 .

[68]  Cathryn M. Trott,et al.  Epoch of reionization window. II. Statistical methods for foreground wedge reduction , 2014, 1404.4372.

[69]  Roger J. Cappallo,et al.  Real-Time Calibration of the Murchison Widefield Array , 2008, IEEE Journal of Selected Topics in Signal Processing.

[70]  J. Pel,et al.  The High Road to Astronomical Photometric Precision: Differential Photometry , 2011 .

[71]  K. Golap,et al.  Wide-field wide-band Interferometric Imaging: The WB A-Projection and Hybrid Algorithms , 2013 .