Abstract
Spectral structures due to the instrument response is the current limiting factor for the experiments attempting to detect the redshifted 21 cm signal from the Epoch of Reionization (EoR). Recent advances in the delay spectrum methodology for measuring the redshifted 21 cm EoR power spectrum brought new attention to the impact of an antenna’s frequency response on the viability of making this challenging measurement. The delay spectrum methodology provides a somewhat straightforward relationship between the time-domain response of an instrument that can be directly measured and the power spectrum modes accessible to a 21 cm EoR experiment. In this paper, we derive the explicit relationship between antenna reflection coefficient (S11) measurements made by a Vector Network Analyzer (VNA) and the extent of additional foreground contaminations in delay space. In the light of this mathematical framework, we examine the chromaticity of a prototype antenna element that will constitute the Hydrogen Epoch of Reionization Array (HERA) between 100 and 200 MHz. These reflectometry measurements exhibit additional structures relative to electromagnetic simulations, but we find that even without any further design improvement, such an antenna element will support measuring spatial k modes with line-of-sight components of k∥ > 0.2h Mpc− 1. We also find that when combined with the powerful inverse covariance weighting method used in optimal quadratic estimation of redshifted 21 cm power spectra the HERA prototype elements can successfully measure the power spectrum at spatial modes as low as k∥ > 0.1h Mpc− 1. This work represents a major step toward understanding the HERA antenna element and highlights a straightforward method for characterizing instrument response for future experiments designed to detect the 21 cm EoR power spectrum.
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Notes
Assuming a flat sky and using appropriate cosmological scalars, the spectral axis, ν, and angle on the sky, \(\vec \theta \), translate to coordinates in a three-dimensional volume at cosmological distances. In describing the spatial power spectrum of emission \(P(\vec k)\) in this volume, we use the three-dimensional wave vector \(\vec k\equiv (k_{\parallel },\vec k_{\perp })\), where k∥ is the line of sight component aligned with the spectral axis, ν, and \(\vec k_{\perp }\) lies in the plane of the sky.
Here, we distinguish the chromaticity of the elements in isolation from the chromaticity inherent to element separation in an interferometric baseline.
References
Ali, Z.S., Parsons, A.R., Zheng, H., et al.: PAPER-64 constraints on reionization: the 21 cm power spectrum at z = 8.4. ApJ 809, 61 (2015)
Barry, N., Hazelton, B., Sullivan, I., Morales, M.F., Pober, J.C.: Calibration requirements for detecting the 21 cm epoch of reionization power spectrum and implications for the SKA. MNRAS 461, 3135 (2016)
Bock, D.C.-J., Large, M.I., Sadler, E.M.: Instrumentation: interferometers, radio continuum, surveys. AJ 117, 1578 (1999)
Bowman, J.D., Morales, M.F., Hewitt, J.N.: Foreground contamination in interferometric measurements of the redshifted 21 cm power spectrum. ApJ 695, 183 (2009)
Bowman, J.D., Rogers, A.E.E.: A lower limit of Δz > 0.06 for the duration of the reionization epoch. Nature 468, 796 (2010)
Condon, J.J., Cotton, W.D., Greisen, E.W., et al.: The NRAO VLA sky survey. AJ 115, 1693 (1998)
Datta, A., Bowman, J.D., Carilli, C.L.: Bright source subtraction requirements for redshifted 21 cm measurements. ApJ 724, 526 (2010)
de Oliveira-Costa, A., Tegmark, M., Gaensler, B.M., et al.: A model of diffuse Galactic radio emission from 10 MHz to 100 GHz. MNRAS 388, 247 (2008)
DeBoer, D.R., Parsons, A.R., Aguirre, J.E., et al.: Hydrogen Epoch of Reionization Array (HERA). Publ. Astron. Soc. Pac. 129(2017), 045001 (2016)
Dillon, J.S., Liu, A., Tegmark, M.: A fast method for power spectrum and foreground analysis for 21 cm cosmology. Phys. Rev. D 87, 043005 (2013)
Dillon, J.S., Liu, A., Williams, C.L., et al.: Overcoming real-world obstacles in 21 cm power spectrum estimation: A method demonstration and results from early Murchison Widefield array data. Phys. Rev. D 89, 023002 (2014)
Ewall-Wice, A., Bradley, R., Deboer, D., et al.: The HERA Dish II: electromagnetic simulations and science implications. Astrophys. J. 831(2), 17 (2016). article id. 196
Furlanetto, S.R., Oh, S.P., Briggs, F.H.: Cosmology at low frequencies: The 21 cm transition and the high-redshift Universe. Phys. Rep. 433, 181 (2006)
Kohn, S.A., Aguirre, J.E., Nunhokee, C.D., et al.: Constraining polarized foregrounds for EoR experiments I: 2D power spectra from the PAPER-32 imaging array. ApJ 823, 88 (2016)
Lidz, A., Zahn, O., McQuinn, M., Zaldarriaga, M., Hernquist, L.: Detecting the rise and fall of 21 cm fluctuations with the Murchison widefield array. ApJ 680, 962 (2008)
Liu, A., Parsons, A.R., Trott, C.M.: Epoch of reionization window. II. statistical methods for foreground wedge reduction. Phys. Rev. D 90, 023018 (2014)
Liu, A., Parsons, A.R., Trott, C.M.: Epoch of reionization window. I. Mathematical formalism. Phys. Rev. D 90, 023019 (2014)
Loeb, A., Zaldarriaga, M.: Measuring the small-scale power spectrum of cosmic density fluctuations through 21cm tomography prior to the epoch of structure formation. Phys. Rev. Lett. 92, 211301 (2004)
Madau, P., Meiksin, A., Rees, M.J.: 21 Centimeter tomography of the intergalactic medium at high redshift. ApJ 475, 429 (1997)
Mauch, T., Murphy, T., Buttery, H.J., et al.: SUMSS: A wide-field radio imaging survey of the southern sky - II. The source catalogue. MNRAS 342, 1117 (2003)
Mellema, G., Koopmans, L.V.E., Abdalla, F.A., et al.: Reionization and the cosmic dawn with the square kilometre array. Exp. Astron. 36, 235 (2013)
Mesinger, A., Furlanetto, S., Cen, R.: 21CMFAST: a fast, seminumerical simulation of the high-redshift 21-cm signal. MNRAS 411, 955 (2011)
Morales, M.F., Hazelton, B., Sullivan, I., Beardsley, A.: Four fundamental foreground power spectrum shapes for 21 cm cosmology observations. ApJ 752, 137 (2012)
Morales, M.F., Wyithe, J.S.B.: Reionization and cosmology with 21-cm fluctuations. ARA&A 48, 127 (2010)
Neben, A.R., Bradley, R.F., Hewitt, J.N., et al.: The hydrogen epoch of reionization array dish. I. Beam pattern measurements and science implications. ApJ 826, 199 (2016)
Paciga, G., Chang, T.-C., Gupta, Y., et al.: The GMRT Epoch of reionization experiment: a new upper limit on the neutral hydrogen power spectrum at z8.6. MNRAS 413, 1174 (2011)
Parsons, A.R., Backer, D.C.: Calibration of low-frequency, wide-field radio interferometers using delay/delay-rate filtering. AJ 138, 219 (2009)
Parsons, A.R., Backer, D.C., Foster, G.S., et al.: The precision array for probing the Epoch of re-ionization: eight station results. AJ 139, 1468 (2010)
Parsons, A., Pober, J., McQuinn, M., Jacobs, D., Aguirre, J.: A sensitivity array-configuration study for measuring the power spectrum of 21 cm emission from reionization. ApJ 753, 81 (2012)
Parsons, A.R., Pober, J.C., Aguirre, J.E., et al.: A Per-baseline, delay-spectrum technique for accessing the 21 cm cosmic reionization signature. ApJ 756, 165 (2012)
Parsons, A.R., Liu, A., Aguirre, J.E., et al.: New limits on 21 cm Epoch of reionization from PAPER-32 consistent with an x-ray heated intergalactic medium at z = 7.7. ApJ 788, 106 (2014)
Patra, N., Subrahmanyan, R., Raghunathan, A., UdayaShankar, N.: Bandpass calibration of a wideband spectrometer using coherent pulse injection. Exp. Astron. 36, 319 (2013)
Patra, N., Subrahmanyan, R., Sethi, S., Udaya Shankar, N., Raghunathan, A.: Saras measurement of the radio background at long wavelengths. ApJ 801, 138 (2015)
Patra, N., Bray, J.D., Roberts, P., Ekers, R.D.: Bandpass calibration of a wideband spectrometer using coherent pulse injection. Exp. Astron. 43(2), 119–129 (2017)
Pober, J.C., Parsons, A.R., Aguirre, J.E., et al.: Opening the 21 cm Epoch of reionization window: measurements of foreground isolation with PAPER. ApJ 768, L36 (2013)
Pober, J.C., Liu, A, Dillon, J.S., Aguirre, J.E., et al.: What next-generation 21 cm power spectrum measurements can teach us about the Epoch of reionization. ApJ 782(2), article id. 66 25 (2014)
Presley, M., Liu, A., Parsons, A.: Measuring the cosmological 21 cm monopole with an interferometer. arXiv:abs/1501.01633 (2015)
Pritchard, J.R., Loeb, A.: Evolution of the 21cm signal throughout cosmic history. Rep. Prog. Phys. 75, 086901 (2012)
Shaver, P.A., Windhorst, R.A., Madau, P., de Bruyn, A.G.: Can the reionization epoch be detected as a global signature in the cosmic background?. A&A 345, 380 (1999)
Sokolowski, M., Tremblay, S.E., Wayth, R.B., Tingay, S.J., et al.: BIGHORNS - Broadband Instrument for Global HydrOgen ReioNisation Signal. Publ. Astron. Soc. Aust. 32, id.e004 18 (2015)
Thyagarajan, N., Udaya Shankar, N., Subrahmanyan, R., et al.: A study of fundamental limitations to statistical detection of redshifted H I from the Epoch of Reionization. ApJ 776, 6 (2013)
Thyagarajan, N., Parsons, A.R., DeBoer, D.R., et al.: Effects of antenna beam chromaticity on redshifted 21 cm power spectrum and implications for hydrogen Epoch of Reionization array. ApJ 825, 9 (2016)
Thyagarajan, N., Jacobs, D.C., Bowman, J.D., et al.: Foregrounds in wide-field redshifted 21 cm power spectra. ApJ 804, 14 (2015)
Tingay, S.J., Goeke, R., Bowman, J.D., Emrich, D., Ord, S.M., Mitchell, D.A., Morales, M.F., et al.: The Murchison widefield array: the square kilometre array precursor at low radio frequencies. Publ. Astron. Soc. Aust. 30, id.e007 21 (2013)
Trott, C.M., Wayth, R.B., Tingay, S.: The impact of point-source subtraction residuals on 21 cm Epoch of Reionization estimation. ApJ 757, 101 (2012)
van Haarlem, M.P., Wise, M.W., Gunst, A.W., et al.: LOFAR: the low-frequency array. A&A 556, A2 (2013)
Vedantham, H., Udaya Shankar, N., Subrahmanyan, R.: Imaging the Epoch of reionization: limitations from foreground confusion and imaging algorithms. Mon. Not. R. Astron. Soc. 450(3), 2291–2305
Voytek, T.C.: PhD thesis, Carnegie Mellon University; Probing the Dark Ages at z20: The SCI-HI 21 cm All-sky Spectrum Experiment (2015)
Acknowledgements
This work was supported by the U.S. National Science Foundation (NSF) through awards AST-1440343 & AST-1410719. ARP acknowledges support from NSF CAREER award 13 52519. AL acknowledges support by NASA through Hubble Fellowship grant #HST-HF2-51363.001-A awarded by the Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. This work is completed as part of the University of California Cosmic Dawn Initiative. AL, ARP, and SRF acknowledge support from the UC Office of the President Multicampus Research Programs and Initiatives through award MR-15-328388.
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Nithyanandan Thyagarajan is a Jansky Fellow of the National Radio Astronomy Observatory.
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Patra, N., Parsons, A.R., DeBoer, D.R. et al. The hydrogen epoch of reionization array dish III: measuring chromaticity of prototype element with reflectometry. Exp Astron 45, 177–199 (2018). https://doi.org/10.1007/s10686-017-9563-0
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DOI: https://doi.org/10.1007/s10686-017-9563-0