A Unified Calibration Framework for 21 cm Cosmology
Ruby Byrne, Miguel F. Morales, Bryna Hazelton, Michael Wilensky
备注：
Accepted for publication in MNRAS. This updated version has a section exploring the effects of the unified calibration framework on simulated data and comparing unified calibration to sky-based and redundant calibration. It also has an expanded discussion of calibration biases
Calibration precision is currently a limiting systematic in 21 cm cosmology experiments. While there are innumerable calibration approaches, most can be categorized as either `sky-based,' relying on an extremely accurate model of astronomical foreground emission, or `redundant,' requiring a precisely regular array with near-identical antenna response patterns. Both of these classes of calibration are inflexible to the realities of interferometric measurement. In practice, errors in the foreground model, antenna position offsets, and beam response inhomogeneities degrade calibration performance and contaminate the cosmological signal. Here we show that sky-based and redundant calibration can be unified into a highly general and physically motivated calibration framework based on a Bayesian statistical formalism. Our new framework includes sky and redundant calibration as special cases but can additionally support relaxing the rigid assumptions implicit in those approaches. Furthermore, we present novel calibration techniques such as redundant calibration for arrays with no redundant baselines, representing an alternative calibration method for imaging arrays such as the MWA Phase I. These new calibration approaches could mitigate systematics and reduce calibration error, thereby improving the precision of cosmological measurements.
Contamination from instrumental effects interacting with bright astrophysical sources is the primary impediment to measuring Epoch of Reionization and BAO 21 cm power spectra---an effect called mode-mixing. In this paper we identify four fundamental power spectrum shapes produced by mode-mixing that will affect all upcoming observations. We are able, for the first time, to explain the wedge-like structure seen in advanced simulations and to forecast the shape of an 'EoR window' that is mostly free of contamination. Understanding the origins of these contaminations also enables us to identify c…
Precise polarisation measurements of the cosmic microwave background (CMB) require accurate knowledge of the instrument orientation relative to the sky frame used to define the cosmological Stokes parameters. Suitable celestial calibration sources that could be used to measure the polarimeter orientation angle are limited, so current experiments commonly `self-calibrate.' The self-calibration method exploits the theoretical fact that the $EB$ and $TB$ cross-spectra of the CMB vanish in the standard cosmological model, so any detected $EB$ and $TB$ signals must be due to systematic errors. Howe…
Detecting cosmological signals from the Epoch of Reionization (EoR) requires high-precision calibration to isolate the cosmological signals from foreground emission. In radio interferometery, perturbed primary beams of antenna elements can disrupt the precise calibration, which results in contaminating the foreground-free region, or the EoR window, in the cylindrically averaged power spectrum. For Hydrogen Epoch of Reionization Array (HERA), we simulate and characterize the perturbed primary beams induced by feed motions such as axial, lateral, and tilting motions, above the 14-meter dish. To …
Observation of redshifted 21-cm signal from the Epoch of Reionization (EoR) is challenging due to contamination from the bright foreground sources that exceed the signal by several orders of magnitude. The removal of this very high foreground relies on accurate calibration to keep the intrinsic property of the foreground with frequency. Commonly employed calibration techniques for these experiments are the sky model-based and the redundant baseline-based calibration approaches. However, the sky model-based and redundant baseline-based calibration methods could suffer from sky-modeling error an…
One of the principal challenges of 21 cm cosmology experiments is overcoming calibration error. Established calibration approaches in the field require an exquisitely accurate sky model, and low-level sky model errors introduce calibration errors that corrupt the cosmological signal. We present a novel calibration approach called Delay-Weighted Calibration, or DWCal, that enables precise calibration even in the presence of sky model error. Sky model error does not affect all power spectrum modes equally, and DWCal fits calibration solutions preferentially from error-free modes. We apply this t…
Detecting the cosmological sky-averaged (global) 21 cm signal as a function of observed frequency will provide a powerful tool to study the ionization and thermal history of the intergalactic medium (IGM) in the early Universe ($\sim$ 400 million years after the Big Bang). The greatest challenge in conventional total-power global 21 cm experiments is the removal of the foreground synchrotron emission ($\sim 10^3$-$10^4$ K) to uncover the weak cosmological signal (tens to hundreds of mK), especially since the intrinsic smoothness of the foreground spectrum is corrupted by instrumental effects. …
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 err…
We introduce CALAMITY, a precision bandpass calibration method for radio interferometry. CALAMITY can solve for direction independent gains with arbitrary frequency structure to the high precision required for 21 cm cosmology with minimal knowledge of foregrounds or antenna beams and does not require any degree of redundancy (repeated identical measurements of the same baseline). We have achieved this through two key innovations. Firstly, we model the foregrounds on each baseline independently using a flexible and highly efficient set of basis functions that have minimal overlap with 21 cm mod…
The separation of cosmological signal from astrophysical foregrounds is a fundamental challenge for any effort to probe the evolution of neutral hydrogen during the Cosmic Dawn and epoch of reionization (EoR) using the 21 cm hyperfine transition. Foreground separation is made possible by their intrinsic spectral smoothness, making them distinguishable from spectrally complex cosmological signal even though they are ~5 orders of magnitude brighter. Precisely calibrated radio interferometers are essential to maintaining the smoothness and thus separability of the foregrounds. One powerful calibr…
The redshifted 21 cm line of neutral hydrogen is a promising probe of the Epoch of Reionization (EoR). However, its detection requires a thorough understanding and control of the systematic errors. We study two systematic biases observed in the LOFAR EoR residual data after calibration and subtraction of bright discrete foreground sources. The first effect is a suppression in the diffuse foregrounds, which could potentially mean a suppression of the 21 cm signal. The second effect is an excess of noise beyond the thermal noise. The excess noise shows fluctuations on small frequency scales, and…
Observation of the redshifted 21-cm signal from Cosmic Dawn and Epoch of Reionization is a challenging endeavor in observational cosmology. Presence of orders of magnitude brighter astrophysical foregrounds and various instrumental systematics increases the complexity of these observations. This work presents an end-to-end pipeline dealing with synthetic interferometric data of sensitive radio observations . The mock sky model includes the redshifted 21-cm signal and astrophysical foregrounds. The effects of calibration error and position error in the extraction of the redshifted 21-cm power s…
Realizing the potential of 21 cm tomography to statistically probe the intergalactic medium before and during the Epoch of Reionization requires large telescopes and precise control of systematics. Next-generation telescopes are now being designed and built to meet these challenges, drawing lessons from first-generation experiments that showed the benefits of densely packed, highly redundant arrays--in which the same mode on the sky is sampled by many antenna pairs--for achieving high sensitivity, precise calibration, and robust foreground mitigation. In this work, we focus on the Hydrogen Epo…
Maximally Smooth Functions (MSFs) are a form of constrained functions in which there are no inflection points or zero crossings in high order derivatives. Consequently, they have applications to signal recovery in experiments where signals of interest are expected to be non-smooth features masked by larger smooth signals or foregrounds. They can also act as a powerful tool for diagnosing the presence of systematics. The constrained nature of MSFs makes fitting these functions a non-trivial task. We introduce maxsmooth, an open source package that uses quadratic programming to rapidly fit MSFs.…
The Bayesian Global Sky Model (B-GSM): Validation of a Data Driven Bayesian Simultaneous Component Separation and Calibration Algorithm for EoR Foreground Modelling
21 cm cosmology is a promising new probe of the evolution of visible matter in our universe, especially during the poorly-constrained Cosmic Dawn and Epoch of Reionization. However, in order to separate the 21 cm signal from bright astrophysical foregrounds, we need an exquisite understanding of our telescopes so as to avoid adding spectral structure to spectrally-smooth foregrounds. One powerful calibration method relies on repeated simultaneous measurements of the same interferometric baseline to solve for the sky signal and for instrumental parameters simultaneously. However, certain degree…
Current and future Cosmic Microwave Background (CMB) Radiation experiments are targeting the polarized $B$-mode signal. The small amplitude of this signal makes a successful measurement challenging for current technologies. Therefore, very accurate studies to mitigate and control possible systematic effects are vital to achieve a successful observation. An additional challenge is coming from the presence of polarized Galactic foreground signals that contaminate the CMB signal. When they are combined, the foreground signals dominate the polarized CMB signal at almost every relevant frequency. F…
In order to study the "Cosmic Dawn" and the Epoch of Reionization with 21 cm tomography, we need to statistically separate the cosmological signal from foregrounds known to be orders of magnitude brighter. Over the last few years, we have learned much about the role our telescopes play in creating a putatively foreground-free region called the "EoR window." In this work, we examine how an interferometer's effects can be taken into account in a way that allows for the rigorous estimation of 21 cm power spectra from interferometric maps while mitigating foreground contamination and thus increasi…
Polarization leakage of foreground synchrotron emission is a critical issue in HI intensity mapping experiments. While the sought-after HI emission is unpolarized, polarized foregrounds such as Galactic and extragalactic synchrotron radiation, if coupled with instrumental impurity, can mimic or overwhelm the HI signals. In this paper we present the methodology for polarization calibration at 700-900 MHz, applied on data obtained from the Green Bank Telescope (GBT). We use astrophysical sources, both polarized and unpolarized sources including quasars and pulsars, as calibrators to characterize…
In this paper we present observations, simulations, and analysis demonstrating the direct connection between the location of foreground emission on the sky and its location in cosmological power spectra from interferometric redshifted 21 cm experiments. We begin with a heuristic formalism for understanding the mapping of sky coordinates into the cylindrically averaged power spectra measurements used by 21 cm experiments, with a focus on the effects of the instrument beam response and the associated sidelobes. We then demonstrate this mapping by analyzing power spectra with both simulated and o…
We develop a Bayesian model that jointly constrains receiver calibration, foregrounds and cosmic 21cm signal for the EDGES global 21\,cm experiment. This model simultaneously describes calibration data taken in the lab along with sky-data taken with the EDGES low-band antenna. We apply our model to the same data (both sky and calibration) used to report evidence for the first star formation in 2018. We find that receiver calibration does not contribute a significant uncertainty to the inferred cosmic signal (<1%), though our joint model is able to more robustly estimate the cosmic signal for f…
Current-generation low frequency interferometers constructed with the objective of detecting the high-redshift 21 cm background, aim to generate power spectra of the brightness-temperature contrast of neutral hydrogen in primordial intergalactic medium. Two-dimensional power spectra (power in Fourier modes parallel and perpendicular to the line of sight) formed from interferometric visibilities have been shown to delineate a boundary between spectrally-smooth foregrounds (known as the wedge) and spectrally-structured 21 cm background emission (the EoR-window). However, polarized foregrounds ar…
Recently, the common methodology used to transform type Ia supernovae (SNe Ia) into genuine standard candles has been suffering criticism. Indeed, it assumes a particular cosmological model (namely the flat $Λ$CDM) to calibrate the standardisation corrections parameters, i.e. the dependency of the supernova peak absolute magnitude on its colour, post-maximum decline rate and host galaxy mass. As a result, this assumption could make the data compliant to the assumed cosmology and thus nullify all works previously conducted on model comparison. In this work, we verify the viability of these hypo…
Quantifying Foreground Contamination in the Dark Ages 21 cm Power Spectrum Using an Electromagnetically Simulated Dipole Antenna Atop a Dielectric Surface
Brown University（布朗大学）；National Radio Astronomy Observatory（国家射电天文台）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Lunar Resources, Inc.（月球资源公司）
The redshifted cosmological 21 cm signal emitted by neutral hydrogen during the first billion years of the universe is much fainter relative to other galactic and extragalactic radio emissions, posing a great challenge towards detection of the signal. Therefore, precise instrumental calibration is a vital prerequisite for the success of radio interferometers such as the Murchison Widefield Array (MWA), which aim for a 21 cm detection. Over the previous years, novel calibration techniques targeting the power spectrum paradigm of EoR science have been actively researched and where possible imple…
We study the impact of sky-based calibration errors from source mismodeling on 21\,cm power spectrum measurements with an interferometer and propose a method for suppressing their effects. While emission from faint sources that are not accounted for in calibration catalogs is believed to be spectrally smooth, deviations of true visibilities from model visibilities are not, due to the inherent chromaticity of the interferometer's sky-response (the "wedge"). Thus, unmodeled foregrounds, below the confusion limit of many instruments, introduce frequency structure into gain solutions on the same l…
CosmicWeb-21cm array: A New Radio Observation Array Design for 21cm Cosmology
Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences（中国科学院天体结构与演化重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；College of Information Engineering, Kunming University（昆明学院信息工程学院）；College of Big Data, Yunnan Agricultural University（云南农业大学大数据学院）；College of Physics and Electronic Engineering, Qujing Normal University（曲靖师范学院物理与电子工程学院）
We extend a general maximum likelihood foreground estimation for cosmic microwave background polarization data to include estimation of instrumental systematic effects. We focus on two particular effects: frequency band measurement uncertainty, and instrumentally induced frequency dependent polarization rotation. We assess the bias induced on the estimation of the $B$-mode polarization signal by these two systematic effects in the presence of instrumental noise and uncertainties in the polarization and spectral index of Galactic dust. Degeneracies between uncertainties in the band and polariza…
Foreground mitigation is critical to all next-generation radio interferometers that target cosmology using the redshifted neutral hydrogen 21 cm emission line. Attempts to remove this foreground emission have led to new analysis techniques as well as new developments in hardware specifically dedicated to instrument beam and gain calibration, including stabilized signal injection into the interferometric array and drone-based platforms for beam mapping. The radio calibration sources currently used in the literature are broad-band incoherent sources that can only be detected as excess power and …
Calibration requirements for Epoch of Reionization 21-cm signal observations -- IV. Bias and variance with time and frequency correlated residual gains
Observation of redshifted 21-cm signals from neutral hydrogen holds the key to understanding the structure formation and its evolution during the reionization and post-reionization era. Apart from the presence of orders of magnitude larger foregrounds in the observed frequency range, the instrumental effects of the interferometers combined with the ionospheric effects present a considerable challenge in the extraction of 21-cm signals from strong foregrounds. The systematic effects of time and frequency correlated residual gain errors originating from the measurement process introduce a bias a…
The EDGES High-Band experiment aims to detect the sky-average brightness temperature of the $21$-cm signal from the Epoch of Reionization (EoR) in the redshift range $14.8 \gtrsim z \gtrsim 6.5$. To probe this redshifted signal, EDGES High-Band conducts single-antenna measurements in the frequency range $90-190$ MHz from the Murchison Radio-astronomy Observatory in Western Australia. In this paper, we describe the current strategy for calibration of the EDGES High-Band receiver and report calibration results for the instrument used in the $2015-2016$ observational campaign. We propagate uncert…
We present a new calibration method based on cross-correlations with WMAP and apply it to data from the Atacama Cosmology Telescope (ACT). ACT's observing strategy and map making procedure allows an unbiased reconstruction of the modes in the maps over a wide range of multipoles. By directly matching the ACT maps to WMAP observations in the multipole range of 400 < ell < 1000, we determine the absolute calibration with an uncertainty of 2% in temperature. The precise measurement of the calibration error directly impacts the uncertainties in the cosmological parameters estimated from the ACT po…
The Q&U Bolometric Interferometer for Cosmology (QUBIC) is a novel kind of polarimeter optimized for the measurement of the $B$-mode polarization of the Cosmic Microwave Background (CMB), which is one of the major challenges of observational cosmology. The signal is expected to be of the order of a few tens of nK, prone to instrumental systematic effects and polluted by various astrophysical foregrounds which can only be controlled through multichroic observations. QUBIC is designed to address these observational issues with a novel approach that combines the advantages of interferometry in te…
Detecting a signal from the Epoch of Reionisation (EoR) requires an exquisite understanding of galactic and extra-galactic foregrounds, low frequency radio instruments, instrumental calibration, and data analysis pipelines. In this work we build upon existing work that aims to understand the impact of calibration errors on 21-cm power spectrum (PS) measurements. It is well established that calibration errors have the potential to inhibit EoR detections by introducing additional spectral features that mimic the structure of EoR signals. We present a straightforward way to estimate the impact of…
Differential Polarization Calibration: A Consistency Test for Cosmic Birefringence
Department of Physics, University of California, San Diego（加州大学圣地亚哥分校物理系）；Department of Astronomy & Astrophysics, University of California, San Diego（加州大学圣地亚哥分校天文与天体物理系）
The Primordial Inflation Explorer (PIXIE) is an Explorer-class mission concept to measure cosmological signals from both linear polarization of the cosmic microwave background and spectral distortions from a perfect blackbody. The targeted measurement sensitivity is 2--4 orders of magnitude below competing astrophysical foregrounds, placing stringent requirements on instrument calibration. An on-board blackbody calibrator presents a polarizing Fourier transform spectrometer with a known signal to enable conversion of the sampled interference fringe patterns from telemetry units to physical uni…
Global 21cm cosmology aims to investigate the cosmic dawn and epoch of reionisation by measuring the sky averaged HI absorption signal, which requires, accurate modelling of, or correction for, the bright radio foregrounds and distortions arising from chromaticity of the antenna beam. We investigate the effect of improving foreground modelling by fitting data sets from many observation times simultaneously in a single Bayesian analysis, fitting for the same parameter set by performing these fits on simulated data. We find that for a hexagonal dipole antenna, this simultaneous fitting produces …
The 21~cm transition from neutral Hydrogen promises to be the best observational probe of the Epoch of Reionisation. The main difficulty in measuring the 21 cm signal is the presence of bright foregrounds that require very accurate interferometric calibration. Closure quantities may circumvent the calibration requirements but may be, however, affected by direction dependent effects, particularly antenna primary beam responses. This work investigates the impact of antenna primary beams affected by mutual coupling on the closure phase and its power spectrum. Our simulations show that primary bea…
PEACC - Precision Emitter for 21 cm Array Coherent Calibration
Lane Department of Computer Science and Electrical Engineering, West Virginia University（西弗吉尼亚大学兰恩计算机科学与工程系）；Center for Gravitational Waves and Cosmology, West Virginia University（西弗吉尼亚大学引力波与宇宙学中心）；Department of Physics, Yale University（耶鲁大学物理系）；Department of Astronomy, University of Virginia（弗吉尼亚大学天文学系）；Trottier Space Institute, McGill University（麦吉尔大学特罗蒂尔太空研究所）
The redshifted 21 cm line is an emerging tool in cosmology, in principle permitting three-dimensional surveys of our Universe that reach unprecedentedly large volumes, previously inaccessible length scales, and hitherto unexplored epochs of our cosmic timeline. Large radio telescopes have been constructed for this purpose, and in recent years there has been considerable progress in transforming 21 cm cosmology from a field of considerable theoretical promise to one of observational reality. Increasingly, practitioners in the field are coming to the realization that the success of observational…
The Atacama Cosmology Telescope Polarimeter (ACTPol) is a polarization sensitive upgrade to the Atacama Cosmology Telescope. Located at an elevation of 5190 m, ACTPol measures the Cosmic Microwave Background (CMB) temperature and polarization with arcminute-scale angular resolution. Calibration of the detector angles is a critical step in producing maps of the CMB polarization. Polarization angle offsets in the detector calibration can cause leakage in polarization from E to B modes and induce a spurious signal in the EB and TB cross correlations, which eliminates our ability to measure potent…
Observations of the redshifted 21-cm signal emitted by neutral hydrogen represent a promising probe of large-scale structure in the universe. However, cosmological 21-cm signal is challenging to observe due to astrophysical foregrounds which are several orders of magnitude brighter. Traditional linear foreground removal methods can optimally remove foregrounds for a known telescope response but are sensitive to telescope systematic errors such as antenna gain and delay errors, leaving foreground contamination in the recovered signal. Non-linear methods such as principal component analysis, on …
Detection of the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn and the Epoch of Reionization is one of the final frontiers of modern observational cosmology. The inherently faint signal makes it susceptible to contamination by several sources like astrophysical foregrounds and instrumental systematics. Nevertheless, developments achieved in the recent times will combine to make signal detection possible with the upcoming Square Kilometer Array (SKA), both statistically and via tomography. This review describes an indigenously developed end-to-end pipeline that simulates sens…
As observations of the Epoch of Reionization (EoR) in redshifted 21cm emission begin, we asses the accuracy of the early catalog results from the Precision Array for Probing the Epoch of Reionization (PAPER) and the Murchison Widefield Array. The MWA EoR approach derives much of its sensitivity from subtracting foregrounds to <1% precision while the PAPER approach relies on the stability and symmetry of the primary beam. Both require an accurate flux calibration to set the amplitude of the measured power spectrum. The two instruments are very similar in resolution, sensitivity, sky coverage an…
HI intensity mapping (IM) is an exciting new probe that could revolutionize the future of cosmology. However, the relative faintness of the HI signal when compared to foregrounds of astrophysical or terrestrial origin will make HI IM extremely challenging. The imprint of these foregrounds may result in systematic errors in the recovered cosmological signal. We discuss an IM simulation pipeline developed at Manchester that can introduce systematic errors at the TOD level in order to help assess their impact. We will present results for two potential sources of systematics for HI IM surveys: 1/f…
We study the behavior of internal signal chain reflections and antenna cross coupling as systematics for 21 cm cosmological surveys. We outline the mathematics for how these systematics appear in interferometric visibilities and describe their phenomenology. We then describe techniques for modeling and removing these systematics without attenuating the 21 cm signal in the data. This has critical implications for low-frequency radio surveys aiming to characterize the 21cm signal from the Epoch of Reionization and Cosmic Dawn, as systematics can cause bright foreground emission to contaminate th…
The impact of diffuse Galactic emission on direction-independent gain calibration in high-redshift 21 cm observations
Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）；INAF – Instituto di Radioastronomia（意大利国家天体物理研究所射电天文研究所）；LUX, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université（巴黎天文台卢克斯实验室，PSL研究大学，法国国家科学研究中心，索邦大学）；Astron（荷兰射电天文研究所）
We report on the MIT Epoch of Reionization (MITEoR) experiment, a pathfinder low-frequency radio interferometer whose goal is to test technologies that improve the calibration precision and reduce the cost of the high-sensitivity 3D mapping required for 21 cm cosmology. MITEoR accomplishes this by using massive baseline redundancy, which enables both automated precision calibration and correlator cost reduction. We demonstrate and quantify the power and robustness of redundancy for scalability and precision. We find that the calibration parameters precisely describe the effect of the instrumen…
Contamination due to foregrounds (Galactic and Extra-galactic), calibration errors and ionospheric effects pose major challenges in detection of the cosmic 21 cm signal in various Epoch of Reionization (EoR) experiments. We present the results of a pilot study of a field centered on 3C196 using LOFAR Low Band (56-70 MHz) observations, where we quantify various wide field and calibration effects such as gain errors, polarized foregrounds, and ionospheric effects. We observe a `pitchfork' structure in the 2D power spectrum of the polarized intensity in delay-baseline space, which leaks into the …
