scholarly journals Fundamental uncertainty levels of 21 cm power spectra from a delay analysis

2019 ◽  
Vol 487 (4) ◽  
pp. 5840-5853 ◽  
Author(s):  
Adam E Lanman ◽  
Jonathan C Pober
Keyword(s):  
Power Spectrum ◽  
Power Spectra ◽  
Low Frequency ◽  
Sample Variance ◽  
Model Parameters ◽  
Delay Analysis ◽  
Analysis Strategies ◽  
Murchison Widefield Array ◽  
Fundamental Uncertainty ◽  
Combining Estimates

Abstract Several experimental efforts are underway to measure the power spectrum of 21 cm fluctuations from the epoch of reionization (EoR) using low-frequency radio interferometers. Experiments like the Hydrogen Epoch of Reionization Array (HERA) and Murchison Widefield Array Phase II (MWA) feature highly redundant antenna layouts, building sensitivity through redundant measurements of the same angular Fourier modes, at the expense of diminished UV coverage. This strategy limits the numbers of independent samples of each power spectrum mode, thereby increasing the effect of sample variance on the final power spectrum uncertainty. To better quantify this effect, we measure the sample variance of a delay-transform based power spectrum estimator, using both analytic calculations and simulations of flat-spectrum EoR-like signals. We find that for the shortest baselines in HERA, the sample variance can reach as high as 20 per cent, and up to 30 per cent for the wider fields of view of the MWA. Combining estimates from all the baselines in a HERA- or MWA-like 37 element redundant hexagonal array can lower the variance to 1−3 per cent for some Fourier modes. These results have important implications for observing and analysis strategies, and suggest that sample variance can be non-negligible when constraining EoR model parameters from upcoming 21 cm data.

scholarly journals Comparison of Observing Modes for Statistical Estimation of the 21 cm Signal from the Epoch of Reionisation

2014 ◽  
Vol 31 ◽  
Author(s):  
Cathryn M. Trott
Keyword(s):  
Power Spectrum ◽  
Signal To Noise Ratio ◽  
High Redshift ◽  
Power Spectra ◽  
Low Frequency ◽  
Neutral Hydrogen ◽  
Beam Shape ◽  
Drift Scan ◽  
Murchison Widefield Array ◽  
Aperture Arrays

AbstractNoise considerations for experiments that aim to statistically estimate the 21 cm signal from high redshift neutral hydrogen during the Epoch of Reionisation (EoR) using interferometric data are typically computed assuming a tracked observation, where the telescope pointing centre and instrument phase centre are the same over the observation. Current low frequency interferometers use aperture arrays of fixed dipoles, which are steered electronically on the sky, and have different properties to mechanically-steered single apertures, such as reduced sensitivity away from zenith, and discrete pointing positions on the sky. These properties encourage the use of two additional observing modes: (1) zenith drift, where the pointing centre remains fixed at the zenith, and the phase centre tracks the sky, and (2) drift + shift, a hybrid mode where the telescope uses discrete pointing centres, and the sky drifts during each fixed pointing. These three observing modes view the sky differently, and therefore yield different uncertainties in the power spectrum according to the balance of radiometric noise and cosmic variance. The coherence of measurements made by the instrument in these modes dictates the optimal reduction in thermal noise by combination of coherent modes, and the reduction in cosmic variance by combination of incoherent modes (views of different patches of the sky). Along with calibration and instrument stability considerations, the balance between these noise components provides one measure for the utility of these three modes for measuring a statistical signature of the EoR signal. We provide a general framework for estimating the uncertainty in the power spectrum for a given observing mode, telescope beam shape, and interferometer antenna distribution. We then apply this framework to the Murchison Widefield Array (MWA) using an analysis of the two-dimensional (2D) and one-dimensional (1D) power spectra for 900 hours of observing. We demonstrate that zenith drift scans can yield marginally lower uncertainty in the signal power compared with tracked scans for the MWA EoR experiment, and that moderately higher signal-to-noise ratio (S/N) estimates of the amplitude (3%) and slope (1%) of the 1D power spectrum are accessible, translating directly into a reduction in the required observing time to reach the same estimation precision. We find that the additional sensitivity of pointing at zenith, and the reduction in cosmic variance available with a zenith drift scan, makes this an attractive observing mode for current and future arrays.

scholarly journals Random recurrent networks near criticality capture the broadband power distribution of human ECoG dynamics

2016 ◽  
Author(s):  
Rishidev Chaudhuri ◽  
Biyu He ◽  
Xiao-Jing Wang
Keyword(s):  
Power Spectrum ◽  
Power Distribution ◽  
Random Network ◽  
Field Potential ◽  
Power Spectra ◽  
Low Frequency ◽  
Recurrent Network ◽  
Network Activity ◽  
Brain Diseases ◽  
Low Frequency Power

The power spectrum of brain electric field potential recordings is dominated by an arrhythmic broadband signal but a mechanistic account of its underlying neural network dynamics is lacking. Here we show how the broadband power spectrum of field potential recordings can be explained by a simple random network of nodes near criticality. Such a recurrent network produces activity with a combination of a fast and a slow autocorrelation time constant, with the fast mode corresponding to local dynamics and the slow mode resulting from recurrent excitatory connections across the network. These modes are combined to produce a power spectrum similar to that observed in human intracranial EEG (i.e., electrocorticography, ECoG) recordings. Moreover, such a network naturally converts input correlations across nodes into temporal autocorrelation of the network activity. Consequently, increased independence between nodes results in a reduction in low-frequency power, which offers a possible explanation for observed changes in ECoG power spectra during task performance. Lastly, changes in network coupling produce changes in network activity power spectra reminiscent of those seen in human ECoG recordings across different arousal states. This model thus links macroscopic features of the empirical ECoG power spectrum to a parsimonious underlying network structure and proposes potential mechanisms for changes in ECoG power spectra observed across behavioral and arousal states. This provides a computational framework within which to generate and test hypotheses about the cellular and network mechanisms underlying whole brain electrical dynamics, their variations across behavioral states as well as abnormalities associated with brain diseases.

scholarly journals Simulations of ionospheric refraction on radio interferometric data

2021 ◽  
Vol 38 ◽  
Author(s):  
J. Kariuki Chege ◽  
C. H. Jordan ◽  
C. Lynch ◽  
J. L. B. Line ◽  
C. M. Trott
Keyword(s):  
Power Spectra ◽  
Low Frequency ◽  
Neutral Hydrogen ◽  
Simulated Data ◽  
Software Tool ◽  
Calibration Procedure ◽  
Murchison Widefield Array ◽  
The Impact ◽  
Thin Screen ◽  
Data Calibration

Abstract The Epoch of Reionisation (EoR) is the period within which the neutral universe transitioned to an ionised one. This period remains unobserved using low-frequency radio interferometers, which target the 21 cm signal of neutral hydrogen emitted in this era. The Murchison Widefield Array (MWA) radio telescope was built with the detection of this signal as one of its major science goals. One of the most significant challenges towards a successful detection is that of calibration, especially in the presence of the Earth’s ionosphere. By introducing refractive source shifts, distorting source shapes, and scintillating flux densities, the ionosphere is a major nuisance in low-frequency radio astronomy. We introduce sivio, a software tool developed for simulating observations of the MWA through different ionospheric conditions, which is estimated using thin screen approximation models and propagated into the visibilities. This enables us to directly assess the impact of the ionosphere on observed EoR data and the resulting power spectra. We show that the simulated data captures the dispersive behaviour of ionospheric effects. We show that the spatial structure of the simulated ionospheric media is accurately reconstructed either from the resultant source positional offsets or from parameters evaluated during the data calibration procedure. In turn, this will inform on the best strategies of identifying and efficiently eliminating ionospheric contamination in EoR data moving into the Square Kilometre Array era.

scholarly journals Deep multiredshift limits on Epoch of Reionization 21 cm power spectra from four seasons of Murchison Widefield Array observations

2020 ◽  
Vol 493 (4) ◽  
pp. 4711-4727 ◽  
Author(s):  
Cathryn M Trott ◽  
C H Jordan ◽  
S Midgley ◽  
N Barry ◽  
B Greig ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Thermal Noise ◽  
Power Spectra ◽  
Time System ◽  
Field Frequency ◽  
Real Time System ◽  
Four Seasons ◽  
Murchison Widefield Array ◽  
Averaged Power Spectrum ◽  
High Band

Abstract We compute the spherically averaged power spectrum from four seasons of data obtained for the Epoch of Reionization (EoR) project observed with the Murchison Widefield Array (MWA). We measure the EoR power spectrum over k = 0.07–3.0 h Mpc−1 at redshifts $z$ = 6.5–8.7. The largest aggregation of 110 h on EoR0 high band (3340 observations), yields a lowest measurement of (43 mK)2 = 1.8 × 103 mK2 at k  = 0.14 h Mpc−1 and $z$ = 6.5 (2σ thermal noise plus sample variance). Using the Real-Time System to calibrate and the CHIPS pipeline to estimate power spectra, we select the best observations from the central five pointings within the 2013–2016 observing seasons, observing three independent fields and in two frequency bands. This yields 13 591 2-min snapshots (453 h), based on a quality assurance metric that measures ionospheric activity. We perform another cut to remove poorly calibrated data, based on power in the foreground-dominated and EoR-dominated regions of the two-dimensional power spectrum, reducing the set to 12 569 observations (419 h). These data are processed in groups of 20 observations, to retain the capacity to identify poor data, and used to analyse the evolution and structure of the data over field, frequency, and data quality. We subsequently choose the cleanest 8935 observations (298 h of data) to form integrated power spectra over the different fields, pointings, and redshift ranges.

scholarly journals Long Term X-ray Variability of NGC 4151

1994 ◽  
Vol 159 ◽  
pp. 402-402
Author(s):  
I. E. Papadakis ◽  
I. M. McHardy
Keyword(s):  
Power Spectrum ◽  
Light Curve ◽  
Power Spectra ◽  
Low Frequency ◽  
Short Time Scale ◽  
Low Frequencies ◽  
X Ray ◽  
Ngc 4151 ◽  
Short Time

Short time scale X-ray power spectra of AGN are in general well fitted by a power law with slopes between −1 and −2 but we expect these slopes to flatten at low frequencies (indication of such a flattening has already been seen in NGC 5506). We have searched for such a low-frequency break in the power spectrum of NGC 4151 by investigating its long term X-ray light curve (2–10 keV). To construct this light curve we used Ariel V SSI, OSO-8, HEAO-1, Ariel VI, EXOSAT ME and GINGA LAC data.

On the Application of Selected Wave Group Spectra for the Experimental Investigation of Low Frequency Motions of a Moored Structure

2009 ◽  
Author(s):  
Janou Hennig ◽  
Antonio Carlos Fernandes ◽  
Hans Cozijn ◽  
Marcio Maia Domingues
Keyword(s):  
Power Spectrum ◽  
Wave Train ◽  
Power Spectra ◽  
Low Frequency ◽  
Model Tests ◽  
Wave Power ◽  
Wave Group ◽  
Sea State ◽  
Alternative Approach ◽  
First Results

A moored structure shows both wave and low frequency motions in waves. Wave frequency motions are related to the wave elevation and wave power spectrum of the sea state while low frequency motions are driven by wave groups and the corresponding wave group spectrum. Wave power spectra can be calibrated for model tests. The corresponding wave group spectrum follows from the wave power spectrum together with the applied wave seed or phasing of the wave train. Thus, in common practice (both in simulations and model tests), the wave group spectrum follows from the arbitrary choice of a random seed. This can lead to an under- or overestimation of the resulting low frequency motions of the moored object as compared to the theoretical group spectrum. As an alternative approach, the seeds which give the highest and lowest wave group spectra can be applied in the tests. In this paper, first results of model tests with a moored tanker based on an intentional choice of wave group spectra are presented.

scholarly journals Precision requirements for interferometric gridding in the analysis of a 21 cm power spectrum

2019 ◽  
Vol 631 ◽  
pp. A12 ◽  
Author(s):  
A. R. Offringa ◽  
F. Mertens ◽  
S. van der Tol ◽  
B. Veenboer ◽  
B. K. Gehlot ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Power Spectra ◽  
Low Frequency ◽  
Projection Algorithm ◽  
Wide Field ◽  
Kernel Size ◽  
Image Domain ◽  
Projection Image ◽  
Excess Power ◽  
Convolutional Gridding

Context. Experiments that try to observe the 21 cm redshifted signals from the epoch of reionisation (EoR) using interferometric low-frequency instruments have stringent requirements on the processing accuracy. Aims. We analyse the accuracy of radio interferometric gridding of visibilities with the aim to quantify the power spectrum bias caused by gridding. We do this ultimately to determine the suitability of different imaging algorithms and gridding settings for an analysis of a 21 cm power spectrum. Methods. We simulated realistic Low-Frequency Array (LOFAR) data and constructed power spectra with convolutional gridding and w stacking, w projection, image-domain gridding, and without w correction. These were compared against data that were directly Fourier transformed. The influence of oversampling, kernel size, w-quantization, kernel windowing function, and image padding were quantified. The gridding excess power was measured with a foreground subtraction strategy, for which foregrounds were subtracted using Gaussian progress regression, as well as with a foreground avoidance strategy. Results. Constructing a power spectrum with a significantly lower bias than the expected EoR signals is possible with the methods we tested, but requires a kernel oversampling factor of at least 4000, and when w-correction is used, at least 500 w-quantization levels. These values are higher than typically used values for imaging, but they are computationally feasible. The kernel size and padding factor parameters are less crucial. Of the tested methods, image-domain gridding shows the highest accuracy with the lowest imaging time. Conclusions. LOFAR 21 cm power spectrum results are not affected by gridding. Image-domain gridding is overall the most suitable algorithm for 21 cm EoR power spectrum experiments, including for future analyses of data from the Square Kilometre Array (SKA) EoR. Nevertheless, convolutional gridding with tuned parameters results in sufficient accuracy for interferometric 21 cm EoR experiments. This also holds for w stacking for wide-field imaging. The w-projection algorithm is less suitable because of the requirements for kernel oversampling, and a faceting approach is unsuitable because it causes spatial discontinuities.

scholarly journals Calibration and 21-cm power spectrum estimation in the presence of antenna beam variations

2019 ◽  
Vol 492 (2) ◽  
pp. 2017-2028 ◽  
Author(s):  
Ronniy C Joseph ◽  
C M Trott ◽  
R B Wayth ◽  
A Nasirudin
Keyword(s):  
Data Analysis ◽  
Power Spectrum ◽  
Low Frequency ◽  
Analytic Description ◽  
Spectral Features ◽  
Spectrum Estimation ◽  
Power Spectrum Estimation ◽  
Murchison Widefield Array ◽  
The Impact ◽  
Expected Signal

ABSTRACT Detecting a signal from the Epoch of Reionization (EoR) requires an exquisite understanding of Galactic and extragalactic 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 a wide variety of modelling residuals in EoR PS estimation. We apply this framework to the specific case of broken dipoles in Murchison Widefield Array (MWA) to understand its effect and estimate its impact on PS estimation. Combining an estimate of the percentage of MWA tiles that have at least one broken dipole (15–40 per cent) with an analytic description of beam errors induced by such dipoles, we compute the residuals of the foregrounds after calibration and source subtraction. We find that that incorrect beam modelling introduces bias in the 2D-PS on the order of $\sim 10^3\, \mathrm{mK}^2 \, h^{-3}\, \mathrm{Mpc}^{3}$. Although this is three orders of magnitude lower than current lowest limits, it is two orders of magnitude higher than the expected signal. Determining the accuracy of both current beam models and direction-dependent calibration pipelines is therefore crucial in our search for an EoR signal.

Log-log scale roughness spectroscopy of surfaces

1993 ◽  
Vol 51 ◽  
pp. 224-225
Author(s):  
P. Fraundorf ◽  
B. Armbruster
Keyword(s):  
Power Spectrum ◽  
Autocorrelation Function ◽  
Power Spectra ◽  
Scanning Force Microscopy ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
Scanning Force ◽  
Lateral Structure ◽  
Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

scholarly journals The anisotropy of the power spectrum in periodic cosmological simulations

2021 ◽  
Vol 503 (4) ◽  
pp. 5638-5645
Author(s):  
Gábor Rácz ◽  
István Szapudi ◽  
István Csabai ◽  
László Dobos
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Power Spectra ◽  
Cosmological Simulations ◽  
Spherical Collapse ◽  
Lower Amplitude ◽  
Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

Sign in / Sign up

Export Citation Format

Share Document