Nonlinear redshift-space distortions in the harmonic-space galaxy power spectrum

Henry S. Grasshorn Gebhardt; Donghui Jeong

doi:10.1103/physrevd.102.083521

Dark Energy Survey Year 1 results: measurement of the galaxy angular power spectrum

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1514 ◽

2019 ◽

Vol 487 (3) ◽

pp. 3870-3883 ◽

Cited By ~ 6

Author(s):

H Camacho ◽

N Kokron ◽

F Andrade-Oliveira ◽

R Rosenfeld ◽

M Lima ◽

...

Keyword(s):

Power Spectrum ◽

Covariance Matrix ◽

Goodness Of Fit ◽

Effective Area ◽

Real Space ◽

Harmonic Space ◽

Angular Power Spectrum ◽

Space Analysis ◽

The Galaxy ◽

The Impact

ABSTRACT We use data from the first-year observations of the DES collaboration to measure the galaxy angular power spectrum (APS), and search for its BAO feature. We test our methodology in a sample of 1800 DES Y1-like mock catalogues. We use the pseudo-Cℓ method to estimate the APS and the mock catalogues to estimate its covariance matrix. We use templates to model the measured spectra and estimate template parameters firstly from the Cℓ’s of the mocks using two different methods, a maximum likelihood estimator and a Markov Chain Monte Carlo, finding consistent results with a good reduced χ2. Robustness tests are performed to estimate the impact of different choices of settings used in our analysis. Finally, we apply our method to a galaxy sample constructed from DES Y1 data specifically for LSS studies. This catalogue comprises galaxies within an effective area of 1318 deg2 and 0.6 < z < 1.0. We find that the DES Y1 data favour a model with BAO at the $2.6 \sigma$ C.L. However, the goodness of fit is somewhat poor, with χ2/(d.o.f.) = 1.49. We identify a possible cause showing that using a theoretical covariance matrix obtained from Cℓ’s that are better adjusted to data results in an improved value of χ2/(dof) = 1.36 which is similar to the value obtained with the real-space analysis. Our results correspond to a distance measurement of DA(zeff = 0.81)/rd = 10.65 ± 0.49, consistent with the main DES BAO findings. This is a companion paper to the main DES BAO article showing the details of the harmonic space analysis.

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The on-line use of histogram data for high-speed correction and alignment of electron microscope images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100112713 ◽

1984 ◽

Vol 42 ◽

pp. 556-557

Author(s):

William Krakow

Keyword(s):

Power Spectrum ◽

High Speed ◽

Direct Memory Access ◽

Digital Television ◽

Contrast Transfer Function ◽

The Past ◽

High Resolution Tem ◽

On Line ◽

Correction Of Astigmatism ◽

The Fourier Transform

In the past few years on-line digital television frame store devices coupled to computers have been employed to attempt to measure the microscope parameters of defocus and astigmatism. The ultimate goal of such tasks is to fully adjust the operating parameters of the microscope and obtain an optimum image for viewing in terms of its information content. The initial approach to this problem, for high resolution TEM imaging, was to obtain the power spectrum from the Fourier transform of an image, find the contrast transfer function oscillation maxima, and subsequently correct the image. This technique requires a fast computer, a direct memory access device and even an array processor to accomplish these tasks on limited size arrays in a few seconds per image. It is not clear that the power spectrum could be used for more than defocus correction since the correction of astigmatism is a formidable problem of pattern recognition.

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Log-log scale roughness spectroscopy of surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146965 ◽

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.

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