Weak lensing effects on the galaxy three-point correlation function

The two point correlation function w(θ) has been evaluated for the galaxies measured by the COSMOS machine at the Royal Observatory, Edinburgh, in an area of about 2 square degrees on a 2 hour exposure J plate and a 2 hour exposure R plate (Phillipps, S., Fong, R., Ellis, R.S., Fall, S.M. and MacGillivray, H.T., 1977, Mon. Not. R. astr. Soc., in press). in each case w(θ) is found to be in agreement with the form w = Aθ−0.8 found previously by Peebles and coworkers. Since the samples are not magnitude limited the selection function, i.e. the distribution in distance, was determined by using models of the galaxy distribution to fit the observed angular diameter counts. However, when these selection functions are used to scale the amplitudes found for our samples, the amplitudes are found to be lower than those expected from Peebles' results by a factor of about 3. We consider that this is likely to be due to a lack of clusters in the small area of sky which we have studied: analysis of further areas should show whether this is the case.

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Measuring the galaxy-galaxy-mass three-point correlation function with weak gravitational lensing

Monthly Notices of the Royal Astronomical Society ◽

10.1111/j.1365-2966.2006.10011.x ◽

2006 ◽

Vol 367 (3) ◽

pp. 1222-1240 ◽

Cited By ~ 6

Author(s):

D. E. Johnston

Keyword(s):

Correlation Function ◽

Gravitational Lensing ◽

Weak Gravitational Lensing ◽

The Galaxy ◽

Point Correlation ◽

Point Correlation Function

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Estimating the galaxy two-point correlation function using a split random catalog

Astronomy and Astrophysics ◽

10.1051/0004-6361/201935828 ◽

2019 ◽

Vol 631 ◽

pp. A73 ◽

Cited By ~ 2

Author(s):

E. Keihänen ◽

H. Kurki-Suonio ◽

V. Lindholm ◽

A. Viitanen ◽

A.-S. Suur-Uski ◽

...

Keyword(s):

Correlation Function ◽

Computational Cost ◽

Computation Time ◽

Monte Carlo Sampling ◽

Sampling Errors ◽

The Galaxy ◽

Data Pair ◽

Point Correlation ◽

Point Correlation Function ◽

Percent Accuracy

The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the galaxy positions and the expected galaxy density field. The expected field is commonly specified using a Monte-Carlo sampling of the volume covered by the survey and, to minimize additional sampling errors, this random catalog has to be much larger than the data catalog. Correlation function estimators compare data–data pair counts to data–random and random–random pair counts, where random–random pairs usually dominate the computational cost. Future redshift surveys will deliver spectroscopic catalogs of tens of millions of galaxies. Given the large number of random objects required to guarantee sub-percent accuracy, it is of paramount importance to improve the efficiency of the algorithm without degrading its precision. We show both analytically and numerically that splitting the random catalog into a number of subcatalogs of the same size as the data catalog when calculating random–random pairs and excluding pairs across different subcatalogs provides the optimal error at fixed computational cost. For a random catalog fifty times larger than the data catalog, this reduces the computation time by a factor of more than ten without affecting estimator variance or bias.

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The weak lensing bispectrum induced by gravity

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa296 ◽

2020 ◽

Vol 493 (3) ◽

pp. 3985-3995 ◽

Cited By ~ 6

Author(s):

D Munshi ◽

T Namikawa ◽

T D Kitching ◽

J D McEwen ◽

R Takahashi ◽

...

Keyword(s):

Correlation Function ◽

Signal To Noise Ratio ◽

Theoretical Modelling ◽

Weak Lensing ◽

High Signal ◽

Signal To Noise ◽

The Third ◽

Theoretical Predictions ◽

Point Correlation ◽

Point Correlation Function

ABSTRACT Recent studies have demonstrated that secondary non-Gaussianity induced by gravity will be detected with a high signal-to-noise ratio (S/N) by future and even by on-going weak lensing surveys. One way to characterize such non-Gaussianity is through the detection of a non-zero three-point correlation function of the lensing convergence field, or of its harmonic transform, the bispectrum. A recent study analysed the properties of the squeezed configuration of the bispectrum, when two wavenumbers are much larger than the third one. We extend this work by estimating the amplitude of the (reduced) bispectrum in four generic configurations, i.e. squeezed, equilateral, isosceles and folded, and for four different source redshifts zs = 0.5, 1.0, 1.5, 2.0, by using an ensemble of all-sky high-resolution simulations. We compare these results against theoretical predictions. We find that, while the theoretical expectations based on widely used fitting functions can predict the general trends of the reduced bispectra, a more accurate theoretical modelling will be required to analyse the next generation of all-sky weak lensing surveys. The disagreement is particularly pronounced in the squeezed limit.

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Weak lensing cosmology with convolutional neural networks on noisy data

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2610 ◽

2019 ◽

Vol 490 (2) ◽

pp. 1843-1860 ◽

Cited By ~ 8

Author(s):

Dezső Ribli ◽

Bálint Ármin Pataki ◽

José Manuel Zorrilla Matilla ◽

Daniel Hsu ◽

Zoltán Haiman ◽

...

Keyword(s):

Neural Networks ◽

Correlation Function ◽

Power Spectrum ◽

Convolutional Neural Networks ◽

Higher Order ◽

Weak Lensing ◽

Noise Levels ◽

Point Correlation ◽

Point Correlation Function ◽

Non Gaussian

ABSTRACT Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, Euclid, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher order statistics such as the three-point correlation function, peak counts, or Minkowski functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2D or 3D astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of (σ8, Ωm) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4–2.8 times smaller credible contours than the power spectrum, and 3.5–4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4–2.1 times smaller contours than peak counts, a higher order statistic capable of extracting non-Gaussian information from weak lensing maps.

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