85 research outputs found
Non-negative matrix factorization for self-calibration of photometric redshift scatter in weak lensing surveys
Photo-z error is one of the major sources of systematics degrading the
accuracy of weak lensing cosmological inferences. Zhang et al. (2010) proposed
a self-calibration method combining galaxy-galaxy correlations and galaxy-shear
correlations between different photo-z bins. Fisher matrix analysis shows that
it can determine the rate of photo-z outliers at a level of 0.01-1% merely
using photometric data and do not rely on any prior knowledge. In this paper,
we develop a new algorithm to implement this method by solving a constrained
nonlinear optimization problem arising in the self-calibration process. Based
on the techniques of fixed-point iteration and non-negative matrix
factorization, the proposed algorithm can efficiently and robustly reconstruct
the scattering probabilities between the true-z and photo-z bins. The algorithm
has been tested extensively by applying it to mock data from simulated stage IV
weak lensing projects. We find that the algorithm provides a successful
recovery of the scatter rates at the level of 0.01-1%, and the true mean
redshifts of photo-z bins at the level of 0.001, which may satisfy the
requirements in future lensing surveys.Comment: 12 pages, 6 figures. Accepted for publication in ApJ. Updated to
match the published versio
Weak lensing power spectrum reconstruction by counting galaxies.-- I: the ABS method
We propose an Analytical method of Blind Separation (ABS) of cosmic
magnification from the intrinsic fluctuations of galaxy number density in the
observed galaxy number density distribution. The ABS method utilizes the
different dependences of the signal (cosmic magnification) and contamination
(galaxy intrinsic clustering) on galaxy flux, to separate the two. It works
directly on the measured cross galaxy angular power spectra between different
flux bins. It determines/reconstructs the lensing power spectrum analytically,
without assumptions of galaxy intrinsic clustering and cosmology. It is
unbiased in the limit of infinite number of galaxies. In reality the lensing
reconstruction accuracy depends on survey configurations, galaxy biases, and
other complexities, due to finite number of galaxies and the resulting shot
noise fluctuations in the cross galaxy power spectra. We estimate its
performance (systematic and statistical errors) in various cases. We find that,
stage IV dark energy surveys such as SKA and LSST are capable of reconstructing
the lensing power spectrum at and \ell\la 5000 accurately. This
lensing reconstruction only requires counting galaxies, and is therefore highly
complementary to the cosmic shear measurement by the same surveys.Comment: v1: 13 pages, 10 figures. v2: minor revisions. ApJ in pres
The source-lens clustering effect in the context of lensing tomography and its self-calibration
Cosmic shear can only be measured where there are galaxies. This source-lens
clustering (SLC) effect has two sources, intrinsic source clustering and cosmic
magnification (magnification/size bias). Lensing tomography can suppress the
former. However, this reduction is limited by the existence of photo-z error
and nonzero redshift bin width. Furthermore, SLC induced by cosmic
magnification cannot be reduced by lensing tomography. Through N-body
simulations, we quantify the impact of SLC on the lensing power spectrum in the
context of lensing tomography. We consider both the standard estimator and the
pixel-based estimator. We find that none of them can satisfactorily handle both
sources of SLC. (1) For the standard estimator, SLC induced by both sources can
bias the lensing power spectrum by O(1)-O(10)%. Intrinsic source clustering
also increases statistical uncertainties in the measured lensing power
spectrum. However, the standard estimator suppresses intrinsic source
clustering in the cross-spectrum. (2) In contrast, the pixel-based estimator
suppresses SLC through cosmic magnification. However, it fails to suppress SLC
through intrinsic source clustering and the measured lensing power spectrum can
be biased low by O(1)-O(10)%. In short, for typical photo-z errors
(sigma_z/(1+z)=0.05) and photo-z bin sizes (Delta_z^P=0.2), SLC alters the
lensing E-mode power spectrum by 1-10%, with ell~10^3$ and z_s~1 being of
particular interest to weak lensing cosmology. Therefore the SLC is a severe
systematic for cosmology in Stage-IV lensing surveys. We present useful scaling
relations to self-calibrate the SLC effect.Comment: 13 pages, 10 figures, Accepted by AP
Kriging Interpolating Cosmic Velocity Field
[abridged] Volume-weighted statistics of large scale peculiar velocity is
preferred by peculiar velocity cosmology, since it is free of uncertainties of
galaxy density bias entangled in mass-weighted statistics. However, measuring
the volume-weighted velocity statistics from galaxy (halo/simulation particle)
velocity data is challenging. For the first time, we apply the Kriging
interpolation to obtain the volume-weighted velocity field. Kriging is a
minimum variance estimator. It predicts the most likely velocity for each place
based on the velocity at other places. We test the performance of Kriging
quantified by the E-mode velocity power spectrum from simulations. Dependences
on the variogram prior used in Kriging, the number of the nearby
particles to interpolate and the density of the observed sample are
investigated. First, we find that Kriging induces and systematics
at when
and , respectively. The deviation
increases for decreasing and increasing . When , a smoothing effect dominates small scales, causing
significant underestimation of the velocity power spectrum. Second, increasing
helps to recover small scale power. However, for cases, the recovery is limited. Finally, Kriging is
more sensitive to the variogram prior for lower sample density. The most
straightforward application of Kriging on the cosmic velocity field does not
show obvious advantages over the nearest-particle method (Zheng et al. 2013)
and could not be directly applied to cosmology so far. However, whether
potential improvements may be achieved by more delicate versions of Kriging is
worth further investigation.Comment: 11 pages, 5 figures, published in PR
Gaussianizing the non-Gaussian lensing convergence field I: the performance of the Gaussianization
Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010,
we proposed a Gaussianization transform to Gaussianize the non-Gaussian lensing
convergence field . It performs a local monotonic transformation
pixel by pixel to make the unsmoothed one-point
probability distribution function of the new variable Gaussian. We tested
whether the whole field is Gaussian against N-body simulations. (1) We
found that the proposed Gaussianization suppresses the non-Gaussianity by
orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and
6th-order cumulants of the field smoothed over various angular scales
relative to that of the corresponding smoothed field. The residual
non-Gaussianities are often consistent with zero within the statistical errors.
(2) The Gaussianization significantly suppresses the bispectrum. Furthermore,
the residual scatters around zero, depending on the configuration in the
Fourier space. (3) The Gaussianization works with even better performance for
the 2D fields of the matter density projected over \sim 300 \mpch distance
interval centered at , which can be reconstructed from the weak
lensing tomography. (4) We identified imperfectness and complexities of the
proposed Gaussianization. We noticed weak residual non-Gaussianity in the
field. We verified the widely used logarithmic transformation as a good
approximation to the Gaussianization transformation. However, we also found
noticeable deviations.Comment: 13 pages, 15 figures, accepted by PR
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