135 research outputs found
Fast Edge Corrected Measurement of the Two-Point Correlation Function and the Power Spectrum
We present two related techniques to measure the two-point correlation
function and the power spectrum with edge correction in any spatial dimensions.
The underlying algorithm uses fast Fourier transforms for calculating the
two-point function with an heuristically weighted edge corrected estimator.
Once the correlation function is measured, we estimate the power spectrum via
numerical integration of the Hankel transform connecting the two. We introduce
an efficient numerical technique based on Gauss-Bessel-quadrature and double
exponential transformation. This, combined with our, or any similar, two-point
function estimator leads to a novel edge corrected estimator for power spectra.
The pair of techniques presented are the Euclidean analogs of those developed
and widely used in cosmic microwave background research for spherical maps.Comment: 4 pages, 2 figures, submitted to ApJ
Effects of Sampling on Statistics of Large Scale Structure
The effects of sampling are investigated on measurements of counts-in-cells
in three-dimensional magnitude limited galaxy surveys, with emphasis on moments
of the underlying smooth galaxy density field convolved with a spherical
window. A new estimator is proposed for measuring the k-th order moment < rho^k
>: the weighted factorial moment F_k[w], corrected for the effects of the
varying selection function.
The cosmic error on the measurement of F_k[w] is computed via the the
formalism of Szapudi & Colombi (1996), which is generalized to include
selection effects. The integral equation for finding the minimum variance
weight is solved numerically, and an intuitive analytical approximation is
derived. The resulting estimator is more accurate than the traditional method
of counts-in-cells in volume limited samples, which discards useful
information. As a practical example we consider the case of the future Sloan
Digital Sky Survey.
Optimal (sparse) sampling strategies for designing magnitude limited redshift
surveys are investigated as well. It is found that the optimal strategy depends
greatly on the statistics and scales considered.
Finally we consider the issue of designing the geometry of a catalog, when it
covers only a small fraction of the sky.Comment: 24 pages, 9 figures, Latex (MN format), accepted for publication in
MNRA
Evidence for a high-z ISW signal from supervoids in the distribution of eBOSS quasars
The late-time integrated Sachs-Wolfe (ISW) imprint of super-structures is sourced by evolving large-scale
potentials due to a dominant dark energy component in the CDM model.
The aspect that makes the ISW effect distinctly interesting is the repeated
observation of stronger-than-expected imprints from supervoids at
. Here we analyze the un-probed key redshift range
where the ISW signal is expected to fade in CDM, due to a weakening
dark energy component, and eventually become consistent with zero in the matter
dominated epoch. On the contrary, alternative cosmological models, proposed to
explain the excess low- ISW signals, predicted a sign-change in the ISW
effect at due to the possible growth of large-scale potentials
that is absent in the standard model. To discriminate, we estimated the
high- CDM ISW signal using the Millennium XXL mock catalogue, and
compared it to our measurements from about 800 supervoids identified in the
eBOSS DR16 quasar catalogue. At , we found an excess ISW signal with
amplitude. The signal is then consistent with
the CDM expectation () at where the
standard and alternative models predict similar amplitudes. Most interestingly,
we also detected an opposite-sign ISW signal at that is in
tension with the CDM prediction. Taken at face value,
these moderately significant detections of ISW anomalies suggest an alternative
growth rate of structure in low-density environments at scales.Comment: 12 pages, 9 figures, submitted to MNRA
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