1,115 research outputs found
Biased-estimations of the Variance and Skewness
Nonlinear combinations of direct observables are often used to estimate
quantities of theoretical interest. Without sufficient caution, this could lead
to biased estimations. An example of great interest is the skewness of
the galaxy distribution, defined as the ratio of the third moment \xibar_3
and the variance squared \xibar_2^2. Suppose one is given unbiased estimators
for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does
not necessarily result in an unbiased estimator of . Exactly such an
estimation-bias affects most existing measurements of . Furthermore,
common estimators for \xibar_3 and \xibar_2 suffer also from this kind of
estimation-bias themselves: for \xibar_2, it is equivalent to what is
commonly known as the integral constraint. We present a unifying treatment
allowing all these estimation-biases to be calculated analytically. They are in
general negative, and decrease in significance as the survey volume increases,
for a given smoothing scale. We present a re-analysis of some existing
measurements of the variance and skewness and show that most of the well-known
systematic discrepancies between surveys with similar selection criteria, but
different sizes, can be attributed to the volume-dependent estimation-biases.
This affects the inference of the galaxy-bias(es) from these surveys. Our
methodology can be adapted to measurements of analogous quantities in quasar
spectra and weak-lensing maps. We suggest methods to reduce the above
estimation-biases, and point out other examples in LSS studies which might
suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap
Observational Constraints on Higher Order Clustering up to $z\simeq 1
Constraints on the validity of the hierarchical gravitational instability
theory and the evolution of biasing are presented based upon measurements of
higher order clustering statistics in the Deeprange Survey, a catalog of
galaxies with derived from a KPNO 4m CCD imaging
survey of a contiguous region. We compute the
3-point and 4-point angular correlation functions using a direct estimation for
the former and the counts-in-cells technique for both. The skewness
decreases by a factor of as galaxy magnitude increases over the
range (). This decrease is
consistent with a small {\it increase} of the bias with increasing redshift,
but not by more than a factor of 2 for the highest redshifts probed. Our
results are strongly inconsistent, at about the level, with
typical cosmic string models in which the initial perturbations follow a
non-Gaussian distribution - such models generally predict an opposite trend in
the degree of bias as a function of redshift. We also find that the scaling
relation between the 3-point and 4-point correlation functions remains
approximately invariant over the above magnitude range. The simplest model that
is consistent with these constraints is a universe in which an initially
Gaussian perturbation spectrum evolves under the influence of gravity combined
with a low level of bias between the matter and the galaxies that decreases
slightly from to the current epoch.Comment: 28 pages, 4 figures included, ApJ, accepted, minor change
A Comparison of Semi-Analytic and Smoothed Particle Hydrodynamics Galaxy Formation
We compare the statistical properties of galaxies found in two different
models of hierarchical galaxy formation: the semi-analytic model of Cole et al.
and the smoothed particle hydrodynamics (SPH) simulations of Pearce et al.
Using a `stripped-down' version of the semi-analytic model which mimics the
resolution of the SPH simulations and excludes physical processes not included
in them, we find that the two models produce an ensemble of galaxies with
remarkably similar properties, although there are some differences in the gas
cooling rates and in the number of galaxies that populate halos of different
mass. The full semi-analytic model, which has effectively no resolution limit
and includes a treatment of star formation and supernovae feedback, produces
somewhat different (but readily understandable) results. Agreement is
particularly good for the present-day global fractions of hot gas, cold dense
(i.e. galactic) gas and uncollapsed gas, for which the SPH and stripped-down
semi-analytic calculations differ by at most 25%. In the most massive halos,
the stripped-down semi-analytic model predicts, on the whole, up to 50% less
gas in galaxies than is seen in the SPH simulations. The two techniques
apportion this cold gas somewhat differently amongst galaxies in a given halo.
This difference can be tracked down to the greater cooling rate in massive
halos in the SPH simulation compared to the semi-analytic model. (abridged)Comment: 19 pages, 13 figures, to appear in MNRAS. Significantly extended to
explore galaxy progenitor distributions and behaviour of models at high
redshift
Large Scale Fluctuations in the X-Ray Background
We present an attempt to measure the large angular scale fluctuations in the
X-Ray Background (XRB) from the HEAO1-A2 data, expressed in terms of spherical
harmonics. We model the harmonic coefficients assuming a power spectrum and an
epoch-dependent bias parameter, and using a phenomenological scenario
describing the evolution of the X-ray sources. From the few low-order
multipoles detected above shot noise, we estimate the power-spectrum
normalization on scales intermediate between those explored by local galaxy
redshift surveys (~ 100 Mpc) and by the COBE Microwave Background measurements
(~ 1000 Mpc). We find that the HEAO1 harmonics are consistent with present
epoch rms fluctuations of the X-ray sources bx(0)sigma8 ~ 1-2 in 8 Mpc spheres.
Therefore the observed fluctuations in the XRB are roughly as expected from
interpolating between the local galaxy surveys and the COBE CMB experiment. We
predict that an X-ray all-sky surface brightness survey resolving sources a
factor of 10 fainter than HEAO1, may reveal fluctuations to significantly
larger angular scales and therefore more strongly constrain the large scale
structure of the Universe on scales of hundreds of Mpcs.Comment: 14 pages, 3 Postscript figures, uses aaspp4.sty and psfig. Revised
following referee's report. Accepted for publication in Ap
Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog
We present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy
Redshift Survey. There are ten reconstructions of galaxy density fields in real
space spanning the range to , where
, is the present dimensionless density and
is the bias factor. Our method uses the growth of the largest cluster
statistic to characterize the topology of a density field, where Gaussian
randomized versions of the reconstructions are used as standards for analysis.
For the reconstruction volume of radius, Mpc,
percolation analysis reveals a slight `meatball' topology for the real space,
galaxy distribution of the IRAS survey.
cosmology-galaxies:clustering-methods:numericalComment: Revised version accepted for publication in The Astrophysical
Journal, January 10, 1997 issue, Vol.47
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