113 research outputs found
Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure
We derive analytical formulae for the Minkowski Functions of the cosmic
microwave background (CMB) and large-scale structure (LSS) from primordial
non-Gaussianity. These formulae enable us to estimate a non-linear coupling
parameter, f_NL, directly from the CMB and LSS data without relying on
numerical simulations of non-Gaussian primordial fluctuations. One can use
these formulae to estimate statistical errors on f_NL from Gaussian
realizations, which are much faster to generate than non-Gaussian ones, fully
taking into account the cosmic/sampling variance, beam smearing, survey mask,
etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe
should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck
data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time
non-Gaussianity arising from gravitational instability and galaxy biasing makes
it more challenging to detect primordial non-Gaussianity at low redshifts. The
late-time effects obscure the primordial signals at small spatial scales.
High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be
required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are
nicely complementary to the bispectrum because the Minkowski Functionals are
defined in real space and the bispectrum is defined in Fourier space. This
property makes the Minksowski Functionals a useful tool in the presence of
real-world issues such as anisotropic noise, foreground and survey masks. Our
formalism can be extended to scale-dependent f_NL easily.Comment: 16 pages, 5 figures, accepted for publication in ApJ (Vol. 653, 2006
Galaxy clustering constraints on deviations from Newtonian gravity at cosmological scales II: Perturbative and numerical analyses of power spectrum and bispectrum
We explore observational constraints on possible deviations from Newtonian
gravity by means of large-scale clustering of galaxies. We measure the power
spectrum and the bispectrum of Sloan Digital Sky Survey galaxies and compare
the result with predictions in an empirical model of modified gravity. Our
model assumes an additional Yukawa-like term with two parameters that
characterize the amplitude and the length scale of the modified gravity. The
model predictions are calculated using two methods; the second-order
perturbation theory and direct N-body simulations. These methods allow us to
study non-linear evolution of large-scale structure. Using the simulation
results, we find that perturbation theory provides reliable estimates for the
power spectrum and the bispectrum in the modified Newtonian model. We also
construct mock galaxy catalogues from the simulations, and derive constraints
on the amplitude and the length scale of deviations from Newtonian gravity. The
resulting constraints from power spectrum are consistent with those obtained in
our earlier work, indicating the validity of the previous empirical modeling of
gravitational nonlinearity in the modified Newtonian model. If linear biasing
is adopted, the bispectrum of the SDSS galaxies yields constraints very similar
to those from the power spectrum. If we allow for the nonlinear biasing
instead, we find that the ratio of the quadratic to linear biasing
coefficients, b_2/b_1, should satisfy -0.4 < b_2/b_1<0.3 in the modified
Newtonian model.Comment: 12 pages, 7 figure
Higher-Order Angular Galaxy Correlations in the SDSS: Redshift and Color Dependence of non-Linear Bias
We present estimates of the N-point galaxy, area-averaged, angular
correlation functions () for = 2,...,7 for
galaxies from the fifth data release of the Sloan Digital Sky Survey. Our
parent sample is selected from galaxies with , and is the
largest ever used to study higher-order correlations. We subdivide this parent
sample into two volume limited samples using photometric redshifts, and these
two samples are further subdivided by magnitude, redshift, and color (producing
early- and late-type galaxy samples) to determine the dependence of
() on luminosity, redshift, and galaxy-type. We
measure () using oversampling techniques and use them
to calculate the projected, . Using models derived from theoretical
power-spectra and perturbation theory, we measure the bias parameters and
, finding that the large differences in both bias parameters ( and
) between early- and late-type galaxies are robust against changes in
redshift, luminosity, and , and that both terms are consistently
smaller for late-type galaxies. By directly comparing their higher-order
correlation measurements, we find large differences in the clustering of
late-type galaxies at redshifts lower than 0.3 and those at redshifts higher
than 0.3, both at large scales ( is larger by at ) and
small scales (large amplitudes are measured at small scales only for ,
suggesting much more merger driven star formation at ). Finally, our
measurements of suggest both that and is negative.Comment: 46 pages, 19 figures, Accepted to Ap
Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?
In this paper, we investigate the utility of Minkowski Functionals as a probe
of cold/hot disk-like structures in the CMB. In order to construct an accurate
estimator, we resolve a long-standing issue with the use of Minkowski
Functionals as probes of the CMB sky -- namely that of systematic differences
("residuals") when numerical and analytical MF are compared. We show that such
residuals are in fact by-products of binning, and not caused by pixelation or
masking as originally thought. We then derive a map-independent estimator that
encodes the effects of binning, applicable to beyond our present work. Using
this residual-free estimator, we show that small disk-like effects (as claimed
by Vielva et al.) can be detected only when a large sample of such maps are
averaged over. In other words, our estimator is noise-dominated for small disk
sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to
the WMAP7 data to obtain a null result.Comment: 15 pages, 13 figure
Topology of structure in the Sloan Digital Sky Survey: model testing
We measure the three-dimensional topology of large-scale structure in the
Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured
with unprecedented statistical accuracy. The sample size is now sufficiently
large to allow the topology to be an important tool for testing galaxy
formation models. For comparison, we make mock SDSS samples using several
state-of-the-art N-body simulations: the Millennium run of Springel et al.
(2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billion
particles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billion
cell hydro mesh). Each of these simulations uses a different method for
modeling galaxy formation. The SDSS data show a genus curve that is broadly
characteristic of that produced by Gaussian random phase initial conditions.
Thus the data strongly support the standard model of inflation where Gaussian
random phase initial conditions are produced by random quantum fluctuations in
the early universe. But on top of this general shape there are measurable
differences produced by non-linear gravitational effects (cf. Matsubara 1994),
and biasing connected with galaxy formation. The N-body simulations have been
tuned to reproduce the power spectrum and multiplicity function but not
topology, so topology is an acid test for these models. The data show a
``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; this
shift also appears in a sub-sample not containing the Wall) which differs at
the 2.5\sigma level from the results of the Millennium run and the Kim & Park
dark halo models, even including the effects of cosmic variance.Comment: 13 Apj pages, 7 figures High-resolution stereo graphic available at
http://www.astro.princeton.edu/~dclayh/stereo50.ep
Note on Redshift Distortion in Fourier Space
We explore features of redshift distortion in Fourier analysis of N-body
simulations. The phases of the Fourier modes of the dark matter density
fluctuation are generally shifted by the peculiar motion along the line of
sight, the induced phase shift is stochastic and has probability distribution
function (PDF) symmetric to the peak at zero shift while the exact shape
depends on the wave vector, except on very large scales where phases are
invariant by linear perturbation theory. Analysis of the phase shifts motivates
our phenomenological models for the bispectrum in redshift space. Comparison
with simulations shows that our toy models are very successful in modeling
bispectrum of equilateral and isosceles triangles at large scales. In the
second part we compare the monopole of the power spectrum and bispectrum in the
radial and plane-parallel distortion to test the plane-parallel approximation.
We confirm the results of Scoccimarro (2000) that difference of power spectrum
is at the level of 10%, in the reduced bispectrum such difference is as small
as a few percents. However, on the plane perpendicular to the line of sight of
k_z=0, the difference in power spectrum between the radial and plane-parallel
approximation can be more than 10%, and even worse on very small scales. Such
difference is prominent for bispectrum, especially for those configurations of
tilted triangles. The non-Gaussian signals under radial distortion on small
scales are systematically biased downside than that in plane-parallel
approximation, while amplitudes of differences depend on the opening angle of
the sample to the observer. The observation gives warning to the practice of
using the power spectrum and bispectrum measured on the k_z=0 plane as
estimation of the real space statistics.Comment: 15 pages, 8 figures. Accepted for publication in ChJA
A Map of the Universe
We have produced a new conformal map of the universe illustrating recent
discoveries, ranging from Kuiper belt objects in the Solar system, to the
galaxies and quasars from the Sloan Digital Sky Survey. This map projection,
based on the logarithm map of the complex plane, preserves shapes locally, and
yet is able to display the entire range of astronomical scales from the Earth's
neighborhood to the cosmic microwave background. The conformal nature of the
projection, preserving shapes locally, may be of particular use for analyzing
large scale structure. Prominent in the map is a Sloan Great Wall of galaxies
1.37 billion light years long, 80% longer than the Great Wall discovered by
Geller and Huchra and therefore the largest observed structure in the universe.Comment: Figure 8, and additional material accessible on the web at:
http://www.astro.princeton.edu/~mjuric/universe
The defect variance of random spherical harmonics
The defect of a function is defined as the
difference between the measure of the positive and negative regions. In this
paper, we begin the analysis of the distribution of defect of random Gaussian
spherical harmonics. By an easy argument, the defect is non-trivial only for
even degree and the expected value always vanishes. Our principal result is
obtaining the asymptotic shape of the defect variance, in the high frequency
limit. As other geometric functionals of random eigenfunctions, the defect may
be used as a tool to probe the statistical properties of spherical random
fields, a topic of great interest for modern Cosmological data analysis.Comment: 19 page
Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies
We present an analysis of the Minkowski Functionals (MFs) describing the WMAP
three-year temperature maps to place limits on possible levels of primordial
non-Gaussianity. In particular, we apply perturbative formulae for the MFs to
give constraints on the usual non-linear coupling constant fNL. The theoretical
predictions are found to agree with the MFs of simulated CMB maps including the
full effects of radiative transfer. The agreement is also very good even when
the simulation maps include various observational artifacts, including the
pixel window function, beam smearing, inhomogeneous noise and the survey mask.
We find accordingly that these analytical formulae can be applied directly to
observational measurements of fNL without relying on non-Gaussian simulations.
Considering the bin-to-bin covariance of the MFs in WMAP in a chi-square
analysis, we find that the primordial non-Gaussianity parameter is constrained
to lie in the range -70<fNL<91 at 95% C.L. using the Q+V+W co-added maps.Comment: 9 pages, 4 figures, accpeted for publication in MNRA
Primordial non-Gaussianity: large-scale structure signature in the perturbative bias model
I compute the effect on the power spectrum of tracers of the large-scale
mass-density field (e.g., galaxies) of primordial non-Gaussianity of the form
Phi=phi+fNL (phi-)+gNL phi^3+..., where Phi is proportional to the
initial potential fluctuations and phi is a Gaussian field, using
beyond-linear-order perturbation theory. I find that the need to eliminate
large higher-order corrections necessitates the addition of a new term to the
bias model, proportional to phi, i.e., delta_g=b_delta delta+b_phi fNL phi+...,
with all the consequences this implies for clustering statistics, e.g.,
P_gg(k)=b_delta^2 P_deltadelta(k)+2 b_delta b_phi fNL P_phidelta(k)+b_phi^2
fNL^2 P_phiphi(k)+... . This result is consistent with calculations based on a
model for dark matter halo clustering, showing that the form is quite general,
not requiring assumptions about peaks, or the formation or existence of halos.
The halo model plays the same role it does in the usual bias picture, giving a
prediction for b_phi for galaxies known to sit in a certain type of halo.
Previous projections for future constraints based on this effect have been very
conservative -- there is enough volume at z<~2 to measure fNL to ~+-1, with
much more volume at higher z. As a prelude to the bias calculation, I point out
that the beyond-linear (in phi) corrections to the power spectrum of
mass-density perturbations are naively infinite, so it is dangerous to assume
they are negligible; however, the infinite part can be removed by a
renormalization of the fluctuation amplitude, with the residual k-dependent
corrections negligible for models allowed by current constraints.Comment: 11 pg, 2 fig, v2: added illustrative figure, minor improvements, v3:
added references, version accepted by PR
- …