221 research outputs found
Non Gaussian Minkowski functionals and extrema counts for 2D sky maps
In the conference presentation we have reviewed the theory of non-Gaussian
geometrical measures for the 3D Cosmic Web of the matter distribution in the
Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that
was developed in a series of our papers. The theory leverages symmetry of
isotropic statistics such as Minkowski functionals and extrema counts to
develop post- Gaussian expansion of the statistics in orthogonal polynomials of
invariant descriptors of the field, its first and second derivatives. The
application of the approach to 2D fields defined on a spherical sky was
suggested, but never rigorously developed. In this paper we present such
development treating effects of the curvature and finiteness of the spherical
space exactly, without relying on the flat-sky approximation. We present
Minkowski functionals, including Euler characteristic and extrema counts to the
first non-Gaussian correction, suitable for weakly non-Gaussian fields on a
sphere, of which CMB is the prime example.Comment: 6 pages, to appear as proceedings of the IAU Symposium No. 308, 2014
The Zeldovich Universe, Genesis and Growth of the Cosmic Web Rien van de
Weygaert, Sergei Shandarin, Enn Saar and Jaan Einast
Statistics of cosmic density profiles from perturbation theory
The joint probability distribution function (PDF) of the density within
multiple concentric spherical cells is considered. It is shown how its cumulant
generating function can be obtained at tree order in perturbation theory as the
Legendre transform of a function directly built in terms of the initial
moments. In the context of the upcoming generation of large-scale structure
surveys, it is conjectured that this result correctly models such a function
for finite values of the variance. Detailed consequences of this assumption are
explored. In particular the corresponding one-cell density probability
distribution at finite variance is computed for realistic power spectra, taking
into account its scale variation. It is found to be in agreement with
-CDM simulations at the few percent level for a wide range of density
values and parameters. Related explicit analytic expansions at the low and high
density tails are given. The conditional (at fixed density) and marginal
probability of the slope -- the density difference between adjacent cells --
and its fluctuations is also computed from the two-cells joint PDF; it also
compares very well to simulations, in particular in under-dense regions, with a
significant reduced cosmic scatter compared to over-dense regions. It is
emphasized that this could prove useful when studying the statistical
properties of voids as it can serve as a statistical indicator to test gravity
models and/or probe key cosmological parameters.Comment: 22 pages, 15 figures, submitted to PR
The large-scale correlations of multi-cell densities and profiles, implications for cosmic variance estimates
In order to quantify the error budget in the measured probability
distribution functions of cell densities, the two-point statistics of cosmic
densities in concentric spheres is investigated. Bias functions are introduced
as the ratio of their two-point correlation function to the two-point
correlation of the underlying dark matter distribution. They describe how cell
densities are spatially correlated. They are computed here via the so-called
large deviation principle in the quasi-linear regime. Their large-separation
limit is presented and successfully compared to simulations for density and
density slopes: this regime is shown to be rapidly reached allowing to get
sub-percent precision for a wide range of densities and variances. The
corresponding asymptotic limit provides an estimate of the cosmic variance of
standard concentric cell statistics applied to finite surveys. More generally,
no assumption on the separation is required for some specific moments of the
two-point statistics, for instance when predicting the generating function of
cumulants containing any powers of concentric densities in one location and one
power of density at some arbitrary distance from the rest. This exact "one
external leg" cumulant generating function is used in particular to probe the
rate of convergence of the large-separation approximation.Comment: 17 pages, 10 figures, replaced to match the MNRAS accepted versio
BEYOND THE POWER SPECTRUM WITH LARGE DEVIATION THEORY
International audienceA large-deviation principle is used to model the time-evolution of the large-scale structure of the Universe. This approach allows for analytical predictions in the mildly non-linear regime, beyond what is commonly achievable via other statistics such as correlation functions. The idea is to measure the mean cosmic densities within concentric spheres and study their joint statistics.The spherical symmetry then leads to surprisingly accurate predictions where standard calculations of perturbation theory usually break down. Results for the one-point statistics of the cosmic density field are shown and implications for future large galaxy surveys are discussed
Peak exclusion, stochasticity and convergence of perturbative bias expansions in 1+1 gravity
The Lagrangian peaks of a 1D cosmological random field representing dark
matter are used as a proxy for a catalogue of biased tracers in order to
investigate the small-scale exclusion in the two-halo term. The two-point
correlation function of peaks of a given height is numerically estimated and
analytical approximations that are valid inside the exclusion zone are derived.
The resulting power spectrum of these tracers is investigated and shows clear
deviations from Poisson noise at low frequencies. On large scales, the
convergence of a perturbative bias expansion is discussed. Finally, we go
beyond Gaussian statistics for the initial conditions and investigate the
subsequent evolution of the two-point clustering of peaks through their
Zel'dovich ballistic displacement, to clarify how exclusion effects mix up with
scale-dependencies induced by nonlinear gravitational evolution. While the
expected large-scale separation limit is recovered, significant deviations are
found in the exclusion zone that tends in particular to be reduced at later
times. Even though these findings apply to the clustering of one-dimensional
tracers, they provide useful insights into halo exclusion and its impact on the
two-halo term.Comment: 16 pages, 9 figures, accepted for publication in MNRA
Non-Gaussian Minkowski functionals & extrema counts in redshift space
In the context of upcoming large-scale structure surveys such as Euclid, it
is of prime importance to quantify the effect of peculiar velocities on
geometric probes. Hence the formalism to compute in redshift space the
geometrical and topological one-point statistics of mildly non-Gaussian 2D and
3D cosmic fields is developed. Leveraging the partial isotropy of the target
statistics, the Gram-Charlier expansion of the joint probability distribution
of the field and its derivatives is reformulated in terms of the corresponding
anisotropic variables. In particular, the cosmic non-linear evolution of the
Minkowski functionals, together with the statistics of extrema are investigated
in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian
redshift distortion correction is estimated for these geometric probes. In 3D,
gravitational perturbation theory is implemented in redshift space to predict
the cosmic evolution of all relevant Gram-Charlier coefficients. Applications
to the estimation of the cosmic parameters sigma(z) and beta=f/b1 from upcoming
surveys is discussed. Such statistics are of interest for anisotropic fields
beyond cosmology.Comment: 35 pages, 15 figures, matches version published in MNRAS with a typo
corrected in eq A1
Encircling the dark: constraining dark energy via cosmic density in spheres
The recently published analytic probability density function for the mildly
non-linear cosmic density field within spherical cells is used to build a
simple but accurate maximum likelihood estimate for the redshift evolution of
the variance of the density, which, as expected, is shown to have smaller
relative error than the sample variance. This estimator provides a competitive
probe for the equation of state of dark energy, reaching a few percent accuracy
on wp and wa for a Euclid-like survey. The corresponding likelihood function
can take into account the configuration of the cells via their relative
separations. A code to compute one-cell density probability density functions
for arbitrary initial power spectrum, top-hat smoothing and various spherical
collapse dynamics is made available online so as to provide straightforward
means of testing the effect of alternative dark energy models and initial
power-spectra on the low-redshift matter distribution.Comment: 7 pages, replaced to match the MNRAS accepted versio
Caught in the rhythm II: Competitive alignments of satellites with their inner halo and central galaxy
The anisotropic distribution of satellites around the central galaxy of their
host halo is well-documented. However the relative impact of baryons and dark
matter in shaping this distribution is still debated. Using the simulation
Horizon-AGN, the angular distribution of satellite galaxies with respect to
their central counterpart and halo is quantified. Below one Rvir, satellites
cluster more strongly in the plane of the central, rather than merely tracing
the shape of their host halo. This is due to the increased isotropy of inner
haloes acquired through their inside-out assembly in vorticity-rich flows along
the cosmic web. While the effect of centrals decreases with distance, halos'
triaxiality increases, impacting more and more the satellite's distribution.
Effects become comparable just outside one virial radius. Above this scale, the
filamentary infall also impacts the satellites distribution, dominating above
two virial radii. The central's morphology plays a governing role: the
alignment w.r.t. the central plane is four times stronger in haloes hosting
stellar discs than in spheroids. But the impact of the galactic plane decreases
for lower satellite-to-central mass ratios, suggesting this might not hold for
dwarf satellites of the Local group. The orientation of the Milky-Way's
satellites traces their cosmic filament, their level of coplanarity is
consistent with systems of similar mass and cosmic location in Horizon-AGN.
However, the strong impact of galactic planes in massive groups and clusters
bounds the likelihood of finding a relaxed region where satellites can be used
to infer halo shape. The minor-to-major axis ratios for haloes with
log(M0/Msun)>13.5 is underestimated by 10%. This error soars quickly to 30-40%
for individual halo measurements.Comment: 30 pages, 28 figures, submitted to A&
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