scholarly journals Quantifying the redshift space distortion of the bispectrum I: primordial non-Gaussianity

2020 ◽  
Vol 493 (1) ◽  
pp. 594-602 ◽  
Author(s):  
Somnath Bharadwaj ◽  
Arindam Mazumdar ◽  
Debanjan Sarkar
Keyword(s):  
Spherical Harmonics ◽  
Real Space ◽  
Line Of Sight ◽  
Multipole Moments ◽  
Distortion Parameter ◽  
Redshift Surveys ◽  
Space Distortion ◽  
Zero Values ◽  
Parallel Approximation ◽  
Analytical Expressions

ABSTRACT The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors $\boldsymbol {k_1},\boldsymbol {k_2},\boldsymbol {k_3}$ with respect to the line of sight. Here, we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this, we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane-parallel approximation, only the first four even ℓ multipoles have non-zero values, and we present explicit analytical expressions for all the non-zero multipoles, that is, upto ℓ = 6 and m = 4. The ratio of the different multipole moments to the real-space bispectrum depends only on β1 the linear redshift distortion parameter and the shape of the triangle. Considering triangles of all possible shapes, we have studied how this ratio depends on the shape of the triangle for β1 = 1. We have also studied the β1 dependence for some of the extreme triangle shapes. If measured in future, these multipole moments hold the potential of constraining β1. The results presented here are also important if one wishes to constrain fNL using redshift surveys.

scholarly journals Quantifying the redshift space distortion of the bispectrum II: induced non-Gaussianity at second-order perturbation

2020 ◽  
Vol 498 (3) ◽  
pp. 3975-3984 ◽  
Author(s):  
Arindam Mazumdar ◽  
Somnath Bharadwaj ◽  
Debanjan Sarkar
Keyword(s):  
Second Order ◽  
Order Perturbation ◽  
Multipole Moments ◽  
Distortion Parameter ◽  
Shape Dependence ◽  
Gravitational Clustering ◽  
Non Linear ◽  
Equilateral Triangles ◽  
Space Distortion ◽  
Analytical Expressions

ABSTRACT The anisotrpy of the redshift space bispectrum $B^s(\boldsymbol {k_1},\boldsymbol {k_2},\boldsymbol {k_3})$, which contains a wealth of cosmological information, is completely quantified using multipole moments $\bar{B}^m_{\ell }(k_1,\mu ,t)$, where k1, the length of the largest side, and (μ, t), respectively, quantify the size and the shape of the triangle $(\boldsymbol {k_1},\boldsymbol {k_2},\boldsymbol {k_3})$. We present analytical expressions for all the multipoles that are predicted to be non-zero (ℓ ≤ 8, m ≤ 6) at second-order perturbation theory. The multipoles also depend on β1, b1, and γ2, which quantify the linear redshift distortion parameter, linear bias and quadratic bias, respectively. Considering triangles of all possible shapes, we analyse the shape dependence of all of the multipoles holding $k_1=0.2 \, {\rm Mpc}^{-1}, \beta _1=1, b_1=1$, and γ2 = 0 fixed. The monopole $\bar{B}^0_0$, which is positive everywhere, is minimum for equilateral triangles. $\bar{B}_0^0$ increases towards linear triangles, and is maximum for linear triangles close to the squeezed limit. Both $\bar{B}^0_{2}$ and $\bar{B}^0_4$ are similar to $\bar{B}^0_0$, however, the quadrupole $\bar{B}^0_2$ exceeds $\bar{B}^0_0$ over a significant range of shapes. The other multipoles, many of which become negative, have magnitudes smaller than $\bar{B}^0_0$. In most cases, the maxima or minima, or both, occur very close to the squeezed limit. $\mid \bar{B}^m_{\ell } \mid$ is found to decrease rapidly if ℓ or m are increased. The shape dependence shown here is characteristic of non-linear gravitational clustering. Non-linear bias, if present, will lead to a different shape dependence.

scholarly journals The Alcock Paczynski test with voids in 21 cm intensity field

2020 ◽  
Vol 499 (1) ◽  
pp. 587-596
Author(s):  
Takao Endo ◽  
Hiroyuki Tashiro ◽  
Atsushi J Nishizawa
Keyword(s):  
Parameter Estimation ◽  
Linear Prediction ◽  
Real Space ◽  
Line Of Sight ◽  
Peculiar Velocities ◽  
The Galaxy ◽  
Intensity Field ◽  
Space Distortion ◽  
Intensity Map ◽  
Free Parameters

ABSTRACT Feasibility of the Alcock Paczynski (AP) test by stacking voids in the 21 cm line intensity field is presented. We analyse the IllustrisTNG simulation to obtain the 21 cm signal map. We then randomly distribute particles depending on the 21 cm intensity field to find voids by using publicly available code, VIDE. As in the galaxy clustering, the shape of the stacked void in the 21 cm field is squashed along the line of sight due to the peculiar velocities in redshift space, although it becomes spherical in real space. The redshift-space distortion for the stacked void weakly depends on redshift and we show that the dependency can be well described by the linear prediction, with the amplitude of the offset being free parameters. We find that the AP test using the stacked voids in a 21 cm intensity map is feasible and the parameter estimation on Ωm and w is unbiased.

scholarly journals Measuring the cosmic bulk flow with 6dFGSv

2014 ◽  
Vol 11 (S308) ◽  
pp. 336-339 ◽  
Author(s):  
Christina Magoulas ◽  
Christopher Springob ◽  
Matthew Colless ◽  
Jeremy Mould ◽  
John Lucey ◽  
...  
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Cosmological Parameters ◽  
Distortion Parameter ◽  
Peculiar Velocity ◽  
Peculiar Velocities ◽  
Redshift Surveys ◽  
Luminous Matter ◽  
The Galaxy ◽  
Space Distortion

AbstractWhile recent years have seen rapid growth in the number of galaxy peculiar velocity measurements, disagreements remain about the extent to which the peculiar velocity field - a tracer of the large-scale distribution of mass - agrees with both ΛCDM expectations and with velocity field models derived from redshift surveys. The 6dF Galaxy Survey includes peculiar velocities for nearly 9 000 early-type galaxies (6dFGSv), making it the largest and most homogeneous galaxy peculiar velocity sample to date. We have used the 6dFGS velocity field to determine the amplitude and scale of large-scale cosmic flows in the local universe and test standard cosmological models. We also compare the galaxy density and peculiar velocity fields to establish the distribution of dark and luminous matter and better constrain key cosmological parameters such as the redshift-space distortion parameter.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

scholarly journals Redshift-space effects in voids and their impact on cosmological tests. Part I: the void size function

2020 ◽  
Vol 500 (1) ◽  
pp. 911-925
Author(s):  
Carlos M Correa ◽  
Dante J Paz ◽  
Ariel G Sánchez ◽  
Andrés N Ruiz ◽  
Nelson D Padilla ◽  
...  
Keyword(s):  
Theoretical Framework ◽  
Real Space ◽  
Global Dynamics ◽  
Void Size ◽  
Spherical Void ◽  
Cosmological Constraints ◽  
Redshift Surveys ◽  
Size Function ◽  
Expansion Effect ◽  
Space Effects

ABSTRACT Voids are promising cosmological probes. Nevertheless, every cosmological test based on voids must necessarily employ methods to identify them in redshift space. Therefore, redshift-space distortions (RSD) and the Alcock–Paczyński effect (AP) have an impact on the void identification process itself generating distortion patterns in observations. Using a spherical void finder, we developed a statistical and theoretical framework to describe physically the connection between the identification in real and redshift space. We found that redshift-space voids above the shot noise level have a unique real-space counterpart spanning the same region of space, they are systematically bigger and their centres are preferentially shifted along the line of sight. The expansion effect is a by-product of RSD induced by tracer dynamics at scales around the void radius, whereas the off-centring effect constitutes a different class of RSD induced at larger scales by the global dynamics of the whole region containing the void. The volume of voids is also altered by the fiducial cosmology assumed to measure distances, this is the AP change of volume. These three systematics have an impact on cosmological statistics. In this work, we focus on the void size function. We developed a theoretical framework to model these effects and tested it with a numerical simulation, recovering the statistical properties of the abundance of voids in real space. This description depends strongly on cosmology. Hence, we lay the foundations for improvements in current models of the abundance of voids in order to obtain unbiased cosmological constraints from redshift surveys.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

scholarly journals The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for the quasar sample

2020 ◽  
Vol 499 (1) ◽  
pp. 269-291 ◽  
Author(s):  
Alex Smith ◽  
Etienne Burtin ◽  
Jiamin Hou ◽  
Richard Neveux ◽  
Ashley J Ross ◽  
...  
Keyword(s):  
Final Analysis ◽  
Systematic Errors ◽  
Acoustic Oscillation ◽  
Sloan Digital Sky Survey ◽  
Fourier Space ◽  
Redshift Surveys ◽  
Sky Survey ◽  
History Of ◽  
Space Distortion ◽  
Halo Occupation Distribution

ABSTRACT The growth rate and expansion history of the Universe can be measured from large galaxy redshift surveys using the Alcock–Paczynski effect. We validate the Redshift Space Distortion models used in the final analysis of the Sloan Digital Sky Survey (SDSS) extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 quasar clustering sample, in configuration and Fourier space, using a series of halo occupation distribution mock catalogues generated using the OuterRim N-body simulation. We test three models on a series of non-blind mocks, in the OuterRim cosmology, and blind mocks, which have been rescaled to new cosmologies, and investigate the effects of redshift smearing and catastrophic redshifts. We find that for the non-blind mocks, the models are able to recover fσ8 to within 3 per cent and α∥ and α⊥ to within 1 per cent. The scatter in the measurements is larger for the blind mocks, due to the assumption of an incorrect fiducial cosmology. From this mock challenge, we find that all three models perform well, with similar systematic errors on fσ8, α∥, and α⊥ at the level of $\sigma _{f\sigma _8}=0.013$, $\sigma _{\alpha _\parallel }=0.012$, and $\sigma _{\alpha _\bot }=0.008$. The systematic error on the combined consensus is $\sigma _{f\sigma _8}=0.011$, $\sigma _{\alpha _\parallel }=0.008$, and $\sigma _{\alpha _\bot }=0.005$, which is used in the final DR16 analysis. For baryon acoustic oscillation fits in configuration and Fourier space, we take conservative systematic errors of $\sigma _{\alpha _\parallel }=0.010$ and $\sigma _{\alpha _\bot }=0.007$.

scholarly journals The FMM-BEM Method for the 3D Particulate Stokes Flow

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Hassib Selmi ◽  
Mohamed Abdelwahed ◽  
Hatem Hamda ◽  
Lassaad El Asmi
Keyword(s):  
Spherical Harmonics ◽  
Stokes Flow ◽  
Transfer Functions ◽  
Stokes Problem ◽  
High Accuracy ◽  
Multipole Moments ◽  
Accuracy Level ◽  
Reasonable Cost

This work introduces new functions based on the spherical harmonics and the solid harmonics which have been used to construct a multipole development for the 3D Stokes problem in order to reduce the operations costs in the BEM method. We show that the major properties of those functions are inherited from the solid harmonics. The contribution of this paper is the introduction of new formulas that serve to calculate the multipole moments and the transfer functions that are necessary for the schemes of orderO(NlogN). Moreover, new translation formulas are introduced to obtain anO(N)scheme. The error truncation of the resulting scheme is discussed. In comparison to the BEM that attains a limit storage atO(104), we present here a method based on FMM-BEM that attains a storage at a limit ofO(106). The implementation of the method achieves a high accuracy level at a reasonable cost.

scholarly journals Discovering Orbit and Clock Quality Based on Analysis of Wide-Lane Ambiguities Derived from PPP Models

2018 ◽  
Author(s):  
Gang Chen ◽  
Sijing Liu ◽  
Qile Zhao
Keyword(s):  
Real Time ◽  
Quality Index ◽  
Precise Point Positioning ◽  
Line Of Sight ◽  
New Approach ◽  
Actual Time ◽  
Estimation Procedures ◽  
Wide Lane ◽  
Point Positioning ◽  
Analytical Expressions

Orbit and clock products are used in real-time GNSS precise point positioning without knowing their quality. This study develops a new approach to detect orbit and clock errors through comparing geometry-free and geometry-based wide-lane ambiguities in PPP model. The reparameterization and estimation procedures of the geometry-free and geometry-based ambiguities are described in detail. The effects of orbit and clock errors on ambiguities are given in analytical expressions. The numerical similarity and differences of geometry-free and geometry-based wide-lane ambiguities are analyzed using different orbit and clock products. Furthermore, two types of typical errors in orbit and clock are simulated and their effects on wide-lane ambiguities are numerically produced and analyzed. The contribution discloses that the geometry-free and geometry-based wide-lane ambiguities are equivalent in terms of their formal errors. Although they are very close in terms of their estimates when the used orbit and clock for geometry-based ambiguities are precise enough, they are not the same, in particular, in the case that the used orbit and clock, as a combination, contain significant errors. It is discovered that the discrepancies of geometry-free and geometry-based wide-lane ambiguities are coincided with the actual time-variant errors in the used orbit and clock at the line-of-sight direction. This provides a quality index for real-time users to detect the errors in real-time orbit and clock products, which potentially improves the accuracy of positioning.

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