We present a scheme based on artificial neural networks (ANN) to estimate the line-of-sight velocities of individual galaxies from an observed redshift-space galaxy distribution. We find an estimate of the peculiar velocity at a galaxy based on galaxy counts and barycenters in shells around it. By training the network with environmental characteristics, such as the total mass and mass center within each shell surrounding every galaxy in redshift space, our ANN model can accurately predict the line-of-sight velocity of each individual galaxy. When this velocity is used to eliminate the RSD effect, the two-point correlation function (TPCF) in real space can be recovered with an accuracy better than 1% at $s$ > 8 $h^{-1}\mathrm{Mpc}$, and 4% on all scales compared to ground truth. The real-space power spectrum can be recovered within 3% on $k$< 0.5 $\mathrm{Mpc}^{-1}h$, and less than 5% for all $k$ modes. The quadrupole moment of the TPCF or power spectrum is almost zero down to $s$ = 10 $h^{-1}\mathrm{Mpc}$ or all $k$ modes, indicating an effective correction of the spatial anisotropy caused by the RSD effect. We demonstrate that on large scales, without additional training with new data, our network is adaptable to different galaxy formation models, different cosmological models, and mock galaxy samples at high redshifts and high biases, achieving less than 10% error for scales greater than 15 $h^{-1}\mathrm{Mpc}$. As it is sensitive to large-scale densities, it does not manage to remove Fingers of God in large clusters, but works remarkably well at recovering real-space galaxy positions elsewhere. Our scheme provides a novel way to predict the peculiar velocity of individual galaxies, to eliminate the RSD effect directly in future large galaxy surveys, and to reconstruct the 3-D cosmic velocity field accurately.
We present a new model for the cross-covariance between galaxy redshift-space distortions and peculiar velocities. We combine this with the auto-covariance models of both probes in a fully self-consistent, maximum-likelihood method, allowing us to extract enhanced cosmological parameter constraints. When applying our method to the 6-degree Field Galaxy Survey (6dFGS), our constraint on the growth rate of structure is $fσ_8 = 0.384 \pm 0.052 \rm{(stat)} \pm 0.061 \rm{(sys)}$ and our constraint for the redshift-space distortion parameter is $β= 0.289^{+0.044}_{-0.043} \rm{(stat)} \pm 0.049 \rm{(…
Line-of-sight shear in SLACS strong lenses II: validation tests with an extended sample
University of Cambridge（剑桥大学）；Kavli Institute for Cosmology, University of Cambridge（剑桥大学卡弗里宇宙学研究所）；Laboratoire Univers et Particules de Montpellier, CNRS & Université de Montpellier（蒙彼利埃大学与法国国家科学研究中心宇宙与粒子物理实验室）；University of Chicago（芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Independent University, Bangladesh（孟加拉独立大学）
We present a family of robust tracer mass estimators to compute the enclosed mass of galaxy haloes from samples of discrete positional and kinematical data of tracers, such as halo stars, globular clusters and dwarf satellites. The data may be projected positions, distances, line of sight velocities or proper motions. Forms of the estimator tailored for the Milky Way galaxy and for M31 are given. Monte Carlo simulations are used to quantify the uncertainty as a function of sample size. For the Milky Way, the satellite sample consists of 26 galaxies with line-of-sight velocities. We find that t…
The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as `wide angle' effects in redshift space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work we study how wide-angle effects modify the …
Accurate mock catalogues are essential for assessing systematics in the cosmological analysis of large galaxy surveys. Anisotropic two-point clustering measurements from the same simulation show some scatter for different lines of sight (LOS), but are on average equal, due to cosmic variance. This results in scatter in the measured cosmological parameters. We use the OuterRim N-body simulation halo catalogue to investigate this, considering the 3 simulation axes as LOS. The quadrupole of the 2-point statistics is particularly sensitive to changes in the LOS, with sub-percent level differences …
We present a new technique to measure neutrino masses using their flow field relative to dark matter. Present day streaming motions of neutrinos relative to dark matter and baryons are several hundred km/s, comparable with their thermal velocity dispersion. This results in a unique dipole anisotropic distortion of the matter-neutrino cross power spectrum, which is observable through the dipole distortion in the cross correlation of different galaxy populations. Such a dipole vanishes if not for this relative velocity and so it is a clean signature for neutrino mass. We estimate the size of thi…
We develop a methodology to use the redshift dependence of the galaxy 2-point correlation function (2pCF) across the line-of-sight, $ξ(r_{\bot})$, as a probe of cosmological parameters. The positions of galaxies in comoving Cartesian space varies under different cosmological parameter choices, inducing a {\it redshift-dependent scaling} in the galaxy distribution. This geometrical distortion can be observed as a redshift-dependent rescaling in the measured $ξ(r_{\bot})$. We test this methodology using a sample of 1.75 billion mock galaxies at redshifts 0, 0.5, 1, 1.5, 2, drawn from the Horizon…
Galaxy surveys aim to map the large-scale structure of the Universe and use redshift space distortions to constrain deviations from general relativity and probe the existence of massive neutrinos. However, the amount of information that can be extracted is limited by the accuracy of theoretical models used to analyze the data. Here, by using the L-Galaxies semi-analytical model run over the MXXL N-body simulation, we assess the impact of galaxy formation on satellite kinematics and the theoretical modelling of redshift-space distortions. We show that different galaxy selection criteria lead to…
We show that redshift-space distortions of galaxy correlations have a strong effect on correlation functions with distinct, localized features, like the signature of the baryon acoustic oscillations (BAO). Near the line of sight, the features become sharper as a result of redshift-space distortions. We demonstrate this effect by measuring the correlation function in Gaussian simulations and the Millennium Simulation. We also analyze the SDSS DR7 main-galaxy sample (MGS), splitting the sample into slices 2.5 degrees on the sky in various rotations. Measuring 2D correlation functions in each sli…
Baryonic feedback can significantly modify the spatial distribution of matter on small scales and create a bulk relative velocity between the dominant cold dark matter and the hot gas. We study the consequences of such bulk motions using two high resolution hydrodynamic simulations, one with no feedback and one with very strong feedback. We find that relative velocities of order $100\ \kms$ are produced in the strong feedback simulation whereas it is much smaller when there is no feedback. Such relative motions induce dipole distortions to the gas, which we quantify by computing the dipole cor…
We use the Millennium simulation to probe the correlation between cluster velocities and their shapes and the consequences for measurements of the kinetic Sunyaev-Zeldovich (kSZ) effect. Halos are generally prolate ellipsoids with orientations that are correlated with those of nearby halos. We measure the mean streaming velocities of halos along the lines that separate them, demonstrating that the peculiar velocities and the long axes of halos tend to be somewhat aligned, especially for the most massive halos. Since the kSZ effect is proportional to the line-of-sight velocity and the optical d…
We examine the chemical and emission properties of mildly irradiated (G0=1) magnetised shocks in diffuse media (nH=10^2 to 10^4 /cm3) at low to moderate velocities (from 3 to 40 km/s). Results: The formation of some molecules relies on endoergic reactions. In J-shocks, their abundances are enhanced by several orders of magnitude for shock velocities as low as 7 km/s. Otherwise most chemical properties of J-type shocks vary over less than an order of magnitude between velocities from about 7 to about 30 km/s, where H2 dissociation sets in. C-type shocks display a more gradual molecular enhancem…
The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result fo…
The streaming model describes the mapping between real and redshift space for 2-point clustering statistics. Its key element is the probability density function (PDF) of line-of-sight pairwise peculiar velocities. Following a kinetic-theory approach, we derive the fundamental equations of the streaming model for ordered and unordered pairs. In the first case, we recover the classic equation while we demonstrate that modifications are necessary for unordered pairs. We then discuss several statistical properties of the pairwise velocities for DM particles and haloes by using a suite of high-reso…
We study the impact on the galaxy correlation function of the presence of a vector component in the tracers' peculiar velocities, in the case in which statistical isotropy is violated. We present a general framework - based on the bipolar spherical harmonics expansion - to study this effect in a model independent way, without any hypothesis on the origin or the properties of these vector modes. We construct six new observables, that can be directly measured in galaxy catalogs in addition to the standard monopole, quadrupole and hexadecapole, and we show that they completely describe any deviat…
We study potential systematic effects of assembly bias on cosmological parameter constraints from redshift space distortion measurements. We use a semi-analytic galaxy formation model applied to the Millennium N-body WMAP-7 simulation to study the effects of halo assembly bias on the redshift space distortions of the galaxy correlation function. We look at the pairwise velocities of galaxies living in haloes with concentrations and ages in the upper and lower quintiles, and find that the velocity differences between these are consistent with those reported for real-space clustering analyses, i…
We present improved modelling of the redshift-space distortions of galaxy clustering that arise from peculiar velocities. We create mock galaxy catalogues in the framework of the halo model, using data from the Bolshoi project. These mock galaxy populations are inserted into the haloes with additional degrees of freedom that govern spatial and kinematical biases of the galaxy populations relative to the dark matter. We explore this generalised halo model with an MCMC algorithm, comparing the predictions to data from the Galaxy And Mass Assembly (GAMA) survey, and thus derive one of the first c…
We present a new efficient method to compute the angular power spectra of large-scale structure observables that circumvents the numerical integration over Bessel functions, expanding on a recently proposed algorithm based on FFTlog. This new approach has better convergence properties. The method is explicitly implemented in the CLASS code for the case of number count $C_\ell$'s (including redshift-space distortions, weak lensing, and all other relativistic corrections) and cosmic shear $C_\ell$'s. In both cases our approach speeds up the calculation of the exact $C_\ell$'s (without the Limber…
The accelerating expansion of the Universe at recent epochs has called into question the validity of general relativity on cosmological scales. One probe of gravity is a comparison of expansion history of the Universe with the history of structure growth via gravitational instability: general relativity predicts a specific relation between these two observables. Here we show that the mean pairwise streaming velocity of galaxy clusters provides a useful method of constraining this relation. Galaxy cluster velocities can be measured via the kinetic Sunyaev-Zeldovich distortion of the cosmic micr…
We present tomography of the circum-galactic metal distribution at redshift 1.7 to 4.5 derived from echellete spectroscopy of binary quasars. We find CIV systems at similar redshifts in paired sightlines more often than expected for sightline-independent redshifts. As the separation of the sightlines increases from 36 kpc to 907 kpc, the amplitude of this clustering decreases. At the largest separations, the CIV systems cluster similar to Lyman-break galaxies (Adelberger et al. 2005a). The CIV systems are significantly less correlated than these galaxies, however, at separations less than R_1 …
The highly redshifted 21 cm line of neutral hydrogen has become recognized as a unique probe of cosmology from relatively low redshifts (z ~ 1) up through the Epoch of Reionization (z ~ 8) and even beyond. To date, most work has focused on recovering the spherically averaged power spectrum of the 21 cm signal, since this approach maximizes the signal-to-noise in the initial measurement. However, like galaxy surveys, the 21 cm signal is affected by redshift space distortions, and is inherently anisotropic between the line-of-sight and transverse directions. A measurement of this anisotropy can …
Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at larger radii, where infall velocities are expected to have a sensitivity to cluster masses. First, we construct a two component model of the three-dimensional phase space distribution of haloes surrounding clusters up to 50 $h^{-1}$Mpc from cluster centres based on $N$-body simulations. We find that the three-dimensional phase space distribution shows a clear …
Starting from first principles, we derive the fundamental equations that relate the $n$-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full $n$-point correlation in redshift-space is obtained as an integral of its real-space counterpart times the joint probability density of $n-1$ relative line-of-sight peculiar velocities. Equations for the connected $n$-point correlation functions are obtained by recursively applying the generalised streaming model for decreasing $n$. Our results are exact within …
We report the detection of the kinetic Sunyaev-Zel'dovich (kSZ) effect in galaxy clusters with a 4.9 sigma significance using the latest 217 GHz Planck map from data release 4. For the detection, we stacked the Planck map at the positions of 30,431 galaxy clusters from the Wen-Han-Liu (WHL) catalog. To align the sign of the kSZ signals, the line-of-sight velocities of galaxy clusters were estimated with a machine-learning approach, in which the relation between the galaxy distribution around a cluster and its line-of-sight velocity was trained through a convolutional neural network. To train o…
Redshift space distortions caused by galaxy peculiar velocities provide a window onto the growth rate of large scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index, γ. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1-sigma or more relative to the fiducial at scales as large as k > 0.07 h/Mpc. This bias propagates to es…
We present a formulation of observed number density fluctuations of gravitational-wave (GW) sources in a three dimensional space. In GW observations, redshift identification for each GW source is a challenging issue, in particular, for high redshift sources. The use of observed luminosity distance as a distance indicator will be a simple yet optimal way for measuring the clustering signal. We derive the density fluctuations of GW sources estimated from observed luminosity distance and sky position of each source. The density fluctuations are distorted as similar to the so-called redshift space…
Galaxy peculiar velocities provide an integral source of cosmological information that can be harnessed to measure the growth rate of large scale structure and constrain possible extensions to General Relativity. In this work, we present a method for extracting the information contained within galaxy peculiar velocities through an ensemble of direct peculiar velocity and galaxy clustering correlation statistics, including the effects of redshift space distortions, using data from the 6-degree Field Galaxy Survey. Our method compares the auto- and cross-correlation function multipoles of these …
We investigate the direct determination of expansion history using redshift distortions without plugging into detailed cosmological parameters. The observed spectra in redshift space include a mixture of information: fluctuations of density-density and velocity-velocity spectra, and distance measures of perpendicular and parallel components to the line of sight. Unfortunately it is hard to measure all the components simultaneously without any specific prior assumption. Common prior assumptions include a linear/quasi-linear model of redshift distortions or a model for the shape of the power spe…
We study the comoving relative velocities, v12, of model isolated galaxy pairs at z=0.5. For this purpose, we use the predictions from the GALFORM semi-analytical model of galaxy formation and evolution based on a Lambda cold dark matter cosmology consistent with the results from WMAP7. In real space, we find that isolated pairs of galaxies are predicted to form an angle t with the line-of-sight that is uniformily distributed as expected if the Universe is homogeneous and isotropic. We also find that isolated pairs of galaxies separated by a comoving distance between 1 and 3 Mpc/h are predicte…
We show how to obtain constraints on $β=f/b$, the ratio of the matter growth rate and the bias that quantifies the linear redshift-space distortions, that are independent of the cosmological model, using multiple tracers of large-scale structure. For a single tracer the uncertainties on $β$ are constrained by the uncertainties in the amplitude and shape of the power spectrum, which is limited by cosmic variance. However, for two or more tracers this limit does not apply, since taking the ratio of power spectra cosmic variance cancels out, and in the linear (Kaiser) approximation one measures d…
Our observations of the Universe are fundamentally anisotropic, with data from galaxies separated transverse to the line of sight coming from the same epoch while that from galaxies separated parallel to the line of sight coming from different times. Moreover, galaxy velocities along the line of sight change their redshift, giving redshift space distortions. We perform a full two-dimensional anisotropy analysis of galaxy clustering data, fitting in a substantially model independent manner the angular diameter distance D_A, Hubble parameter H, and growth rate ddelta/dln a without assuming a dar…
The degeneracy between geometric (Alcock-Paczynski) and dynamic (redshift space) distortions in the pattern of the galaxy distribution has been a long standing problem in the study of the large scale structure of the universe. We examine the possibility of lifting this degeneracy and constraining cosmological parameters by using the Baryon Acoustic Oscillation (BAO) scale as a feature of known physical size, the sound horizon r_s ~ 150 Mpc. We callibrate this scale with the equivalent feature in the Cosmic Microwave Background (CMB). First, we construct a toy model of a power spectrum which in…
We develop a model for the redshift-space correlation function, valid for both dark matter particles and halos on scales $>5\,h^{-1}$Mpc. In its simplest formulation, the model requires the knowledge of the first three moments of the line-of-sight pairwise velocity distribution plus two well-defined dimensionless parameters. The model is obtained by extending the Gaussian-Gaussianity prescription for the velocity distribution, developed in a previous paper, to a more general concept allowing for local skewness, which is required to match simulations. We compare the model with the well known Ga…
Peculiar velocities are an important probe of the growth rate of mass density fluctuations in the Universe. Most previous studies have focussed exclusively on measuring peculiar velocities at intermediate ($0.2 < z < 1$) redshifts using statistical redshift-space distortions. Here we emphasize the power of peculiar velocities obtained directly from distance measurements at low redshift ($z \lesssim 0.05$), and show that these data break the usual degeneracies in the Ω_{m,0} -- $σ_{8,0}$ parameter space. Using only peculiar velocity data, we find $Ω_{m,0} = 0.259\pm0.045$ and $σ_{8,0} = 0.748\p…
The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors ${\bf k_1,k_2,k_3}$ 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 $\ell$ multipoles have non-zero values, and we present explicit analytical expressions…
Similar to the magnification of the galaxies' fluxes by gravitational lensing, the extinction of the fluxes by comic dust, whose existence is recently detected by Menard et al (2009), also modify the distribution of a flux-selected galaxy sample. We study the anisotropic distortion by dust extinction to the 3D galaxy correlation function, including magnification bias and redshift distortion at the same time. We find the extinction distortion is most significant along the line of sight and at large separations, similar to that by magnification bias. The correction from dust extinction is negati…
The line of sight direction in the redshifted 21-cm signal coming from the cosmic dawn and the epoch of reionization is quite unique in many ways compared to any other cosmological signal. Different unique effects, such as the evolution history of the signal, non-linear peculiar velocities of the matter etc will imprint their signature along the line of sight axis of the observed signal. One of the major goals of the future SKA-LOW radio interferometer is to observe the cosmic dawn and the epoch of reionization through this 21-cm signal. It is thus important to understand how these various eff…
Long-wavelength matter inhomogeneities contain cleaner information on the nature of primordial perturbations as well as the physics of the early universe. The large-scale coherent overdensity and tidal force, not directly observable for a finite-volume galaxy survey, are both related to the Hessian of large-scale gravitational potential and therefore of equal importance. We show that the coherent tidal force causes a homogeneous anisotropic distortion of the observed distribution of galaxies in all three directions, perpendicular and parallel to the line-of-sight direction. This effect mimics …
Cosmic voids in the large-scale structure of the Universe affect the peculiar motions of objects in their vicinity. Although these motions are difficult to observe directly, the clustering pattern of their surrounding tracers in redshift space is influenced in a unique way. This allows to investigate the interplay between densities and velocities around voids, which is solely dictated by the laws of gravity. With the help of $N$-body simulations and derived mock-galaxy catalogs we calculate the average density fluctuations around voids identified with a watershed algorithm in redshift space an…
Strong lensing by intervening galaxies can produce multiple images of gravitational waves from sources at cosmological distances. These images acquire additional phase-shifts as the over-focused wavefront passes through itself along the line of sight. Time domain waveforms of Type-II images (associated with saddle points of the time delay) exhibit a non-trivial distortion from the unlensed waveforms. This phenomenon is in addition to the usual frequency-independent magnification, and happens even in the geometric limit where the wavelength is much shorter than the deflector's gravitational len…
The peculiar motion of galaxies can be a particularly sensitive probe of gravitational collapse. As such, it can be used to measure the dynamics of dark matter and dark energy as well the nature of the gravitational laws at play on cosmological scales. Peculiar motions manifest themselves as an overall anisotropy in the measured clustering signal as a function of the angle to the line-of-sight, known as redshift-space distortion (RSD). Limiting factors in this measurement include our ability to model non-linear galaxy motions on small scales and the complexities of galaxy bias. The anisotropy …
