Peculiar Velocity Field Research Articles

Alcock-Paczynski effects on wide-angle galaxy statistics

The Alcock-Paczynski (AP) effect is a geometrical distortion in three-dimensional observed galaxy statistics. In anticipation of precision cosmology based on ongoing and upcoming all-sky galaxy surveys, we build an efficient method to compute the AP-distorted correlations of galaxy number density and peculiar velocity fields for any larger angular scale not relying on the conventionally used plane-parallel (PP) approximation. Here, instead of the usual Legendre polynomial basis, the correlation functions are decomposed using tripolar spherical harmonic basis; hence, characteristic angular dependence due to the wide-angle AP effect can be rigorously captured. By means of this, we demonstrate the computation of the AP-distorted correlations over the various scales. Comparing our results with the PP-limit ones, we confirm that the errors due to the PP approximation become more remarkable as the visual angle of separation between target galaxies, $\Theta$, enlarges, and especially for the density auto correlation, the error exceeds $10\%$ when $\Theta \gtrsim 30^\circ$. This highlights the importance of the analysis beyond the PP approximation.

Peculiar-velocity cosmology with Types Ia and II supernovae

ABSTRACT We present the Democratic Samples of Supernovae (DSS), a compilation of 775 low-redshift Type Ia and II supernovae (SNe Ia and II), of which 137 SN Ia distances are derived via the newly developed snapshot distance method. Using the objects in the DSS as tracers of the peculiar-velocity field, we compare against the corresponding reconstruction from the 2M++ galaxy redshift survey. Our analysis – which takes special care to properly weight each DSS subcatalogue and cross-calibrate the relative distance scales between them – results in a measurement of the cosmological parameter combination $f\sigma _8 = 0.390_{-0.022}^{+0.022}$ as well as an external bulk flow velocity of $195_{-23}^{+22}$ km s−1 in the direction $(\ell , b) = (292_{-7}^{+7}, -6_{-4}^{+5})$ deg, which originates from beyond the 2M++ reconstruction. Similarly, we find a bulk flow of $245_{-31}^{+32}$ km s−1 towards $(\ell , b) = (294_{-7}^{+7}, 3_{-5}^{+6})$ deg on a scale of $\sim 30\, h^{-1}$ Mpc if we ignore the reconstructed peculiar-velocity field altogether. Our constraint on fσ8 – the tightest derived from SNe to date (considering only statistical error bars), and the only one to utilize SNe II – is broadly consistent with other results from the literature. We intend for our data accumulation and treatment techniques to become the prototype for future studies that will exploit the unprecedented data volume from upcoming wide-field surveys.

Minimum variance estimation of statistical anisotropy via galaxy survey

We consider the benefits of measuring cosmic statistical anisotropy from redshift-space correlators of the galaxy number density fluctuation and the peculiar velocity field without adopting the plane-parallel (PP) approximation. Since the correlators are decomposed using the general tripolar spherical harmonic (TripoSH) basis, we can deal with wide-angle contributions untreatable by the PP approximation, and at the same time, target anisotropic signatures can be cleanly extracted. We, for the first time, compute the covariance of the TripoSH decomposition coefficient and the Fisher matrix to forecast the detectability of statistical anisotropy. The resultant expression of the covariance is free from nontrivial mixings between each multipole moment caused by the PP approximation and hence the detectability is fully optimized. Compared with the analysis under the PP approximation, the superiority in detectability is always confirmed, and it is highlighted, especially in the cases that the shot noise level is large and that target statistical anisotropy has a blue-tilted shape in Fourier space. The application of the TripoSH-based analysis to forthcoming all-sky survey data could result in constraints on anisotropy comparable to or tighter than the current cosmic microwave background ones.

Large-scale peculiar velocity fields: Newtonian vs relativistic treatment

We employ a perturbative analysis to study the evolution of large-scale peculiar velocity fields within the framework of Newtonian gravity and then compare our results to those of the corresponding relativistic treatment. In so doing, we use the same mathematical formalism and apply the same physical approach. This facilitates a direct and transparent comparison between the two treatments. Our study recovers and extends the familiar Newtonian results on the one hand, while on the other it shows that the Newtonian analysis leads to substantially weaker growth-rates for the peculiar velocity field, compared to the relativistic approach. This implies that, by using Newton's rather than Einstein's theory, one could seriously underestimate the overall kinematic evolution of cosmological peculiar motions. We are also in the position to identify the reason the two theories arrive at such considerably different results and conclusions.

Cosmic birth: efficient Bayesian inference of the evolving cosmic web from galaxy surveys

ABSTRACT We present cosmic birth (COSMological Initial Conditions from Bayesian Inference Reconstructions with THeoretical models): an algorithm to reconstruct the primordial and evolved cosmic density fields from galaxy surveys on the light-cone. The displacement and peculiar velocity fields are obtained from forward modelling at different redshift snapshots given some initial cosmic density field within a Gibbs-sampling scheme. This allows us to map galaxies, observed in a light-cone, to a single high redshift and hereby provide tracers and the corresponding survey completeness in Lagrangian space including tetrahedral tessellation mapping. These Lagrangian tracers in turn permit us to efficiently obtain the primordial density field, making the cosmic birth code general to any structure formation model. Our tests are restricted for the time being to augmented Lagrangian perturbation theory. We show how to robustly compute the non-linear Lagrangian bias from clustering measurements in a numerical way, enabling us to get unbiased dark matter field reconstructions at initial cosmic times. We also show that we can accurately recover the information of the dark matter field from the galaxy distribution based on a detailed simulation. Novel key ingredients to this approach are a higher order Hamiltonian-sampling technique and a non-diagonal Hamiltonian mass matrix. This technique could be used to study the Eulerian galaxy bias from galaxy surveys and could become an ideal baryon acoustic reconstruction technique. In summary, this method represents a general reconstruction technique, including in a self-consistent way a survey mask, non-linear and non-local bias, and redshift-space distortions, with an efficiency about 10 times superior to previous comparable methods.

Fisher matrix for multiple tracers: all you can learn from large-scale structure without assuming a model

The galaxy power spectrum is one of the central quantities in cosmology. It contains information about the primordial inflationary process, the matter clustering, the baryon-photon interaction, the effects of gravity, the galaxy-matter bias, the cosmic expansion, the peculiar velocity field, etc. Most of this information is however difficult to extract without assuming a specific cosmological model, for instance ΛCDM and standard gravity. In this paper we explore instead how much information can be obtained that is independent of the cosmological model, both at background and linear perturbation level. We determine the full set of model-independent statistics that can be constructed by combining two redshift bins and two distinct tracers. We focus in particular on the statistics r(k,z1,z2), defined as the ratio of fσ8(z) at two redshift shells, and we show how to estimate it with a Fisher matrix approach. Finally, we forecast the constraints on r that can be achieved by future galaxy surveys, and compare it with the standard single-tracer result. We find that r can be measured with a precision from 3 to 11%, depending on the survey. Using two tracers, we find improvements in the constraints up to a factor of two.

Nonlinear redshift-space distortions in the harmonic-space galaxy power spectrum

Future high spectroscopic resolution galaxy surveys will observe galaxies with nearly full-sky footprints. Modeling the galaxy clustering for these surveys, therefore, must include the wide-angle effect with narrow redshift binning. In particular, when the redshift-bin size is comparable to the typical peculiar velocity field, the nonlinear redshift-space distortion (RSD) effect becomes important. A naive projection of the Fourier-space RSD model to spherical harmonic space leads to diverging expressions. In this paper we present a general formalism of projecting the higher-order RSD terms into spherical harmonic space. We show that the nonlinear RSD effect, including the fingers-of-God (FoG), can be entirely attributed to a modification of the radial window function. We find that while linear RSD enhances the harmonic-space power spectrum, unlike the three-dimensional case, the enhancement decreases on small angular-scales. The fingers-of-God suppress the angular power spectrum on all transverse scales if the bin size is smaller than $\Delta r \lesssim \pi \sigma_u$; for example, the radial bin sizes corresponding to a spectral resolution $R=\lambda/\Delta \lambda$ of a few hundred satisfy the condition. We also provide the flat-sky approximation which reproduces the full calculation to sub-percent accuracy.

Cosmic flows in the nearby Universe: new peculiar velocities from SNe and cosmological constraints

ABSTRACT The peculiar velocity field offers a unique way to probe dark matter density field on large scales at low redshifts. In this work, we have compiled a new sample of 465 peculiar velocities from low redshift ($z$ < 0.067) Type Ia supernovae. We compare the reconstructed velocity field derived from the 2M++ galaxy redshift compilation to the supernovae, the SFI++ and the 2MTF Tully–Fisher distance catalogues. We used a forward method to jointly infer the distances and the velocities of distance indicators by comparing the observations to the reconstruction. Comparison of the reconstructed peculiar velocity fields to observations allows us to infer the cosmological parameter combination fσ8, and the bulk flow velocity arising from outside the survey volume. The residual bulk flow arising from outside the 2M++ volume is inferred to be $171^{+11}_{-11}$ km s−1 in the direction l = 301° ± 4° and b = 0° ± 3°. We obtain fσ8 = 0.400 ± 0.017, equivalent to S8 ≈ σ8(Ωm/0.3)0.55 = 0.776 ± 0.033, which corresponds to an approximately $4{{\ \rm per\ cent}}\,$ statistical uncertainty on the value of fσ8. Our inferred value is consistent with other low redshift results in the literature.

Relativistic approach to the kinematics of large-scale peculiar motions

We consider the linear kinematics of large-scale peculiar motions in a perturbed Friedmann universe. In so doing, we take the viewpoint of the “real” observers that move along with the peculiar flow, relative to the smooth Hubble expansion. Using relativistic cosmological perturbation theory, we study the linear evolution of the peculiar velocity field, as well as the expansion/contraction, the shear and the rotation of the bulk motion. Our solutions show growth rates considerably stronger than those of the earlier treatments, which were mostly Newtonian. On scales near and beyond the Hubble radius, namely at the long-wavelength limit, peculiar velocities are found to grow as a^2, in terms of the scale factor, instead of the Newtonian a^{1/2}-law. We attribute this to the fact that, in general relativity, the energy flux, triggered here by the peculiar motion of the matter, also contributes to the local gravitational field. In a sense, the bulk flow gravitates, an effect that has been bypassed in related relativistic studies. These stronger growth-rates imply faster peculiar velocities at horizon crossing and higher residual values for the peculiar-velocity field. Alternatively, one could say that our study favours bulk peculiar flows larger and faster than anticipated.

Iterative removal of redshift-space distortions from galaxy clustering

ABSTRACT Observations of galaxy clustering are made in redshift space, which results in distortions to the underlying isotropic distribution of galaxies. These redshift-space distortions (RSDs) not only degrade important features of the matter density field, such as the baryonic acoustic oscillation (BAO) peaks, but also pose challenges for the theoretical modelling of observational probes. Here, we introduce an iterative non-linear reconstruction algorithm to remove RSD effects from galaxy clustering measurements, and assess its performance by using mock galaxy catalogues. The new method is found to be able to recover the real-space galaxy correlation function with an accuracy of $\sim \!1{{\ \rm per\ cent}}$, and restore the quadrupole accurately to 0, on scales $s\gtrsim 20\,h^{-1}\, {\rm Mpc}$. It also leads to an improvement in the reconstruction of the initial density field, which could help to accurately locate the BAO peaks. An ‘internal calibration’ scheme is proposed to determine the values of cosmological parameters, as a part of the reconstruction process, and possibilities to break parameter degeneracies are discussed. RSD reconstruction can offer a potential way to simultaneously extract the cosmological parameters, initial density field, real-space galaxy positions, and large-scale peculiar velocity field (of the real Universe), making it an alternative to standard perturbative approaches in galaxy clustering analysis, bypassing the need for RSD modelling.

On the amount of peculiar velocity field information in supernovae from LSST and beyond

Peculiar velocities introduce correlations between supernova magnitudes, which implies that the supernova Hubble diagram residual carries information on both the matter power spectrum at the present time and its growth rate. By a combination of brute-force exact computations of likelihoods and Fisher matrix analysis, we investigate how this information, which comes from supernova data only, depends on different survey parameters such as covered area, depth, and duration. We show that, for a survey like The Rubin Observatory Legacy Survey of Space and Time (LSST) and a fixed redshift depth, the same observing time provides the same cosmological information whether one observes a larger area, or a smaller area during more years. We also show that although the peculiar velocity information is peaked in the range $z \in [0, 0.2]$, there is yet plenty of information in $z \in [0.2, 0.5]$, and for very high supernova number densities there is even more information in the latter range. We conclude that, after 5 years, LSST could measure $\sigma_8$ with an uncertainty of 0.17 with the current strategy, and that this could be improved to 0.09 if the supernova completeness is improved to 20%. Moreover, we forecast results considering the extra parameter $\gamma$, and show that this creates a non-linear degeneracy with $\sigma_8$ that makes the Fisher matrix analysis inadequate. Finally, we discuss the possibility of achieving competitive results with the current Zwicky Transient Facility.

Secular Extragalactic Parallax: Measurement Methods and Predictions for Gaia

Abstract Secular extragalactic parallax caused by the solar system’s velocity relative to the cosmic microwave background rest frame may be observable as a dipole proper motion field with amplitude 78 μas yr−1 Mpc. Nearby galaxies also exhibit proper motions caused by their transverse peculiar velocities that prevent detection of secular parallax for any single galaxy, although a statistical detection may be made instead. Such a detection could constrain the local Hubble parameter. We present methods to measure secular parallax using correlated extragalactic proper motions and find a first limit on the secular parallax amplitude using proper motions of 232 nearby galaxies from Gaia Data Release 2. The recovered dipole has an insignificant upper limit of 3500 μas yr−1 Mpc. This measurement will be improved by a larger sample size and reduced proper motion uncertainties in future data releases. Using the local peculiar velocity field derived from Cosmicflows-3, we simulate galaxy proper motions and predict that a significant detection (5–10σ) of the secular parallax amplitude will be possible by Gaia's end of mission. The detection does not correspond to a constraint on the Hubble parameter because it depends on nearby (<5 Mpc), bright (G < 15 mag) galaxies and the underlying peculiar motion dipole. We further investigate the implications of our simulations for the study of transverse peculiar velocities. The peculiar velocity field additionally results in low multipole-correlated proper motions on the order of 0.3 μas yr−1 that may be confounded with other cosmological proper motion measurements, such as limits on the gravitational-wave background and the anisotropy of the Hubble expansion.

The velocity field of the Lyra complex

Context. The formation of cosmic structures culminates with the assembly of galaxy clusters, a process that is quite different from cluster to cluster. Aims. We present the study of the structure and dynamics of the Lyra complex, consisting of the two clusters RXC J1825.3+3026 and CIZA J1824.1+3029, which was very recently studied by using both X-ray and radio data. Methods. This is the first analysis based on the kinematics of member galaxies. New spectroscopic data for 285 galaxies were acquired at the Italian Telescopio Nazionale Galileo and were used in combination with PanSTARRS photometry. The result of our member selection is a sample of 198 galaxies. Results. For RXCJ1825 and CIZAJ1824 we report the redshifts, z = 0.0645 and z = 0.0708, the first estimates of velocity dispersion, σv = 995+131−125 km s−1 and σv = 700 ± 50 km s−1, and of dynamical mass, M200 = 1.1 ± 0.4 × 1015 M⊙ and M200 = 4 ± 0.1 × 1014 M⊙. The past assembly of RXCJ1825 is traced by the two dominant galaxies, which are both aligned with the major axis of the galaxy distribution along the east–west direction, and by a minor northeast substructure. We also detect a quite peculiar high velocity field in the southwest region of the Lyra complex. This feature is likely related to a very luminous galaxy, which is characterized by a high velocity. This galaxy is suggested to be the central galaxy of a group that is in interaction with RXCJ1825 according to very recent studies based on X-ray and radio data. The redshift of the whole Lyra complex is z = 0.067. Assuming that the redshift difference between RXCJ1825 and CIZAJ1824 is due to the relative kinematics, the projected distance between the cluster centers is D ∼ 1.3 Mpc and the line–of–sight velocity difference is ∼1750 km s−1. A dynamical analysis of the system shows that the two clusters are likely to be gravitationally bound in a pre-merger phase, and that CIZAJ1824 is moving toward RXCJ1825. Conclusions. Our results corroborate a picture where the Lyra region is the place of a very complex scenario of cluster assembly.

Partitioning the Universe into gravitational basins using the cosmic velocity field

ABSTRACT This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large-scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field to compute flow lines, or streamlines. The local Universe is then partitioned into volumes corresponding to gravitational basins, also called watersheds, among the different end points of the velocity flow lines. This new methodology is first tested on numerical cosmological simulations, used as benchmark for the method, and then applied to the Cosmic-Flows project observational data in order to pay particular attention to the nearby superclusters including ours. More extensive tests on both simulated and observational data will be discussed in an accompanying paper.

Accurate method to determine the systematics due to the peculiar velocities of galaxies in measuring the Hubble constant from gravitational-wave standard sirens

We propose a novel approach to accurately pin down the systematics due to the peculiar velocities of galaxies in measuring the Hubble constant from nearby galaxies in current and future gravitational-wave (GW) standard-siren experiments. Given the precision that future GW standard-siren experiments aim to achieve, the peculiar velocities of nearby galaxies will be a major source of uncertainty. Unlike the conventional backward reconstruction that requires additional redshift-independent distance indicators to recover the peculiar velocity field, we forwardly model the peculiar velocity field by using a high-fidelity mock galaxy catalog built from high-resolution dark matter only (DMO) N-body simulations with a physically motivated subhalo abundance matching technique without introducing any free parameters. Our mock galaxy catalog can impressively well reproduce the observed spectroscopic redshift space distortions (RSDs) in highly non-linear regimes down to very small scales, which is a robust test of the velocity field of our mock galaxy catalog. Based on this mock galaxy catalog, we accurately, for the first time, measure the peculiar velocity probability distributions for the SDSS main galaxy samples. We find that the systematics induced by the peculiar velocities of SDSS like galaxies on the measured Hubble constant can be reduced to below $1\%$($1\sigma$) for GW host galaxies with a Hubble flow redshift just above $0.13$, a distance that can be well probed by future GW experiments and galaxy surveys.

Study on the mapping of halo clustering from real space to redshift space

The mapping of galaxy clustering from real space to redshift space introduces the anisotropic property to the measured galaxy density power spectrum in redshift space, known as the redshift space distortion (RSD) effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite orders of cross correlations between density and velocity fields, and the Finger-of-God (FoG) effect due to the randomness of the galaxy peculiar velocity field. In previous works, we have verified the robustness of advanced TNS mapping formula in our hybrid RSD model in dark matter case, where the halo bias models are not taken into account for the halo mapping formula in redshift space. Using 100 realizations of halo catalogs in N-body simulations, we find that our halo RSD model with the known halo bias model and the effective FoG function accurately predicts the halo power spectrum measurements, within 1∼2% accuracy up to k∼ 0.2 h Mpc-1, depending on different halo masses and redshifts.

The peculiar velocity field up to z ∼ 0.05 by forward-modelling Cosmicflows-3 data

Abstract A hierarchical Bayesian model is applied to the Cosmicflows-3 catalogue of galaxy distances in order to derive the peculiar velocity field and distribution of matter within z ∼ 0.054. The model assumes the ΛCDM model within the linear regime and includes the fit of the galaxy distances together with the underlying density field. By forward modelling the data, the method is able to mitigate biases inherent to peculiar velocity analyses, such as the Homogeneous Malmquist bias or the lognormal distribution of peculiar velocities. The statistical uncertainty on the recovered velocity field is about 150 km s−1 depending on the location, and we study systematics coming from the selection function and calibration of distance indicators. The resulting velocity field and related density fields recover the cosmography of the Local Universe which is presented in an unprecedented volume of our Universe 10 times larger than previously reached. This methodology opens the doors to reconstruction of initial conditions for larger and more accurate constrained cosmological simulations. This work is also preparatory to larger peculiar velocity data sets coming from Wallaby, TAIPAN, or LSST.

No evidence for modifications of gravity from galaxy motions on cosmological scales

The recent discovery of gravitational waves marks the culmination of a sequence of successful tests of the general theory of relativity (GR) since its formulation in 1915. Yet these tests remain confined to the scale of stellar systems or the strong gravity regime. A departure from GR on larger, cosmological scales has been advocated by the proponents of modified gravity theories as an alternative to the Cosmological Constant to account for the observed cosmic expansion history. While indistinguishable in these terms by construction, such models on the other hand yield distinct values for the linear growth rate of density perturbations and, as a consequence, for the associated galaxy peculiar velocity field. Measurements of the resulting anisotropy of galaxy clustering, when spectroscopic redshifts are used to derive distances, have thus been proposed as a powerful probe of the validity of GR on cosmological scales. However, despite significant effort in modelling such redshift space distortions, systematic errors remain comparable to current statistical uncertainties. Here, we present the results of a different forward-modelling approach, which fully exploits the sensitivity of the galaxy velocity field to modifications of GR. We use state-of-the-art, high-resolution N-body simulations of a standard GR and a compelling f(R) model, one of GR's simplest variants, to build simulated catalogues of stellar-mass-selected galaxies through a robust match to the Sloan Digital Sky Survey observations. We find that, well within the uncertainty of this technique, f(R) fails to reproduce the observed redshift-space clustering on scales 1-10 Mpc/h. Instead, the standard LCDM GR model agrees impressively well with the data. This result provides a strong confirmation, on cosmological scales, of the robustness of Einstein's general theory of relativity.

A New Measurement of the Temperature–density Relation of the IGM from Voigt Profile Fitting

Abstract We decompose the Lyman-α (Lyα) forest of an extensive sample of 75 high signal-to-noise ratio and high-resolution quasar spectra into a collection of Voigt profiles. Absorbers located near caustics in the peculiar velocity field have the smallest Doppler parameters, resulting in a low-b cutoff in the b– distribution set primarily by the thermal state of the intergalactic medium (IGM). We fit this cutoff as a function of redshift over the range , which allows us to measure the evolution of the IGM temperature–density ( ) relation parameters T 0 and γ. We calibrate our measurements against mock Lyα forest data generated using 26 hydrodynamic simulations with different thermal histories from the THERMAL suite, also encompassing different values of the IGM pressure smoothing scale. We adopt a forward-modeling approach and self-consistently apply the same algorithms to both data and simulations, propagating both statistical and modeling uncertainties via Monte Carlo. The redshift evolution of T 0 (γ) shows a suggestive peak (dip) at z = 2.9 (z = 3). Our measured evolution of T 0 and γ is generally in good agreement with previous determinations in the literature. Both the peak in the evolution of T 0 at z = 2.8, as well as the high temperatures that we observe at 2.4 < z < 3.4, strongly suggest that a significant episode of heating occurred after the end of H i reionization, which was most likely the cosmic reionization of He ii.

Large Scale Structure in Redshift Space

The mapping of dark matter clustering from real space to redshift space introduces the anisotropic property to the measured density power spectrum in redshift space, known as the redshift space distortion effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite cross correlations between the density and velocity fields, and the Finger–of–God effect due to the randomness of the peculiar velocity field. Whilst the full higher order polynomials remain unknown, the other systematics can be controlled consistently within the same order truncation in the expansion of the mapping formula, as shown in this paper. The systematic due to the unknown non–linear density and velocity fields is removed by separately measuring all terms in the expansion directly using simulations. The uncertainty caused by the velocity randomness is controlled by splitting the FoG term into two pieces, 1) the “one–point” FoG term being independent of the separation vector between two different points, and 2) the “correlated” FoG term appearing as an indefinite polynomials which is expanded in the same order as all other perturbative polynomials. We introduce the recent progress on understanding this mapping, and the application for the future analysis to reveal the nature of cosmic acceleration.