Peculiar Velocity Field Research Articles

Peculiar Velocity Reconstruction from Simulations and Observations Using Deep Learning Algorithms

In this paper, we introduce a U-Net model of deep learning algorithms for reconstructions of the 3D peculiar velocity field, which simplifies the reconstruction process with enhanced precision. We test the adaptability of the U-Net model with simulation data under more realistic conditions, including the redshift space distortion effect and halo mass threshold. Our results show that the U-Net model outperforms the analytical method that runs under ideal conditions, with a 16% improvement in precision, 13% in residuals, 18% in correlation coefficient, and 27% in average coherence. The deep learning algorithm exhibits exceptional capacities to capture velocity features in nonlinear regions and substantially improve reconstruction precision in boundary regions. We then apply the U-Net model trained under Sloan Digital Sky Survey (SDSS) observational conditions to the SDSS Data Release 7 data for observational 3D peculiar velocity reconstructions.

Large-scale motions and growth rate from forward-modelling Tully–Fisher peculiar velocities

ABSTRACT Peculiar velocities are an important probe of the mass distribution in the Universe and the growth rate of structure, directly measuring the effects of gravity on the largest scales and providing a test for theories of gravity. Comparing peculiar velocities predicted from the density field mapped by a galaxy redshift survey with peculiar velocities measured using a distance estimator such as the Tully–Fisher relation yields the growth factor for large-scale structure. We present a method for forward modelling a sample of galaxy magnitudes and velocity widths that simultaneously determines the parameters of the Tully–Fisher relation and the peculiar velocity field. We apply this to the Cosmicflows-4 Tully–Fisher data set, using the peculiar velocities predicted from the 2M++ redshift survey. After validating the method on mock surveys, we measure the product of the growth rate and mass fluctuation amplitude to be fσ8 = 0.35 ± 0.03 at an effective redshift of z = 0.017. This is consistent at 3σ with the Planck CMB prediction, even though the uncertainty does not fully account for all sources of sample variance. We find the residual bulk flow from gravitational influences outside the 2M++ survey volume to be |V| = 227 ± 11 km s−1, (l, b) = (303°, −1°) in Galactic polar coordinates and the CMB frame. Using simulations, we show that applying our methodology to the large new sample of Tully–Fisher peculiar velocities expected from the WALLABY H I survey of the southern sky can improve the constraints on the growth rate by a factor of 2–3.

Vorticity generation in cosmology and the role of shell crossing

There is no source for cosmic vorticity within the cold dark matter cosmology. However, vorticity has been observed in the universe, especially on the scales of clusters, filaments, galaxies, etc. Recent results from high-resolution general relativistic N-body simulation show that the vorticity power spectrum dominates over the power spectrum of the divergence of the peculiar velocity field on scales where the effective field theory of large-scale structure breaks down. Incidentally, this scale also corresponds to the scale where shell-crossing occurs. Several studies have suggested a link between shell crossing in the dark matter fluid and the vorticity generation in the universe, however, no clear proof of how it works within general relativity exists yet. We describe for the first time how vorticity is generated in a universe such as ours with expanding and collapsing regions. We show how vorticity is generated at the boundary of the expanding and collapsing regions. Our result indicates that the amplitude of the generated vorticity is determined by the jump in gradients of the gravitational potential, pressure and the expansion rate at the boundary. In addition, we argue that the presence of vorticity in the matter fields implies a non-vanishing magnetic part of the Weyl tensor. This has implications for the generation of Maxwell's magnetic field and the dynamics of clusters. The impact of accelerated expansion of the universe and the existence of causal limit for massive particles are discussed

Approximations for the divergence of the reconstructed local large-scale structure velocity field and its possible implications for Cosmology

We characterize the peculiar velocity field of the local large-scale structure reconstructed from the 2M++ survey, by treating it as a fluid, extracting the divergence via different approximations over a range of averaged scales. This reconstructed field is important for cosmology, since it was used to correct the peculiar redshifts of the last SNIA compilation Pantheon+. The results have intriguing implications for the LLSS fluid dynamics and particularly for the “Tilted Cosmology” model, although those results have to be taken carefully as the velocity field could contain significant bias due to the reconstruction procedure. Those possible bias and its influence in our results are discussed. Representative values of the apparent deceleration parameter (q̃) are computed, in order to compare our results with the theoretical predictions of the tilted-universe scenario. We conclude that better velocity field reconstructions are necessary in order to constrain the parameters implied in LLSS research and alternative cosmologies.

Biases in velocity reconstruction: investigating the effects on growth rate and expansion measurements in the local universe

ABSTRACT The local galaxy peculiar velocity field can be reconstructed from the surrounding distribution of large-scale structure and plays an important role in calibrating cosmic growth and expansion measurements. In this paper, we investigate the effect of the stochasticity of these velocity reconstructions on the statistical and systematic errors in cosmological inferences. By introducing a simple statistical model between the measured and theoretical velocities, whose terms we calibrate from linear theory, we derive the bias in the model velocity. We then use lognormal realizations to explore the potential impact of this bias when using a cosmic flow model to measure the growth rate of structure, and to sharpen expansion rate measurements from host galaxies for gravitational wave standard sirens with electromagnetic counterparts. Although our illustrative study does not contain fully realistic observational effects, we demonstrate that in some scenarios these corrections are significant and result in a measurable improvement in determinations of the Hubble constant compared to standard forecasts.

Simulating the LOcal Web (SLOW)

Context. Several observations of the Local Universe point toward the existence of very prominent structures: massive galaxy clusters and local superclusters on the one hand, but also large local voids and underdensities on the other. However, it is highly nontrivial to connect such different observational selected tracers to the underlying dark matter (DM) distribution. Aims. Therefore, constructing mock catalogs of such observable tracers using cosmological hydrodynamics simulations is needed. These simulations have to follow galaxy formation physics and also have to be constrained to reproduce the Local Universe. Such constraints should be based on observables that directly probe the full underlying gravitational field, such as the observed peculiar velocity field, to provide an independent test on the robustness of these distinctive structures. Methods. We used a 500 h−1 Mpc constrained simulation of the Local Universe to investigate the anomalies in the local density field, as found in observations. Constructing the initial conditions based on peculiar velocities derived from the CosmicFlows-2 catalog makes the predictions of the simulations completely independent from the distribution of the observed tracer population, and following galaxy formation physics directly in the hydrodynamics simulations also allows the comparison to be based directly on the stellar masses of galaxies or X-ray luminosity of clusters. We also used the 2668 h−1 Mpc large cosmological box from the Magneticum simulations to evaluate the frequency of finding such anomalies in random patches within simulations. Results. We demonstrate that halos and galaxies in our constrained simulation trace the local dark matter density field very differently. Thus, this simulation reproduces the observed 50% underdensity of galaxy clusters and groups within the sphere of ≈100 Mpc when applying the same mass or X-ray luminosity limit used in the observed cluster sample (CLASSIX), which is consistent with a ≈1.5σ feature. At the same time, the simulation reproduces the observed overdensity of massive galaxy clusters within the same sphere, which on its own also corresponds to a ≈1.5σ feature. Interestingly, we find that only 44 out of 15 635 random realizations (i.e., 0.28%) match both anomalies, thus making the Local Universe a ≈3σ environment. We finally compared a mock galaxy catalog with the observed distribution of galaxies in the Local Universe, finding a match to the observed factor of 2 overdensity at ∼16 Mpc as well as the observed 15% underdensity at ∼40 Mpc. Conclusions. Constrained simulations of the Local Universe which reproduce the main features of the local density field open a new window for local field cosmology, where the imprint of the specific density field and the impact on the bias through the observational specific tracers can be investigated in detail.

On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity ρL=1/2 on the smallest scale (r = 0) is a unique feature of collisionless flow (ρL=1 for incompressible flow). On large scale, transverse velocity correlation has an exponential form T2∝e−r/r2 with a constant comoving scale r2=21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of S2l∝r1/4. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.

Bayesian field-level inference of primordial non-Gaussianity using next-generation galaxy surveys

ABSTRACT Detecting and measuring a non-Gaussian signature of primordial origin in the density field is a major science goal of next-generation galaxy surveys. The signal will permit us to determine primordial-physics processes and constrain models of cosmic inflation. While traditional approaches use a limited set of statistical summaries of the galaxy distribution to constrain primordial non-Gaussianity, we present a field-level approach by Bayesian forward modelling the entire three-dimensional galaxy survey. Since our method includes the entire cosmic field in the analysis, it can naturally and fully self-consistently exploit all available information in the large-scale structure, to extract information on the local non-Gaussianity parameter, fnl. Examples include higher order statistics through correlation functions, peculiar velocity fields through redshift-space distortions, and scale-dependent galaxy bias. To illustrate the feasibility of field-level primordial non-Gaussianity inference, we present our approach using a first-order Lagrangian perturbation theory model, approximating structure growth at sufficiently large scales. We demonstrate the performance of our approach through various tests with self-consistent mock galaxy data emulating relevant features of the SDSS-III/BOSS-like survey, and additional tests with a Stage IV mock data set. These tests reveal that the method infers unbiased values of fnl by accurately handling survey geometries, noise, and unknown galaxy biases. We demonstrate that our method can achieve constraints of $\sigma _{{f_\mathrm{nl}}} \approx 8.78$ for SDSS-III/BOSS-like data, indicating potential improvements of a factor ∼2.5 over current published constraints. We perform resolution studies on scales larger than ∼16h−1 Mpc showing the promise of significant constraints with next-generation surveys. Furthermore, the results demonstrate that our method can consistently marginalize all nuisance parameters of the data model. The method further provides an inference of the three-dimensional primordial density field, providing opportunities to explore additional signatures of primordial physics. This first demonstration of a field-level inference pipeline demonstrates a promising complementary path forward for analysing next-generation surveys.

Velocity reconstruction with the cosmic microwave background and galaxy surveys

The kinetic Sunyaev Zel'dovich (kSZ) and moving lens effects, secondary contributions to the cosmic microwave background (CMB), carry significant cosmological information due to their dependence on the large-scale peculiar velocity field. Previous work identified a promising means of extracting this cosmological information using a set of quadratic estimators for the radial and transverse components of the velocity field. These estimators are based on the statistically anisotropic components of the cross-correlation between the CMB and a tracer of large scale structure, such as a galaxy redshift survey. In this work, we assess the challenges to the program of velocity reconstruction posed by various foregrounds and systematics in the CMB and galaxy surveys, as well as biases in the quadratic estimators. To do so, we further develop the quadratic estimator formalism and implement a numerical code for computing properly correlated spectra for all the components of the CMB (primary/secondary blackbody components and foregrounds) and a photometric redshift survey, with associated redshift errors, to allow for accurate forecasting. We create a simulation framework for generating realizations of properly correlated CMB maps and redshift binned galaxy number counts, assuming the underlying fields are Gaussian, and use this to validate a velocity reconstruction pipeline and assess map-based systematics such as masking. We highlight the most significant challenges for velocity reconstruction, which include biases associated with: modelling errors, characterization of redshift errors, and coarse graining of cosmological fields on our past light cone. Despite these challenges, the outlook for velocity reconstruction is quite optimistic, and we use our reconstruction pipeline to confirm that these techniques will be feasible with near-term CMB experiments and photometric galaxy redshift surveys.

Using peculiar velocity surveys to constrain the growth rate of structure with the wide-angle effect

ABSTRACT Amongst the most popular explanations for dark energy are modified theories of gravity. The galaxy overdensity and peculiar velocity fields help us to constrain the growth rate of structure and distinguish different models of gravity. We introduce an improved method for constraining the growth rate of structure with the galaxy overdensity and peculiar velocity fields. This method reduces the modelling systematic error by accounting for the wide-angle effect and the zero-point calibration uncertainty during the modelling process. We also speed up the posterior sampling by around 30 times by first calculating the likelihood at a small number of fiducial points and then interpolating the likelihood values during MCMC sampling. We test the new method on mocks and we find it is able to recover the fiducial growth rate of structure. We applied our new method to the SDSS PV catalogue, which is the largest single peculiar velocity catalogue to date. Our constraint on the growth rate of structure is $f\sigma _8 = 0.405_{-0.071}^{+0.076}$ (stat) ±0.009 (sys) at the effective redshift of 0.073. Our constraint is consistent with a Planck 2018 cosmological model, fσ8 = 0.448, within one standard deviation. Our improved methodology will enable similar analysis on future data, with even larger sample sizes and covering larger angular areas on the sky.

Cosmology from the kinetic polarized Sunyaev Zel'dovich effect

The cosmic microwave background (CMB) photons that scatter off free electrons in the large-scale structure induce a linear polarization pattern proportional to the remote CMB temperature quadrupole observed in the electrons' rest frame. The associated blackbody polarization anisotropies are known as the polarized Sunyaev Zel'dovich (pSZ) effect. Relativistic corrections to the remote quadrupole field give rise to a non-blackbody polarization anisotropy proportional to the square of the transverse peculiar velocity field; this is the kinetic polarized Sunyaev Zel'dovich (kpSZ) effect. In this paper, we forecast the ability of future CMB and galaxy surveys to detect the kpSZ effect, finding that a statistically significant detection is within the reach of planned experiments. We further introduce a quadratic estimator for the square of the peculiar velocity field based on a galaxy survey and CMB polarization. Finally, we outline how the kpSZ effect is a probe of cosmic birefringence and primordial non-Gaussianity, forecasting the reach of future experiments.

Testing the homogeneity of type Ia Supernovae in near-infrared for accurate distance estimations

Since the discovery of the accelerating expansion of the Universe more than two decades ago, Type Ia Supernovae (SNe Ia) have been extensively used as standardisable candles in the optical. However, SNe Ia have shown to be more homogeneous in the near-infrared (NIR), where the effect of dust extinction is also attenuated. In this work, we explore the possibility of using a low number of NIR observations for accurate distance estimations, given the homogeneity at these wavelengths. We found that one epoch in J and/or H band, plus good gr-band coverage, gives an accurate estimation of peak magnitudes in the J (Jmax) and H (Hmax) bands. The use of a single NIR epoch only introduces an additional scatter of ∼0.05 mag for epochs around the time of B-band peak magnitude (Tmax). We also tested the effect of optical cadence and signal-to-noise ratio (S/N) in the estimation of Tmax and its uncertainty propagation to the NIR peak magnitudes. Both cadence and S/N have a similar contribution, where we constrained the introduced scatter of each to < 0.02 mag in Jmax and < 0.01 in Hmax. However, these effects are expected to be negligible, provided the data quality is comparable to that obtained for observations of nearby SNe (z ≲ 0.1). The effect of S/N in the NIR was tested as well. For SNe Ia at 0.08 < z ≲ 0.1, NIR observations with better S/N than that found in the CSP sample is necessary to constrain the introduced scatter to a minimum (≲0.05 mag). These results provide confidence for our FLOWS project that is aimed at using SNe Ia with public ZTF optical light curves and few NIR epochs to map out the peculiar velocity field of the local Universe. This will allow us to determine the distribution of dark matter in our own supercluster, Laniakea, and to test the standard cosmological model by measuring the growth rate of structures, parameterised by fD, and the Hubble-Lemaître constant, H0.

The First Fall is the Hardest: The Importance of Peculiar Galaxy Dynamics at Infall Time for Tidal Stripping Acting at the Centers of Groups and Clusters

Using dark-matter-only N-body cosmological simulations, we measure the pericentre distance of dark matter halos on their first infall into group and cluster halos. We find that the pericentre distance (R peri) is an important parameter as it significantly affects the strength of tidal mass loss in dense environments, and likely other environmental mechanisms as well. We examine what determines the R peri value and find that, for most infallers, the dominant parameter is V ⊥, the tangential component of the orbital velocity as the halo enters the group/cluster halo for the first time. This means that the strength of tidal stripping acting near the cores of groups/clusters are strongly influenced by the external peculiar velocity field of the large-scale structure surrounding them, which differs between clusters and is sensitive to the mass ratio of infaller to host. We find that filament feeding also partially contributes to feeding in low-V ⊥ halos. Dynamical friction can also play a role in reducing R peri but this is only significant for those few relatively massive infallers (>10% of the mass of their host). These results highlight how the response of galaxies to dense environments will sensitively depend on dynamics inherited from far outside those dense environments.

Effects of peculiar velocities on the morphological properties of large-scale structure

It is known that the large-scale structure (LSS) mapped by a galaxy redshift survey is subject to distortions by galaxies' peculiar velocities. Besides the signatures generated in common N-point statistics, such as the anisotropy in the galaxy 2-point correlation function, the peculiar velocities also induce distinct features in LSS's morphological properties, which are fully described by four Minkowski functionals (MFs), i.e., the volume, surface area, integrated mean curvature and Euler characteristic (or genus). In this work, by using large suite of N-body simulations, we present and analyze these important features in the MFs of LSS on both (quasi-)linear and non-linear scales, with a focus on the latter. We also find the MFs can give competitive constraints on cosmological parameters compared to the power spectrum, probablly due to the non-linear information contained. For galaxy number density similar to the DESI BGS galaxies, the constraint on $\sigma_8$ from the MFs with one smoothing scale can be better by $\sim 50\%$ than from the power spectrum. These findings are important for the cosmological applications of MFs of LSS, and probablly open up a new avenue for studying the peculiar velocity field itself.

Second-order peculiar velocity field as a novel probe of scalar-tensor theories

We investigate the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to constrain degenerate higher-order scalar tensor (DHOST) theories. We find that the signal obtained from the leading kernel of second-order density fluctuations is partially hidden by the uncertainty in the nonlinear galaxy bias, and that the kernel of second-order velocity fields instead provides unbiased information on the modification of gravity theory. Based on this fact, we propose new phenomenological time-dependent functions, written as a combination of the coefficients of the second-order kernels, which is expected to trace the higher-order growth history. We then present approximate expressions for these variables in terms of parameters that characterize the DHOST theories. We also show that the resultant formulae provides new constraints on the parameter space of the DHOST theories.

Sensitivity tests of cosmic velocity fields to massive neutrinos

ABSTRACT We investigate impacts of massive neutrinos on the cosmic velocity fields, employing high-resolution cosmological N-body simulations provided by the information-optimized CUBE code, where cosmic neutrinos are evolved using collisionless hydrodynamics and their perturbations can be accurately resolved. In this study, we focus, for the first time, on the analysis of massive-neutrino-induced suppression effects in various cosmic velocity field components of velocity magnitude, divergence, vorticity, and dispersion. By varying the neutrino mass sum Mν from 0 to 0.4 eV, the simulations show that the power spectra of vorticity – exclusively sourced by non-linear structure formation that is affected by massive neutrinos significantly – are very sensitive to the mass sum, which potentially provide novel signatures in detecting massive neutrinos. Furthermore, using the χ2 statistic, we quantitatively test the sensitivity of the density and velocity power spectra to the neutrino mass sum. Indeed, we find that the vorticity spectrum has the highest sensitivity, and the null hypothesis of massless neutrinos is incompatible with both vorticity and divergence spectra from Mν = 0.1 eV at high significance (P-value = 0.03 and 0.07, respectively). These results demonstrate clearly the importance of peculiar velocity field measurements, in particular of vorticity and divergence components, in determination of neutrino mass and mass hierarchy.

The effect of inhomogeneous reionization on the Lyman α forest power spectrum at redshift z > 4: implications for thermal parameter recovery

ABSTRACT We use the Sherwood–Relics suite of hybrid hydrodynamical and radiative transfer simulations to model the effect of inhomogeneous reionization on the 1D power spectrum of the Lyman α (Lyα) forest transmitted flux at redshifts 4.2 ≤ z ≤ 5. Relative to models that assume a homogeneous ultraviolet background, reionization suppresses the power spectrum at small scales, k ∼ 0.1 km−1 s, by ∼10 per cent because of spatial variations in the thermal broadening kernel and the divergent peculiar velocity field associated with overpressurized intergalactic gas. On larger scales, $k\lt 0.03\rm \, km^{-1}\, s$, the power spectrum is instead enhanced by 10–50 per cent by large-scale spatial variations in the neutral hydrogen fraction. The effect of inhomogeneous reionization must therefore be accounted for in analyses of forthcoming high precision measurements. We provide a correction for the Lyα forest power spectrum at 4.1 ≤ z ≤ 5.4 that can be easily applied within other parameter inference frameworks using similar reionization models. We perform a Bayesian analysis of mock data to assess the extent of systematic biases that may arise in measurements of the intergalactic medium if ignoring this correction. At the scales probed by current high-resolution Lyα forest data at z > 4, $0.006 \le k \le 0.2 \rm \, km^{-1}\, s$, we find inhomogeneous reionization does not introduce any significant bias in thermal parameter recovery for the current measurement uncertainties of ∼10 per cent. However, for 5 per cent uncertainties, ∼1σ shifts between the estimated and true parameters occur.

Gaussianization of peculiar velocities and bulk flow measurement

The line-of-sight peculiar velocities are good indicators of the gravitational fluctuation of the density field. Techniques have been developed to extract cosmological information from the peculiar velocities in order to test cosmological models. These techniques include measuring cosmic flow, measuring two-point correlation and power spectrum of the peculiar velocity fields, and reconstructing the density field using peculiar velocities. However, some measurements from these techniques are biased due to the non-Gaussianity of the estimated peculiar velocities. Therefore, we rely on the 2MTF survey to explore a power transform that can Gaussianize the estimated peculiar velocities. We find a tight linear relation between the transformation parameters and the measurement errors of log-distance ratio. To show an example for the implementation of Gaussianized peculiar velocities in cosmology, we develop a bulk flow estimator and estimate bulk flow from the Gaussianized peculiar velocities. We use 2MTF mocks to test the algorithm, and we find the algorithm yields unbiased measurements. We also find this technique gives smaller measurement errors compared to other techniques. In Galactic coordinates, at the depth of 30 h −1 Mpc, we measure a bulk flow of 332 ± 27 km s−1 in the direction (l,b) = (293° ± 5°, 13° ± 4°). The measurement is consistent with the ΛCDM prediction.

Exploring the redshift-space peculiar velocity field and its power spectrum

Redshift-space distortions (RSD) generically affect any spatially-dependent observable that is mappedusing redshift information. The effect on the observed clustering of galaxies is the primary example ofthis. This paper is devoted to another example: the effect of RSD on the apparent peculiar motions oftracers as inferred from their positions in redshift space (i.e. the observed distance). Our theoreticalstudy is motivated by practical considerations, mainly, the direct estimation of the velocity powerspectrum, which is preferably carried out using the tracer's redshift-space position (so as to avoiduncertainties in distance measurements).We formulate the redshift-space velocity field and show that RSD enters as a higher-order effect.Physically, this effect may be interpreted as a dissipative correction to the usual perfect-fluiddescription of dark matter. We show that the effect on the power spectrum is a damping on relativelylarge, quasilinear scales (k≳0.01 h-1), as was observed, though unexplained, inN-body simulations elsewhere. This paper presents two power spectrum models for the peculiarvelocity field in redshift space, both of which can be considered velocity analogues of existingclustering models. In particular, we show that the “Finger-of-God” effect, while also present in thevelocity field, cannot be entirely blamed for the observed damping in simulations. Our work providessome of the missing modelling ingredients required for a density-velocity multi-tracer analysis,which has been proposed for upcoming redshift surveys.

Constrained realizations of 2MRS density and peculiar velocity fields: growth rate and local flow

ABSTRACT We generate constrained realizations (CRs) of the density and peculiar velocity fields within $200 \, h^{-1} \, \mathrm{Mpc}$ from the final release of the Two-Micron All-Sky Redshift Survey (2MRS) – the densest all-sky redshift survey to date. The CRs are generated by combining a Wiener filter estimator in spherical Fourier-Bessel space with random realizations of log-normally distributed density fields and Poisson-sampled galaxy positions. The algorithm is tested and calibrated on a set of semi-analytic mock catalogues mimicking the environment of the Local Group (LG), to rigorously account for the statistical and systematic errors of the reconstruction method. By comparing our peculiar velocity CRs with the observed velocities from the Cosmicflows-3 catalogue, we constrain the normalized linear growth rate to $f \sigma _8^{\text{lin}}= 0.367 \pm 0.060$, which is consistent at the 1.1σ level with the latest Planck results as well as other direct probes. Simultaneously, we estimate a bulk flow contribution from sources beyond the 2MRS reconstruction volume of $B^{\text{ext}}= 199 \pm 68 \, \mathrm{km} \, \mathrm{s}^{-1}$ towards l = 299 ± 18°, b = 8 ± 19°. The total reconstructed velocity field at the position of the LG, smoothed with a $1 \, h^{-1} \, \mathrm{Mpc}$ Gaussian, is $685 \pm 75 \, \mathrm{km} \, \mathrm{s}^{-1}$ towards l = 270.6 ± 6.6°, b = 35.5 ± 7.2°, in good agreement with the observed CMB dipole. The total reconstructed bulk flow within different radii is compatible with other measurements. Within a $50 \, h^{-1} \, \mathrm{Mpc}$ Gaussian window we find a bulk flow of $274 \pm 50 \, \mathrm{km} \, \mathrm{s}^{-1}$ towards l = 287 ± 9°, b = 11 ± 10°. The code used to generate the CRs and obtain these results, dubbed coras, is made publicly available.