Testing the minimum variance method for estimating large-scale velocity moments

Monthly Notices of the Royal Astronomical Society (Impact Factor: 5.11). 12/2011; 424(4). DOI: 10.1111/j.1365-2966.2012.21345.x
Source: arXiv


The estimation and analysis of large-scale bulk flow moments of peculiar velocity surveys is complicated by non-spherical
survey geometry, the non-uniform sampling of the matter velocity field by the survey objects and the typically large measurement
errors of the measured line-of-sight velocities. Previously, we have developed an optimal ‘;minimum variance’ (MV) weighting
scheme for using peculiar velocity data to estimate bulk flow moments for idealized, dense and isotropic surveys with Gaussian
radial distributions, that avoids many of these complications. These moments are designed to be easy to interpret and are
comparable between surveys. In this paper, we test the robustness of our MV estimators using numerical simulations. Using
MV weights, we estimate the bulk flow moments for various mock catalogues extracted from the LasDamas and the Horizon Run
numerical simulations and compare these estimates to the moments calculated directly from the simulation boxes. We show that
the MV estimators are unbiased and negligibly affected by non-linear flows.

Download full-text


Available from: Hume A. Feldman
  • Source
    • "Further, [31] also shows the inconsistency of the MLE. Recently, a more consistent and, in fact, optimal estimation method – 1 – was introduced to address these problems, called the Minimum Variance (MV) method [39] [40], and was tested further by citation [48] (for a recent implementation of the MV method see [49] [50]). Various studies have indicated that the BF magnitudes fit Maxwellian distribution (e.g. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The bulk flow is a volume average of the peculiar velocities and a useful probe of the mass distribution on large scales. The gravitational instability model views the bulk flow as a potential flow that obeys a Maxwellian Distribution. We use two N-body simulations, the LasDamas Carmen and the Horizon Run, to calculate the bulk flows of various sized volumes in the simulation boxes. Once we have the bulk flow velocities as a function of scale, we investigate the mass and gravitational potential distribution around the volume. We found that matter densities can be asymmetrical and difficult to detect in real surveys, however, the gravitational potential and its gradient may provide better tools to investigate the underlying matter distribution. This study shows that bulk flows are indeed potential flows and thus provides information on the flow sources. We also show that bulk flow magnitudes follow a Maxwellian distribution on scales $>10\ h^{-1}$Mpc.
    Preview · Article · Dec 2015
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We calculate the cosmic Mach number M – the ratio of the bulk flow of the velocity field on scale R to the velocity dispersion within regions of scale R. M is effectively a measure of the ratio of large-scale to small-scale power and can be a useful tool to constrain the cosmological parameter space. Using a compilation of existing peculiar velocity surveys, we calculate M and compare it to that estimated from mock catalogues extracted from the Large Suite of Dark Matter Simulations (LasDamas, a Λ cold dark matter cosmology) numerical simulations. We find agreement with expectations for the LasDamas cosmology at ∼1.5σ confidence level. We also show that our Mach estimates for the mocks are not biased by selection function effects. To achieve this, we extract dense and nearly isotropic distributions using Gaussian selection functions with the same width as the characteristic depth of the real surveys, and show that the Mach numbers estimated from the mocks are very similar to the values based on Gaussian profiles of the corresponding widths. We discuss the importance of the survey window functions in estimating their effective depths. We investigate the non-linear matter power spectrum interpolator pkann as an alternative to numerical simulations, in the study of Mach number.
    Full-text · Article · Jun 2013 · Monthly Notices of the Royal Astronomical Society
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We introduce a new estimator of the peculiar velocity of a galaxy or group of galaxies from redshift and distance estimates. This estimator results in peculiar velocity estimates which are statistically unbiased and have Gaussian distributed errors, thus complying with the assumptions of analyses that rely on individual peculiar velocities. We apply this estimator to the SFI++ and the Cosmicflows-2 catalogues of galaxy distances and, since peculiar velocity estimates of distant galaxies are error dominated, examine their error distributions. The adoption of the new estimator significantly improves the accuracy and validity of studies of the large-scale peculiar velocity field that assume Gaussian distributed velocity errors and eliminates potential systematic biases, thus helping to bring peculiar velocity analysis into the era of precision cosmology. In addition, our method of examining the distribution of velocity errors should provide a useful check of the statistics of large peculiar velocity catalogues, particularly those that are compiled out of data from multiple sources.
    Full-text · Article · Nov 2014 · Monthly Notices of the Royal Astronomical Society