We create a sample of spectroscopically identified galaxies with z < 0.2 from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7), covering 6813 deg2. Galaxies are chosen to sample the highest ...mass haloes, with an effective bias of 1.5, allowing us to construct 1000 mock galaxy catalogues (described in Paper II), which we use to estimate statistical errors and test our methods. We use an estimate of the gravitational potential to ‘reconstruct’ the linear density fluctuations, enhancing the baryon acoustic oscillation (BAO) signal in the measured correlation function and power spectrum. Fitting to these measurements, we determine D
V
(z
eff = 0.15) = (664 ± 25)(r
d/r
d, fid) Mpc; this is a better than 4 per cent distance measurement. This ‘fills the gap’ in BAO distance ladder between previously measured local and higher redshift measurements, and affords significant improvement in constraining the properties of dark energy. Combining our measurement with other BAO measurements from Baryon Oscillation Spectroscopic Survey and 6-degree Field Galaxy Redshift Survey galaxy samples provides a 15 per cent improvement in the determination of the equation of state of dark energy and the value of the Hubble parameter at z = 0 (H
0). Our measurement is fully consistent with the Planck results and the Λ cold dark matter concordance cosmology, but increases the tension between Planck+BAO H
0 determinations and direct H
0 measurements.
Abstract
In order to be efficient, spectroscopic galaxy redshift surveys do not obtain redshifts for all galaxies in the population targeted. The missing galaxies are often clustered, commonly ...leading to a lower proportion of successful observations in dense regions. One example is the close-pair issue for SDSS spectroscopic galaxy surveys, which have a deficit of pairs of observed galaxies with angular separation closer than the hardware limit on placing neighbouring fibres. Spatially clustered missing observations will exist in the next generations of surveys. Various schemes have previously been suggested to mitigate these effects, but none works for all situations. We argue that the solution is to link the missing galaxies to those observed with statistically equivalent clustering properties, and that the best way to do this is to rerun the targeting algorithm, varying the angular position of the observations. Provided that every pair has a non-zero probability of being observed in one realization of the algorithm, then a pair-upweighting scheme linking targets to successful observations, can correct these issues. We present such a scheme, and demonstrate its validity using realizations of an idealized simple survey strategy.
We develop a model for the redshift-space correlation function, valid for both dark matter particles and haloes on scales >5 h super( -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 Gaussian streaming model and the more recent Edgeworth streaming model. Using N-body simulations as a reference, we show that our model gives a precise description of the redshift-space clustering over a wider range of scales. We do not discuss the theoretical prescription for the evaluation of the velocity moments, leaving this topic to further investigation.
Observed galaxy clustering exhibits local transverse statistical isotropy around the line of sight (LOS). The variation of the LOS across a galaxy survey complicates the measurement of the observed ...clustering as a function of the angle to the LOS, as fast Fourier transforms (FFTs) based on Cartesian grids, cannot individually allow for this. Recent advances in methodology for calculating LOS-dependent clustering in Fourier space include the realization that power spectrum LOS-dependent moments can be constructed from sums over galaxies, based on approximating the LOS to each pair of galaxies by the LOS to one of them. We show that we can implement this method using multiple FFTs, each measuring the LOS-weighted clustering along different axes. The Nlog N nature of FFTs means that the computational speed-up is a factor of >1000 compared with summing over galaxies. This development should be beneficial for future projects such as DESI and Euclid which will provide an order of magnitude more galaxies than current surveys.
ABSTRACT
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the ...maximum a posteriori probability values, as the intervals indicate concordance or discordance between models and with measurements from other data. Intermediate statistics (e.g. the power spectrum) are usually measured and inferences are made by fitting models to these rather than the raw data, assuming that the likelihood for these statistics has multivariate Gaussian form. The covariance matrix used to calculate the likelihood is often estimated from simulations, such that it is itself a random variable. This is a standard problem in Bayesian statistics, which requires a prior to be placed on the true model parameters and covariance matrix, influencing the joint posterior distribution. As an alternative to the commonly used independence Jeffreys prior, we introduce a prior that leads to a posterior that has approximately frequentist matching coverage. This is achieved by matching the covariance of the posterior to that of the distribution of true values of the parameters around the maximum likelihood values in repeated trials, under certain assumptions. Using this prior, credible intervals derived from a Bayesian analysis can be interpreted approximately as confidence intervals, containing the truth a certain proportion of the time for repeated trials. Linking frequentist and Bayesian approaches that have previously appeared in the astronomical literature, this offers a consistent and conservative approach for credible intervals quoted on model parameters for problems where the covariance matrix is itself an estimate.
Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure. In this paper, we develop and test a new ...statistic based on anisotropies in the measured galaxy power spectrum, which is independent of galaxy bias and matches the matter power spectrum shape on large scales. The amplitude provides a constraint on the derivative of the linear growth rate through fσ8(mass). This demonstrates that spectroscopic galaxy surveys offer many of the same advantages as weak lensing surveys, in that they both use galaxies as test particles to probe all matter in the Universe. They are complementary as redshift-space distortions probe non-relativistic velocities and therefore the temporal metric perturbations, while weak lensing tests the sum of the temporal and spatial metric perturbations. The degree to which our estimator can be pushed into the non-linear regime is considered and we show that a simple Gaussian damping model, similar to that previously used to model the behaviour of the power spectrum on very small scales, can also model the quasi-linear behaviour of our estimator. This enhances the information that can be extracted from surveys for Λ cold dark matter (ΛCDM) models.
Abstract
We perform a detailed analysis of the covariance matrix of the spherically averaged galaxy power spectrum and present a new, practical method for estimating this within an arbitrary survey ...without the need for running mock galaxy simulations that cover the full survey volume. The method uses theoretical arguments to modify the covariance matrix measured from a set of small-volume cubic galaxy simulations, which are computationally cheap to produce compared to larger simulations and match the measured small-scale galaxy clustering more accurately than is possible using theoretical modelling. We include prescriptions to analytically account for the window function of the survey, which convolves the measured covariance matrix in a non-trivial way. We also present a new method to include the effects of super-sample covariance and modes outside the small simulation volume which requires no additional simulations and still allows us to scale the covariance matrix. As validation, we compare the covariance matrix estimated using our new method to that from a brute-force calculation using 500 simulations originally created for analysis of the Sloan Digital Sky Survey Main Galaxy Sample. We find excellent agreement on all scales of interest for large-scale structure analysis, including those dominated by the effects of the survey window, and on scales where theoretical models of the clustering normally break down, but the new method produces a covariance matrix with significantly better signal-to-noise ratio. Although only formally correct in real space, we also discuss how our method can be extended to incorporate the effects of redshift space distortions.
We measure redshift space distortions in the two-point correlation function of a sample of 63 163 spectroscopically identified galaxies with z < 0.2, an epoch where there are currently only limited ...measurements, from the Sloan Digital Sky Survey Data Release 7 main galaxy sample (MGS). Our sample, which we denote MGS, covers 6813 deg2 with an effective redshift z
eff = 0.15 and is described in our companion paper (Paper I), which concentrates on baryon acoustic oscillation (BAO) measurements. In order to validate the fitting methods used in both papers, and derive errors, we create and analyse 1000 mock catalogues using a new algorithm called picola to generate accurate dark matter fields. Haloes are then selected using a friends-of-friends algorithm, and populated with galaxies using a halo-occupation distribution fitted to the data. Using errors derived from these mocks, we fit a model to the monopole and quadrupole moments of the MGS correlation function. If we assume no Alcock–Paczynski (AP) effect (valid at z = 0.15 for any smooth model of the expansion history), we measure the amplitude of the velocity field, fσ8, at z = 0.15 to be
$0.49_{-0.14}^{+0.15}$
. We also measure fσ8 including the AP effect. This latter measurement can be freely combined with recent cosmic microwave background results to constrain the growth index of fluctuations, γ. Assuming a background Λ cold dark matter cosmology and combining with current BAO data, we find γ = 0.64 ± 0.09, which is consistent with the prediction of general relativity (γ ≈ 0.55), though with a slight preference for higher γ and hence models with weaker gravitational interactions.
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