Galaxy 2-Point Covariance Matrix Estimation for Next Generation Surveys

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 supersample 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 (SDSS-MGS). 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. Although only formally correct in real-space, we also discuss how our method can be extended to incorporate the effects of Redshift Space Distortions.Comment: 18 pages, 9 figures. Accepted for publication in MNRAS. Added new references to introduction and slightly updated text accordingl

Cosmological Forecasts for Combined and Next Generation Peculiar Velocity Surveys

Peculiar velocity surveys present a very promising route to measuring the growth rate of large-scale structure and its scale dependence. However, individual peculiar velocity surveys suffer from large statistical errors due to the intrinsic scatter in the relations used to infer a galaxy's true distance. In this context we use a Fisher Matrix formalism to investigate the statistical benefits of combining multiple peculiar velocity surveys. We find that for all cases we consider there is a marked improvement on constraints on the linear growth rate $f\sigma_{8}$. For example, the constraining power of only a few peculiar velocity measurements is such that the addition of the 2MASS Tully-Fisher survey (containing only $\sim2,000$ galaxies) to the full redshift and peculiar velocity samples of the 6-degree Field Galaxy Survey (containing $\sim 110,000$ redshifts and $\sim 9,000$ velocities) can improve growth rate constraints by $\sim20\%$. Furthermore, the combination of the future TAIPAN and WALLABY+WNSHS surveys has the potential to reach a $\sim3\%$ error on $f\sigma_{8}$, which will place tight limits on possible extensions to General Relativity. We then turn to look at potential systematics in growth rate measurements that can arise due to incorrect calibration of the peculiar velocity zero-point and from scale-dependent spatial and velocity bias. For next generation surveys, we find that neglecting velocity bias in particular has the potential to bias constraints on the growth rate by over $5\sigma$, but that an offset in the zero-point has negligible impact on the velocity power spectrum.Comment: 24 pages, 11 figures, 7 tables. Accepted for publication in MNRA

Cosmology with Peculiar Velocities: Observational Effects

In this paper we investigate how observational effects could possibly bias cosmological inferences from peculiar velocity measurements. Specifically, we look at how bulk flow measurements are compared with theoretical predictions. Usually bulk flow calculations try to approximate the flow that would occur in a sphere around the observer. Using the Horizon Run 2 simulation we show that the traditional methods for bulk flow estimation can overestimate the magnitude of the bulk flow for two reasons: when the survey geometry is not spherical (the data do not cover the whole sky), and when the observations undersample the velocity distributions. Our results may explain why several bulk flow measurements found bulk flow velocities that seem larger than those expected in standard {\Lambda}CDM cosmologies. We recommend a different approach when comparing bulk flows to cosmological models, in which the theoretical prediction for each bulk flow measurement is calculated specifically for the geometry and sampling rate of that survey. This means that bulk flow values will not be comparable between surveys, but instead they are comparable with cosmological models, which is the more important measure.Comment: 11 pages, 5 figures. Accepted for publication in MNRA

L-PICOLA: A parallel code for fast dark matter simulation

Robust measurements based on current large-scale structure surveys require precise knowledge of statistical and systematic errors. This can be obtained from large numbers of realistic mock galaxy catalogues that mimic the observed distribution of galaxies within the survey volume. To this end we present a fast, distributed-memory, planar-parallel code, L-PICOLA, which can be used to generate and evolve a set of initial conditions into a dark matter field much faster than a full non-linear N-Body simulation. Additionally, L-PICOLA has the ability to include primordial non-Gaussianity in the simulation and simulate the past lightcone at run-time, with optional replication of the simulation volume. Through comparisons to fully non-linear N-Body simulations we find that our code can reproduce the $z=0$ power spectrum and reduced bispectrum of dark matter to within 2% and 5% respectively on all scales of interest to measurements of Baryon Acoustic Oscillations and Redshift Space Distortions, but 3 orders of magnitude faster. The accuracy, speed and scalability of this code, alongside the additional features we have implemented, make it extremely useful for both current and next generation large-scale structure surveys. L-PICOLA is publicly available at https://cullanhowlett.github.io/l-picolaComment: 22 Pages, 20 Figures. Accepted for publication in Astronomy and Computin

Bulk flow and shear in the local Universe: 2MTF and COSMICFLOWS-3

The low-order kinematic moments of galaxies, namely bulk flow and shear, enables us to test whether theoretical models can accurately describe the evolution of the mass density field in the nearby Universe. We use the so-called etaMLE maximum likelihood estimator in logdistance space to measure thesemoments from a combined sample of the 2MASS Tully-Fisher (2MTF) survey and the COSMICFLOWS-3 (CF3) compilation. Galaxies common between 2MTF and CF3 demonstrate a small zero-point difference of -0.016+-0.002 dex.We test the etaMLE on 16 mock 2MTF survey catalogues in order to explore how well the etaMLE recovers the true moments, and the effect of sample anisotropy. On the scale size of 37 Mpc/h, we find that the bulk flow of the local Universe is 259 +- 15 km/h in the direction is (l,b)=(300+-4, 23+-3) (Galactic coordinates). The average shear amplitude is 1.7+-0.4 h km/s/Mpc. We use a variable window function to explore the bulk and shear moments as a function of depth. In all cases, the measurements are consistent with the predictions of the L cold dark matter (LCDM) model.Comment: 11 pages, 10+2 figures, published in MNRAS, Oct/201

Constraining the growth rate of structure with phase correlations

We show that correlations between the phases of the galaxy density field in redshift space provide additional information about the growth rate of large-scale structure that is complementary to the power spectrum multipoles. In particular, we consider the multipoles of the line correlation function (LCF), which correlates phases between three collinear points, and use the Fisher forecasting method to show that the LCF multipoles can break the degeneracy between the measurement of the growth rate of structure $f$ and the amplitude of perturbations $\sigma_8$ that is present in the power spectrum multipoles at large scales. This leads to an improvement in the measurement of $f$ and $\sigma_8$ by up to 220 per cent for $k_{\rm max} = 0.15 \, h\mathrm{Mpc}^{-1}$ and up to 50 per cent for $k_{\rm max} = 0.30 \, h\mathrm{Mpc}^{-1}$ at redshift $z=0.25$, with respect to power spectrum measurements alone for the upcoming generation of galaxy surveys like DESI and Euclid. The average improvements in the constraints on $f$ and $\sigma_8$ for $k_{\rm max} = 0.15 \, h\mathrm{Mpc}^{-1}$ are $\sim 90$ per cent for the DESI BGS sample with mean redshift $\overline{z}=0.25$, $\sim 40$ per cent for the DESI ELG sample with $\overline{z}=1.25$, and $\sim 40$ per cent for the Euclid H$\alpha$ galaxies with $\overline{z}=1.3$. For $k_{\rm max} = 0.30 \, h\mathrm{Mpc}^{-1}$, the average improvements are $\sim 40$ per cent for the DESI BGS sample and $\sim 20$ per cent for both the DESI ELG and Euclid H$\alpha$ galaxies.Comment: 28 pages, 13 figures, 2 tables. v2 has additional discussion on model-independence of the forecasts. v3 matches the MNRAS accepted versio

Measuring the growth rate of structure with Type IA Supernovae from LSST

We investigate measuring the peculiar motions of galaxies up to $z=0.5$ using Type Ia supernovae (SNe Ia) from LSST, and predict the subsequent constraints on the growth rate of structure. We consider two cases. Our first is based on measurements of the volumetric SNe Ia rate and assumes we can obtain spectroscopic redshifts and light curves for varying fractions of objects that are detected pre-peak luminosity by LSST (some of which may be obtained by LSST itself and others which would require additional follow-up). We find that these measurements could produce growth rate constraints at $z<0.5$ that significantly outperform those using Redshift Space Distortions (RSD) with DESI or 4MOST, even though there are $\sim4\times$ fewer objects. For our second case, we use semi-analytic simulations and a prescription for the SNe Ia rate as a function of stellar mass and star formation rate to predict the number of LSST SNe IA whose host redshifts may already have been obtained with the Taipan+WALLABY surveys, or with a future multi-object spectroscopic survey. We find $\sim 18,000$ and $\sim 160,000$ SN Ia with host redshifts for these cases respectively. Whilst this is only a fraction of the total LSST-detected SNe Ia, they could be used to significantly augment and improve the growth rate constraints compared to only RSD. Ultimately, we find that combining LSST SNe Ia with large numbers of galaxy redshifts will provide the most powerful probe of large scale gravity in the $z<0.5$ regime over the coming decades.Comment: 12 pages, 1 table, 5 figures. Accepted for publication in ApJ. The Fisher matrix forecast code used in this paper can be found at: https://github.com/CullanHowlett/PV_fisher. Updated to fix error in Eq. 1 (thanks to Eric Linder for pointing this out

The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15

We create a sample of spectroscopically identified galaxies with $z < 0.2$ from the Sloan Digital Sky Survey (SDSS) Data Release 7, covering 6813 deg$^2$. Galaxies are chosen to sample the highest mass haloes, with an effective bias of 1.5, allowing us to construct 1000 mock galaxy catalogs (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 $D_{V}(z_{\rm eff}=0.15) = (664\pm25)(r_d/r_{d,{\rm fid}})$ 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 BOSS and 6dFGS 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 $\Lambda$CDM concordance cosmology, but increases the tension between Planck$+$BAO $H_0$ determinations and direct $H_0$ measurements.Comment: Accepted by MNRAS, distance likelihood is available in source file

Standard siren speeds: improving velocities in gravitational-wave measurements of H0

We re-analyse data from the gravitational-wave event GW170817 and its host galaxy NGC 4993 to demonstrate the importance of accurate total and peculiar velocities when measuring the Hubble constant using this nearby standard siren. We show that a number of reasonable choices can be made to estimate the velocities for this event, but that systematic differences remain between these measurements depending on the data used. This leads to significant changes in the Hubble constant inferred from GW170817. We present Bayesian model averaging as one way to account for these differences, and obtain H-0 = 66.8(-9.2)(+13.4) km s(-1)Mpc(-1). Adding additional information on the viewing angle from high-resolution imaging of the radio counterpart refines this to H-0 = 64.8(-7.2)(+7.3) km s(-1) Mpc(-1). During this analysis, we also present an alternative Bayesian model for the posterior on H-0 from standard sirens that works more closely with observed quantities from redshift and peculiar velocity surveys. Our results more accurately capture the true uncertainty on the total and peculiar velocities of NGC 4993 and show that exploring how well different data sets characterize galaxy groups and the velocity field in the local Universe could improve this measurement further. These considerations impact any low-redshift distance measurement, and the improvements we suggest here can also be applied to standard candles like Type Ia supernovae. GW170817 is particularly sensitive to peculiar velocity uncertainties because it is so close. For future standard siren measurements, the importance of this error will decrease as (i) we will measure more distant standard sirens and (ii) the random direction of peculiar velocities will average out with more detections