Search

As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is performing triplet counts of synthetic data points in random catalogues. Since triplet counting algorithms scale at best as $\mathcal{O}(N^2\log N)$ with the number of particles and the random catalogues are typically at least 50 times denser than the data; this tends to be by far the most time-consuming part of the measurements. Here we present a simple method of computing the necessary triplet counts involving uniform random distributions through simple one-dimensional integrals. The method speeds up the computation of the three-point function by orders of magnitude, eliminating the need for random catalogues, with the simultaneous pair and triplet counting of the data points alone being sufficient., Comment: Accepted to MNRAS Letters

We present the first high significance detection ($4.1\sigma$) of the Baryon Acoustic Oscillations (BAO) feature in the galaxy bispectrum of the twelfth data release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS sample ($0.43 \leq z \leq 0.7$). We measured the scale dilation parameter, $\alpha$, using the power spectrum, bispectrum, and both simultaneously for DR12, plus 2048 MultiDark-PATCHY mocks in the North and South Galactic Caps (NGC and SGC, respectively), and the volume weighted averages of those two samples (N+SGC). The fitting to the mocks validated our analysis pipeline, yielding values consistent with the mock cosmology. By fitting to the power spectrum and bispectrum separately, we tested the robustness of our results, finding consistent values from the NGC, SGC and N+SGC in all cases. We found $D_{\mathrm{V}} = 2032 \pm 24 (\mathrm{stat.}) \pm 15 (\mathrm{sys.})$ Mpc, $D_{\mathrm{V}} = 2038 \pm 55 (\mathrm{stat.}) \pm 15 (\mathrm{sys.})$ Mpc, and $D_{\mathrm{V}} = 2031 \pm 22 (\mathrm{stat.}) \pm 10 (\mathrm{sys.})$ Mpc from the N+SGC power spectrum, bispectrum and simultaneous fitting, respectively., Comment: Submitted to Monthly Notices of the Royal Astronomical Society. 13 pages, 11 figures

Since the volume accessible to galaxy surveys is fundamentally limited, it is extremely important to analyse available data in the most optimal fashion. One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region (FKP weights) and their bias with respect to the dark matter field (PVP weights). They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. We develop a procedure for computing the optimal weights and test them against mock catalogues for which the values of all fitting parameters, as well as the input power-spectrum are known. We show that by applying these weights to the joint power-spectrum of Emission Line Galaxies and Luminous Red Galaxies from the Dark Energy Spectroscopic Instrument survey, the variance in the measured growth rate parameter can be reduced by as much as 36 per cent., Comment: 9 pages, 3 figures, 3 tables. Matches accepted version in Monthly Notices of the Royal Astronomical Society

The covariance matrices of power-spectrum (P(k)) measurements from galaxy surveys are difficult to compute theoretically. The current best practice is to estimate covariance matrices by computing a sample covariance of a large number of mock catalogues. The next generation of galaxy surveys will require thousands of large volume mocks to determine the covariance matrices to desired accuracy. The errors in the inverse covariance matrix are larger and scale with the number of P(k) bins, making the problem even more acute. We develop a method of estimating covariance matrices using a theoretically justified, few-parameter model, calibrated with mock catalogues. Using a set of 600 BOSS DR11 mock catalogues, we show that a seven parameter model is sufficient to fit the covariance matrix of BOSS DR11 P(k) measurements. The covariance computed with this method is better than the sample covariance at any number of mocks and only ~100 mocks are required for it to fully converge and the inverse covariance matrix converges at the same rate. This method should work equally well for the next generation of galaxy surveys, although a demand for higher accuracy may require adding extra parameters to the fitting function., Comment: 7 pages, 7 figures

A new analytical model for constraining the extent of gravitationally bound structure in the Universe is presented. This model is based on a simple modification of the spherical collapse model (SCM), and its performance in predicting the limits of bound structure in N-body simulations is compared to that of two previous models with the aid of new software named COLDGaS-- compute unified device architecture (CUDA) object location determination in GADGET2 snapshots -- which was developed by the author. All of these models can be distilled down to a single unique parameter {\xi}, here named the critical parameter, which was found to have values of 3 and 1.18 from the previous studies, and a value of 1.89 from the modified SCM. While still on the conservative side, this new model tends to better identify what structure is gravitationally bound in simulations. All three analytical models are applied to the Corona Borealis supercluster, with the modified SCM and {\xi} = 1.18 model making predictions that are in agreement with recent work showing that A2056, A2061, A2065, A2067, and A2089 comprise a gravitationally bound supercluster. As an additional test, the modified SCM is used to estimate the mass within the turn around radius of the Virgo cluster, providing results in good agreement with studies relating the virial mass of clusters to the total mass within turn around., Comment: 11 pages, 6 figures

Recent simulations of the densest portion of the Corona Borealis supercluster (A2061, A2065, A2067, and A2089) have shown virtually no possibility of extended gravitationally bound structure without inter-cluster matter (Pearson & Batuski). In contrast, recent analyses of the dynamics found that the clusters had significant peculiar velocities towards the supercluster centroid (Batiste & Batuski). In this paper we present the results of a thorough investigation of the CSC: we determine redshifts and virial masses for all 8 clusters associated with the CSC; repeat the analysis of Batiste & Batuski with the inclusion of A2056 and CL1529+29; estimate the mass of the supercluster by applying the virial theorem on the supercluster scale (e.g. Small et al.), the caustics method (e.g. Reisenegger et al.), and a new procedure using the spherical collapse model (SCM) with the results of the dynamical analysis (SCM+FP); and perform a series of simulations to assess the likelihood of the CSC being a gravitationally bound supercluster. We find that the mass of the CSC is between 0.6 and 12 x 10^{16} h^{-1} M_{sun}. The dynamical analysis, caustics method and the SCM+FP indicate that the structure is collapsing, with the latter two both indicating a turn around radius of about 12.5 h^{-1} Mpc. Lastly, the simulations show that with a reasonable amount of inter-cluster mass, there is likely extended bound structure in the CSC. Our results suggest that A2056, A2061, A2065, A2067, and A2089 form a gravitationally bound supercluster.

Given the overwhelming evidence that the universe is currently undergoing an accelerated expansion, the question of what are the largest gravitationally bound structures remains. A couple of groups, Busha et al. 2003 (B03) and Dunner et al. 2006 (D06), have attempted to analytically define these limits, arriving at substantially different estimates due to differences in their assumptions about the velocities at the present epoch. In an effort to locate the largest bound structures in the universe, we selected the Aquarius (ASC), Microscopium (MSC), Corona Borealis (CBSC), and Shapley (SSC) superclusters for study, due to their high number density of rich Abell clusters. Simple N-body simulations, which assumed negligible intercluster mass, were used to assess the likelihood of these structures being gravitationally bound, and the predictions of the models of B03 and D06 were compared with those results. We find that ASC, and MSC contain pairs of clusters which are gravitationally bound, A2541/A2546 and A3695/A3696 respectively, with no other structures having a significant chance of being bound. For SSC, we find a group of five clusters, A3554, A3556, A3558, A3560, and A3562 that are bound, with an additional pair, A1736/A3559, having a slight chance of being bound. We find that CBSC has no extended bound structure, contrary to the findings of Small et al. 1998, who claim that the entire supercluster is bound. In regards to the analytical models, we find that B03 will identify structure that is definitely bound, but tends to underestimate the true extent of the structure, while D06 will identify all structure that is bound while overestimating its extent. Combined, the two models can provide lower and upper limits to the extent of bound structures so long as there are no other significant structures nearby or no significant dark matter exterior to the clusters.