Random Catalogs Research Articles

Cosmology from LOFAR Two-metre Sky Survey Data Release 2: angular clustering of radio sources

ABSTRACT Covering $\sim 5600\, \deg ^2$ to rms sensitivities of ∼70−100 $\mu$Jy beam−1, the LOFAR Two-metre Sky Survey Data Release 2 (LoTSS-DR2) provides the largest low-frequency (∼150 MHz) radio catalogue to date, making it an excellent tool for large-area radio cosmology studies. In this work, we use LoTSS-DR2 sources to investigate the angular two-point correlation function of galaxies within the survey. We discuss systematics in the data and an improved methodology for generating random catalogues, compared to that used for LoTSS-DR1, before presenting the angular clustering for ∼900 000 sources ≥1.5 mJy and a peak signal-to-noise ≥ 7.5 across ∼80 per cent of the observed area. Using the clustering, we infer the bias assuming two evolutionary models. When fitting angular scales of $0.5 \le \theta \lt 5{^\circ }$, using a linear bias model, we find LoTSS-DR2 sources are biased tracers of the underlying matter, with a bias of $b_{\rm C}= 2.14^{+0.22}_{-0.20}$ (assuming constant bias) and $b_{\rm E}(z=0)= 1.79^{+0.15}_{-0.14}$ (for an evolving model, inversely proportional to the growth factor), corresponding to $b_{\rm E}= 2.81^{+0.24}_{-0.22}$ at the median redshift of our sample, assuming the LoTSS Deep Fields redshift distribution is representative of our data. This reduces to $b_{\rm C}= 2.02^{+0.17}_{-0.16}$ and $b_{\rm E}(z=0)= 1.67^{+0.12}_{-0.12}$ when allowing preferential redshift distributions from the Deep Fields to model our data. Whilst the clustering amplitude is slightly lower than LoTSS-DR1 (≥2 mJy), our study benefits from larger samples and improved redshift estimates.

Probing cosmic homogeneity in the Local Universe

ABSTRACT We investigate the transition scale to homogeneity, RH, using as cosmic tracer the spectroscopic sample of blue galaxies from the Sloan Digital Sky Survey (SDSS). Considering the spatial distribution of the galaxy sample, we compute the two point correlation function ξ(r), the scaled counts in spheres $\mathcal {N}(\lt r)$, and the fractal dimension $\mathcal {D}_2(r)$ to quantify the homogeneity scale in the Local Universe (0.04 < z < 0.20). The sample in analysis is compared with random and mock catalogues with the same geometry, and the same number of synthetic cosmic objects as the data set, to calculate the covariance matrix for the errors determination. The criteria adopted for the transition-to-homogeneity follows the literature, it is attained when $\mathcal {D}_2(r)$ reaches the 1 per cent level of the limit value 3 (i.e. where it reaches 2.97) as the scale increases. We obtain RH = 70.33 ± 10.74 Mpc h−1, at the effective redshift zeff = 0.128, for a sample containing $150\, 302$ SDSS blue galaxies with 0.04 < z < 0.20. Additionally, we perform robustness tests by analysing the homogeneity scale in sub-volumes of the original one, obtaining coherent results; we also check for a possible artefact in our procedure examining a homogeneous synthetic data set as a pseudo-data, verifying that such systematic is absent. Because our analyses concentrate in data at low redshifts, z < 0.20, we find interesting to use cosmography to calculate the radial comoving distances; therefore in this subject our analyses do not use fiducial cosmological model. For completeness, we evaluate the difference of the comoving distances estimation using cosmography and fiducial cosmology.

Glass-like random catalogues for two-point estimates on the light-cone

ABSTRACT We introduce grlic, a publicly available Python tool for generating glass-like point distributions with a radial density profile n(r) as it is observed in large-scale surveys of galaxy distributions on the past light-cone. Utilizing these glass-like catalogues, we assess the bias and variance of the Landy–Szalay (LS) estimator of the first three two-point correlation function (2PCF) multipoles in halo and particle catalogues created with the cosmological N-body code gevolution. Our results demonstrate that the LS estimator calculated with the glass-like catalogues is biased by less than 10−4 with respect to the estimate derived from Poisson-sampled random catalogues, for all multipoles considered and on all but the smallest scales. Additionally, the estimates derived from glass-like catalogues exhibit significantly smaller standard deviation σ than estimates based on commonly used Poisson-sampled random catalogues of comparable size. The standard deviation of the estimate depends on a power of the number of objects NR in the random catalogue; we find a power law $\sigma \propto N_\mathit{R}^{-0.9}$ for glass-like catalogues as opposed to $\sigma \propto N_\mathit{R}^{-0.48}$ using Poisson-sampled random catalogues. Given a required precision, this allows for a much reduced number of objects in the glass-like catalogues used for the LS estimate of the 2PCF multipoles, significantly reducing the computational costs of each estimate.

Toward Accurate Measurement of Property-dependent Galaxy Clustering. II. Tests of the Smoothed Density-corrected V max Method

We present a smoothed density-corrected V max technique for building a random catalog for property-dependent galaxy clustering estimation. This approach is essentially based on the density-corrected V max method of Cole, with three improvements to the original method. To validate the improved method, we generate two sets of flux-limited samples from two independent mock catalogs with different k + e corrections. By comparing the two-point correlation functions, our results demonstrate that the random catalog created by the smoothed density-corrected V max approach provides a more accurate and precise measurement for both sets of mock samples than the commonly used V max and redshift shuffled methods. For the flux-limited samples and color-dependent subsamples, the accuracy of the projected correlation function is well constrained within 1% on the scale of 0.07–30 h −1 Mpc. The accuracy of the redshift-space correlation function is less than 2% as well. Currently, it is the only approach that holds promise for achieving the goal of high-accuracy clustering measures for next-generation surveys.

The Target-selection Pipeline for the Dark Energy Spectroscopic Instrument

In 2021 May, the Dark Energy Spectroscopic Instrument (DESI) began a 5 yr survey of approximately 50 million total extragalactic and Galactic targets. The primary DESI dark-time targets are emission line galaxies, luminous red galaxies, and quasars. In bright time, DESI will focus on two surveys known as the Bright Galaxy Survey and the Milky Way Survey. DESI also observes a selection of “secondary” targets for bespoke science goals. This paper gives an overview of the publicly available pipeline (desitarget) used to process targets for DESI observations. Highlights include details of the different DESI survey targeting phases, the targeting ID (TARGETID) used to define unique targets, the bitmasks used to indicate a particular type of target, the data model and structure of DESI targeting files, and examples of how to access and use the desitarget code base. This paper will also describe “supporting” DESI target classes, such as standard stars, sky locations, and random catalogs that mimic the angular selection function of DESI targets. The DESI target-selection pipeline is complex and sizable; this paper attempts to summarize the most salient information required to understand and work with DESI targeting data.

Euclid: Fast two-point correlation function covariance through linear construction

We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy–Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (random-to-data objects’ ratio M ≫ 1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs with a size of M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of the two. We show that the LC covariance estimate is unbiased. We validated the method with PINOCCHIO simulations in the range r = 20 − 200 h−1 Mpc. With M = 50 and with 2 h−1 Mpc bins, the theoretical speedup of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and present a formula for the covariance of covariance.

Seasonal Variations in the b-Value of the Reservoir-Triggered Seismicity in the Koyna–Warna Region, Western India

—The analysis of the local earthquake catalog revealed fine features in the behavior of seasonal components of induced seismicity in the Koyna–Warna region, western India. The seasonal variations in seismicity associated with annual fluctuations in water levels in the Koyna and Warna reservoirs have local maxima during the year, corresponding to the known mechanisms of immediate and delayed responses of reservoir-triggered seismicity (RTS). The superposed epoch analysis combined with the stochastic modeling of random earthquake catalogs revealed regular changes in the b-value of the frequency–magnitude relationship of the earthquakes within the annual cycle of seasonal seismicity fluctuations. The minimum b-values fall in the intervals of the maxima of both the immediate and delayed seismic responses. The maximum b-values are observed during the rise and fall phases of water levels in the reservoirs. The pattern of changes in the seismicity together with the b-value behavior at the activation phase of the immediate RTS response is consistent with the scenario of gradual redistribution of the failure process from the lower to higher scales, characteristic of the activation of transient seismicity. A pilot laboratory experiment on cyclic initiation of fracture process by pore pressure in a granite sample extracted from a well in the Koyna–Warna region of reservoir-triggered seismicity demonstrated the patterns of changes in the acoustic regime similar to the seasonal features of the Koyna–Warna region seismicity.

Improved two-point correlation function estimates using glass-like distributions as a reference sample

ABSTRACT All estimators of the two-point correlation function are based on a random catalogue, a set of points with no intrinsic clustering following the selection function of a survey. High-accuracy estimates require the use of large random catalogues, which imply a high computational cost. We propose to replace the standard random catalogues by glass-like point distributions or glass catalogues whose power spectrum P(k) ∝ k4 exhibits significantly less power on scales larger than the mean interparticle separation than a Poisson distribution with the same number of points. We show that these distributions can be obtained by iteratively applying the technique of Zeldovich reconstruction commonly used in studies of baryon acoustic oscillations (BAO). We provide a modified version of the widely used Landy–Szalay estimator of the correlation function adapted to the use of glass catalogues and compare its performance with the results obtained using random samples. Our results show that glass-like samples do not add any bias with respect to the results obtained using Poisson distributions. On scales larger than the mean interparticle separation of the glass catalogues, the modified estimator leads to a significant reduction of the variance of the Legendre multipoles ξℓ(s) with respect to the standard Landy–Szalay results with the same number of points. The size of the glass catalogue required to achieve a given accuracy in the correlation function is significantly smaller than when using random samples. Their use could help us to drastically reduce the computational cost of configuration-space clustering analysis of future surveys while maintaining high-accuracy requirements.

Organised randoms: Learning and correcting for systematic galaxy clustering patterns in KiDS using self-organising maps

We present a new method for the mitigation of observational systematic effects in angular galaxy clustering through the use of corrective random galaxy catalogues. Real and synthetic galaxy data from the Kilo Degree Survey’s (KiDS) 4th Data Release (KiDS-1000) and the Full-sky Lognormal Astro-fields Simulation Kit package, respectively, are used to train self-organising maps to learn the multivariate relationships between observed galaxy number density and up to six systematic-tracer variables, including seeing, Galactic dust extinction, and Galactic stellar density. We then create ‘organised’ randoms; random galaxy catalogues with spatially variable number densities, mimicking the learnt systematic density modes in the data. Using realistically biased mock data, we show that these organised randoms consistently subtract spurious density modes from the two-point angular correlation function w(ϑ), correcting biases of up to 12σ in the mean clustering amplitude to as low as 0.1σ, over an angular range of 7 − 100 arcmin with high signal-to-noise ratio. Their performance is also validated for angular clustering cross-correlations in a bright, flux-limited subset of KiDS-1000, comparing against an analogous sample constructed from highly complete spectroscopic redshift data. Each organised random catalogue object is a clone carrying the properties of a real galaxy, and is distributed throughout the survey footprint according to the position of the parent galaxy in systematics space. Thus, sub-sample randoms are readily derived from a single master random catalogue through the same selection as applied to the real galaxies. Our method is expected to improve in performance with increased survey area, galaxy number density, and systematic contamination, making organised randoms extremely promising for current and future clustering analyses of faint samples.

Fast analytical calculation of the random pair counts for realistic survey geometry

Galaxy clustering is a standard cosmological probe that is commonly analysed through two-point statistics. In observations, the estimation of the two-point correlation function crucially relies on counting pairs in a random catalogue. The latter contains a large number of randomly distributed points, which accounts for the survey window function. Random pair counts can also be advantageously used for modelling the window function in the observed power spectrum. Since pair counting scales as 𝒪(N2), where N is the number of points, the computational time to measure random pair counts can be very expensive for large surveys. In this work, we present an alternative approach for estimating those counts that does not rely on the use of a random catalogue. We derived an analytical expression for the anisotropic random-random pair counts that accounts for the galaxy radial distance distribution, survey geometry, and possible galaxy weights. We show that a prerequisite is the estimation of the two-point correlation function of the angular selection function, which can be obtained efficiently using pixelated angular maps. Considering the cases of the VIPERS and SDSS-BOSS redshift surveys, we find that the analytical calculation is in excellent agreement with the pair counts obtained from random catalogues. The main advantage of this approach is that the primary calculation only takes a few minutes on a single CPU and it does not depend on the number of random points. Furthermore, it allows for an accuracy on the monopole equivalent to what we would otherwise obtain when using a random catalogue with about 1500 times more points than in the data at hand. We also describe and test an approximate expression for data-random pair counts that is less accurate than for random-random counts, but still provides subpercent accuracy on the monopole. The presented formalism should be very useful in accounting for the window function in next-generation surveys, which will necessitate accurate two-point window function estimates over huge observed cosmological volumes.

The PAU Survey: Intrinsic alignments and clustering of narrow-band photometric galaxies

We present the first measurements of the projected clustering and intrinsic alignments (IA) of galaxies observed by the Physics of the Accelerating Universe Survey (PAUS). With photometry in 40 narrow optical passbands (4500 Å–8500 Å), the quality of photometric redshift estimation is σz ∼ 0.01(1 + z) for galaxies in the 19 deg2 Canada-France-Hawaii Telescope Legacy Survey W3 field, allowing us to measure the projected 3D clustering and IA for flux-limited, faint galaxies (i < 22.5) out to z ∼ 0.8. To measure two-point statistics, we developed, and tested with mock photometric redshift samples, ‘cloned’ random galaxy catalogues which can reproduce data selection functions in 3D and account for photometric redshift errors. In our fiducial colour-split analysis, we made robust null detections of IA for blue galaxies and tentative detections of radial alignments for red galaxies (∼1 − 3σ), over scales of 0.1 − 18 h−1 Mpc. The galaxy clustering correlation functions in the PAUS samples are comparable to their counterparts in a spectroscopic population from the Galaxy and Mass Assembly survey, modulo the impact of photometric redshift uncertainty which tends to flatten the blue galaxy correlation function, whilst steepening that of red galaxies. We investigate the sensitivity of our correlation function measurements to choices in the random catalogue creation and the galaxy pair-binning along the line of sight, in preparation for an optimised analysis over the full PAUS area.

Improving estimates of the growth rate using galaxy–velocity correlations: a simulation study

ABSTRACT We present an improved framework for estimating the growth rate of large-scale structure, using measurements of the galaxy–velocity cross-correlation in configuration space. We consider standard estimators of the velocity autocorrelation function, ψ1 and ψ2, the two-point galaxy correlation function, ξgg, and introduce a new estimator of the galaxy–velocity cross-correlation function, ψ3. By including pair counts measured from random catalogues of velocities and positions sampled from distributions characteristic of the true data, we find that the variance in the galaxy–velocity cross-correlation function is significantly reduced. Applying a covariance analysis and χ2 minimization procedure to these statistics, we determine estimates and errors for the normalized growth rate fσ8 and the parameter β = f/b, where b is the galaxy bias factor. We test this framework on mock hemisphere data sets for redshift z < 0.1 with realistic velocity noise constructed from the l-picola simulation code, and find that we are able to recover the fiducial value of fσ8 from the joint combination of ψ1 + ψ2 + ψ3 + ξgg, with 15 per cent accuracy from individual mocks. We also recover the fiducial fσ8 to within 1σ regardless of the combination of correlation statistics used. When we consider all four statistics together we find that the statistical uncertainty in our measurement of the growth rate is reduced by $59{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ2, by $53{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ1, and by $52{{\ \rm per\ cent}}$ compared to the same analysis jointly considering ψ1 and ψ2.

Long-term statistical evidence proving the correspondence between tir anomalies and earthquakes is still absent

Recently, researchers have conducted long-term statistical studies to prove the correspondence between earthquakes and thermal infrared (TIR) anomalies. Upon obtaining relatively high true positive rates (TPR), it was concluded that TIR anomalies are closely related to earthquakes. However, the temporal-spatial clustering of earthquakes and overly large temporal-spatial windows will also contribute to high TPRs, and it is improper to correlate TIR anomalies with earthquakes without excluding these influences. In this paper, relevant studies will be tested according to the prior probability, random earthquake catalogs and Molchan diagram weighted by the Relative Intensity (RI) index. Our results show that the high TPR in the previous studies were caused by overly large determining windows, and the result was close to random guessing, which means that the extracted TIR anomalies make no contributions to predicting the timing, epicenter and magnitude of earthquakes. By comparing the original Molchan diagram and the Molchan diagram weighted by the RI index, we found that simply taking the fraction of space-time occupied by alarm may give a wrong evaluation for alarm. Moreover, long-term statistical evidence proving the correspondence between earthquakes and TIR anomalies in Greece and Taiwan are still absent.

Experimental evaluation of complete safe coordination of astrobots for Sloan Digital Sky Survey V

The data throughput of massive spectroscopic surveys in the course of each observation is directly coordinated with the number of optical fibers which reach their target. In this paper, we evaluate the safety and the performance of the astrobots coordination in SDSS-V by conducting various experimental and simulated tests. We illustrate that our strategy provides a complete coordination condition which depends on the operational characteristics of astrobots, their configurations, and their targets. Namely, a coordination method based on the notion of cooperative artificial potential fields is used to generate safe and complete trajectories for astrobots. Optimal target assignment further improves the performance of the used algorithm in terms of faster convergences and less oscillatory movements. Both random targets and galaxy catalog targets are employed to observe the coordination success of the algorithm in various target distributions. The proposed method is capable of handling all potential collisions in the course of coordination. Once the completeness condition is fulfilled according to initial configuration of astrobots and their targets, the algorithm reaches full convergence of astrobots. Should one assign targets to astrobots using efficient strategies, convergence time as well as the number of oscillations decrease in the course of coordination. Rare incomplete scenarios are simply resolved by trivial modifications of astrobots swarms’ parameters.

A faster Fourier transform? Computing small-scale power spectra and bispectra for cosmological simulations in 𝒪(N2) time

ABSTRACT We present $\mathcal {O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales, requiring orders of magnitude less computation time than Fast Fourier Transform based approaches alone. These methods are applicable to any tracer; simulation particles, haloes or galaxies, and take advantage of the simple geometry of the box and periodicity to remove almost all dependence on large random particle catalogues. By working in configuration-space, both power spectra and bispectra can be computed via a weighted sum of particle pairs up to some radius, which can be reduced at larger k, leading to algorithms with decreasing complexity on small scales. These do not suffer from aliasing or shot-noise, allowing spectra to be computed to arbitrarily large wavenumbers. The estimators are rigorously derived and tested against simulations, and their covariances discussed. The accompanying code, hipster, has been publicly released, incorporating these algorithms. Such estimators will be of great use in the analysis of large sets of high-resolution simulations.

On the fast random sampling and other properties of the three point correlation function in galaxy surveys

In the forthcoming large volume galaxy surveys, the use of higher order statistics will prove important to obtain complementary information to the usual two point statistics. In particular, one of those higher order statistical tools is the Three Point Correlation Function (3PCF) over discrete data points, whose lowest variance estimators count triangle configurations with vertices mixing data and random catalogues. A popular choice is to use large density random catalogues, which reduces the shot noise but leads to a computational cost of one or two orders of magnitude more than the pure data histogram calculation. In this paper, we explore ideas to time reduce the random sampling without using random catalogues. We focus on the isotropic 3PCF case over periodic boxes. In a first approach, based on Hamilton's construction of his famous two point estimator, we use an ad-hoc two point correlation piece for the mixed random-data histograms. A second approach relies on operators constructed from a geometrical viewpoint, using two sides and one angle to define the three dependencies of the isotropic 3PCF . We map the last result to the three triangle side basis either numerically or analytically, and show that the latter method performs best when applied to synthetic data. In addition, we elaborate on relaxing the no boundary condition, discuss other low variance n-point estimators and present useful 3PCF visualization schemes.

Estimating the galaxy two-point correlation function using a split random catalog

The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the galaxy positions and the expected galaxy density field. The expected field is commonly specified using a Monte-Carlo sampling of the volume covered by the survey and, to minimize additional sampling errors, this random catalog has to be much larger than the data catalog. Correlation function estimators compare data–data pair counts to data–random and random–random pair counts, where random–random pairs usually dominate the computational cost. Future redshift surveys will deliver spectroscopic catalogs of tens of millions of galaxies. Given the large number of random objects required to guarantee sub-percent accuracy, it is of paramount importance to improve the efficiency of the algorithm without degrading its precision. We show both analytically and numerically that splitting the random catalog into a number of subcatalogs of the same size as the data catalog when calculating random–random pairs and excluding pairs across different subcatalogs provides the optimal error at fixed computational cost. For a random catalog fifty times larger than the data catalog, this reduces the computation time by a factor of more than ten without affecting estimator variance or bias.

Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries

ABSTRACT We present configuration-space estimators for the auto- and cross-covariance of two- and three-point correlation functions (2PCF and 3PCF) in general survey geometries. These are derived in the Gaussian limit (setting higher order correlation functions to zero), but for arbitrary non-linear 2PCFs (which may be estimated from the survey itself), with a shot-noise rescaling parameter included to capture non-Gaussianity. We generalize previous approaches to include Legendre moments via a geometry-correction function calibrated from measured pair and triple counts. Making use of importance sampling and random particle catalogues, we can estimate model covariances in fractions of the time required to do so with mocks, obtaining estimates with negligible sampling noise in ∼10 (∼100) CPU-hours for the 2PCF (3PCF) autocovariance. We compare results to sample covariances from a suite of BOSS DR12 mocks and find the matrices to be in good agreement, assuming a shot-noise rescaling parameter of 1.03 (1.20) for the 2PCF (3PCF). To obtain strongest constraints on cosmological parameters, we must use multiple statistics in concert; having robust methods to measure their covariances at low computational cost is thus of great relevance to upcoming surveys.

Computing three-point correlation function randoms counts without the randoms catalogue

ABSTRACT 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.

Effect of the Galactic Disk and Satellite Galaxies on the Spatial Distribution of Globular Clusters

The distribution anisotropy in systems of globular clusters (GCs) in satellite galaxies of the Milky Way is considered using the inertia tensor. The statistical significance of the results is estimated by repeating this analysis for random catalogs. This method reproduces a known planar structure in the distribution of satellite galaxies; however, the significance of this structure is slightly lower than that for other methods used in the literature. For the GCs at distances 2 < R < 10 kpc, the structure is coplanar with the galactic plane. At large distances, the structure orientation is close to the orientations of the satellite galaxies, i.e., is perpendicular to the Galaxy plane. The probability of stochastic realization of such distribution is 1.7%. The GC distribution anisotropy is also measured without the GCs belonging to the Sagittarius tidal stream. Measurements show that the effect of the stream on the GC perturbation is weak.