Two-point Angular Correlation Function 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.

Unraveling the CMB lack-of-correlation anomaly with the cosmological gravitational wave background

Since the very first observations, the Cosmic Microwave Background (CMB) has revealed on large-scales unexpected features known as anomalies, which challenge the standard Λ cold dark matter (ΛCDM) cosmological model. One such anomaly is the “lack-of-correlation”, where the measured two-point angular correlation function of CMB temperature anisotropies is compatible with zero, differently from the predictions of the standard model. This anomaly could indicate a deviation from the standard model, unknown systematics, or simply a rare realization of the model itself. In this study, we explore the possibility that the lack-of-correlation anomaly is a consequence of living in a rare realization of the standard model, by leveraging the potential information provided by the cosmological gravitational wave background (CGWB) detectable by future gravitational wave (GW) interferometers. We analyze both constrained and unconstrained realizations of the CGWB to investigate the extent of information that GWs can offer. To quantify the impact of the CGWB on the lack-of-correlation anomaly, we employ established estimators and introduce a new estimator that addresses the “look-elsewhere” effect. Additionally, we consider three different maximum multipoles, denoted as ℓ max, to account for the anticipated capabilities of future GW detectors (ℓ max = 4, 6, 10). Summarizing our findings for the case of ℓ max = 4, we identify the angular range [63∘ - 180∘] as the region where future observations of the CGWB maximize the probability of rejecting the standard model. Furthermore, we calculate the expected significance of this observation, demonstrating that 98.81% (81.67%) of the constrained GW realizations enhance the current significance of the anomaly when considering the full-sky (masked) Planck SMICA map as our CMB sky.

The formation of supermassive black holes from Population III.1 seeds. II. Evolution to the local universe

ABSTRACT We present predictions for cosmic evolution of populations of supermassive black holes (SMBHs) forming from Population III.1 seeds, i.e. early, metal-free dark matter minihaloes forming far from other sources, parametrized by isolation distance, diso. Extending previous work that explored this scenario to z = 10, we follow evolution of a $(60\, {\rm {Mpc}})^3$ volume to z = 0. We focus on evolution of SMBH comoving number densities, halo occupation fractions, angular clustering, and 3D clustering, exploring a range of diso constrained by observed local number densities of SMBHs. We also compute synthetic projected observational fields, in particular, a case comparable to the Hubble Ultra Deep Field. We compare Pop III.1 seeding to a simple halo mass threshold model, commonly adopted in cosmological simulations of galaxy formation. Major predictions of the Pop III.1 model include that all SMBHs form by z ∼ 25, after which their comoving number densities are near-constant, with low merger rates. Occupation fractions evolve to concentrate SMBHs in the most massive haloes by z = 0, but with rare cases of SMBHs in haloes down to $\sim 10^8\, M_\odot$. The diso scale at epoch of formation, e.g. $100\,$kpc-proper at z ∼ 30, i.e. $\sim 3\,$Mpc-comoving, is imprinted in the SMBH two-point angular correlation function, remaining discernible as a low-amplitude feature to z ∼ 1. The SMBH 3D two-point correlation function at z = 0 also shows lower amplitude compared to equivalently massive haloes. We discuss prospects for testing these predictions with observational surveys of SMBH populations.

Mapping the milky way’s stellar halo with 2D data

ABSTRACT We propose a new method for measuring the spatial density distribution of the stellar halo of the Milky Way. Our method is based on a pairwise statistic of the distribution of stars in the sky, the angular two-point correlation function (ATPCF). The ATPCF utilizes two-dimensional data of stars only and is therefore immune to the large uncertainties in the determination of distances to stars. We test our method using mock stellar data coming from various models including the single power-law (SPL) and the broken power-law (BPL) density profiles. We also test the influence of axisymmetric flattening factors using both constant and varying values. We find that the ATPCF is a powerful tool for recovering the spatial distributions of the stellar haloes in our models. We apply our method to observational data from the type ab RR Lyrae catalogue in the Catalina Survey Data Release 1. In the 3-parameter BPL model, we find that $s_{1}=2.46_{-0.20}^{+0.18}, s_{2}=3.99_{-1.33}^{+0.75}$, and $r_{0}=31.11_{-5.88}^{+7.61}$, which are in good agreement with previous results. We also find that introducing an extra parameter, the radially varying flattening factor, greatly improves our ability to model accurately the observed data distribution. This implies perhaps that the stellar halo of the Milky Way should be regarded as oblate.

Clustering of red sequence galaxies in the fourth data release of the Kilo-Degree Survey

We present a sample of luminous red sequence galaxies as the basis for a study of the large-scale structure in the fourth data release of the Kilo-Degree Survey. The selected galaxies are defined by a red sequence template, in the form of a data-driven model of the colour-magnitude relation conditioned on redshift. In this work, the red sequence template was built using the broad-band optical+near infrared photometry of KiDS-VIKING and the overlapping spectroscopic data sets. The selection process involved estimating the red sequence redshifts, assessing the purity of the sample and estimating the underlying redshift distributions of redshift bins. After performing the selection, we mitigated the impact of survey properties on the observed number density of galaxies by assigning photometric weights to the galaxies. We measured the angular two-point correlation function of the red galaxies in four redshift bins and constrain the large-scale bias of our red sequence sample assuming a fixed ΛCDM cosmology. We find consistent linear biases for two luminosity-threshold samples (‘dense’ and ‘luminous’). We find that our constraints are well characterised by the passive evolution model.

Primordial non-Gaussianity with angular correlation function: integral constraint and validation for DES

ABSTRACT Local primordial non-Gaussianity (PNG) is a promising observable of the underlying physics of inflation, characterized by $f_{\rm NL}^{\rm loc}$. We present the methodology to measure $f_{\rm NL}^{\rm loc}$ from the Dark Energy Survey (DES) data using the two-point angular correlation function (ACF) with scale-dependent bias. One of the focuses of the work is the integral constraint (IC). This condition appears when estimating the mean number density of galaxies from the data and is key in obtaining unbiased $f_{\rm NL}^{\rm loc}$ constraints. The methods are analysed for two types of simulations: ∼246 goliat-png N-body small area simulations with fNL equal to −100 and 100, and 1952 Gaussian ice-cola mocks with fNL = 0 that follow the DES angular and redshift distribution. We use the ensemble of goliat-png mocks to show the importance of the IC when measuring PNG, where we recover the fiducial values of fNL within the 1σ when including the IC. In contrast, we found a bias of ΔfNL ∼ 100 when not including it. For a DES-like scenario, we forecast a bias of ΔfNL ∼ 23, equivalent to 1.8σ, when not using the IC for a fiducial value of fNL = 100. We use the ice-cola mocks to validate our analysis in a realistic DES-like set-up finding it robust to different analysis choices: best-fitting estimator, the effect of IC, BAO damping, covariance, and scale choices. We forecast a measurement of fNL within σ(fNL) = 31 when using the DES-Y3 BAO sample, with the ACF in the 1 deg < θ < 20 deg range.

CMB two-point angular correlation function in the Ellipsoidal Universe

We suggest that the Ellipsoidal Universe cosmological model, proposed several years ago to account for the low quadrupole temperature–temperature correlation of the Cosmic Microwave Background, can also provide temperature–temperature two-point angular correlation function in reasonable agreement with Planck observations.

Semi-analytic forecasts for Roman – the beginning of a new era of deep-wide galaxy surveys

ABSTRACT The Nancy Grace Roman Space Telescope, NASA’s next flagship observatory, will redefine deep-field galaxy survey with a field of view two orders of magnitude larger than Hubble and an angular resolution of matching quality. These future deep-wide galaxy surveys necessitate new simulations to forecast their scientific output and to optimize survey strategies. In this work, we present five realizations of 2-deg2 light cones, containing a total of ≳25 million simulated galaxies with −16 ≳ MUV ≳ −25 spanning z ∼ 0 to 10. This data set enables a new set of experiments with the impacts of survey size on the derived galaxy formation and cosmological constraints. The intrinsic and observable galaxy properties are predicted using a well-established, physics-based semi-analytic modelling approach. We provide forecasts for number density, cosmic SFR, field-to-field variance, and angular two-point correlation functions, and demonstrate how the future wide-field surveys will be able to improve these measurements relative to current generation surveys. We also present a comparison between these light cones and others that have been constructed with empirical models. The mock light cones are designed to facilitate the exploration of multi-instrument synergies and connecting with current generation instruments and legacy surveys. In addition to Roman, we also provide photometry for a number of other instruments on upcoming facilities, including Euclid and Rubin, as well as the instruments, that are part of many legacy surveys. Full object catalogues and data tables for the results presented in this work are made available through a web-based, interactive portal.

The BINGO project

Context. A new and promising technique for observing the Universe and study the dark sector is the intensity mapping of the redshifted 21 cm line of neutral hydrogen (H I). The Baryon Acoustic Oscillations [BAO] from Integrated Neutral Gas Observations (BINGO) radio telescope will use the 21 cm line to map the Universe in the redshift range 0.127 ≤ z ≤ 0.449 in a tomographic approach, with the main goal of probing the BAO. Aims. This work presents the forecasts of measuring the transversal BAO signal during the BINGO phase 1 operation. Methods. We used two clustering estimators: the two-point angular correlation function (ACF) in configuration space, and the angular power spectrum (APS) in harmonic space. We also used a template-based method to model the ACF and APS estimated from simulations of the BINGO region and to extract the BAO information. The tomographic approach allows the combination of redshift bins to improve the template fitting performance. We computed the ACF and APS for each of the 30 redshift bins and measured the BAO signal in three consecutive redshift blocks (lower, intermediate, and higher) of ten channels each. Robustness tests were used to evaluate several aspects of the BAO fitting pipeline for the two clustering estimators. Results. We find that each clustering estimator shows different sensitivities to specific redshift ranges, although both of them perform better at higher redshifts. In general, the APS estimator provides slightly better estimates, with smaller uncertainties and a higher probability of detecting the BAO signal, achieving ≳90% at higher redshifts. We investigate the contribution from instrumental noise and residual foreground signals and find that the former has the greater impact. It becomes more significant with increasing redshift, in particular for the APS estimator. When noise is included in the analysis, the uncertainty increases by up to a factor of ∼2.2 at higher redshifts. Foreground residuals, in contrast, do not significantly affect our final uncertainties. Conclusions. In summary, our results show that even when semi-realistic systematic effects are included, BINGO has the potential to successfully measure the BAO scale at radio frequencies.

COSMOS2020: Cosmic evolution of the stellar-to-halo mass relation for central and satellite galaxies up to z ∼ 5

We used the COSMOS2020 catalog to measure the stellar-to-halo mass relation (SHMR) divided by central and satellite galaxies from z = 0.2 to z = 5.5. Starting from accurate photometric redshifts, we measured the near-infrared selected two-point angular correlation and stellar mass functions in ten redshift bins. We used a phenomenological model that parametrizes the stellar-to-halo mass relation for central galaxies and the number of galaxies inside each halo to describe our observations. This model qualitatively reproduces our measurements and their dependence on the stellar mass threshold. Surprisingly, the mean halo occupation distribution only shows a mild evolution with redshift suggesting that galaxies occupy halos similarly throughout cosmic time. At each redshift, we measured the ratio of stellar mass to halo mass, M*/Mh, which shows the characteristic strong dependence of halo mass with a peak at Mhpeak ∼ 2 × 1012 M⊙. For the first time, using a joint modeling of clustering and abundances, we measured the evolution of Mhpeak from z = 0.2 to z = 5.5. Mhpeak increases gradually with redshift from log Mhpeak/M⊙ ∼ 12.1 at z ∼ 0.3 to log Mhpeak/M⊙ ∼ 12.3 at z ∼ 2, and up to log Mhpeak/M⊙ ∼ 12.9 at z ∼ 5. Similarly, the stellar mass peak M∗peak increases with redshift from log M∗peak/M⊙ ∼ 10.5 at z ∼ 0.3 to log M∗peak/M⊙ ∼ 10.9 at z ∼ 3. The SHMR ratio at the peak halo mass remains almost constant with redshift. These results are in accordance with the scenario in which the peak of star-formation efficiency moves toward more massive halos at higher redshifts. We also measured the fraction of satellites as a function of stellar mass and redshift. For all stellar mass thresholds, the satellite fraction decreases at higher redshifts. At a given redshift, there is a higher fraction of low-mass satellites and this fraction reaches a plateau at ∼25% at z ∼ 1. The satellite contribution to the total stellar mass budget in halos becomes more important than that of the central at halo masses of about Mh > 1013 M⊙ and always stays below the peak, indicating that quenching mechanisms are present in massive halos that keep the star-formation efficiency low. Finally, we compared our results with three hydrodynamical simulations: HORIZON-AGN, TNG100 of the ILLUSTRISTNG project, and EAGLE. We find that the most significant discrepancy is at the high-mass end, where the simulations generally show that satellites have a higher contribution to the total stellar mass budget than the observations. This, together with the finding that the fraction of satellites is higher in the simulations, indicates that the feedback mechanisms acting in both group- and cluster-scale halos appear to be less efficient in quenching the mass assembly of satellites – and that quenching occurs much later in the simulations.

Semi-analytic forecasts for JWST – VI. Simulated light-cones and galaxy clustering predictions

ABSTRACT In anticipation of the new era of high-redshift exploration marked by the commissioning of the James Webb Space Telescope (JWST), we present two sets of galaxy catalogues that are designed to aid the planning and interpretation of observing programs. We provide a set of 40 wide-field light-cones with footprints spanning approximately ∼1000 arcmin2 containing galaxies up to z = 10, and a new set of eight ultradeep light-cones with 132 arcmin2 footprints, containing galaxies up to z ∼ 12 down to the magnitudes expected to be reached in the deepest JWST surveys. These mock light-cones are extracted from dissipationless N-body simulations and populated with galaxies using the well-established, computationally efficient Santa Cruz semi-analytic model for galaxy formation. We provide a wide range of predicted physical properties, and simulated photometry from Near-Infrared Camera (NIRCam) and many other instruments. We explore the predicted counts and luminosity functions and angular two-point correlation functions for galaxies in these simulated light-cones. We also explore the predicted field-to-field variance using multiple light-cone realizations. We find that these light-cones reproduce the available measurements of observed clustering from 0.2 ≲ z ≲ 7.5 very well. We provide predictions for galaxy clustering at high redshift that may be obtained from future JWST observations. All of the light-cones presented here are made available through a web-based interactive data release portal.

Stringy Signals from Large-Angle Correlations in the Cosmic Microwave Background?

We interpret the lack of large-angle temperature correlations and the even-odd parity imbalance observed in the cosmic microwave background (CMB) by COBE, WMAP and Planck satellite missions as a possible stringy signal ultimately stemming from a composite inflaton field (e.g., a fermionic condensate). Based on causality arguments and a Fourier analysis of the angular two-point correlation function, two infrared cutoffs kmineven,odd (satisfying kmineven≃2kminodd) are introduced to the CMB power spectrum associated, respectively, with periodic and antiperiodic boundary conditions of the fermionic constituents (echoing the Neveu–Schwarz–Ramond model in superstring theory), without resorting to any particular model.

Euclid: Constraining ensemble photometric redshift distributions with stacked spectroscopy

Context. The ESA Euclid mission will produce photometric galaxy samples over 15 000 square degrees of the sky that will be rich for clustering and weak lensing statistics. The accuracy of the cosmological constraints derived from these measurements will depend on the knowledge of the underlying redshift distributions based on photometric redshift calibrations. Aims. A new approach is proposed to use the stacked spectra from Euclid slitless spectroscopy to augment broad-band photometric information to constrain the redshift distribution with spectral energy distribution fitting. The high spectral resolution available in the stacked spectra complements the photometry and helps to break the colour-redshift degeneracy and constrain the redshift distribution of galaxy samples. Methods. We modelled the stacked spectra as a linear mixture of spectral templates. The mixture may be inverted to infer the underlying redshift distribution using constrained regression algorithms. We demonstrate the method on simulated Vera C. Rubin Observatory and Euclid mock survey data sets based on the Euclid Flagship mock galaxy catalogue. We assess the accuracy of the reconstruction by considering the inference of the baryon acoustic scale from angular two-point correlation function measurements. Results. We selected mock photometric galaxy samples at redshift z > 1 using the self-organising map algorithm. Considering the idealised case without dust attenuation, we find that the redshift distributions of these samples can be recovered with 0.5% accuracy on the baryon acoustic scale. The estimates are not significantly degraded by the spectroscopic measurement noise due to the large sample size. However, the error degrades to 2% when the dust attenuation model is left free. We find that the colour degeneracies introduced by attenuation limit the accuracy considering the wavelength coverage of Euclid near-infrared spectroscopy.

The dependence of the hierarchical distribution of star clusters on galactic environment

ABSTRACT We use the angular two-point correlation function (TPCF) to investigate the hierarchical distribution of young star clusters in 12 local (3–18 Mpc) star-forming galaxies using star cluster catalogs obtained with the Hubble Space Telescope (HST) as part of the Treasury Program Legacy ExtraGalactic UV Survey. The sample spans a range of different morphological types, allowing us to infer how the physical properties of the galaxy affect the spatial distribution of the clusters. We also prepare a range of physically motivated toy models to compare with and interpret the observed features in the TPCFs. We find that, conforming to earlier studies, young clusters ($T \lesssim 10\, \mathrm{Myr}$) have power-law TPCFs that are characteristic of fractal distributions with a fractal dimension D2, and this scale-free nature extends out to a maximum scale lcorr beyond which the distribution becomes Poissonian. However, lcorr, and D2 vary significantly across the sample, and are correlated with a number of host galaxy physical properties, suggesting that there are physical differences in the underlying star cluster distributions. We also find that hierarchical structuring weakens with age, evidenced by flatter TPCFs for older clusters ($T \gtrsim 10\, \mathrm{Myr}$), that eventually converges to the residual correlation expected from a completely random large-scale radial distribution of clusters in the galaxy in $\sim 100 \, \mathrm{Myr}$. Our study demonstrates that the hierarchical distribution of star clusters evolves with age, and is strongly dependent on the properties of the host galaxy environment.

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.

Statistical modelling of the cosmological dispersion measure

ABSTRACT We have investigated the basic statistics of the cosmological dispersion measure (DM)—such as its mean, variance, probability distribution, angular power spectrum, and correlation function—using the state-of-the-art hydrodynamic simulations, IllustrisTNG300, for the fast radio burst cosmology. To model the DM statistics, we first measured the free-electron abundance and the power spectrum of its spatial fluctuations. The free-electron power spectrum turns out to be consistent with the dark matter power spectrum at large scales, but it is strongly damped at small scales (≲ Mpc) owing to the stellar and active galactic nucleus feedback. The free-electron power spectrum is well modelled using a scale-dependent bias factor (the ratio of its fluctuation amplitude to that of the dark matter). We provide analytical fitting functions for the free-electron abundance and its bias factor. We next constructed mock sky maps of the DM by performing standard ray-tracing simulations with the TNG300 data. The DM statistics are calculated analytically from the fitting functions of the free-electron distribution, which agree well with the simulation results measured from the mock maps. We have also obtained the probability distribution of source redshift for a given DM, which helps in identifying the host galaxies of FRBs from the measured DMs. The angular two-point correlation function of the DM is described by a simple power law, $\xi (\theta) \approx 2400 (\theta /{\rm deg})^{-1} \, {\rm pc}^2 \, {\rm cm}^{-6}$, which we anticipate will be confirmed by future observations when thousands of FRBs are available.

Constraining reionization in progress at z = 5.7 with Lyman-α emitters: voids, peaks, and cosmic variance

ABSTRACT A number of independent observations suggest that the intergalactic medium was significantly neutral at z = 7 and that reionization was, perhaps, still in progress at z = 5.7. The narrowband survey, SILVERRUSH, has mapped over 2000 Lyman-α emitters (LAEs) at these redshifts ( G58). Previous analyses have assumed that reionization was over by z = 5.7, but this data may actually sample the final stages of reionization when the last neutral islands were relegated to the cosmic voids. Motivated by these developments, we re-examine LAE void and peak statistics and their ability to constrain reionization. We construct models of the LAE distribution in (1 Gpc h−1)3 volumes, spanning a range of neutral fractions at z = 5.7 and 6.6. Models with a higher neutral fraction show an enhanced probability of finding holes in the LAE distribution. When comparing models at fixed mean surface density, however, LAEs obscured by neutral gas in the voids must be compensated by visible LAEs elsewhere. Hence, in these models, the likelihood of finding an overdense peak is also enhanced in the latter half of reionization. Compared to the widely used angular two-point correlation function (2PCF), we find that the void probability function (VPF) provides a more sensitive test of models during the latter half of reionization. By comparison, at neutral fractions $\sim 50{{\ \rm per\ cent}}$, the VPF and a simple peak thresholding statistic are both similar to the 2PCF in constraining power. Lastly, we find that the cosmic variance and large-scale asymmetries observed in the SILVERRUSH fields are consistent with large-scale structure in a ΛCDM universe.

One- and two-point source statistics from the LOFAR Two-metre Sky Survey first data release

Context.The LOFAR Two-metre Sky Survey (LoTSS) will eventually map the complete Northern sky and provide an excellent opportunity to study the distribution and evolution of the large-scale structure of the Universe.Aims.We test the quality of LoTSS observations through a statistical comparison of the LoTSS first data release (DR1) catalogues to expectations from the established cosmological model of a statistically isotropic and homogeneous Universe.Methods.We study the point-source completeness and define several quality cuts, in order to determine the count-in-cell statistics and differential source count statistics, and measure the angular two-point correlation function. We use the photometric redshift estimates, which are available for about half of the LoTSS-DR1 radio sources, to compare the clustering throughout the history of the Universe.Results.For the masked LoTSS-DR1 value-added source catalogue, we find a point-source completeness of 99% above flux densities of 0.8 mJy. The counts-in-cell statistic reveals that the distribution of radio sources cannot be described by a spatial Poisson process. Instead, a good fit is provided by a compound Poisson distribution. The differential source counts are in good agreement with previous findings in deep fields at low radio frequencies and with simulated catalogues from the SKA Design Study and the Tiered Radio Extragalactic Continuum Simulation. Restricting the value added source catalogue to low-noise regions and applying a flux density threshold of 2 mJy provides our most reliable estimate of the angular two-point correlation. Based on the distribution of photometric redshifts and thePlanck2018 best-fit cosmological model, the theoretically predicted angular two-point correlation between 0.1 deg and 6 deg agrees reasonably well with the measured clustering for the sub-sample of radio sources with redshift information.Conclusions.The deviation from a Poissonian distribution might be a consequence of the multi-component nature of a large number of resolved radio sources and/or of uncertainties on the flux density calibration. The angular two-point correlation function is < 10−2at angular scales > 1 deg and up to the largest scales probed. At a 2 mJy flux density threshold and at a pivot angle of 1 deg, we find a clustering amplitude ofA = (5.1 ± 0.6) × 10−3with a slope parameter ofγ = 0.74 ± 0.16. For smaller flux density thresholds, systematic issues are identified, which are most likely related to the flux density calibration of the individual pointings. We conclude that we find agreement with the expectation of large-scale statistical isotropy of the radio sky at the per cent level. The angular two-point correlation agrees well with the expectation of the cosmological standard model.

The transverse baryonic acoustic scale from the SDSS DR11 galaxies

We report five measurements of the transverse baryonic acoustic scale, θBAO, obtained from the angular two-point correlation function calculation for Luminous Red Galaxies of the eleventh data release of the Sloan Digital Sky Survey (SDSS). Each measurement has been obtained by considering a thin redshift shell (Δz=0.01 and 0.02) in the interval z ∈ [0.565, 0.660], which contains a large density of galaxies ( ~ 20, 000 galaxies/redshift shell). Differently from the three-dimensional Baryon Acoustic Oscillations (BAO) measurements, these data points are obtained almost model-independently and provide a Cosmic Microwave Background (CMB)-independent way to estimate the sound horizon rs. Assuming a time-dependent equation-of-state parameter for the dark energy, we also discuss constraints on the main cosmological parameters from θBAO and CMB data.

Baryon acoustic oscillations signature in the three-point angular correlation function from the SDSS-DR12 quasar survey

ABSTRACTThe clustering properties of the Universe at large scales are currently being probed at various redshifts through several cosmological tracers and with diverse statistical estimators. Here we use the three-point angular correlation function (3PACF) to probe the baryon acoustic oscillation (BAO) features in the quasars catalogue from the Sloan Digital Sky Survey Data Release 12, with mean redshift $\overline{z} = 2.225$, detecting the BAO imprint with a statistical significance of $2.9 \sigma$, obtained using lognormal mocks. Following a quasi-model-independent approach for the 3PACF, we find the BAO transversal signature for triangles with sides θ1 = $1{^{\circ}_{.}}0$ and θ2 = $1{^{\circ}_{.}}5$ and the angle between them of α = 1.59 ± 0.17 rad, a value that corresponds to the angular BAO scale $\theta_{\rm BAO}=1{^{\circ}_{.}}82 \pm 0{^{\circ}_{.}}21$, in excellent agreement with the value found in a recent work ($\theta_{\rm BAO}=1{^{\circ}_{.}}77 \pm 0{^{\circ}_{.}}31$) applying the two-point angular correlation function (2PACF) to similar data. Moreover, we performed two types of test: one to confirm the robustness of the BAO signal in the 3PACF through random displacements in the data set, and the other to verify the suitability of our random samples, a null test that in fact does not show any signature that could bias our results.