We use the scaled counts in spherical caps $\mathcal{N}(<θ)$ and the fractal correlation dimension $ \mathcal{D}_{2}(θ) $ procedures to search for a transition scale to homogeneity in the local universe as given by the ALFALFA catalogue (a sample of extragalactic HI line sources, in the redshift range $0 < z < 0.06$). Our analyses, in the 2-dimensional sky projected data, show a transition to homogeneity at $θ_H = 16.49^{\circ} \pm 0.29^{\circ}$, in remarkable accordance with the angular scale expected from simulations, a result that strengthens the validity of the cosmological principle in the local universe. We test the robustness of our results by analysing the data sample using three versions of the $\mathcal{N}(<θ)$ estimator, which show a well agreement between them. These statistical estimators were validated using mock realizations generated assuming a fractal distribution of points, successfully recovering the input information. In addition, we perform further analyses showing that our approach is also able to indicate the presence of under- and over-densities in the data. Finally, we verify the influence of the sample size to the $θ_H$ estimates by using segment Cox processes of different projected areas, confirming the suitability of the ALFALFA surveyed area for the current analyses.
Using the 2MASS Photometric Redshift catalogue we perform a number of statistical tests aimed at detecting possible departures from statistical homogeneity and isotropy in the large-scale structure of the Universe. Making use of the angular homogeneity index, an observable proposed in a previous publication, as well as studying the scaling of the angular clustering and number counts with magnitude limit, we place constraints on the fractal nature of the galaxy distribution. We find that the statistical properties of our sample are in excellent agreement with the standard cosmological model, an…
We investigate the growth rate of structures in the local Universe. For this, we use as a cosmological tracer the HI line extra-galactic sources from the Arecibo Legacy Fast ALFA (ALFALFA) survey to obtain a measurement of the normalized growth rate parameter, $f σ_{8}$, considered a powerful tool to constrain alternative models of gravity. For these analyses, we calculate the Local Group velocity due to the matter structures distribution in the ALFALFA catalogue and compare it with the Local Group velocity relative to the Cosmic Microwave Background frame to obtain the velocity scale paramete…
Clowes et al. (2013) have recently reported the discovery of a Large Quasar Group (LQG), dubbed the Huge-LQG, at redshift z~1.3 in the DR7 quasar catalogue of the Sloan Digital Sky Survey. On the basis of its characteristic size ~500 Mpc and longest dimension >1 Gpc, it is claimed that this structure is incompatible with large-scale homogeneity and the cosmological principle. If true, this would represent a serious challenge to the standard cosmological model. However, the homogeneity scale is an average property which is not necessarily affected by the discovery of a single large structure. I…
We probe the angular scale of homogeneity in the local Universe using blue galaxies from the SDSS survey as a cosmological tracer. Through the scaled counts in spherical caps, $ \mathcal{N}(<θ) $, and the fractal correlation dimension, $\mathcal{D}_{2}(θ)$, we find an angular scale of transition to homogeneity for this sample of $θ_{\text{H}} = 22.19^{\circ} \pm 1.02^{\circ}$. A comparison of this measurement with another obtained using a different cosmic tracer at a similar redshift range ($z < 0.06$), namely, the HI extragalactic sources from the ALFALFA catalogue, confirms that both results…
New observations of high-redshift objects are crucial for the improvement of the standard $Λ$CDM cosmological model and our understanding of the Universe. One of the main directions of modern observational cosmology is the analysis of the large-scale structure of Universe, in particular, in deep fields. We study the large-scale structure of the Universe along the line of sight using the latest version of the COSMOS2015 catalogue, which contains 518,404 high quality photometric redshifts of galaxies selected in the optical range of the COSMOS field ($2\times 2$ deg$^2$), with depth up to the re…
Dark matter (DM) clustering at the present epoch is investigated from a fractal viewpoint in order to determine the scale where the self-similar scaling property of the DM halo distribution transits to homogeneity. Methods based on well-established `counts-in-cells' as well as new methods based on anomalous diffusion and random walks are investigated. Both are applied to DM halos of the biggest N-Body simulation in the `Dark Sky Simulations' (DS) catalogue and an equivalent randomly distributed catalogue. Results based on the smaller `Millennium Run' (MR) simulation are revisited and improved.…
A Large Quasar Group (LQG) of particularly large size and high membership has been identified in the DR7QSO catalogue of the Sloan Digital Sky Survey. It has characteristic size (volume^1/3) ~ 500 Mpc (proper size, present epoch), longest dimension ~ 1240 Mpc, membership of 73 quasars, and mean redshift <z> = 1.27. In terms of both size and membership it is the most extreme LQG found in the DR7QSO catalogue for the redshift range 1.0 <= z <= 1.8 of our current investigation. Its location on the sky is ~ 8.8 deg north (~ 615 Mpc projected) of the Clowes & Campusano LQG at the same redshift, <z>…
We report measurements of the angular scale of cosmic homogeneity ($θ_{H}$) using the recently released luminous red galaxy sample of the sixteenth data release of the Sloan Digital Sky Survey (SDSS-IV LRG DR16). It consists of a model-independent method, as we only use the celestial coordinates of these objects to carry out such an analysis. The observational data is divided into thin redshift bins, namely $0.67<z<0.68$, $0.70<z<0.71$, and $0.73<z<0.74$, in order to avoid projection biases, and we estimate our uncertainties through a bootstrap method and a suite of mock catalogues. We find th…
It is well known that both the star formation rate and the cold gas content of a galaxy depend on the local density out to distances of a few Megaparsecs. In this paper, we compare the environmental density dependence of the atomic gas mass fractions of nearby galaxies with the density dependence of their central and global specific star formation rates. We stack HI line spectra extracted from the Arecibo Legacy Fast ALFA survey centered on galaxies with UV imaging from GALEX and optical imaging/spectroscopy from SDSS. We use these stacked spectra to evaluate the mean atomic gas mass fraction …
In this paper, we study the characteristic scale of transition to cosmic homogeneity of the universe, $\mathcal{R}_H$, as a standard ruler, to constrain cosmological parameters on mock galaxy catalogues. We use mock galaxy catalogues that simulate the CMASS galaxy sample of the BOSS survey in the redshift range $0.43 \leq z \leq 0.7$. In each redshift bin we obtain the homogeneity scale, defined as the scale at which the universe becomes homogeneous to $1\%$, i.e. $D_2(\mathcal{R}_H) = 2.97$. With a simple Fisher analysis, we find that the performance of measuring the cosmological parameters w…
This is the second paper of two reporting results from a study of the HI content and stellar properties of nearby galaxies detected by the Arecibo Legacy Fast ALFA blind 21-cm line survey and the Sloan Digital Sky Survey in a 2160 deg^2 region covered by both surveys. We apply strategies of multivariate data analysis to a complete HI flux-limited subset of 1624 objects extracted from the control sample of HI emitters assembled by Toribio et al. (2011a) in order to: i) investigate the correlation structure of the space defined by an extensive set of observables describing gas-rich systems; ii) …
We analyze a set of volume limited samples from SDSS DR12 to quantify the degree of inhomogeneity at different length scales using Shannon entropy. We find that the galaxy distributions exhibit a higher degree of inhomogeneity as compared to a Poisson point process at all length scales. Our analysis indicates that signatures of inhomogeneities in the galaxy distributions persist at least upto a length scale of $120 \, h^{-1}\, {\rm Mpc}$. The galaxy distributions appear to be homogeneous on a scale of $140 \, h^{-1}\, {\rm Mpc}$ and beyond. Analyzing a set of mock galaxy samples from a semi an…
In this paper, we study the homogeneity of the GRB distribution using a subsample of the Greiner GRB catalogue, which contains 314 objects with redshift $0<z<2.5$ (244 of them discovered by the Swift GRB Mission). We try to reconcile the dilemma between the new observations and the current theory of structure formation and growth. To test the results against the possible biases in redshift determination and the incompleteness of the Greiner sample, we also apply our analysis to the 244 GRBs discovered by Swift and the subsample presented by the Swift Gamma-Ray Burst Host Galaxy Legacy Survey (…
The homogeneity of matter distribution at large scales, known as the cosmological principle, is a central assumption in the standard cosmological model. The case is testable though, thus no longer needs to be a principle. Here we perform a test for spatial homogeneity using the Sloan Digital Sky Survey Luminous Red Galaxies (LRG) sample by counting galaxies within a specified volume with the radius scale varying up to 300 Mpc/h. We directly confront the large-scale structure data with the definition of spatial homogeneity by comparing the averages and dispersions of galaxy number counts with a…
Observations reveal that the Universe has a hierarchy of galaxy clustering with transition to homogeneity on large scales according to the $Λ$CDM model. On the other hand some observational estimates suggest a multifractal behavior where galactic clustering is based on generalization of the correlation dimension. We study the influence of veto areas on fractal measurements in masks of galaxy surveys. We investigate if these holes can produce fractal behaviors or modify the scale of cosmic homogeneity. From the footprint of BOSS-DR12, we build a homogeneous sample following the radial selection…
We present the final distance measurements for the 2MASS Tully-Fisher (2MTF) survey. The final 2MTF catalogue contains 2,062 nearby spiral galaxies in the CMB frame velocity range of 600 km s$^{-1}$ $< cz < 10,000$ km s$^{-1}$ with a mean velocity of 4,805 km s$^{-1}$. The main update in this release is the replacement of some archival HI data with newer ALFALFA data. Using the 2MTF template relation, we calculate the distances and peculiar velocities of all 2MTF galaxies. The mean uncertainties of the linear distance measurements are around 22\% in all three infrared bands. 2MTF measurements …
In this work, we develop a statistical analysis of the large-scale clustering of matter in the Universe from the fractal point of view using galaxies from the Ninth Sloan Digital Sky Survey (SDSS) Data Release (DR9). From the total set of galaxies, a magnitude-limited sample of galaxies with redshifts in the range 0 < z < 0.15 was created. The sample covers the largest completely connected area of the celestial sphere within the catalogue, with limits in right ascension from 120 to 240 degrees and declination from 0 to 60 degrees, which is a region that includes the largest galactic samples th…
The Stellar Mass Function of Gas-Rich Galaxies and the Underlying $M_{\rm HI}-M_{\rm star}$ Scaling Relation in the Local Universe
School of Physical Sciences, National Institute of Science Education and Research（国家科学教育与研究研究所物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立大学）；National Centre for Radio Astrophysics, Tata Institute of Fundamental Research（塔塔基础研究院国家射电天文中心）
