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We estimate the two-point angular correlation function (CF) of quasars from SDSS DR3 using a special method of comparison random catalog generation. The best-fit value for the CF power-law index is found to be $alpha=0.78pm0.18$ on the $2<theta<250$ $arcmin$ interval. This is lower (though in marginal agreement) than earlier result of markcite{{it Myers et al.} (2005)} based on SDSS DR1 catalogue of photometrically-classified quasars.
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The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local Universe. In this Letter we present some of the initial results on the angular 2-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18<r*<22, is shown to be consistent with results from existing wide-field, photographic-based surveys and narrower CCD galaxy surveys. On scales between 1 arcminute and 1 degree the correlation function is well described by a power-law with an exponent of ~ -0.7. The amplitude of the correlation function, within this angular interval, decreases with fainter magnitudes in good agreement with analyses from existing galaxy surveys. There is a characteristic break in the correlation function on scales of approximately 1-2 degrees. On small scales, < 1, the SDSS correlation function does not appear to be consistent with the power-law form fitted to the 1< theta <0.5 deg data. With a data set that is less than 2% of the full SDSS survey area, we have obtained high precision measurements of the power-law angular correlation function on angular scales 1 < theta < 1 deg, which are robust to systematic uncertainties. Because of the limited area and the highly correlated nature of the error covariance matrix, these initial results do not yet provide a definitive characterization of departures from the power-law form at smaller and larger angles. In the near future, however, the area of the SDSS imaging survey will be sufficient to allow detailed analysis of the small and large scale regimes, measurements of higher-order correlations, and studies of angular clustering as a function of redshift and galaxy type.
The 2-point angular correlation function $w(theta)$ (2PACF), where $theta$ is the angular separation between pairs of galaxies, provides the transversal Baryon Acoustic Oscillation (BAO) signal almost model-independently. In this paper we use 409,337 luminous red galaxies in the redshift range $z = [0.440,0.555]$ obtained from the tenth data release of the Sloan Digital Sky Survey (SDSS DR10) to estimate $theta_{rm{BAO}}(z)$ from the 2PACF at six redshift {shells}. Since noise and systematics can hide the BAO signature in the $w - theta$ plane, we also discuss some criteria to localize the acoustic bump. We identify two sources of model-dependence in the analysis, namely, the value of the acoustic scale from Cosmic Microwave Background (CMB) measurements and the correction in the $theta_{rm{BAO}}(z)$ position due to projection effects. Constraints on the dark energy equation-of-state parameter w$(z)$ from the $theta_{rm{BAO}}(z)$ diagram are derived, as well as from a joint analysis with current CMB measurements. We find that the standard $Lambda$CDM model as well as some of its extensions are in good agreement with these $theta_{rm{BAO}}(z)$ measurements.
The two point angular correlation function is an excellent measure of structure in the universe. To extract from it the three dimensional power spectrum, one must invert Limbers Equation. Here we perform this inversion using a Bayesian prior constraining the smoothness of the power spectrum. Among other virtues, this technique allows for the possibility that the estimates of the angular correlation function are correlated from bin to bin. The output of this technique are estimators for the binned power spectrum and a full covariance matrix. Angular correlations mix small and large scales but after the inversion, small scale data can be trivially eliminated, thereby allowing for realistic constraints on theories of large scale structure. We analyze the APM catalogue as an example, comparing our results with previous results. As a byproduct of these tests, we find -- in rough agreement with previous work -- that APM places stringent constraints on Cold Dark Matter inspired models, with the shape parameter constrained to be $0.25pm 0.04$ (using data with wavenumber $k le 0.1 h{rm Mpc}^{-1}$). This range of allowed values use the full power spectrum covariance matrix, but assumes negligible covariance in the off-diagonal angular correlation error matrix, which is estimated with a large angular resolution of 0.5degrees (in the range 0.5 and 20 degrees).
We analyse the large-scale angular correlation function (ACF) of the CMASS luminous galaxies (LGs), a photometric-redshift catalogue based on the Data Release 8 (DR8) of the Sloan Digital Sky Survey-III. This catalogue contains over $600 , , 000$ LGs in the range $0.45 leq z leq 0.65$, which was split into four redshift shells of constant width. First, we estimate the constraints on the redshift-space distortion (RSD) parameters $bsigma_8$ and $fsigma_8$, where $b$ is the galaxy bias, $f$ the growth rate and $sigma_8$ is the normalization of the perturbations, finding that they vary appreciably among different redshift shells, in agreement with previous results using DR7 data. When assuming constant RSD parameters over the survey redshift range, we obtain $fsigma_8 = 0.69 pm 0.21$, which agrees at the $1.5sigma$ level with Baryon Oscillation Spectroscopic Survey DR9 spectroscopic results. Next, we performed two cosmological analyses, where relevant parameters not fitted were kept fixed at their fiducial values. In the first analysis, we extracted the baryon acoustic oscillation peak position for the four redshift shells, and combined with the sound horizon scale from 7-year textit{Wilkinson Microwave Anisotropy Probe} $(WMAP7)$ to produce the constraints $Omega_{m}=0.249 pm 0.031$ and $w=-0.885 pm 0.145$. In the second analysis, we used the ACF full shape information to constrain cosmology using real data for the first time, finding $Omega_{m} = 0.280 pm 0.022$ and $f_b = Omega_b/Omega_m = 0.211 pm 0.026$. These results are in good agreement with $WMAP7$ findings, showing that the ACF can be efficiently applied to constrain cosmology in future photometric galaxy surveys.
The 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 twelfth data release of the Sloan Digital Sky Survey, with mean redshift 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 $theta_1 = 1.0^circ$ and $theta_2 = 1.5^circ$ and the angle between them of $alpha = 1.59 pm 0.17$ rad, a value that corresponds to the angular BAO scale ${theta}_{BAO} = 1.82^circ pm 0.21^circ$ , in excellent agreement with the value found in a recent work (${theta}_{BAO} = 1.77^circ pm 0.31^circ$ ) applying the 2PACF to similar data. Moreover, we performed two type of tests: one to confirm the robustness of the BAO signal in the 3PACF through random displacements in the dataset, 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.
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