arXiv subjects

Alexander S. Szalay

Publications and source records attributed to Alexander S. Szalay.

At least 127 records · Page 7Linked to original sources

arXiv2001

KL Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early SDSS Data

We present measurements of parameters of the 3-dimensional power spectrum of galaxy clustering from 222 square degrees of early imaging data in the Sloan Digital Sky Survey. The projected galaxy distribution on the sky is expanded over a set of Karhunen-Loeve eigenfunctions, which optimize the signal-to-noise ratio in our analysis. A maximum likelihood analysis is used to estimate parameters that set the shape and amplitude of the 3-dimensional power spectrum. Our best estimates are Gamma=0.188 +/- 0.04 and sigma_8L = 0.915 +/- 0.06 (statistical errors only), for a flat Universe with a cosmological constant. We demonstrate that our measurements contain signal from scales at or beyond the peak of the 3D power spectrum. We discuss how the results scale with systematic uncertainties, like the radial selection function. We find that the central values satisfy the analytically estimated scaling relation. We have also explored the effects of evolutionary corrections, various truncations of the KL basis, seeing, sample size and limiting magnitude. We find that the impact of most of these uncertainties stay within the 2-sigma uncertainties of our fiducial result.

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arXiv2001

The Angular Correlation Function of Galaxies from Early SDSS Data

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.

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arXiv2001

The 3D Power Spectrum from Angular Clustering of Galaxies in Early SDSS Data

Early photometric data from the Sloan Digital Sky Survey (SDSS) contain angular positions for 1.5 million galaxies. In companion papers, the angular correlation function $w(θ)$ and 2D power spectrum $C_l$ of these galaxies are presented. Here we invert Limber's equation to extract the 3D power spectrum from the angular results. We accomplish this using an estimate of $dn/dz$, the redshift distribution of galaxies in four different magnitude slices in the SDSS photometric catalog. The resulting 3D power spectrum estimates from $w(θ)$ and $C_l$ agree with each other and with previous estimates over a range in wavenumbers $0.03 < k/{\rm h Mpc}^{-1} < 1$. The galaxies in the faintest magnitude bin ($21 < \rstar < 22$, which have median redshift $z_m=0.43$) are less clustered than the galaxies in the brightest magnitude bin ($18 < \rstar < 19$ with $z_m=0.17$), especially on scales where nonlinearities are important. The derived power spectrum agrees with that of Szalay et al. (2001) who go directly from the raw data to a parametric estimate of the power spectrum. The strongest constraints on the shape parameter $Γ$ come from the faintest galaxies (in the magnitude bin $21 < \rstar < 22$), from which we infer $Γ= 0.14^{+0.11}_{-0.06}$ (95% C.L.).

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arXiv2001

Optimal multihump filter for photometric redshifts

We propose a novel type filter for multicolor imaging to improve on the photometric redshift estimation of galaxies. An extra filter - specific to a certain photometric system - may be utilized with high efficiency. We present a case study of the Hubble Space Telescope's Advanced Camera for Surveys and show that one extra exposure could cut down the mean square error on photometric redshifts by 34% over the z<1.3 redshift range.

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arXiv2001

Photometric redshifts from reconstructed QSO templates

From SDSS commissioning photometric and spectroscopic data, we investigate the utility of photometric redshift techniques to the task of estimating QSO redshifts. We consider empirical methods (e.g. nearest-neighbor searches and polynomial fitting), standard spectral template fitting and hybrid approaches (i.e. training spectral templates from spectroscopic and photometric observations of QSOs). We find that in all cases, due to the presence of strong emission-lines within the QSO spectra, the nearest-neighbor and template fitting methods are superior to the polynomial fitting approach. Applying a novel reconstruction technique, we can, from the SDSS multicolor photometry, reconstruct a statistical representation of the underlying SEDs of the SDSS QSOs. Although, the reconstructed templates are based on only broadband photometry the common emission lines present within the QSO spectra can be recovered in the resulting spectral energy distributions. The technique should be useful in searching for spectral differences among QSOs at a given redshift, in searching for spectral evolution of QSOs, in comparing photometric redshifts for objects beyond the SDSS spectroscopic sample with those in the well calibrated photometric redshifts for objects brighter than 20th magnitude and in searching for systematic and time variable effects in the SDSS broad band photometric and spectral photometric calibrations.

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arXiv2001

Constraining the Cosmological Constant from Large-Scale Redshift-Space Clustering

We show how the cosmological constant can be estimated from redshift surveys at different redshifts, using maximum-likelihood techniques. The apparent redshift-space clustering on large scales (\simgt 20 \himpc) are affected in the radial direction by infall, and curvature influences the apparent correlations in the transverse direction. The relative strengths of the two effects will strongly vary with redshift. Using a simple idealized survey geometry, we compute the smoothed correlation matrix of the redshift-space correlation function, and the Fisher matrix for $\omm$ and $\oml$. These represent the best possible measurement of these parameters given the geometry. We find that the likelihood contours are turning, according to the behavior of the angular-diameter distance relation. The clustering measures from redshift surveys at intermediate-to-high redshifts can provide a surprisingly tight constraint on $\oml$. We also estimate confidence contours for real survey geometries, using the SDSS LRG and QSO surveys as specific examples. We believe that this method will become a practical tool to constrain the nature of the dark energy.

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arXiv2000

Fast CMB Analyses via Correlation Functions

We propose and implement a fast, universally applicable method for extracting the angular power spectrum C_l from CMB temperature maps by first estimating the correlation function ξ(θ). Our procedure recovers the C_l's using N^2 (but potentially N logN), operations, where N is the number of pixels. This is in contrast with standard maximum likelihood techniques which require N^3 operations. Our method makes no special assumptions about the map, unlike present fast techniques which rely on symmetries of the underlying noise matrix, sky coverage, scanning strategy, and geometry. This enables for the first time the analysis of megapixel maps without symmetries. The key element of our technique is the accurate multipole decomposition of ξ(θ). The C_l error bars and cross-correlations are found by a Monte-Carlo approach. We applied our technique to a large number of simulated maps with Boomerang sky coverage in 81000 pixels. We used a diagonal noise matrix, with approximately the same amplitude as Boomerang. These studies demonstrate that our technique provides an unbiased estimator of the C_l's. Even though our method is approximate, the error bars obtained are nearly optimal, and converged only after few tens of Monte-Carlo realizations. Our method is directly applicable for the non-diagonal noise matrix. This, and other generalizations, such as minimum variance weighting schemes, polarization, and higher order statistics are also discussed.

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arXiv2000

Spectral Templates from Multicolor Redshift Surveys

Understanding how the physical properties of galaxies (e.g. their spectral type or age) evolve as a function of redshift relies on having an accurate representation of galaxy spectral energy distributions. While it has been known for some time that galaxy spectra can be reconstructed from a handful of orthogonal basis templates, the underlying basis is poorly constrained. The limiting factor has been the lack of large samples of galaxies (covering a wide range in spectral type) with high signal-to-noise spectrophotometric observations. To alleviate this problem we introduce here a new technique for reconstructing galaxy spectral energy distributions directly from samples of galaxies with broadband photometric data and spectroscopic redshifts. Exploiting the statistical approach of the Karhunen-Loeve expansion, our iterative training procedure increasingly improves the eigenbasis, so that it provides better agreement with the photometry. We demonstrate the utility of this approach by applying these improved spectral energy distributions to the estimation of photometric redshifts for the HDF sample of galaxies. We find that in a small number of iterations the dispersion in the photometric redshifts estimator (a comparison between predicted and measured redshifts) can decrease by up to a factor of 2.

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arXiv2000

Cosmological Parameters from the Eigenmode Analysis of the Las Campanas Redshift Survey

We present the first results of the Karhunen-Loève (KL) eigenmodes applied to real data of the Las Campanas Redshift Survey (LCRS) to simultaneously measure the values of the redshift-distortion parameter, $β= Ω_0^{0.6}/b$, the linearly extrapolated normalization, $σ_8^{\rm L}$, and the CDM shape parameter, $Γ= Ω_0 h$. The results of our numerical likelihood analysis indicate a low value of $β= 0.30 \pm 0.39$, a shape parameter $Γ= 0.16 \pm 0.10$, and a linearly extrapolated normalization $σ_8^{\rm L} = 0.79 \pm 0.08$, which are consistent with a low density universe, $Ω_0 \simlt 0.5$.

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arXiv1999

The Sloan Digital Sky Survey and its Archive

The next-generation astronomy archives will cover most of the universe at fine resolution in many wavelengths. One of the first of these projects, the Sloan Digital Sky Survey (SDSS) will create a 5-wavelength catalog over 10,000 square degrees of the sky. The 200 million objects in the multi-terabyte database will have mostly numerical attributes, defining a space of 100+ dimensions. Points in this space have highly correlated distributions. The archive will enable astronomers to explore the data interactively. Data access will be aided by multidimensional spatial indices. The data will be partitioned in many ways. Small tag objects consisting of the most popular attributes speed up frequent searches. Splitting the data among multiple servers enables parallel, scalable I/O. Hashing techniques allow efficient clustering and pairwise comparison algorithms. Randomly sampled subsets allow debugging otherwise large queries at the desktop. Central servers will operate a data pump that supports sweeping searches that touch most of the data.

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arXiv1999

The Unusual Infrared Object HDF-N J123656.3+621322

We describe an object in the Hubble Deep Field North with very unusual near-infrared properties. It is readily visible in Hubble Space Telescope NICMOS images at 1.6um and from the ground at 2.2um, but is undetected (with signal-to-noise <~ 2) in very deep WFPC2 and NICMOS data from 0.3 to 1.1um. The f_nu flux density drops by a factor >~ 8.3 (97.7% confidence) from 1.6 to 1.1um. The object is compact but may be slightly resolved in the NICMOS 1.6um image. In a low-resolution, near-infrared spectrogram, we find a possible emission line at 1.643um, but a reobservation at higher spectral resolution failed to confirm the line, leaving its reality in doubt. We consider various hypotheses for the nature of this object. Its colors are unlike those of known galactic stars, except perhaps the most extreme carbon stars or Mira variables with thick circumstellar dust shells. It does not appear to be possible to explain its spectral energy distribution as that of a normal galaxy at any redshift without additional opacity from either dust or intergalactic neutral hydrogen. The colors can be matched by those of a dusty galaxy at z >~ 2, by a maximally old elliptical galaxy at z >~ 3 (perhaps with some additional reddening), or by an object at z >~ 10 whose optical and 1.1um light have been suppressed by the intergalactic medium. Under the latter hypothesis, if the luminosity results from stars and not an AGN, the object would resemble a classical, unobscured protogalaxy, with a star formation rate >~ 100 M_sun/yr. Such UV-bright objects are evidently rare at 2 < z < 12.5, however, with a space density several hundred times lower than that of present-day L* galaxies.

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arXiv1999

Designing and Mining Multi-Terabyte Astronomy Archives: The Sloan Digital Sky Survey

The next-generation astronomy digital archives will cover most of the universe at fine resolution in many wave-lengths, from X-rays to ultraviolet, optical, and infrared. The archives will be stored at diverse geographical locations. One of the first of these projects, the Sloan Digital Sky Survey (SDSS) will create a 5-wavelength catalog over 10,000 square degrees of the sky (see http://www.sdss.org/). The 200 million objects in the multi-terabyte database will have mostly numerical attributes, defining a space of 100+ dimensions. Points in this space have highly correlated distributions. The archive will enable astronomers to explore the data interactively. Data access will be aided by a multidimensional spatial index and other indices. The data will be partitioned in many ways. Small tag objects consisting of the most popular attributes speed up frequent searches. Splitting the data among multiple servers enables parallel, scalable I/O and applies parallel processing to the data. Hashing techniques allow efficient clustering and pair-wise comparison algorithms that parallelize nicely. Randomly sampled subsets allow debugging otherwise large queries at the desktop. Central servers will operate a data pump that supports sweeping searches that touch most of the data. The anticipated queries require special operators related to angular distances and complex similarity tests of object properties, like shapes, colors, velocity vectors, or temporal behaviors. These issues pose interesting data management challenges.

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arXiv1999

The Variance of a New Class of N-point Correlation Estimators in Poisson and Binomial Point Processes

We describe a set of new estimators for the N-point correlation functions of point processes. The variance of these estimators is calculated for the Poisson and binomial cases. It is shown that the variance of the unbiased estimator converges to the continuum value much faster than with any previously used alternative, all terms with slower convergence exactly cancel. We compare our estimators with Ripley's $\tK_0$ and $\tK_2$.

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arXiv1998

Cumulant Correlators from the APM

This work presents a set of new statistics, the cumulant correlators, aimed at high precision analysis of the galaxy distribution. They form a symmetric matrix, $Q_{NM}$, related to moment correlators the same way as cumulants are related to the moments of the distribution. They encode more information than the usual cumulants, $S_N$'s, and their extraction from data is similar to the calculation of the two-point correlation function. Perturbation theory (PT), its generalization, the extended perturbation theory (EPT), and the hierarchical assumption (HA) have simple predictions for these statistics. As an example, the factorial moment correlators measured by Szapudi, Dalton, Efstathiou & Szalay (1996) in the APM catalog are reanalyzed using this technique. While the previous analysis assumed hierarchical structure constants, this method can directly investigate the validity of HA, along with PT, and EPT. The results in agreement with previous findings indicate that, at the small scales used for this analysis, the APM data supports HA. When all non-linear corrections are taken into account it is a good approximation at the 20 percent level. It appears that PT, and a natural generalization of EPT for cumulant correlators does not provide such a good fit for the APM at small scales. Once the validity the HA is approximately established, cumulant correlators can separate the amplitudes of different tree-types in the hierarchy up to fifth order. As an example, the weights for the fourth order tree topologies are calculated including all non-linear corrections.

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arXiv1998

A blind test of photometric redshift prediction

Results of a blind test of photometric redshift predictions against spectroscopic galaxy redshifts obtained in the Hubble Deep Field with the Keck Telescope are presented. The best photometric redshift schemes predict spectroscopic redshifts with a redshift accuracy of |Delta-z|<0.1 for more than 68 percent of sources and with |Delta-z|<0.3 for 100 percent, when single-feature spectroscopic redshifts are removed from consideration. This test shows that photometric redshift schemes work well at least when the photometric data are of high quality and when the sources are at moderate redshifts.

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arXiv1997

Redshift Space Distortions of the Correlation Function in Wide Angle Galaxy Surveys

Using a novel two-dimensional coordinate system, we have derived a particularly simple way to express the redshift distortions in galaxy redshift surveys with arbitrary geometry in closed form. This method provides an almost ideal way to measure the value of $β=Ω_0^{0.6}/b$ in wide area surveys, since all pairs in the survey can be used for the analysis. In the limit of small angles, this result straightforwardly reduces to the plane-parallel approximation. This expansion can also be used together with more sophisticated methods such as for the calculation of Karhunen-Loeve eigenvectors in redshift space for an arbitrary survey geometry. Therefore, these results should provide for more precise methods in which to measure the large scale power spectrum and the value of $β$ simultaneously.

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arXiv1997

The Pairwise Velocity Distribution of Galaxies in the Las Campanas Redshift Survey

We present a novel measurement of the pairwise peculiar velocity distribution function of galaxies on scales $r<3200$ \kmsec in the Las Campanas Redshift Survey. The distribution is well described by a scale-independent exponential with a width $τ$ where $\sig =\sqrt{2}τ=363$ \kmsec. The signal is very stable. Results from the Northern and Southern sets of slices agree within $\pm13$ \kmsec and the fluctuations among the six individual survey slices vary as $\pm44$ \kmsec. The distribution was determined using a Fourier-space deconvolution of the redshift-space distortions in the correlation function. This technique is insensitive to the effect of rich clusters in the survey and recovers the entire distribution function rather than just its second moment. Taken together with the large effective volume of the survey $6.0\times10^6 \Mpc^3$, we believe this to be a definitive result for $r$-band selected galaxies with absolute magnitudes $-18.5 <M_r<-22.5$ and $z<0.2$.

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arXiv1997

A New Class of Estimators for the N-point Correlations

A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to the continuum value much faster than with any alternative, all terms giving rise to a slower convergence exactly cancel. Explicit variance formulae are provided for both Poisson and multinomial point processes using techniques for spatial statistics reported by Ripley (1988). The formalism naturally includes most previously used statistical tools such as N-point correlation functions and their Fourier counterparts, moments of counts-in-cells, and moment correlators. For all these, and perhaps some other statistics our estimator provides a straightforward means for efficient edge corrections.

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