A Modified Magnitude System that Produces Well-Behaved Magnitudes, Colors, and Errors Even for Low Signal-to-Noise Ratio Measurements

We describe a modification of the usual definition of astronomical magnitudes, replacing the usual logarithm with an inverse hyperbolic sine function; we call these modified magnitudes `asinh magnitudes'. For objects detected at signal-to-noise ratios of greater than about five, our modified definition is essentially identical to the traditional one; for fainter objects (including those with a formally negative flux) our definition is well behaved, tending to a definite value with finite errors as the flux goes to zero. This new definition is especially useful when considering the colors of faint objects, as the difference of two `asinh' magnitudes measures the usual flux ratio for bright objects, while avoiding the problems caused by dividing two very uncertain values for faint objects. The Sloan Digital Sky Survey (SDSS) data products will use this scheme to express all magnitudes in their catalogs.Comment: 11 pages, including 3 postscript figures. Submitted to A

Constraining Large Scale Structure Theories with the Cosmic Background Radiation

We review the relevant 10+ parameters associated with inflation and matter content; the relation between LSS and primary and secondary CMB anisotropy probes; COBE constraints on energy injection; current anisotropy band-powers which strongly support the gravitational instability theory and suggest the universe could not have reionized too early. We use Bayesian analysis methods to determine what current CMB and CMB+LSS data imply for inflation-based Gaussian fluctuations in tilted $\Lambda$CDM, $\Lambda$hCDM and oCDM model sequences with age 11-15 Gyr, consisting of mixtures of baryons, cold (and possibly hot) dark matter, vacuum energy, and curvature energy in open cosmologies. For example, we find the slope of the initial spectrum is within about 5% of the (preferred) scale invariant form when just the CMB data is used, and for $\Lambda$CDM when LSS data is combined with CMB; with both, a nonzero value of $\Omega_\Lambda$ is strongly preferred ($\approx 2/3$ for a 13 Gyr sequence, similar to the value from SNIa). The $o$CDM sequence prefers $\Omega_{tot}<1$, but is overall much less likely than the flat $\Omega_\Lambda \ne 0$ sequence with CMB+LSS. We also review the rosy forecasts of angular power spectra and parameter estimates from future balloon and satellite experiments when foreground and systematic effects are ignored.Comment: 20 pages, LaTeX, 5 figures, 2 tables, uses rspublic.sty To appear in Philosophical Transactions of the Royal Society of London A, 1998. "Discussion Meeting on Large Scale Structure in the Universe," Royal Society, London, March 1998. Text and colour figures also available at ftp://ftp.cita.utoronto.ca/bond/roysoc9

Photometric Response Functions of the SDSS Imager

The monochromatic illumination system is constructed to carry out in situ measurements of the response function of the mosaicked CCD imager used in the Sloan Digital Sky Survey (SDSS). The system is outlined and the results of the measurements, mostly during the first 6 years of the SDSS, are described. We present the reference response functions for the five colour passbands derived from these measurements, and discuss column to column variations and variations in time, and also their effects on photometry. We also discuss the effect arising from various, slightly different response functions of the associated detector systems that were used to give SDSS photometry. We show that the calibration procedures of SDSS remove these variations reasonably well with the resulting final errors from variant response functions being unlikely to be larger than 0.01 mag for g, r, i, and z bands over the entire duration of the survey. The considerable aging effect is uncovered in the u band, the response function showing a 30% decrease in the throughput in the short wavelength side during the survey years, which potentially causes a systematic error in photometry. The aging effect is consistent with variation of the instrumental sensitivity in u-band, which is calibrated out. The expected colour variation is consistent with measured colour variation in the catalog of repeated photometry. The colour variation is delta (u-g) ~ 0.01 for most stars, and at most delta (u-g) ~ 0.02 mag for those with extreme colours. We verified in the final catalogue that no systematic variations in excess of 0.01 mag are detected in the photometry which can be ascribed to aging and/or seasonal effects except for the secular u-g colour variation for stars with extreme colours.Comment: 54 pages, 18 figures, 7 tables, accepted for publication in A

A LARGE-VOLUME RADIO-METRIC CALORIMETER

An isothermal heat-flow calorimeter with a sample chamber of 13-in. diameter and 14-in. length is described. The detection limit is about 1 mW and the precision for large samples is within a few tenths of a percent. A 96junction thermopile is used for the temperature measurement. (auth

The evolution of clustering and bias in the galaxy distribution

This paper reviews the measurements of galaxy correlations at high redshifts, and discusses how these may be understood in models of hierarchical gravitational collapse. The clustering of galaxies at redshift one is much weaker than at present, and this is consistent with the rate of growth of structure expected in an open universe. If $\Omega=1$, this observation would imply that bias increases at high redshift, in conflict with observed $M/L$ values for known high-$z$ clusters. At redshift 3, the population of Lyman-limit galaxies displays clustering which is of similar amplitude to that seen today. This is most naturally understood if the Lyman-limit population is a set of rare recently-formed objects. Knowing both the clustering and the abundance of these objects, it is possible to deduce empirically the fluctuation spectrum required on scales which cannot be measured today owing to gravitational nonlinearities. Of existing physical models for the fluctuation spectrum, the results are most closely matched by a low-density spatially flat universe. This conclusion is reinforced by an empirical analysis of CMB anisotropies, in which the present-day fluctuation spectrum is forced to have the observed form. Open models are strongly disfavoured, leaving $\Lambda$CDM as the most successful simple model for structure formation.Comment: Invited review at the Royal Society Meeting `Large-scale structure in the universe', London, March 1998. 20 Pages LaTe