Higher-Order Properties of Analytic Wavelets

The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a two-parameter family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a mapping between scale and frequency, and the bias involved in estimating properties of modulated oscillatory signals, are proposed as important considerations. Wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain, as quantified by the third central moments. A particular subset of the generalized Morse wavelets, recognized as deriving from an inhomogeneous Airy function, emerge as having particularly desirable properties. These "Airy wavelets" substantially outperform the only approximately analytic Morlet wavelets for high time localization. Special cases of the generalized Morse wavelets are examined, revealing a broad range of behaviors which can be matched to the characteristics of a signal.Comment: 15 pages, 6 Postscript figure

On the relation between sSFR and metallicity

In this paper we present an exact general analytic expression $Z(sSFR)=y/\Lambda(sSFR)+I(sSFR)$ linking the gas metallicity Z to the specific star formation rate (sSFR), that validates and extends the approximate relation put forward by Lilly et al. (2013, L13), where $y$ is the yield per stellar generation, $\Lambda(sSFR)$ is the instantaneous ratio between inflow and star formation rate expressed as a function of the sSFR, and $I$ is the integral of the past enrichment history, respectively. We then demonstrate that the instantaneous metallicity of a self-regulating system, such that its sSFR decreases with decreasing redshift, can be well approximated by the first term on the right-hand side in the above formula, which provides an upper bound to the metallicity. The metallicity is well approximated also by the L13 ideal regulator case, which provides a lower bound to the actual metallicity. We compare these approximate analytic formulae to numerical results and infer a discrepancy <0.1 dex in a range of metallicities and almost three orders of magnitude in the sSFR. We explore the consequences of the L13 model on the mass-weighted metallicity in the stellar component of the galaxies. We find that the stellar average metallicity lags 0.1-0.2 dex behind the gas-phase metallicity relation, in agreement with the data. (abridged)Comment: 14 pages, 6 figures, MNRAS accepte

THE CANADA-FRANCE REDSHIFT SURVEY V: Global Properties of the Sample

The photometric and spectroscopic data of the CFRS survey of objects with 17.5 < I_{AB} < 22.5 are combined and analysed. The overall completeness is 85%. The redshift histogram of the sample is presented for 591 field galaxies with secure redshifts. The median redshift is z = 0.56, and the highest redshift observed is z = 1.3; 25 galaxies have z > 1 The distributions of magnitudes and colors demonstrate that galaxies at these high redshifts have very similar colors to those observed locally. The survey thus represents a major improvement in our knowledge of field galaxies at large look-back times. Only ~1% of the galaxies are as compact as stars (on images with FWHM ~ 0.9") and comparisons of the photometric and spectroscopic data show that only one galaxy was initially incorrectly classified spectroscopically as a star, and only two stars were misclassified as galaxies. It is demonstrated that the redshift distributions in the five fields are statistically consistent with each other, once the reduction in the effective number of independent galaxies due to small-scale clustering in redshift is taken into account. The photometric properties of the spectroscopically-unidentified objects indicate that most are likely to be galaxies rather than stars. At least half of these must have the same redshift distribution as the identified galaxies, and a combination of magnitudes, colors and compactness of the remaining unidentified galaxies is used to predict their redshifts. The majority are probably ordinary galaxies at the high redshift end of our sample, including some quiescent galaxies at z > 1.0, rather than some new or unusual population.Comment: 20 uuencoded postscript pages (first part) with 12 figures (second part). Also available at http://www.dao.nrc.ca/DAO/SCIENCE/science.html and coming soon on a CFRS homepage. Accepted June 19, scheduled for Dec 10 issue of Ap

zCOSMOS: A large VLT/VIMOS redshift survey covering 0 < z < 3 in the COSMOS field

zCOSMOS is a large-redshift survey that is being undertaken in the COSMOS field using 600 hr of observation with the VIMOS spectrograph on the 8 m VLT. The survey is designed to characterize the environments of COSMOS galaxies from the 100 kpc scales of galaxy groups up to the 100 Mpc scale of the cosmic web and to produce diagnostic information on galaxies and active galactic nuclei. The zCOSMOS survey consists of two parts: (1) zCOSMOSbright, a magnitude-limited I-band I_(AB) < 22.5 sample of about 20,000 galaxies with 0.1 < z < 1.2 covering the whole 1.7 deg^2 COSMOS ACS field, for which the survey parameters at z ~ 0.7 are designed to be directly comparable to those of the 2dFGRS at z ~ 0.1; and (2) zCOSMOS-deep, a survey of approximately 10,000 galaxies selected through color-selection criteria to have 1.4 < z < 3.0, within the central 1 deg^2. This paper describes the survey design and the construction of the target catalogs and briefly outlines the observational program and the data pipeline. In the first observing season, spectra of 1303 zCOSMOS-bright targets and 977 zCOSMOS-deep targets have been obtained. These are briefly analyzed to demonstrate the characteristics that may be expected from zCOSMOS, and particularly zCOSMOS-bright, when it is finally completed between 2008 and 2009. The power of combining spectroscopic and photometric redshifts is demonstrated, especially in correctly identifying the emission line in single-line spectra and in determining which of the less reliable spectroscopic redshifts are correct and which are incorrect. These techniques bring the overall success rate in the zCOSMOS-bright so far to almost 90% and to above 97% in the 0.5 < z < 0.8 redshift range. Our zCOSMOS-deep spectra demonstrate the power of our selection techniques to isolate high-redshift galaxies at 1.4 < z < 3.0 and of VIMOS to measure their redshifts using ultraviolet absorption lines

THE CANADA-FRANCE REDSHIFT SURVEY II: Spectroscopic Program; Data for the 0000-00 and 1000+25 Fields

This paper describes the methods used to obtain the spectroscopic data and construct redshift catalogs for the Canada-France deep Redshift Survey (CFRS). The full data set consists of more than one thousand spectra, of objects with 17.5 < I_{AB} < 22.5, obtained from deep multi-slit data with the MARLIN and MOS-SIS spectrographs at the CFHT. The final spectroscopic catalog contains 200 stars, 591 galaxies with secure redshifts in the range 0 < z < 1.3, 6 QSOs, and 146 objects with very uncertain or unknown redshifts, leading to an overall success rate of identification of 85%. Additionally, 67 objects affected by observational problems have been placed in a supplemental list. We describe here the instrumental set up, and the observing procedures used to efficiently gather this large data set. New optimal ways of packing spectra on the detector to significantly increase the multiplexing gain offered by multi-slit spectroscopy are described. Dedicated data reduction procedures have been developed under the IRAF environment to allow for fast and accurate processing. Very strict procedures have been followed to establish a reliable list of final spectroscopic measurements. Fully independent processing of the data has been carried out by three members of the team for each data set associated with a multi-slit mask, and final redshifts were assigned only after the careful comparison of the three independent measurements. A confidence class scheme was established. We strongly emphasize the benefits of such procedures. Finally, we present the spectroscopic data obtained for 303 objects in the 0000-00 and 1000+25 fields. The success rate in spectroscopic identification isComment: 16 uuencoded postcript pages with figures 4,5,8,9 and 12. Other (large) figures available from the authors. Large data table not yet released. Also available at http://www.dao.nrc.ca/DAO/SCIENCE/science.html and coming soon on a CFRS homepage. Accepted June 19, scheduled for the Dec 10 issue of Ap

The CANADA-FRANCE REDSHIFT SURVEY I: Introduction to the Survey, Photometric Catalogs and Surface Brightness Selection Effects

The Canada-France Redshift Survey has been undertaken to provide a large well-defined sample of faint galaxies at high redshift in which the selection criteria match as closely as possible those of samples of nearby galaxies. The survey is designed to have a median redshift of z ~ 0.6 corresponding to a look-back time of half the present age of the Universe for Omega ~ 1. Such a survey can then be used for studying many different aspects of the evolution of galaxies over the interval 0 < z < 1. In this paper we describe the selection of the fields, the multicolor imaging observations and the construction and validation of the photometric catalogs. Particular attention is paid to quantifying the unavoidable selection effects in surface brightness and their impact on the survey is assessed in the context of the properties of known populations of galaxies. The photometric catalogs contain several thousand objects brighter than I_{AB}< 22.5 and are essentially complete for central surface brightnesses as faint as $\mu_{AB}(I)$ $\sim$ 24.5 mag arcsec$^{-2}$. This should be sufficient to include both normal surface brightness galaxies and prototypes of extreme low surface brightness galaxies.Comment: 17 pages, 2 tables, 10 postscript figures (in 2 parts), uses aaspp.sty Also available at http://www.dao.nrc.ca/DAO/SCIENCE/science.html and coming soon on a CFRS homepag

Photo-z Performance for Precision Cosmology II : Empirical Verification

The success of future large scale weak lensing surveys will critically depend on the accurate estimation of photometric redshifts of very large samples of galaxies. This in turn depends on both the quality of the photometric data and the photo-z estimators. In a previous study, (Bordoloi et al. 2010) we focussed primarily on the impact of photometric quality on photo-z estimates and on the development of novel techniques to construct the N(z) of tomographic bins at the high level of precision required for precision cosmology, as well as the correction of issues such as imprecise corrections for Galactic reddening. We used the same set of templates to generate the simulated photometry as were then used in the photo-z code, thereby removing any effects of "template error". In this work we now include the effects of "template error" by generating simulated photometric data set from actual COSMOS photometry. We use the trick of simulating redder photometry of galaxies at higher redshifts by using a bluer set of passbands on low z galaxies with known redshifts. We find that "template error" is a rather small factor in photo-z performance, at the photometric precision and filter complement expected for all-sky surveys. With only a small sub-set of training galaxies with spectroscopic redshifts, it is in principle possible to construct tomographic redshift bins whose mean redshift is known, from photo-z alone, to the required accuracy of 0.002(1+z).Comment: 7 pages, 5 figures, accepted for publication in MNRA