The principle of symmetric bracket invariance as the origin of first and second quantization

The principle of invariance of the c-number symmetric bracket is used to derive both the quantum operator commutator relation $[\hat q, \hat p]=i\hbar$ and the time-dependent Schr\"odinger equation. A c-number dynamical equation is found which leads to the second quantized field theory of bosons and fermions.Comment: 14 pages. Contributed Paper: XIX International Symposium on Lepton and Photon Interactions at High Energies, Stanford University, August 9-14, 199

Infalling Faint [OII] Emitters in Abell 851. I. Spectroscopic Confirmation of Narrowband-Selected Objects

We report on a spectroscopic confirmation of narrowband-selected [OII] emitters in Abell 851 catalogued by Martin et al. (2000). The optical spectra obtained from the Keck I Low Resolution Imaging Spectrometer (LRIS) and Keck II Deep Imaging Multi-Object Spectrograph (DEIMOS) have confirmed [OII]3727 emission in narrowband-selected cluster [OII] candidates at a 85% success rate for faint (i <~ 25) blue (g-i < 1) galaxies. The rate for the successful detection of [OII] emission is a strong function of galaxy color, generally proving the efficacy of narrowband [OII] search supplemented with broadband colors in selecting faint cluster galaxies with recent star formation. Balmer decrement-derived reddening measurements show a high degree of reddening [E(B-V) >~ 0.5] in a significant fraction of this population. Even after correcting for dust extinction, the [OII]/Ha line flux ratio for the high-E(B-V) galaxies remains generally lower by a factor of ~2 than the mean [OII]/Ha ratios reported by the studies of nearby galaxies. The strength of [OII] equivalent width shows a negative trend with galaxy luminosity while the Ha equivalent width does not appear to depend as strongly on luminosity. This in part is due to the high amount of reddening observed in luminous galaxies. Furthermore, emission line ratio diagnostics show that AGN-like galaxies are abundant in the high luminosity end of the cluster [OII]-emitting sample, with only moderately strong [OII] equivalent widths, consistent with a scenario of galaxy evolution connecting AGNs and suppression of star-forming activity in massive galaxies.Comment: 11 pages (LaTeX emulateapj), 8 figures, to appear in ApJ. A version with high resolution figures available from the lead autho

Limits on the evolution of galaxies from the statistics of gravitational lenses

We use gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS) to constrain the evolution of galaxies since redshift $z \sim 1$ in the current \LCDM cosmology. This constraint is unique as it is based on a mass-selected lens sample of galaxies. Our method of statistical analysis is the same as in Chae (2003). We parametrise the early-type number density evolution in the form of $(1+z)^{\nu_n}$ and the velocity dispersion as $(1+z)^{\nu_v}$. We find that $\nu_n=-0.11^{+0.82}_{-0.89}$ ($1\sigma$) if we assume $\nu_v =0$, implying that the number density of early-type galaxies is within 50% to 164% of the present-day value at redshift $z=1$. Allowing the velocity dispersion to evolve, we find that $\nu_v=-0.4^{+0.5}_{-0.4}$ ($1\sigma$), indicating that the velocity dispersion must be within 57% and 107% of the present-day value at $z=1$. These results are consistent with the early formation and passive evolution of early-type galaxies. More stringent limits from lensing can be obtained from future large lens surveys and by using very high-redshift quasars (z \ga 5) such as those found from the Sloan Digital Sky Survey.Comment: 10 pages (preprint format), 2 figures, ApJL in press (December 20th issue

The Massive End of the Stellar Mass Function

We derive average flux corrections to the \texttt{Model} magnitudes of the Sloan Digital Sky Survey (SDSS) galaxies by stacking together mosaics of similar galaxies in bins of stellar mass and concentration. Extra flux is detected in the outer low surface brightness part of the galaxies, leading to corrections ranging from 0.05 to 0.32 mag for the highest stellar mass galaxies. We apply these corrections to the MPA-JHU (Max-Planck Institute for Astrophysics - John Hopkins University) stellar masses for a complete sample of half a million galaxies from the SDSS survey to derive a corrected galaxy stellar mass function at $z=0.1$ in the stellar mass range $9.5<\log(M_\ast/M_\odot)<12.0$. We find that the flux corrections and the use of the MPA-JHU stellar masses have a significant impact on the massive end of the stellar mass function, making the slope significantly shallower than that estimated by Li \& White (2009), but steeper than derived by Bernardi et al. (2013). This corresponds to a mean comoving stellar mass density of galaxies with stellar masses $\log(M_\ast/M_\odot) \ge 11.0$ that is a factor of 3.36 larger than the estimate by Li \& White (2009), but is 43\% smaller than reported by Bernardi et al. (2013).Comment: 11 pages, 8 figures, Accepted to MNRA

Defining And Measuring Green FDI: An Exploratory Review Of Existing Work And Evidence

This paper was developed at the request of the OECD Working Party of the Investment Committee to document efforts to date to define and measure green FDI and to investigate the practicability of various possible definitions, as well as to identify investment policy restrictions to green FDI. It does so by reviewing the literature and existing work on the contributions of FDI to the environment; by providing a two-part definition of green FDI; and by discussing various assumptions necessary to estimate the magnitude of \u27green\u27 FDI

The scale-dependence of relative galaxy bias: encouragement for the halo model description

We investigate the relationship between the colors, luminosities, and environments of galaxies in the Sloan Digital Sky Survey spectroscopic sample, using environmental measurements on scales ranging from 0.2 to 6 Mpc/h. We find: (1) that the relationship between color and environment persists even to the lowest luminosities we probe (absolute magnitude in the r band of about -14 for h=1); (2) at luminosities and colors for which the galaxy correlation function has a large amplitude, it also has a steep slope; and (3) in regions of a given overdensity on small scales (1 Mpc/h), the overdensity on large scales (6 Mpc/h) does not appear to relate to the recent star formation history of the galaxies. Of these results, the last has the most immediate application to galaxy formation theory. In particular, it lends support to the notion that a galaxy's properties are related only to the mass of its host dark matter halo, and not to the larger scale environment.Comment: submitted to ApJ; full resolution figures and slide material available at http://cosmo.nyu.edu/blanton/scale_density.htm

Parametrizing the Stellar Haloes of Galaxies

We study the stellar haloes of galaxies out to 70-100 kpc as a function of stellar mass and galaxy type by stacking aligned $r$ and $g$ band images from a sample of 45508 galaxies from SDSS DR9 in the redshift range $0.06\,\le\,z\,\le\,0.1$ and in the mass range $10^{10.0} M_{\odot} < M_{*} < 10^{11.4} M_{\odot}$r. We derive surface brightness profiles to a depth of almost $\mu_r \sim 32 \,\mathrm{mag\,arcsec}^{-2}$. We find that the ellipticity of the stellar halo is a function of galaxy stellar mass and that the haloes of high concentration ($C > 2.6$) galaxies are more elliptical than those of low concentration ($C < 2.6$) galaxies. The $g$-$r$ colour profile of high concentration galaxies reveals that the $g$-$r$ colour of the stellar population in the stellar halo is bluer than in the main galaxy, and the colour of the stellar halo is redder for higher mass galaxies. We further demonstrate that the full two-dimensional surface intensity distribution of our galaxy stacks can only be fit through multi-component S\'{e}rsic models. Using the fraction of light in the outer component of the models as a proxy for the fraction of accreted stellar light, we show that this fraction is a function of stellar mass and galaxy type. For high concentration galaxies, the fraction of accreted stellar light rises from $30\%$ to $70\%$ for galaxies in the stellar mass range from $10^{10.0} M_{\odot}$ to $10^{11.4} M_{\odot}$. The fraction of accreted light is much smaller in low concentration systems, increasing from $2\%$ to $25\%$ over the same mass range. This work provides important constraints for the theoretical understanding of the formation of stellar haloes of galaxies.Comment: Submitted to MNRAS, 18 pages, 19 figure