The Tolman Surface Brightness Test for the Reality of the Expansion. II. The Effect of the Point-Spread Function and Galaxy Ellipticity on the Derived Photometric Parameters

To complete the Tolman surface brightness test on the reality of the expansion of the Universe, we need to measure accurately the surface brightness profiles of the high-redshift galaxy sample. We, therefore, investigate the effects of various sizes of point-spread-functions composed of telescope diffraction, CCD pixel resolutions, and ground-based seeing on the measurements of mean surface brightness. We have done the calculations using two synthetic galaxies of effective radii of 0.70" and 0.25" with point-spread functions of 0.1, 0.3, and 0.9 arcseconds. We have also compared actual observations of three high-redshift galaxies in the cluster Cl 1324 + 3011 (z = 0.76) made both with the Keck telescopes in seeing of about 0.9" and with HST which has a PSF that is approximately ten times smaller. The conclusion is that HST data can be used as far into the galaxy image as a Petrosian metric radius of eta = 1.3 magnitudes, whereas the ground-based data will have systematic errors of up to 2.9 magnitudes in the mean surface brightness at eta values of less than 2.2 magnitudes. In the final section, we compare the differences in derived average surface brightness for nearly circular galaxy images compared with highly flattened images. The comparison is made by using the two reduction procedures of (1) integrating the profile curves using circular apertures, and (2) approximating an ``equivalent circular'' galaxy that is highly elongated by using an ``effective'' radius of sqrt{ab}, where a and b are the semi-major and semi-minor axis, respectively, of the best-fitting ellipse. The conclusion is that the two methods of reduction give nearly identical results and that either method can be used to analyze the low and high-redshift galaxy samples used in the Tolman test.Comment: 15 pages, 9 figures; accepted for publication in Astronomical Journa

Angular Power Spectrum of the Microwave Background Anisotropy seen by the COBE Differential Microwave Radiometer

The angular power spectrum estimator developed by Peebles (1973) and Hauser & Peebles (1973) has been modified and applied to the 2 year maps produced by the COBE DMR. The power spectrum of the real sky has been compared to the power spectra of a large number of simulated random skies produced with noise equal to the observed noise and primordial density fluctuation power spectra of power law form, with $P(k) \propto k^n$. Within the limited range of spatial scales covered by the COBE DMR, corresponding to spherical harmonic indices 3 \leq \ell \lsim 30, the best fitting value of the spectral index is $n = 1.25^{+0.4}_{-0.45}$ with the Harrison-Zeldovich value $n = 1$ approximately 0.5$\sigma$ below the best fit. For 3 \leq \ell \lsim 19, the best fit is $n = 1.46^{+0.39}_{-0.44}$. Comparing the COBE DMR $\Delta T/T$ at small $\ell$ to the $\Delta T/T$ at $\ell \approx 50$ from degree scale anisotropy experiments gives a smaller range of acceptable spectral indices which includes $n = 1$.Comment: 22 pages of LaTex using aaspp.sty and epsf.sty with appended Postscript figures, COBE Preprint 94-0

The CFH Optical PDCS survey (COP) I: The Data

This paper presents and gives the COP (COP: CFHT Optical PDCS; CFHT: Canada-France-Hawaii Telescope; PDCS: Palomar Distant Cluster Survey) survey data. We describe our photometric and spectroscopic observations with the MOS multi-slit spectrograph at the CFH telescope. A comparison of the photometry from the PDCS (Postman et al. 1996) catalogs and from the new images we have obtained at the CFH telescope shows that the different magnitude systems can be cross-calibrated. After identification between the PDCS catalogues and our new images, we built catalogues with redshift, coordinates and V, I and Rmagnitudes. We have classified the galaxies along the lines of sight into field and structure galaxies using a gap technique (Katgert et al. 1996). In total we have observed 18 significant structures along the 10 lines of sight.Comment: 40 pages, 13 figures, accepted in A

The Kast Ground Based UV Spectral Survey of 79 QSOs at Redshift 2 for Lyman Alpha Forest and Metal Absorption

We present a moderate resolution (~1.15 Angstroms/pixel) survey of 79 quasars obtained using the Kast spectrograph on the Shane 3m telescope at Lick observatory. The spectra span the wavelength range of 3175-5880 Angstroms, and have typical signal to noise of 6-20 in the regions of the spectra showing Lyman alpha forest absorption. The quasars have a mean emission redshift of z=2.17, and nearly all cover the entire Lyman alpha forest between Lyman alpha and Lyman beta. Although the quasars were selected to avoid BAL, two quasars in the survey are BAL, one of which is a new discovery. We list the HI and metal ions observed in a total of 140 absorption systems. We also identify 526 emission lines, and list their observed wavelengths, along with new redshifts of the quasars. We determine the rest wavelengths of 3 emission lines or line blends in the forest to be 1070.95 +/- 1.00, 1123.13 +/- 0.51, and 1175.88 +/- 0.30 Angstroms.Comment: Submitted to the Astronomical Journa

Mass along the Line of Sight to the Gravitational Lens B1608+656: Galaxy Groups and Implications for H_0

We report the discovery of four groups of galaxies along the line of sight to the B1608+656 gravitational lens system. One group is at the redshift of the primary lensing galaxy (z = 0.631) and appears to have a low mass, with eight spectroscopically confirmed members and an estimated velocity dispersion of 150 ± 60 km s^(-1). The three other groups are in the foreground of the lens. These groups contain ~10 confirmed members each and are located at redshifts of 0.265, 0.426, and 0.52. Two of the three additional groups are centered roughly on the lens system, while the third is centered ~1' south of the lens. We investigate the effect of each of the four groups on the gravitational lensing potential of the B1608+656 system, with a particular focus on the implications for the value of H_0 derived from this system. We find that each group provides an external convergence of ~0.005-0.060, depending on the assumptions made in the calculation. For the B1608+656 system, the stellar velocity dispersion of the lensing galaxy has been measured, thus breaking the mass sheet degeneracy due to the group that is physically associated with the lens. The effect of the other groups along the line of sight can be folded into the overall uncertainties due to large-scale structure (LSS) along the line of sight. Because B1608+656 appears to lie along an overdense line of sight, the LSS will cause the measurement of H_0 to be biased high for this system. This effect could be 5% or greater

Operations on integral lifts of K(n)

This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence that operations on lifts of the functors K(n) to cohomology theories with values in modules over valuation rings of local number fields, indexed by Lubin-Tate groups of such fields, are extensions of the groups of automorphisms of the indexing group laws, by the exterior algebras on the normal bundle to the orbits of the group laws in the space of lifts.Comment: \S 2.0 hopefully less cryptic. To appear in the proceedings of the 2015 Nagoya conference honoring T Ohkawa. Comments very welcome