On \mu-Compatible Metrics and Measurable Sensitivity

We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving case they are W-measurably sensitive or measurably isomorphic to an ergodic isometry on a compact metric space.Comment: Many improvements in exposition, a technical assumption removed, as suggested by the reviewe

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 Origin of [O II] Emission in Recently Quenched Active Galaxy Nucleus Hosts

We have employed emission-line diagnostics derived from DEIMOS and NIRSPEC spectroscopy to determine the origin of the [O II] emission line observed in six active galactic nucleus (AGN) hosts at z ~ 0.9. These galaxies are a subsample of AGN hosts detected in the Cl1604 supercluster that exhibit strong Balmer absorption lines in their spectra and appear to be in a post-starburst or post-quenched phase, if not for their [O II] emission. Examining the flux ratio of the [N II] to Hα lines, we find that in five of the six hosts the dominant source of ionizing flux is AGN continuum emission. Furthermore, we find that four of the six galaxies have over twice the [O II] line luminosity that could be generated by star formation alone given their Hα line luminosities. This strongly suggests that AGN-excited narrow-line emission is contaminating the [O II] line flux. A comparison of star formation rates calculated from extinction-corrected [O II] and Hα line luminosities indicates that the former yields a five-fold overestimate of the current activity in these galaxies. Our findings reveal the [O II] line to be a poor indicator of star formation activity in a majority of these moderate-luminosity Seyferts. This result bolsters our previous findings that an increased fraction of AGN at high redshifts is hosted by galaxies in a post-starburst phase. The relatively high fraction of AGN hosts in the Cl1604 supercluster that show signs of recently truncated star formation activity may suggest that AGN feedback plays an increasingly important role in suppressing ongoing activity in large-scale structures at high redshift

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

A z=0.9 supercluster of X-ray luminous, optically-selected, massive galaxy clusters

We report the discovery of a compact supercluster structure at z=0.9. The structure comprises three optically-selected clusters, all of which are detected in X-rays and spectroscopically confirmed to lie at the same redshift. The Chandra X-ray temperatures imply individual masses of ~5x10^14 Msun. The X-ray masses are consistent with those inferred from optical--X-ray scaling relations established at lower redshift. A strongly-lensed z~4 Lyman break galaxy behind one of the clusters allows a strong-lensing mass to be estimated for this cluster, which is in good agreement with the X-ray measurement. Optical spectroscopy of this cluster gives a dynamical mass in good agreement with the other independent mass estimates. The three components of the RCS2319+00 supercluster are separated from their nearest neighbor by a mere <3 Mpc in the plane of the sky and likely <10 Mpc along the line-of-sight, and we interpret this structure as the high-redshift antecedent of massive (~10^15 Msun) z~0.5 clusters such as MS0451.5-0305.Comment: ApJ Letters accepted. 5 pages in emulateapj, 3 figure

Search For Unresolved Sources In The COBE-DMR Two-Year Sky Maps

We have searched the temperature maps from the COBE Differential Microwave Radiometers (DMR) first two years of data for evidence of unresolved sources. The high-latitude sky (|b| > 30\deg) contains no sources brighter than 192 uK thermodynamic temperature (322 Jy at 53 GHz). The cumulative count of sources brighter than threshold T, N(> T), is consistent with a superposition of instrument noise plus a scale-invariant spectrum of cosmic temperature fluctuations normalized to Qrms-PS = 17 uK. We examine the temperature maps toward nearby clusters and find no evidence for any Sunyaev-Zel'dovich effect, \Delta y < 7.3 x 10^{-6} (95% CL) averaged over the DMR beam. We examine the temperature maps near the brightest expected radio sources and detect no evidence of significant emission. The lack of bright unresolved sources in the DMR maps, taken with anisotropy measurements on smaller angular scales, places a weak constraint on the integral number density of any unresolved Planck-spectrum sources brighter than flux density S, n(> S) < 2 x 10^4 (S/1 Jy)^{-2} sr^{-1}.Comment: 16 pages including 2 figures, uuencoded PostScript, COBE preprint 94-0

Keck spectroscopy of CLASS gravitational lenses

We present the optical spectra of four newly discovered gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS). These observations were carried out using the Low Resolution Imaging Spectrograph on the W. M. Keck-I Telescope as part of a program to study galaxy-scale gravitational lenses. From our spectra we found the redshift of the background source in CLASS B0128+437 (z_s=3.1240+-0.0042) and the lensing galaxy redshifts in CLASS B0445+123 (z_l=0.5583+-0.0003) and CLASS B0850+054 (z_l=0.5883+-0.0006). Intriguingly, we also discovered that CLASS B0631+519 may have two lensing galaxies (z_l,1=0.0896+-0.0001, z_l,2=0.6196+-0.0004). We also found a single unidentified emission line from the lensing galaxy in CLASS B0128+437 and the lensed source in CLASS B0850+054. We find the lensing galaxies in CLASS B0445+123 and CLASS B0631+519 (l,2) to be early-type galaxies with Einstein Radii of 2.8-3.0 h^{-1} kpc. The deflector in CLASS B0850+054 is a late-type galaxy with an Einstein Radius of 1.6 h^{-1} kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA

The Assembly of the Red Sequence at z ~ 1: The Color and Spectral Properties of Galaxies in the Cl1604 Supercluster

We investigate the properties of the 525 spectroscopically confirmed members of the Cl1604 supercluster at z ~ 0.9 as part of the Observations of Redshift Evolution in Large Scale Environments survey. In particular, we focus on the photometric, stellar mass, morphological, and spectral properties of the 305 member galaxies of the eight clusters and groups that comprise the Cl1604 supercluster. Using an extensive Keck Low-Resolution Imaging Spectrometer (LRIS)/DEep Imaging Multi-Object Spectrograph (DEIMOS) spectroscopic database in conjunction with ten-band ground-based, Spitzer, and Hubble Space Telescope imaging, we investigate the buildup of the red sequence in groups and clusters at high redshift. Nearly all of the brightest and most massive red-sequence galaxies present in the supercluster environment are found to lie within the bounds of the cluster and group systems, with a surprisingly large number of such galaxies present in low-mass group systems. Despite the prevalence of these red-sequence galaxies, we find that the average cluster galaxy has a spectrum indicative of a star-forming galaxy, with a star formation rate between those of z ~ 1 field galaxies and moderate-redshift cluster galaxies. The average group galaxy is even more active, exhibiting spectral properties indicative of a starburst. The presence of massive, red galaxies and the high fraction of starbursting galaxies present in the group environment suggest that significant processing is occurring in group environments at z ~ 1 and earlier. There is a deficit of low-luminosity red-sequence galaxies in all Cl1604 clusters and groups, suggesting that such galaxies transition to the red sequence at later times. Extremely massive (~10^(12)M_☉) red-sequence galaxies routinely observed in rich clusters at z ~ 0 are also absent from the Cl1604 clusters and groups. We suggest that such galaxies form at later times through merging processes. There are significant populations of transition galaxies at intermediate stellar masses (log(M_*)=10.25-10.75) present in the group and cluster environments, suggesting that this range is important for the buildup of the red-sequence mass function at z ~ 1. Through a comparison of the transitional populations present in the Cl1604 cluster and group systems, we find evidence that massive blue-cloud galaxies are quenched earliest in the most dynamically relaxed systems and at progressively later times in dynamically unrelaxed systems