Old high-redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at $z\simeq 1.5$ which have apparent stellar ages of \gs 3 Gyr, based on detailed spectroscopy in the rest-frame ultraviolet. In order for galaxies to have existed at the high collapse redshifts indicated by these ages, there must be a minimum level of power in the density fluctuation spectrum on galaxy scales. This paper compares the required power with that inferred from other high-redshift populations. If the collapse redshifts for the old red galaxies are in the range $z_c\simeq 6$ -- 8, there is general agreement between the various tracers on the required inhomogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately $\nu\simeq 3.0$ fluctuations, implying a very large bias parameter $b\simeq 6$. The high collapse redshifts of the red galaxies as deduced from gravitational collapse provides independent support for the ages estimated from their stellar populations. Such early-forming galaxies are rare, and their contribution to the cosmological stellar density is consistent with an extrapolation to higher redshifts of the star-formation rate measured at $z<5$; there is no evidence for a general era of spheroid formation at extreme redshifts.Comment: 9 Pages MNRAS in press. Uses MNRAS Plain TeX macro

Further redshifts of 1-Jy radio sources

We have firm redshifts for a further 12 faint radio source identifications from the ‘1-Jy’ complete radio-selected sample, two of which are galaxies with redshifts z > 1.5. Another object has a provisional redshift that requires confirmation. Five of these identifications had previously been classified as QSOs on the basis of their optical morphology. Our spectroscopy shows that of these, one is definitely a galaxy and two have characteristics intermediate between those of ‘normal’ radio galaxies and those of ‘normal’ quasars, for instance broad Balmer emission but an extended optical image. Two of the eight identifications previously classified as galaxies have similar ‘intermediate’ properties. The remaining identifications have low-excitation narrow emission-line systems of the type seen in other 1-Jy radio sources by Allington-Smith et al. We confirm that the 1-Jy emission lines are a factor 2 weaker than those of 3C galaxies in the same redshift interval

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure

A New Einstein Cross: A Highly Magnified, Intrinsically Faint Lyman-Alpha Emitter at z=2.7

We report the discovery of a new Einstein cross at redshift z_S = 2.701 based on Lyman-alpha emission in a cruciform configuration around an SDSS luminous red galaxy (z_L = 0.331). The system was targeted as a possible lens based on an anomalous emission line in the SDSS spectrum. Imaging and spectroscopy from the W. M. Keck Observatory confirm the lensing nature of this system. This is one of the widest-separation galaxy-scale lenses known, with an Einstein radius of ~1.84 arcsec. We present simple gravitational lens models for the system and compute the intrinsic properties of the lensed galaxy. The total mass of the lensing galaxy within the 8.8 +/- 0.1 kpc enclosed by the lensed images is (5.2 +/- 0.1) x 10^11 M_sun. The lensed galaxy is a low mass galaxy (0.2 L*) with a high equivalent-width Lyman-alpha line (EW_Lya_rest = 46 +/- 5 Angstroms). Follow-up studies of this lens system can probe the mass structure of the lensing galaxy, and can provide a unique view of an intrinsically faint, high-redshift, star-forming galaxy at high signal-to-noise ratio.Comment: ApJ Letters, in pres

The Intracluster Medium in z > 1 Galaxy Clusters

The Chandra X-ray Observatory was used to obtain a 190 ks image of three high redshift galaxy clusters in one observation. The results of our analysis of these data are reported for the two z > 1 clusters in this Lynx field, including the most distant known X-ray selected cluster. Spatially-extended X-ray emission was detected from both these clusters, indicating the presence of hot gas in their intracluster media. A fit to the X-ray spectrum of RX J0849+4452, at z=1.26, yields a temperature of kT = 5.8^{+2.8}_{-1.7} keV. Using this temperature and the assumption of an isothermal sphere, the total mass of RX J0849+4452 is found to be 4.0^{+2.4}_{-1.9} X 10^{14} h_{65}^{-1} M_{\sun} within r = 1 h_{65}^{-1} Mpc. The T_x for RX J0849+4452 approximately agrees with the expectation based on its L_{bol} = 3.3^{+0.9}_{-0.5} X 10^{44}$erg s$^{-1} according to the low redshift L_x - T_x relation. The very different distributions of X-ray emitting gas and of the red member galaxies in the two z > 1 clusters, in contrast to the similarity of the optical/IR colors of those galaxies, suggests that the early-type galaxies mostly formed before their host clusters.Comment: 4 pages in emulateapj style plus 2 color jpegs for Figure 3. Accepted by The Astrophysical Journa

Serendipitously Detected Galaxies in the Hubble Deep Field

We present a catalog of 74 galaxies detected serendipitously during a campaign of spectroscopic observations of the Hubble Deep Field North (HDF) and its environs. Among the identified objects are five candidate Ly-alpha emitters at z > 5, a galaxy cluster at z = 0.85, and a Chandra source with a heretofore undetermined redshift of z = 2.011. We report redshifts for 25 galaxies in the central HDF, 13 of which had no prior published spectroscopic redshift. Of the remaining 49 galaxies, 30 are located in the single-orbit HDF Flanking Fields. We discuss the redshift distribution of the serendipitous sample, which contains galaxies in the range 0.10 < z < 5.77 with a median redshift of z = 0.85, and we present strong evidence for redshift clustering. By comparing our spectroscopic redshifts to optical/IR photometric studies of the HDF, we find that photometric redshifts are in most cases capable of producing reasonable predictions of galaxy redshifts. Finally, we estimate the line-of-sight velocity dispersion and the corresponding mass and expected X-ray luminosity of the galaxy cluster, we present strong arguments for interpreting the Chandra source as an obscured AGN, and we discuss in detail the spectrum of one of the candidate z > 5 Ly-alpha emitters.Comment: 18 pages, 9 figures, accepted for publication in the Astronomical Journa

Structural parameterizations for boxicity

The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number. Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the pathwidth of the input graph. Finally, we provide evidence in favor of a conjecture of Adiga et al. that boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page