Computing NodeTrix Representations of Clustered Graphs

NodeTrix representations are a popular way to visualize clustered graphs; they represent clusters as adjacency matrices and inter-cluster edges as curves connecting the matrix boundaries. We study the complexity of constructing NodeTrix representations focusing on planarity testing problems, and we show several NP-completeness results and some polynomial-time algorithms. Building on such algorithms we develop a JavaScript library for NodeTrix representations aimed at reducing the crossings between edges incident to the same matrix.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

First Results from the Large Area Lyman Alpha Survey

We report on a new survey for z=4.5 Lyman alpha sources, the Large Area Lyman Alpha (LALA) survey. Our survey achieves an unprecedented combination of volume and sensitivity by using narrow-band filters on the new 8192x8192 pixel CCD Mosaic Camera at the 4 meter Mayall telescope of Kitt Peak National Observatory. Well-detected sources with flux and equivalent width matching known high redshift Lyman alpha galaxies (i.e., observed equivalent width above 80 Angstroms and line+continuum flux between 2.6e-17 and 5.2e-17 erg/cm^2/sec in an 80 Angstrom filter) have an observed surface density corresponding to 11000 +- 700 per square degree per unit redshift at z=4.5. Spatial variation in this surface density is apparent on comparison between counts in 6561 and 6730 Angstrom filters. Early spectroscopic followup results from the Keck telescope included three sources meeting our criteria for good Lyman alpha candidates. Of these, one is confirmed as a z=4.52 source, while another remains consistent with either z=4.55 or z=0.81. We infer that 30 to 50% of our good candidates are bona fide Lyman alpha emitters, implying a net density of about 4000 Lyman alpha galaxies per square degree per unit redshift.Comment: 10 pages, 2 figures (3 .ps files), uses AASTeX 4. Submitted to The Astrophysical Journal Letter

A Chandra X-ray Study of Cygnus A - II. The Nucleus

We report Chandra ACIS and quasi-simultaneous RXTE observations of the nearby, powerful radio galaxy Cygnus A, with the present paper focusing on the properties of the active nucleus. In the Chandra observation, the hard (> a few keV) X-ray emission is spatially unresolved with a size \approxlt 1 arcsec (1.5 kpc, H_0 = 50 km s^-1 Mpc^-1) and coincides with the radio and near infrared nuclei. In contrast, the soft (< 2 keV) emission exhibits a bi-polar nebulosity that aligns with the optical bi-polar continuum and emission-line structures and approximately with the radio jet. In particular, the soft X-ray emission corresponds very well with the [O III] \lambda 5007 and H\alpha + [N II] \lambda\lambda 6548, 6583 nebulosity imaged with HST. At the location of the nucleus there is only weak soft X-ray emission, an effect that may be intrinsic or result from a dust lane that crosses the nucleus perpendicular to the source axis. The spectra of the various X-ray components have been obtained by simultaneous fits to the 6 detectors. The compact nucleus is detected to 100 keV and is well described by a heavily absorbed power law spectrum with \Gamma_h = 1.52^{+0.12}_{-0.12} (similar to other narrow line radio galaxies) and equivalent hydrogen column N_H (nuc) = 2.0^{+0.1}_{-0.2} \times 10^{23} cm^-2. (Abstract truncated).Comment: To be published in the Astrophysical Journal, v564 January 1, 2002 issue; 34 pages, 11 figures (1 color

Scattered Nuclear Continuum and Broad H-alpha in Cygnus A

We have discovered scattered broad Balmer emission lines in the spectrum of Cygnus A, using the Keck II telescope. Broad H-alpha appears in polarized flux from components on either side of the nucleus, and to a lesser extent in the nucleus. The full-width at half-maximum of broad H-alpha is 26,000 km/s, comparable to the widest emission lines seen in broad-line radio galaxies. Scattered AGN light provides a significant contribution to the total flux at 3800 Angstroms (rest) of the western component, where the polarization rises to 16%. The spatially integrated flux of Cygnus A at 5500 Angstroms can be decomposed into an elliptical galaxy fraction (Fg=0.70), a highly polarized blue component (FC1=0.15), a less polarized red component (FC=0.09), and a contribution from the nebular continuum (0.06). Imaging polarimetry shows a double fan of polarization vectors with circular symmetry which corresponds to the ionization cone seen in HST images. Our results are consistent with scattering of light from a hidden quasar of modest luminosity by an extended, dusty narrow-line region.Comment: 13 pages, 4 figures, Latex, to appear in ApJ Letter

Probing the time dependence of dark energy

A new method to investigate a possible time-dependence of the dark energy equation of state $w$ is proposed. We apply this methodology to two of the most recent data sets of type Ia supernova (Union2 and SDSS) and the baryon acoustic oscillation peak at $z = 0.35$. For some combinations of these data, we show that there is a clear departure from the standard $\Lambda$CDM model at intermediary redshifts, although a non-evolving dark energy component ($dw/dz = 0$) cannot be ruled out by these data. The approach developed here may be useful to probe a possible evolving dark energy component when applied to upcoming observational data.Comment: 6 pages, 3 figures, LaTe

RC J0311+0507: A Candidate for Superpowerful Radio Galaxies in the Early Universe at Redshift z=4.514

A strong emission line at 6703A has been detected in the optical spectrum for the host galaxy (R=23.1) of the radio source RC J0311+0507 (4C+04.11). This radio galaxy, with a spectral index of 1.31 in the frequency range 365-4850 MHz, is one of the ultrasteep spectrum objects from the deep survey of a sky strip conducted with RATAN-600 in 1980-1981. We present arguments in favor of the identification of this line with Ly\alpha at redshift z=4.514. In this case, the object belongs to the group of extremely distant radio galaxies of ultrahigh radio luminosity (P_{1400}=1.3 x 10^{29}W Hz^{-1}). Such power can be provided only by a fairly massive black hole (~10^9M_\sun}) that formed in a time less than the age of the Universe at the observed z(1.3 Gyr) or had a primordial origin.Comment: 8 pages, 3 figure

On strongly chordal graphs that are not leaf powers

A common task in phylogenetics is to find an evolutionary tree representing proximity relationships between species. This motivates the notion of leaf powers: a graph G = (V, E) is a leaf power if there exist a tree T on leafset V and a threshold k such that uv is an edge if and only if the distance between u and v in T is at most k. Characterizing leaf powers is a challenging open problem, along with determining the complexity of their recognition. This is in part due to the fact that few graphs are known to not be leaf powers, as such graphs are difficult to construct. Recently, Nevries and Rosenke asked if leaf powers could be characterized by strong chordality and a finite set of forbidden subgraphs. In this paper, we provide a negative answer to this question, by exhibiting an infinite family \G of (minimal) strongly chordal graphs that are not leaf powers. During the process, we establish a connection between leaf powers, alternating cycles and quartet compatibility. We also show that deciding if a chordal graph is \G-free is NP-complete, which may provide insight on the complexity of the leaf power recognition problem

Stellar population gradients in Fornax Cluster S0 galaxies: connecting bulge and disk evolution

We present absorption-line index gradients for a sample of S0 galaxies in the Fornax Cluster. The sample has been selected to span a wide range in galaxy mass, and the deep VLT-FORS2 spectroscopy allows us to explore the stellar populations all the way to the outer disk-dominated regions of these galaxies. We find that globally, in both bulges and disks, star formation ceased earliest in the most massive systems, as a further manifestation of downsizing. However, within many galaxies, we find an age gradient which indicates that star formation ended first in the outermost regions. Metallicity gradients, when detected, are always negative such that the galaxy centres are more metal-rich. This finding fits with a picture in which star formation continued in the central regions, with enriched material, after it had stopped in the outskirts. Age and metallicity gradients are correlated, suggesting that large differences in star formation history between the inner and outer parts of S0 galaxies yield large differences in their chemical enrichment. In agreement with previous results, we conclude that the radial variations in the stellar populations of S0 galaxies are compatible with the hypothesis that these galaxies are the descendants of spiral galaxies whose star formation has ceased. With the addition of radial gradient information, we are able to show that this shutdown of star formation occurred from the outside inward, with the later star formation in the central regions offering a plausible mechanism for enhancing the bulge light in these systems, as the transformation to more bulge-dominated S0 galaxies requires.Comment: 9 pages, 4 figures and Appendix, accepted for publication in MNRA

CENSORS: A Combined EIS-NVSS Survey Of Radio Sources. I. Sample definition, radio data and optical identifications

A new sample of radio sources, with the designated name CENSORS (A Combined EIS-NVSS Survey Of Radio Sources), has been defined by combining the NRAO VLA Sky Survey (NVSS) at 1.4 GHz with the ESO Imaging Survey (EIS) Patch D, a 3 by 2 degree region of sky centred at 09 51 36.0, -21 00 00 (J2000). New radio observations of 199 NVSS radio sources with NVSS flux densities S(1.4GHz) > 7.8mJy are presented, and compared with the EIS I-band imaging observations which reach a depth of I~23; optical identifications are obtained for over two-thirds of the ~150 confirmed radio sources within the EIS field. The radio sources have a median linear size of 6 arcseconds, consistent with the trend for lower flux density radio sources to be less extended. Other radio source properties, such as the lobe flux density ratios, are consistent with those of brighter radio source samples. From the optical information, 30-40% of the sources are expected to lie at redshifts z >~ 1.5. One of the key goals of this survey is to accurately determine the high redshift evolution of the radio luminosity function. These radio sources are at the ideal flux density level to achieve this goal; at redshifts z~2 they have luminosities which are around the break of the luminosity function and so provide a much more accurate census of the radio source population at those redshifts than the existing studies of extreme, high radio power sources. Other survey goals include investigating the dual--population unification schemes for radio sources, studying the radio luminosity dependence of the evolution of radio source environments, and understanding the radio power dependence of the K-z relation for radio galaxies.Comment: Accepted for publication in MNRAS. 28 pages plus 36 reduced resolution jpeg figures. A postscript version with full resolution figures included in the text is available from http://www.roe.ac.uk/~pnb/censors.ps.g

Spectroscopy of the near-nuclear regions of Cygnus A: estimating the mass of the supermassive black hole

We use a combination of high spatial resolution optical and near-IR spectroscopic data to make a detailed study of the kinematics of the NLR gas in the near-nuclear regions of the powerful, FRII radio galaxy Cygnus A (z=0.0560), with the overall goal of placing limits on the mass of any supermassive black hole in the core. Our K-band infrared observations (0.75 arcsec seeing) -- taken with NIRSPEC on the Keck II telescope -- show a smooth rotation pattern across the nucleus in the Paschen alpha and H_2 emission lines along a slit position (PA180) close to perpendicular to the radio axis, however, there is no evidence for such rotation along the radio axis (PA105). Higher spatial resolution observations of the [OIII]5007 emission line -- taken with STIS on the Hubble Space Telescope (HST) -- confirm the general rotation pattern of the gas in the direction perpendicular to the radio axis, and provide evidence for steep velocity gradients within a radius of 0.1 arcsec of the core. The circular velocities measured from both the Keck and HST data lead to an estimate of the mass of the supermassive black hole of 2.5+/-0.7x10^9 solar masses. For the host galaxy properties of Cygnus A, this mass is consistent with the global correlations between black hole mass and host galaxy properties deduced for non-active galaxies. Therefore, despite the extreme power of its radio source and the quasar-like luminosity of its AGN, the black hole in Cygnus A is not unusually massive considering theluminosity of its host galaxy. Indeed, the estimated mass of the black hole in Cygnus A is similar to that inferred for the supermassive black hole in the FRI radio galaxy M87, despite the fact that the AGN and radio jets of Cygnus A are 2 -- 3 orders of magnitude more powerful.Comment: 17 pages, 12 figure