Root Cover Pebbling on Graphs

Consider a graph, G, with pebbles on its vertices. A pebbling move is defined to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The cover pebbling number of a graph, γ(G), is the minimum number of pebbles such that, given any configuration of γ(G) pebbles on the vertices of G, pebbling moves can be used to place one pebble on each vertex of G. We define the root vertex of a graph and fix an initial configuration of pebbles on G where we place all pebbles on the root vertex of G. We define the root cover pebbling number, R(G), of a graph to be the minimum number of pebbles needed so that, if R(G) pebbles are placed on the root vertex, pebbling moves can be used to place one pebble on each vertex. We obtain formulas for root cover pebbling numbers of two types of graphs. We use these formulas to compare the cover pebbling number with the root cover pebbling number of paths, stars and fuses. We also determine ways to minimize the root cover pebbling number of a graph

IUE observations of the 1987 superoutburst of the dwarf nova Z Cha

Low resolution IUE observations of the dwarf nova Z Cha during superoutburst are presented. These cover most of the development of the outburst and have sufficient time resolution to probe continuum and line behavior on orbital phase. The observed modulation on this phase is very similar to that observed in the related object OY Car. The results imply the presence of a cool spot on the edge of the edge of the accretion disk, which periodically occults the brighter inner disk. Details of the line behavior suggest that the line originated in an extended wind-emitting region. In contrast to archive spectra obtained in normal outburst, the continuum is fainter and redder, indicating that the entire superoutburst disk may be geometrically thicker than during a normal outburst

Identification of a Class of Low-Mass Asymptotic Giant Branch Stars Struggling to Become Carbon Stars in the Magellanic Clouds

We have identified a new class of Asymptotic Giant Branch (AGB) stars in the Small and Large Magellanic Clouds (SMC/LMC) using optical to infrared photometry, light curves, and optical spectroscopy. The strong dust production and long-period pulsations of these stars indicate that they are at the very end of their AGB evolution. Period-mass-radius relations for the fundamental-mode pulsators give median current stellar masses of 1.14 M_sun in the LMC and 0.94 M_sun in the SMC (with dispersions of 0.21 and 0.18 M_sun, respectively), and models suggest initial masses of <1.5 M_sun and <1.25 M_sun, respectively. This new class of stars includes both O-rich and C-rich chemistries, placing the limit where dredge-up allows carbon star production below these masses. A high fraction of the brightest among them should show S star characteristics indicative of atmospheric C/O ~ 1, and many will form O-rich dust prior to their C-rich phase. These stars can be separated from their less-evolved counterparts by their characteristically red J-[8] colors.Comment: 16 pages, 18 figures, accepted for publication in Ap

Testing Binary Population Synthesis Models with Hot Subdwarfs

Models of binary star interactions have been successful in explaining the origin of field hot subdwarf (sdB) stars in short period systems, but longer-period systems that formed via Roche-lobe overflow (RLOF) mass transfer from the present sdB to its companion have received less attention. We map sets of initial binaries into present-day binaries that include sdBs and main-sequence stars, distinguishing "observable" sdBs from "hidden" ones. We aim to find out whether (1) the existing catalogues of sdBs are sufficiently fair samples of all the kinds of sdB binaries that theory predicts; or instead whether (2) large predicted hidden populations mandate the construction of new catalogues, perhaps using wide-field imaging surveys such as 2MASS, SDSS, and Galex. We also report on a pilot study to identify hidden subdwarfs, using 2MASS and GALEX data.Comment: 3 pages with 2 figures. Uses AIP style files. To appear in Future Directions in Ultraviolet Astronomy, ed. Michael E. VanSteenberg (AIP Conf Proc

Far-UV FUSE spectroscopy of the OVI resonance doublet in Sand2 (WO)

We present Far-Ultraviolet Spectroscopic Explorer (FUSE) spectroscopy of Sand 2, a LMC WO-type Wolf-Rayet star, revealing the OVI resonance P Cygni doublet at 1032-38A. These data are combined with HST/FOS ultraviolet and Mt Stromlo 2.3m optical spectroscopy, and analysed using a spherical, non-LTE, line-blanketed code. Our study reveals exceptional stellar parameters: T*=150,000K, v_inf=4100 km/s, log (L/Lo)=5.3, and Mdot=10^-5 Mo/yr if we adopt a volume filling factor of 10%. Elemental abundances of C/He=0.7+-0.2 and O/He=0.15(-0.05+0.10) by number qualitatively support previous recombination line studies. We confirm that Sand 2 is more chemically enriched in carbon than LMC WC stars, and is expected to undergo a supernova explosion within the next 50,000 yr.Comment: 17 pages, 4 figures, AASTeX preprint format. This paper will appear in a special issue of ApJ Letters devoted to the first scientific results from the FUSE missio