HST Images of a Galaxy Group at z=2.81, and the Sizes of Damped Lyman Alpha Galaxies

We present HST WFPC2 observations in three bands (F450W, F467M and F814W) of a group of three galaxies at z=2.8 discovered in a ground-based narrow-band search for Lyman alpha emission near the z=2.8 quasar PKS0528-250. One of the galaxies is a damped (DLA) absorber and these observations bear on the relation between the DLA clouds and the Lyman-break galaxies and the stage in the evolution of galaxies they represent. We describe a procedure for combining the undersampled WFPC2 images pointed on a sub-pixel grid, which largely recovers the full sampling of the WFPC2 point spread function (psf). These three galaxies have similar properties to the Lyman-break galaxies except that they have strong Lyman alpha emission. The three galaxies are detected in all three bands, with average B~26, I~25. Two of the galaxies are compact with intrinsic (i.e. after correcting for the effect of the psf) half-light radii of ~0.1 arcsec (~0.4/h kpc, q_o=0.5). The third galaxy comprises two similarly compact components separated by 0.3 arcsec. The HST images and a new ground-based Lyman alpha image of the field provide evidence that the three galaxies are more extended in the light of Lyman alpha than in the continuum. The measured impact parameters for this DLA galaxy (1.17 arcsec), for a second confirmed system, and for several candidates, provide a preliminary estimate of the cross-section-weighted mean radius of the DLA gas clouds at z~3 of less than 13/h kpc, for q_o=0.5. Given the observed sky covering factor of the absorbers this implies that for q_o=0.5 the space density of DLA clouds at these redshifts is more than five times the space density of spiral galaxies locally, with the actual ratio probably considerably greater. For q_o=0.0 there is no evidence as yet that DLA clouds are more common than spiral galaxies locally.Comment: 11 pages, LaTeX, 6 Figures total (4 colour GIF-format, 2 PostScript), accepted for publication in MNRA

Macroscopic-Microscopic Mass Models

We discuss recent developments in macroscopic-microscopic mass models, including the 1992 finite-range droplet model, the 1992 extended-Thomas-Fermi Strutinsky-integral model, and the 1994 Thomas-Fermi model, with particular emphasis on how well they extrapolate to new regions of nuclei. We also address what recent developments in macroscopic-microscopic mass models are teaching us about such physically relevant issues as the nuclear curvature energy, a new congruence energy arising from a greater-than-average overlap of neutron and proton wave functions, the nuclear incompressibility coefficient, and the Coulomb redistribution energy arising from a central density depression. We conclude with a brief discussion of the recently discovered rock of metastable superheavy nuclei near 272:110 that had been correctly predicted by macroscopic-microscopic models, along with a possible new tack for reaching an island near 290:110 beyond our present horizon.Comment: 10 pages. LaTeX. Presented at International Conference on Exotic Nuclei and Atomic Masses (ENAM 95), Arles, France, June 19-23, 1995. To be published in conference proceedings by Les Editions Frontieres, Gif sur Yvette, France. Seven figures not included here. PostScript version with figures available at http://t2.lanl.gov/pub/publications/publications.html or by anonymous ftp at ftp://t2.lanl.gov/pub/publications/enam9

Self-shrinkers with a rotational symmetry

In this paper we present a new family of non-compact properly embedded, self-shrinking, asymptotically conical, positive mean curvature ends $\Sigma^n\subseteq\mathbb{R}^{n+1}$ that are hypersurfaces of revolution with circular boundaries. These hypersurface families interpolate between the plane and half-cylinder in $\mathbb{R}^{n+1}$, and any rotationally symmetric self-shrinking non-compact end belongs to our family. The proofs involve the global analysis of a cubic-derivative quasi-linear ODE. We also prove the following classification result: a given complete, embedded, self-shrinking hypersurface of revolution $\Sigma^n$ is either a hyperplane $\mathbb{R}^{n}$, the round cylinder $\mathbb{R}\times S^{n-1}$ of radius $\sqrt{2(n-1)}$, the round sphere $S^n$ of radius $\sqrt{2n}$, or is diffeomorphic to an $S^1\times S^{n-1}$ (i.e. a "doughnut" as in [Ang], which when $n=2$ is a torus). In particular for self-shrinkers there is no direct analogue of the Delaunay unduloid family. The proof of the classification uses translation and rotation of pieces, replacing the method of moving planes in the absence of isometries.Comment: Trans. Amer. Math. Soc. (2011), to appear; 23 pages, 1 figur