Deconstructing Approximate Offsets

We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using CGAL, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter \delta; its running time additionally depends on \delta. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.Comment: 18 pages, 11 figures, previous version accepted at SoCG 2011, submitted to DC

Deconstructing the Antlia cluster core

The present literature does not give a satisfactory answer to the question about the nature of the "Antlia galaxy cluster". The radial velocities of galaxies found in the region around the giant ellipticals NGC 3258/3268 range from about 1000 km/s to 4000 km/s. We characterise this region and its possible kinematical and population substructure. We have obtained VLT--VIMOS multi-object spectra of the galaxy population in the inner part of the Antlia cluster and measure radial velocities for 45 potential members. We supplement our galaxy sample with literature data, ending up with 105 galaxy velocities. We find a large radial velocity dispersion for the entire sample as reported in previous papers. However, we find three groups at about 1900 km/s, 2800 km/s, and 3700 km/s, which we interpret as differences in the recession velocities rather than peculiar velocities. The high radial velocity dispersion of galaxies in the Antlia region reflects a considerable extension along the line of sight.Comment: 11 pages, 7 figures, accepted in A&

Holographic Electroweak Symmetry Breaking from D-branes

We observe several interesting phenomena in a technicolor-like model of electroweak symmetry breaking based on the D4-D8-D8bar system of Sakai and Sugimoto. The benefit of holographic models based on D-brane configurations is that both sides of the holographic duality are well understood. We find that the lightest technicolor resonances contribute negatively to the Peskin-Takeuchi S-parameter, but heavy resonances do not decouple and lead generically to large, positive values of S, consistent with standard estimates in QCD-like theories. We study how the S parameter and the masses and decay constants of the vector and axial-vector techni-resonances vary over a one-parameter family of D8-brane configurations. We discuss possibilities for the consistent truncation of the theory to the first few resonances and suggest some generic predictions of stringy holographic technicolor models.Comment: REVTeX, 25 pages, 8 eps figures, version published in PR

Probing Outflows in z= 1~2 Galaxies through FeII/FeII* Multiplets

We report on a study of the 2300-2600\AA FeII/FeII* multiplets in the rest-UV spectra of star-forming galaxies at 1.0<z<2.6 as probes of galactic-scale outflows. We extracted a mass-limited sample of 97 galaxies at z~1.0-2.6 from ultra-deep spectra obtained during the GMASS spetroscopic survey in the GOODS South field with the VLT and FORS2. We obtain robust measures of the rest equivalent width of the FeII absorption lines down to a limit of W_r>1.5 \AA and of the FeII* emission lines to W_r>0.5 \AA. Whenever we can measure the systemic redshift of the galaxies from the [OII] emission line, we find that both the FeII and MgII absorption lines are blueshifted, indicative that both species trace gaseous outflows. We also find, however, that the FeII gas has generally lower outflow velocity relative to that of MgII. We investigate the variation of FeII line profiles as a function of the radiative transfer properties of the lines, and find that transitions with higher oscillator strengths are more blueshifted in terms of both line centroids and line wings. We discuss the possibility that FeII lines are suppressed by stellar absorptions. The lower velocities of the FeII lines relative to the MgII doublet, as well as the absence of spatially extended FeII* emission in 2D stacked spectra, suggest that most clouds responsible for the FeII absorption lie close (3~4 kpc) to the disks of galaxies. We show that the FeII/FeII* multiplets offer unique probes of the kinematic structure of galactic outflows.Comment: 53 pages, 22 Figures, accepted for publication in ApJ, revised according to referee comment

Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters

We test the performance of our analysis technique for integrated-light spectra by applying it to seven well-studied Galactic GCs that span a wide range of metallicities. Integrated-light spectra were obtained by scanning the slit of the UVES spectrograph on the ESO Very Large Telescope across the half-light diameters of the clusters. We modelled the spectra using resolved HST colour-magnitude diagrams (CMDs), as well as theoretical isochrones, in combination with standard stellar atmosphere and spectral synthesis codes. The abundances of Fe, Na, Mg, Ca, Ti, Cr, and Ba were compared with literature data for individual stars in the clusters. The typical differences between iron abundances derived from our integrated-light spectra and those compiled from the literature are less than 0.1 dex. A larger difference is found for one cluster (NGC 6752), and is most likely caused primarily by stochastic fluctuations in the numbers of bright red giants within the scanned area. As expected, the alpha-elements (Ca, Ti) are enhanced by about 0.3 dex compared to the Solar-scaled composition, while the [Cr/Fe] ratios are close to Solar. When using up-to-date line lists, our [Mg/Fe] ratios also agree well with literature data. Our [Na/Fe] ratios are, on average, 0.08-0.14 dex lower than average values quoted in the literature, and our [Ba/Fe] ratios may be overestimated by 0.20-0.35 dex at the lowest metallicities. We find that analyses based on theoretical isochrones give very similar results to those based on resolved CMDs. Overall, the agreement between our integrated-light abundance measurements and the literature data is satisfactory. Refinements of the modelling procedure, such as corrections for stellar evolutionary and non-LTE effects, might further reduce some of the remaining offsets.Comment: 35 pages, 16 figures, accepted for A&

A 2MASS All-Sky View of the Sagittarius Dwarf Galaxy: Variation of the Metallicity Distribution Function Along the Sagittarius Stream

We present reliable measurements of the metallicity distribution function (MDF) at different points along the tidal stream of the Sagittarius (Sgr) dwarf spheroidal (dSph) galaxy, based on high resolution, echelle spectroscopy of candidate M giant members of the Sgr system. The Sgr MDF is found to evolve significantly from a median [Fe/H] ~-0.4 in the core to ~-1.1 dex over a Sgr leading arm length representing ~2.5-3.0 Gyr of dynamical (i.e. tidal stripping) age. This is direct evidence that there can be significant chemical differences between current dSph satellites and the bulk of the stars they have contributed to the halo. Our results suggest that Sgr experienced a significant change in binding energy over the past several Gyr, which has substantially decreased its tidal boundary across a radial range over which there must have been a significant metallicity gradient in the progenitor galaxy. By accounting for MDF variation along the debris arms, we approximate the MDF Sgr would have had several Gyr ago. We also analyze the MDF of a moving group of M giants we previously discovered towards the North Galactic Cap having opposite radial velocities to the infalling Sgr leading arm stars there and propose that most of these represent Sgr trailing arm stars overlapping the Sgr leading arm in this part of the sky. If so, these trailing arm stars further demonstrate the strong MDF evolution within the Sgr stream.Comment: The new version is a much-expanded version moved from ApJL to ApJ and will appear in Dec. 1 editio