Symmetry as a sufficient condition for a finite flex

We show that if the joints of a bar and joint framework $(G,p)$ are positioned as `generically' as possible subject to given symmetry constraints and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous non-symmetric methods.Comment: 26 pages, 10 figure

About the Algebraic Solutions of Smallest Enclosing Cylinders Problems

Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication (previous version is a copy of the original one of 2010

The Nuclear Gas Dynamics and Star Formation of Markarian 231

We report adaptive optics H- and K-band spectroscopy of the inner few arcsec of the luminous merger/ULIRG/QSO Mkn231, at spatial resolutions as small as 0.085". For the first time we have been able to resolve the active star forming region close to the AGN using stellar absorption features, finding that its luminosity profile is well represented by an exponential function with a disk scale length 0.18-0.24" (150-200pc), and implying that the stars exist in a disk rather than a spheroid. The stars in this region are also young (10-100Myr), and it therefore seems likely that they have formed in situ in the gas disk, which itself resulted from the merger. The value of the stellar velocity dispersion is a result of the large mass surface density of the disk. The stars in this region have a combined mass of at least 1.6x10^9M_sun, and account for 25-40% of the bolometric luminosity of the entire galaxy. We have detected the 2.12um 1-0S(1) H_2 and 1.64um [FeII] lines out to radii exceeding 0.5". The kinematics for the two lines are very similar to each other as well as to the stellar kinematics, and broadly consistent with the nearly face-on rotating disk reported in the literature and based on interferometric CO1-0 and CO2-1 measurements of the cold gas. However, they suggest a more complex situation in which the inner 0.2-0.3" (200pc) is warped out of its original disk plane. Such a scenario is supported by other observations.Comment: accepted for publication in ApJ; abstract given here is slightly shortene

Bar Diagnostics in Edge-On Spiral Galaxies. III. N-Body Simulations of Disks

Present in over 45% of local spirals, boxy and peanut-shaped bulges are generally interpreted as edge-on bars and may represent a key phase in the evolution of bulges. Aiming to test such claims, the kinematic properties of self-consistent 3D N-body simulations of bar-unstable disks are studied. Using Gauss-Hermite polynomials to describe the stellar kinematics, a number of characteristic bar signatures are identified in edge-on disks: 1) a major-axis light profile with a quasi-exponential central peak and a plateau at moderate radii (Freeman Type II profile); 2) a ``double-hump'' rotation curve; 3) a sometime flat central velocity dispersion peak with a plateau at moderate radii and occasional local central minimum and secondary peak; 4) an h3-V correlation over the projected bar length. All those kinematic features are spatially correlated and can easily be understood from the orbital structure of barred disks. They thus provide a reliable and easy-to-use tool to identify edge-on bars. Interestingly, they are all produced without dissipation and are increasingly realized to be common in spirals, lending support to bar-driven evolution scenarios for bulge formation. So called ``figure-of-eight'' position-velocity diagrams are never observed, as expected for realistic orbital configurations. Although not uniquely related to triaxiality, line-of-sight velocity distributions with a high velocity tail (i.e. an h3-V correlation) appear as particularly promising tracers of bars. The stellar kinematic features identified grow in strength as the bar evolves and vary little for small inclination variations. Many can be used to trace the bar length. Comparisons with observations are encouraging and support the view that boxy and peanut-shaped bulges are simply thick bars viewed edge-on.Comment: 32 pages, 4 figures, AASTeX preprint. Revised following referees' comments. Now accepted for publication in The Astrophysical Journal. We strongly suggest you download the version with full resolution figures at http://www.astro.columbia.edu/~bureau/Publications/Nbody_ApJ04.ps.g

A Search for Kinematic Evidence of Radial Gas Flows in Spiral Galaxies

CO and HI velocity fields of seven nearby spiral galaxies, derived from radio-interferometric observations, are decomposed into Fourier components whose radial variation is used to search for evidence of radial gas flows. Additional information provided by optical or near-infrared isophotes is also considered, including the relationship between the morphological and kinematic position angles. To assist in interpreting the data, we present detailed modeling that demonstrates the effects of bar streaming, inflow, and a warp on the observed Fourier components. We find in all of the galaxies evidence for either elliptical streaming or a warped disk over some range in radius, with deviations from pure circular rotation at the level of ~20-60 km/s. Evidence for kinematic warps is observed in several cases well inside R_{25}. No unambiguous evidence for radial inflows is seen in any of the seven galaxies, and we are able to place an upper limit of ~5-10 km/s (3-5% of the circular speed) on the magnitude of any radial inflow in the inner regions of NGC 4414, 5033 and 5055. We conclude that the inherent non-axisymmetry of spiral galaxies is the greatest limitation to the direct detection of radial inflows.Comment: 22 emulateapj pages with bitmapped colour figures, to appear in ApJ (April 2004). For full resolution figures go to http://www.atnf.csiro.au/people/twong/preprints

Breaking the Disk/Halo Degeneracy with Gravitational Lensing

The degeneracy between the disk and the dark matter contribution to galaxy rotation curves remains an important uncertainty in our understanding of disk galaxies. Here we discuss a new method for breaking this degeneracy using gravitational lensing by spiral galaxies, and apply this method to the spiral lens B1600+434 as an example. The combined image and lens photometry constraints allow models for B1600+434 with either a nearly singular dark matter halo, or a halo with a sizable core. A maximum disk model is ruled out with high confidence. Further information, such as the circular velocity of this galaxy, will help break the degeneracies. Future studies of spiral galaxy lenses will be able to determine the relative contribution of disk, bulge, and halo to the mass in the inner parts of galaxies.Comment: Replaced with minor revisions, a typo fixed, and reference added; 21 pages, 8 figures, ApJ accepte

Feedback in the Antennae Galaxies (NGC 4038/9): I. High-Resolution Infrared Spectroscopy of Winds from Super Star Clusters

We present high-resolution (R ~ 24,600) near-IR spectroscopy of the youngest super star clusters (SSCs) in the prototypical starburst merger, the Antennae Galaxies. These SSCs are young (3-7 Myr old) and massive (10^5 - 10^7 M_sun for a Kroupa IMF) and their spectra are characterized by broad, extended Br-gamma emission, so we refer to them as emission-line clusters (ELCs) to distinguish them from older SSCs. The Brgamma lines of most ELCs have supersonic widths (60-110 km/s FWHM) and non-Gaussian wings whose velocities exceed the clusters' escape velocities. This high-velocity unbound gas is flowing out in winds that are powered by the clusters' massive O and W-R stars over the course of at least several crossing times. The large sizes of some ELCs relative to those of older SSCs may be due to expansion caused by these outflows; many of the ELCs may not survive as bound stellar systems, but rather dissipate rapidly into the field population. The observed tendency of older ELCs to be more compact than young ones is consistent with the preferential survival of the most concentrated clusters at a given age.Comment: Accepted to Ap