Constraining the History of the Sagittarius Dwarf Galaxy Using Observations of its Tidal Debris

We present a comparison of semi-analytic models of the phase-space structure of tidal debris with observations of stars associated with the Sagittarius dwarf galaxy (Sgr). We find that many features in the data can be explained by these models. The properties of stars 10-15 degrees away from the center of Sgr --- in particular, the orientation of material perpendicular to Sgr's orbit (c.f. Alard 1996) and the kink in the velocity gradient (Ibata et al 1997) --- are consistent with those expected for unbound material stripped during the most recent pericentric passage ~50 Myrs ago. The break in the slope of the surface density seen by Mateo, Olszewski & Morrison (1998) at ~ b=-35 can be understood as marking the end of this material. However, the detections beyond this point are unlikely to represent debris in a trailing streamer, torn from Sgr during the immediately preceding passage ~0.7 Gyrs ago, but are more plausibly explained by a leading streamer of material that was lost more that 1 Gyr ago and has wrapped all the way around the Galaxy. The observations reported in Majewski et al (1999) also support this hypothesis. We determine debris models with these properties on orbits that are consistent with the currently known positions and velocities of Sgr in Galactic potentials with halo components that have circular velocities v_circ=140-200 km/s. The best match to the data is obtained in models where Sgr currently has a mass of ~10^9 M_sun and has orbited the Galaxy for at least the last 1 Gyr, during which time it has reduced its mass by a factor of 2-3, or luminosity by an amount equivalent to ~10% of the total luminosity of the Galactic halo. These numbers suggest that Sgr is rapidly disrupting and unlikely to survive beyond a few more pericentric passages.Comment: 19 pages, 5 figures, accepted to Astronomical Journa

Two-Time Physics with gravitational and gauge field backgrounds

It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained by generalizing the worldline formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d+2 dimensions to (d-1) +1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target d+2 dimensional spacetime. The gravitational background obeys a null homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher d+2 dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden.Comment: Latex, 19 pages, references adde

Conformal Symmetry and Duality between Free Particle, H-atom and Harmonic Oscillator

We establish a duality between the free massless relativistic particle in d dimensions, the non-relativistic hydrogen atom (1/r potential) in (d-1) space dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass given as the lightcone momentum of an additional dimension. The duality is in the sense that the classical action of these systems are gauge fixed forms of the same worldline gauge theory action at the classical level, and they are all described by the same unitary representation of the conformal group SO(d,2) at the quantum level. The worldline action has a gauge symmetry Sp(2) which treats canonical variables (x,p) as doublets and exists only with a target spacetime that has d spacelike dimensions and two timelike dimensions. This spacetime is constrained due to the gauge symmetry, and the various dual solutions correspond to solutions of the constraints with different topologies. For example, for the H-atom the two timelike dimensions X^{0'},X^{0} live on a circle. The model provides an example of how realistic physics can be viewed as existing in a larger covariant space that includes two timelike coordinates, and how the covariance in the larger space unifies different looking physics into a single system.Comment: Latex, 23 pages, minor improvements. In v3 a better gauge choice for u for the H-atom is made; the results are the sam

Gauge symmetry in phase space with spin, a basis for conformal symmetry and duality among many interactions

We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space (X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime with two times X^0,, X^0', unifies many physical systems which ordinarily are described by a 1-time formulation. Different systems of 1-time physics emerge by choosing gauges that embed ordinary time in d+2 dimensions in different ways. The embeddings have different topology and geometry for the choice of time among the d+2 dimensions. Thus, 2-time physics unifies an infinite number of 1-time physical interacting systems, and establishes a kind of duality among them. One manifestation of the two times is that all of these physical systems have the same quantum Hilbert space in the form of a unique representation of SO(d,2) with the same Casimir eigenvalues. By changing the number n of spinning degrees of freedom the gauge group changes to OSp(n/2). Then the eigenvalue of the Casimirs of SO(d,2) depend on n and then the content of the 1-time physical systems that are unified in the same representation depend on n. The models we study raise new questions about the nature of spacetime.Comment: Latex, 42 pages. v2 improvements in AdS section. In v3 sec.6.2 is modified; the more general potential is limited to a smaller clas

A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

The ACS Survey of Galactic Globular Clusters: M54 and Young Populations in the Sagittarius Dwarf Spheroidal Galaxy

We present new Hubble Space Telescope photometry of the massive globular cluster M54 (NGC 6715) and the superposed core of the tidally disrupted Sagittarius (Sgr) dSph galaxy as part of the ACS Survey of Galactic Globular Clusters. Our deep (F606W~26.5), high-precision photometry yields an unprecedentedly detailed color-magnitude diagram showing the extended blue horizontal branch and multiple main sequences of the M54+Sgr system. The distance and reddening to M54 are revised usingboth isochrone and main-sequence fitting to (m-M)_0=17.27 and E(B-V)=0.15. Preliminary assessment finds the M54+Sgr field to be dominated by the old metal-poor populations of Sgr and the globular cluster. Multiple turnoffs indicate the presence of at least two intermediate-aged star formation epochs with 4 and 6 Gyr ages and [Fe/H]=-0.4 to -0.6. We also clearly show, for the first time, a prominent, 2.3 Gyr old Sgr population of near-solar abundance. A trace population of even younger (0.1-0.8 Gyr old), more metal-rich ([Fe/H]\sim0.6) stars is also indicated. The Sgr age-metallicity relation is consistent with a closed-box model and multiple (4-5) star formation bursts over the entire life of the satellite, including the time since Sgr began disrupting.Comment: Accepted to ApJ Letter; 11 pages, 2 figures; figure 1 uploaded as jpg; paper in ApJ format with full-resolution figures available at: http://www.astro.ufl.edu/~ata/public_hstgc/paperIV/paperIV.p

Generic Twistless Bifurcations

We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurcation that creates a ``twistless'' torus. At this bifurcation, the twist, which is the derivative of the rotation number with respect to the action, vanishes. The twistless torus moves outward after it is created, and eventually collides with the saddle-center bifurcation that creates the period three orbits. The existence of the twistless bifurcation is responsible for the breakdown of the nondegeneracy condition required in the proof of the KAM theorem for flows or the Moser twist theorem for maps. When the twistless torus has a rational rotation number, there are typically reconnection bifurcations of periodic orbits with that rotation number.Comment: 29 pages, 9 figure

Spherically symmetric spacetimes in massive gravity

We explore spherically symmetric stationary solutions, generated by ``stars'' with regular interiors, in purely massive gravity. We reexamine the claim that the resummation of non-linear effects can cure, in a domain near the source, the discontinuity exhibited by the linearized theory as the mass m of the graviton tends to zero. First, we find analytical difficulties with this claim, which appears not to be robust under slight changes in the form of the mass term. Second, by numerically exploring the inward continuation of the class of asymptotically flat solutions, we find that, when m is ``small'', they all end up in a singularity at a finite radius, well outside the source, instead of joining some conjectured ``continuous'' solution near the source. We reopen, however, the possibility of reconciling massive gravity with phenomenology by exhibiting a special class of solutions, with ``spontaneous symmetry breaking'' features, which are close, near the source, to general relativistic solutions and asymptote, for large radii, a de Sitter solution of curvature ~m^2.Comment: 57 pages, references addde

The effect of relationship status on communicating emotions through touch

Research into emotional communication to date has largely focused on facial and vocal expressions. In contrast, recent studies by Hertenstein, Keltner, App, Bulleit, and Jaskolka (2006) and Hertenstein, Holmes, McCullough, and Keltner (2009) exploring nonverbal communication of emotion discovered that people could identify anger, disgust, fear, gratitude, happiness, love, sadness and sympathy from the experience of being touched on either the arm or body by a stranger, without seeing the touch. The study showed that strangers were unable to communicate the self-focused emotions embarrassment, envy and pride, or the universal emotion surprise. Literature relating to touch indicates that the interpretation of a tactile experience is significantly influenced by the relationship between the touchers (Coan, Schaefer, & Davidson, 2006). The present study compared the ability of romantic couples and strangers to communicate emotions solely via touch. Results showed that both strangers and romantic couples were able to communicate universal and prosocial emotions, whereas only romantic couples were able to communicate the self-focused emotions envy and pride