Detection of a Stellar Stream Behind Open Cluster NGC 188: Another Part of the Monoceros Stream

We present results from a WIYN/OPTIC photometric and astrometric survey of the field of the open cluster NGC 188 ((l,b) = (122.8\arcdeg, 22.5\arcdeg)). We combine these results with the proper-motion and photometry catalog of Platais et al. and demonstrate the existence of a stellar overdensity in the background of NGC 188. The theoretical isochrone fits to the color-magnitude diagram of the overdensity are consistent with an age between 6 and 10 Gyr and an intermediately metal poor population ([Fe/H] = -0.5 to -1.0). The distance to the overdensity is estimated to be between 10.0 and 12.6 kpc. The proper-motions indicate that the stellar population of the overdensity is kinematically cold. The distance estimate and the absolute proper motion of the overdensity agree reasonably well with the predictions of the Pe\~{n}arrubia et al. model of the formation of the Monoceros stream. Orbits for this material constructed with plausible radial-velocity values, indicate that dynamically, this material is unlikely to belong to the thick disk. Taken together, this evidence suggests that the newly-found overdensity is part of the Monoceros stream.Comment: accepted by A

Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX

Kinematics in Kapteyn's Selected Area 76: Orbital Motions Within the Highly Substructured Anticenter Stream

We have measured the mean three-dimensional kinematics of stars in Kapteyn's Selected Area (SA) 76 (l=209.3, b=26.4 degrees) that were selected to be Anticenter Stream (ACS) members on the basis of their radial velocities, proper motions, and location in the color-magnitude diagram. From a total of 31 stars ascertained to be ACS members primarily from its main sequence turnoff, a mean ACS radial velocity (derived from spectra obtained with the Hydra multi-object spectrograph on the WIYN 3.5m telescope) of V_helio = 97.0 +/- 2.8 km/s was determined, with an intrinsic velocity dispersion sigma_0 = 12.8 \pm 2.1 km/s. The mean absolute proper motions of these 31 ACS members are mu_alpha cos (delta) = -1.20 +/- 0.34 mas/yr and mu_delta = -0.78 \pm 0.36 mas/yr. At a distance to the ACS of 10 \pm 3 kpc, these measured kinematical quantities produce an orbit that deviates by ~30 degrees from the well-defined swath of stellar overdensity constituting the Anticenter Stream in the western portion of the Sloan Digital Sky Survey footprint. We explore possible explanations for this, and suggest that our data in SA 76 are measuring the motion of a kinematically cold sub-stream among the ACS debris that was likely a fragment of the same infalling structure that created the larger ACS system. The ACS is clearly separated spatially from the majority of claimed Monoceros ring detections in this region of the sky; however, with the data in hand, we are unable to either confirm or rule out an association between the ACS and the poorly-understood Monoceros structure.Comment: Accepted to ApJ. 48 pages, 20 figures, preprint forma

Energy landscape and phase transitions in the self-gravitating ring model

We apply a recently proposed criterion for the existence of phase transitions, which is based on the properties of the saddles of the energy landscape, to a simplified model of a system with gravitational interactions, referred to as the self-gravitating ring model. We show analytically that the criterion correctly singles out the phase transition between a homogeneous and a clustered phase and also suggests the presence of another phase transition, not previously known. On the basis of the properties of the energy landscape we conjecture on the nature of the latter transition

Geometry of dynamics, Lyapunov exponents and phase transitions

The Hamiltonian dynamics of classical planar Heisenberg model is numerically investigated in two and three dimensions. By considering the dynamics as a geodesic flow on a suitable Riemannian manifold, it is possible to analytically estimate the largest Lyapunov exponent in terms of some curvature fluctuations. The agreement between numerical and analytical values for Lyapunov exponents is very good in a wide range of temperatures. Moreover, in the three dimensional case, in correspondence with the second order phase transition, the curvature fluctuations exibit a singular behaviour which is reproduced in an abstract geometric model suggesting that the phase transition might correspond to a change in the topology of the manifold whose geodesics are the motions of the system.Comment: REVTeX, 10 pages, 5 PostScript figures, published versio