A new test for the Galactic formation and evolution -- prediction for the orbital eccentricity distribution of the halo stars

We present theoretical calculations for the differential distribution of stellar orbital eccentricity in a galaxy halo, assuming that the stars constitute a spherical, collisionless system in dynamical equilibrium with a dark matter halo. In order to define the eccentricity e of a halo star for given energy E and angular momentum L, we adopt two types of gravitational potential, such as an isochrone potential and a Navarro-Frenk-White potential, that could form two ends covering in-between any realistic potential of dark matter halo. Based on a distribution function of the form f(E,L) that allows constant anisotropy in velocity dispersions characterized by a parameter \beta, we find that the eccentricity distribution is a monotonically increasing function of e for the case of highly radially anisotropic velocity dispersions (\beta > 0.6), while showing a hump-like shape for the cases from radial through tangential velocity anisotropy (\beta < 0.6). We also find that when the velocity anisotropy agrees with that observed for the Milky Way halo stars (\beta = 0.5-0.7), a nearly linear eccentricity distribution of N(e) \alpha e results at e < 0.7, largely independent of the potential adopted. Our theoretical eccentricity distribution would be a vital tool of examining how far out in the halo the dynamical equilibrium has been achieved, through comparison with kinematics of halo stars sampled at greater distances. Given that large surveys of the SEGUE and Gaia projects would be in progress, we discuss how our results would serve as a new guide in exploring the formation and evolution of the Milky Way halo.Comment: 13 pages, 7 figure

The symmetries and scaling of tidal tails in galaxies

(Abriged) We present analytic models for the formation and evolution of tidal tails and related structures following impulsive disturbances in galaxy collisions. Since the epicyclic approximation is not valid for large radial excursions, we use orbital equations of the form we call p-ellipses. These have been shown to provide accurate representations of orbits in power-law halo potentials. In the case of a purely tidal disturbance the resulting tidal tails have simple structure. Scalings for their maximum lengths and other characteristics as functions of the tidal amplitude and the exponent of the power-law potentials are described. The analytic model shows that azimuthal caustics (orbit crossing zones) are produced generically in these tails at a fixed azimuth relative to the point of closest approach. Long tails, with high order caustics at their base are also produced at larger amplitudes. The analysis is extended to nonlinear disturbances and multiple encounters, which break the symmetries of tidal perturbations. As the strength of the nonlinear terms is varied the structure of the resulting forms varies from symmetric tails to one-armed plumes. Cases with two or more impulse disturbances are also considered as the simplest analytic models distinguishing between prograde and retrograde encounters. A specific mechanism for the formation of tidal dwarf galaxies at the end of tails is suggested as a consequence of resonance effects in prolonged encounters. Qualitative comparisons to Arp Atlas systems suggest that the limiting analytic cases are realized in real systems. We identify a few Arp systems which may have swallowtail caustics, where dissipative gas streams converge and trigger star formation. UV and optical images reveal luminous knots of young stars at these 'hinge clump' locations.Comment: MNRAS accepted, 24 pages, 21 figure

Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model

We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel characterization takes effect at the level of the microcanonical and canonical equilibrium distributions of states. For this reason it may be viewed as a statistical characterization of nonequivalent ensembles which extends and complements the common thermodynamic characterization of nonequivalent ensembles based on nonconcave anomalies of the microcanonical entropy. By computing numerically both the microcanonical and canonical sets of equilibrium distributions of states of the BEG model, we show that for values of the mean energy where the microcanonical entropy is nonconcave, the microcanonical distributions of states are nowhere realized in the canonical ensemble. Moreover, we show that for values of the mean energy where the microcanonical entropy is strictly concave, the equilibrium microcanonical distributions of states can be put in one-to-one correspondence with equivalent canonical equilibrium distributions of states. Our numerical computations illustrate general results relating thermodynamic and statistical equivalence and nonequivalence of ensembles proved by Ellis, Haven, and Turkington [J. Stat. Phys. 101, 999 (2000)].Comment: 13 pages, 4 figures, minor typos corrected and one reference adde

Partial equivalence of statistical ensembles and kinetic energy

The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore, the configurational microcanonical entropy is a smooth function, whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble. In the presence of a standard kinetic energy contribution, partial equivalence is removed and a nonanalyticity arises also microcanonically. Hence in contrast to the common belief, kinetic energy, even though a quadratic form in the momenta, has a non-trivial effect on the thermodynamic behaviour. As a by-product we present the microcanonical solution of the mean-field spherical model with kinetic energy for finite and infinite system sizes.Comment: 21 pages, 11 figure

Negative magnetic susceptibility and nonequivalent ensembles for the mean-field ϕ4\phi^4 spin model

We calculate the thermodynamic entropy of the mean-field $\phi^4$ spin model in the microcanonical ensemble as a function of the energy and magnetization of the model. The entropy and its derivative are obtained from the theory of large deviations, as well as from Rugh's microcanonical formalism, which is implemented by computing averages of suitable observables in microcanonical molecular dynamics simulations. Our main finding is that the entropy is a concave function of the energy for all values of the magnetization, but is nonconcave as a function of the magnetization for some values of the energy. This last property implies that the magnetic susceptibility of the model can be negative when calculated microcanonically for fixed values of the energy and magnetization. This provides a magnetization analog of negative heat capacities, which are well-known to be associated in general with the nonequivalence of the microcanonical and canonical ensembles. Here, the two ensembles that are nonequivalent are the microcanonical ensemble in which the energy and magnetization are held fixed and the canonical ensemble in which the energy and magnetization are fixed only on average by fixing the temperature and magnetic field.Comment: 14 pages, 4 figures, 2 appendices, REVTeX

Exact Optics: A unification of optical telescope design

A perfect focus telescope is one in which all rays parallel to the axis meet at a point and give equal magnification there. It is shown that these two conditions define the shapes of both primary and secondary mirrors. Apart from scale, the solution depends upon two parameters, $s$, which gives the mirror separation in terms of the effective focal length, and $K$, which gives the relative position of the final focus in that unit. The two conditions ensure that the optical systems have neither spherical aberration nor coma, no matter how fast the $f$ ratio. All known coma--free systems emerge as approximate special cases. In his classical paper, K. Schwarzschild studied all two mirror systems whose profiles were conic sections. We make no such a priori shape conditions but demand a perfect focus and solve for the mirrors' shapes.Comment: 11 pages, LaTex ([alleqno,epsfig]{mn}), 7 Figures (eps), accepted by MNRA

Identification of Moving Groups and Member Selection using Hipparcos Data

A new method to identify coherent structures in velocity space --- moving groups --- in astrometric catalogues is presented: the Spaghetti method. It relies on positions, parallaxes, and proper motions and is ideally suited to search for moving groups in the Hipparcos Catalogue. No radial velocity information is required. The method has been tested extensively on synthetic data, and applied to the Hipparcos measurements for the Hyades and IC2602 open clusters. The resulting lists of members agree very well with those of Perryman et al. for the Hyades and of Whiteoak and Braes for IC2602.Comment: 14 pages, 9 encapsulated postscript figures, LaTeX using mn.sty; accepted for publication in the MNRA

Mapping the Galactic Halo with blue horizontal branch stars from the 2dF quasar redshift survey

We use 666 blue horizontal branch (BHB) stars from the 2Qz redshift survey to map the Galactic halo in four dimensions (position, distance and velocity). We find that the halo extends to at least 100 kpc in Galactocentric distance, and obeys a single power-law density profile of index ~-2.5 in two different directions separated by 150 degrees on the sky. This suggests that the halo is spherical. Our map shows no large kinematically coherent structures (streams, clouds or plumes) and appears homogeneous. However, we find that at least 20% of the stars in the halo reside in substructures and that these substructures are dynamically young. The velocity dispersion profile of the halo appears to increase towards large radii while the stellar velocity distribution is non Gaussian beyond 60 kpc. We argue that the outer halo consists of a multitude of low luminosity overlapping tidal streams from recently accreted objects.Comment: Accepted for publication in the Astrophysical Journal Requires emulateapj to proces

Effects of galactic dark halo rotation on WIMP direct detection

The effects of a possible rotation of the galactic dark halo on the calculation of the direct detection rates for particle dark matter are analyzed, with special attention to the extraction of the upper limits on the WIMP--nucleon scalar cross section from the experimental data. We employ a model of dark halo rotation which describes the maximal possible effects. For WIMP masses above 50 GeV, the upper limit exclusion plot is modified by less than a factor of two when rotation is included. For lighter masses the effect can be stronger, suggesting the necessity to develop specific models of halo rotation in order to provide more accurate conclusions.Comment: 14 pages, 7 figures included as PS file

Superhumps: Confronting Theory with Observation

We review the theory and observations related to the ``superhump'' precession of eccentric accretion discs in close binary sytems. We agree with earlier work, although for different reasons, that the discrepancy between observation and dynamical theory implies that the effect of pressure in the disc cannot be neglected. We extend earlier work that investigates this effect to include the correct expression for the radius at which resonant orbits occur. Using analytic expressions for the accretion disc structure, we derive a relationship between the period excess and mass-ratio with the pressure effects included. This is compared to the observed data, recently derived results for detailed integration of the disc equations and the equivalent empirically derived relations and used to predict values for the mass ratio based on measured values of the period excess for 88 systems.Comment: 11 pages, 7 figures, 4 tables, accepted for publication in MNRA