Radial Mixing in Galactic Discs

We show that spiral waves in galaxy discs churn the stars and gas in a manner that largely preserves the overall angular momentum distribution and leads to little increase in random motion. Changes in the angular momenta of individual stars are typically as large as ~50% over the lifetime of the disk. The changes are concentrated around the corotation radius for an individual spiral wave, but since transient waves with a wide range of pattern speeds develop in rapid succession, the entire disk is affected. This behaviour has profound consequences for the metallicity gradients with radius in both stars and gas. The ISM is also stirred by the same mechanism. We find observational support for stirring, propose a simple model for the distribution of stars over metallicity and age, and discuss other possible consequences.Comment: Accepted to appear in MNRAS, 13 pages, 16 figures, LaTeX uses mn2e.cls Minor additions to text and one extra figur

Is Galactic Structure Compatible with Microlensing Data?

We generalize to elliptical models the argument of Kuijken (1997), which connects the microlensing optical depth towards the Galactic bulge to the Galactic rotation curve. When applied to the latest value from the MACHO collaboration for the optical depth for microlensing of bulge sources, the argument implies that the Galactic bar cannot plausibly reconcile the measured values of the optical depth, the rotation curve and the local mass density. Either there is a problem with the interpretation of the microlensing data, or our line of sight to the Galactic centre is highly atypical in that it passes through a massive structure that wraps only a small distance around the Galactic centre.Comment: Submitted to ApJ Letters. 8 pages LaTeX, 3 figures. Corrected error in description of microlensing observation

Stellar Orbits and the Interstellar Gas Temperature in Elliptical Galaxies

We draw attention to the close relationship between the anisotropy parameter beta(r) for stellar orbits in elliptical galaxies and the temperature profile T(r) of the hot interstellar gas. For nearly spherical galaxies the gas density can be accurately determined from X-ray observations and the stellar luminosity density can be accurately found from the optical surface brightness. The Jeans equation and hydrostatic equilibrium establish a connection between beta(r) and T(r) that must be consistent with the observed stellar velocity dispersion. Purely optical observations of the bright elliptical galaxy NGC 4472 indicate beta(r) < 0.35 within the effective radius. However, the X-ray gas temperature profile T(r) for NGC 4472 requires significantly larger anisotropy, beta = 0.6 - 0.7, about twice the optical value. This strong preference for radial stellar orbits must be understood in terms of the formation history of massive elliptical galaxies. Conversely, if the smaller, optically determined anisotropy is indeed correct, we are led to the important conclusion that the temperature profile T(r) of the hot interstellar gas in NGC 4472 must differ from that indicated by X-ray observations, or that the hot gas is not in hydrostatic equilibrium.Comment: 6 pages (emulateapj5) with 4 figures; accepted by The Astrophysical Journa

Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are q_c=0.091(2) and q_c=0.134(3) for (3,4,6,4) and (3^4,6) Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for this model are 0.103(6), 1.596(54), 0.872(85) for (3,4,6,4) and 0.114(3), 1.632(35), 0.978(104) for (3^4,6) Archimedean lattices. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionality of the system [D_{eff}(3,4,6,4)=1.802(55) and D_{eff}(3^4,6)=1.860(34)] for these networks are reasonably close to the embedding dimension two.Comment: 6 pages, 7 figures in 12 eps files, RevTex

The Anisotropic Distribution of Galactic Satellites

We present a study of the spatial distribution of subhalos in galactic dark matter halos using dissipationless cosmological simulations of the concordance LCDM model. We find that subhalos are distributed anisotropically and are preferentially located along the major axes of the triaxial mass distributions of their hosts. The Kolmogorov-Smirnov probability for drawing our simulated subhalo sample from an isotropic distribution is P_KS \simeq 1.5 \times 10^{-4}. An isotropic distribution of subhalos is thus not the correct null hypothesis for testing the CDM paradigm. The nearly planar distribution of observed Milky Way (MW) satellites is marginally consistent (probability \simeq 0.02) with being drawn randomly from the subhalo distribution in our simulations. Furthermore, if we select the subhalos likely to be luminous, we find a distribution that is consistent with the observed MW satellites. In fact, we show that subsamples of the subhalo population with a centrally-concentrated radial distribution, similar to that of the MW dwarfs, typically exhibit a comparable degree of planarity. We explore the origin of the observed subhalo anisotropy and conclude that it is likely due to (1) preferential accretion of subhalos along filaments, often closely aligned with the major axis of the host halo, and (2) evolution of satellite orbits within the prolate, triaxial potentials typical of CDM halos. Agreement between predictions and observations requires the major axis of the outer dark matter halo of the Milky Way to be nearly perpendicular to the disk. We discuss possible observational tests of such disk-halo alignment with current large galaxy surveys.Comment: 14 pages (including appendix), 9 figures. Accepted for Publication in ApJ. Minor changes to reflect referee's comment

The Pattern Speed of the Galactic Bar

Most late-type stars in the solar neighborhood have velocities similar to the local standard of rest (LSR), but there is a clearly separated secondary component corresponding to a slower rotation and a mean outward motion. Detailed simulations of the response of a stellar disk to a central bar show that such a bi-modality is expected from outer-Lindblad resonant scattering. When constraining the run of the rotation curve by the proper motion of Sgr A* and the terminal gas velocities, the value observed for the rotation velocity separating the two components results in a value of (53+/-3)km/s/kpc for the pattern speed of the bar, only weakly dependent on the precise values for Ro and bar angle phi.Comment: 5 pages LaTeX, 2 Figs, accepted for publication in ApJ Letter

On the kinematic signature of a central Galactic bar in observed star samples

A quasi self-consistent model for a barred structure in the central regions of our Galaxy is used to calculate the signature of such a triaxial structure on the kinematical properties of star samples. We argue that, due to the presence of a velocity dispersion, such effects are much harder to detect in the stellar component than in the gas. It might be almost impossible to detect stellar kinematical evidence for a bar using only l-v diagrams, if there is no a priori knowledge of the potential. Therefore, we propose some test parameters that can easily be applied to observed star samples, and that also incorporate distances or proper motions. We discus the diagnostic power of these tests as a function of the sample size and the bar strength. We conclude that about 1000 stars would be necessary to diagnose triaxiality with some statistical confidence.Comment: 9 pages + 8 PS figures, uses aas2pp4.sty. Accepted by Ap

Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question---correlation, predictability, predictive cost, observer synchronization, and the like---induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along the way, we establish special properties of the projection operators that demonstrate how they capture the organization of subprocesses within a complex system. Circumventing the spurious infinities of alternative calculi, this leads in the sequel, Part II, to the first closed-form expressions for complexity measures, couched either in terms of the Drazin inverse (negative-one power of a singular operator) or the eigenvalues and projection operators of the appropriate transition dynamic.Comment: 24 pages, 3 figures, 4 tables; current version always at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt1.ht

Local Kinematics and the Local Standard of Rest

We re-examine the stellar kinematics of the Solar neighbourhood in terms of the velocity of the Sun with respect to the local standard of rest. We show that the classical determination of its component V_sun in the direction of Galactic rotation via Stroemberg's relation is undermined by the metallicity gradient in the disc, which introduces a correlation between the colour of a group of stars and the radial gradients of its properties. Comparing the local stellar kinematics to a chemodynamical model which accounts for these effects, we obtain (U,V,W)_sun = (11.1 +/- 0.74, 12.24 +/- 0.47, 7.25 +/-0.37) km/s, with additional systematic uncertainties of ~ (1,2,0.5) km/s. In particular, V_sun is 7 km/s larger than previously estimated. The new values of solar motion are extremely insensitive to the metallicity gradient within the disc.Comment: 5 pages, submitted to MNRA

The Fundamental Plane of Gravitational Lens Galaxies and The Evolution of Early-Type Galaxies in Low Density Environments

Most gravitational lenses are early-type galaxies in relatively low density environments -- a ``field'' rather than a ``cluster'' population. We show that field early-type galaxies with 0 < z < 1, as represented by the lens galaxies, lie on the same fundamental plane as those in rich clusters at similar redshifts. We then use the fundamental plane to measure the combined evolutionary and K-corrections for early-type galaxies in the V, I and H bands. Only for passively evolving stellar populations formed at z > 2 (H_0=65 km/s Mpc, Omega_0=0.3, Lambda_0=0.7) can the lens galaxies be matched to the local fundamental plane. The high formation epoch and the lack of significant differences between the field and cluster populations contradict many current models of the formation history of early-type galaxies. Lens galaxy colors and the fundamental plane provide good photometric redshift estimates with an empirical accuracy of -0.03 +/- 0.11 for the 17 lenses with known redshifts. A mass model dominated by dark matter is more consistent with the data than either an isotropic or radially anisotropic constant M/L mass model, and a radially anisotropic model is better than an isotropic model.Comment: 36 pages, 9 figures, 6 tables. ApJ in press. Final version contains more observational dat