Secular Evolution in Disk Galaxies

Disk galaxies evolve over time through processes that may rearrange both the radial mass profile and the metallicity distribution within the disk. This review of such slow changes is largely, though not entirely, restricted to internally-driven processes that can be distinguished from evolution driven by galaxy interactions. It both describes our current understanding of disk evolution, and identifies areas where more work is needed. Stellar disks are heated through spiral scattering, which increases random motion components in the plane, while molecular clouds redirect some fraction of the random energy into vertical motion. The recently discovered process of radial migration at the corotation resonance of a transient spiral mode does not alter the underlying structure of the disk, since it neither heats the disk nor causes it to spread, but it does have a profound effect on the expected distribution of metallicities among the disk stars. Bars in disks are believed to be major drivers of secular evolution through interactions with the outer disk and with the halo. Once the material that makes up galaxy disks is converted into stars, their overall angular momentum distribution cannot change by much, but that of the gas is generally far more liable to rearrangement, allowing rings and pseudo-bulges to form. While simulations are powerful tools from which we have learned a great deal, those of disks may suffer from collisional relaxation that requires some results to be interpreted with caution.Comment: Minor revisions to become as it will appear in the journa

Relaxation in N-body simulations of spherical systems

I present empirical measurements of the rate of relaxation in N-body simulations of stable spherical systems and distinguish two separate types of relaxation: energy diffusion that is largely independent of particle mass, and energy exchange between particles of differing masses. While diffusion is generally regarded as a Fokker-Planck process, it can equivalently be viewed as the consequence of collective oscillations that are driven by shot noise. Empirical diffusion rates scale as N^{-1} in inhomogeneous models, in agreement with Fokker-Planck predictions, but collective effects cause relaxation to scale more nearly as N^{-1/2} in the special case of a uniform sphere. I use four different methods to compute the gravitational field, and a 100-fold range in the numbers of particles in each case. I find the rate at which energy is exchanged between particles of differing masses does not depend at all on the force determination method, but I do find the energy diffusion rate is marginally lower when a field method is used. The relaxation rate in 3D is virtually independent of the method used because it is dominated by distant encounters; any method to estimate the gravitational field that correctly captures the contributions from distant particles must also capture their statistical fluctuations and the collective modes they drive.Comment: 7 pages, 4 figures, accepted to appear in MNRAS. Very minor changes in proof

Bar instability in disk-halo systems

We show that the exponential growth rate of a bar in a stellar disk is substantially greater when the disk is embedded in a live halo than in a rigid one having the same mass distribution. We also find that the vigor of the instability in disk-halo systems varies with the shape of the halo velocity ellipsoid. Disks in rigid halos that are massive enough to be stable by the usual criteria, quickly form bars in isotropic halos and much greater halo mass is needed to avoid a strong bar; thus stability criteria derived for disks in rigid halos do not apply when the halo is responsive. The study presented here is of an idealized family of models with near uniform central rotation and that lack an extended halo; we present more realistic models with extended halos in a companion paper. The puzzle presented by the absence of strong bars in some galaxies having gently rising inner rotation curves is compounded by the results presented here.Comment: 8 pages, 4 figures. Revised version submitted to Ap

Relaxation in N-body simulations of disk galaxies

I use N-body simulations with two mass species of particles to demonstrate that disk galaxy simulations are subject to collisional relaxation at a higher rate than is widely assumed. Relaxation affects the vertical thickness of the disk most strongly, and drives the velocity ellipsoid to a moderately flattened shape similar to that observed for disk stars in the solar neighborhood. The velocity ellipsoid in simulations with small numbers of particles quickly approaches this shape, but shot noise also dominates the in-plane behavior. Simulations with higher, but reachable, numbers of particles relax slowly enough to be considered collisionless, allowing the in-plane dispersions to rise due to spiral activity without heating the vertical motions. Relaxation may have affected many previously published simulations of the formation and evolution of galaxy disks.Comment: Accepted to ApJ Letters April 23, uses emulateapj.st

Disk Mass from Large-scale Dynamics

The radial distribution of mass in a disk galaxy is strongly constrained by its rotation curve. The separate contributions from the individual stellar populations and dark matter (DM) are not easily disentangled, however, especially since there is generally no feature to indicate where the component dominating the central attraction switches from luminous to dark matter. Here I summarize three recent thesis projects at Rutgers University which all suggest that DM has a low density in the inner parts of bright galaxies, and that most of the mass therefore resides in the disk. In addition, I present some preliminary work on the Milky Way.Comment: 3 pages including 1 figure, LaTeX with jd.sty file included, to appear in "Highlights of Astronomy, v11" ed J Anderse

Dynamical Constraints on Disk Masses

While the total interior mass of a galaxy is reasonably well determined by a good rotation curve, the relative contributions from disk, bulge and halo are only weakly constrained by one-dimensional data. Barred galaxies are intrinsically more complicated, but provide much tighter constraints on the disk masses and support the idea that most of the mass in the inner parts of bright galaxies is in their stars. There appears to be no systematic difference in dark matter content between barred and unbarred galaxies, consistent with the theoretical result that the global stability of galaxies with dense centers does not depend on their halo fraction. The rotation curve shapes of lower luminosity and low-surface-brightness galaxies, on the other hand, indicate significant mass in the DM halo even near their centers. We find that most DM halos appear to have large cores, inconsistent with the predictions from cosmological simulations. We also show that such large-core halos can result from compression by disk infall of physically reasonable initial halos. Maximum disks, while apparently required by the data, do seem to present some puzzles; most notably they re-open the old disk-halo ``conspiracy'' issue and incorrectly predict that surface brightness should be a second parameter in the Tully-Fisher relation.Comment: To Appear in "Galaxy Dynamics" eds. Merritt, Sellwood & Valluri, 14 pages, Latex needs paspconf.sty, 6 figure

Spiral Structure as a Recurrent Instability

A long-standing controversy in studies of spiral structure has concerned the lifetimes of individual spiral patterns. Much theoretical work has sought quasi-stationary spiral modes while N-body simulations have consistently displayed recurrent, short-lived patterns. The simulations manifest a recurrent cycle of true instabilities related to small-scale features in the angular momentum distribution of particles, with the decay of each instability seeding the growth of the next. Data from the recent Hipparcos mission seem to offer support for the recurrent transient picture.Comment: To appear in "Astrophysical Dynamics -- in Commemoration of F. D. Kahn", eds. D. Berry, et al. (Dordrecht: Kluwer) - 5 figures, 13 pages, LaTeX uses paspconf.st

Spiral Instabilities in N-body Simulations I: Emergence from Noise

The origin of spiral patterns in galaxies is still not fully understood. Similar features also develop readily in N-body simulations of isolated cool, collisionless disks, yet even here the mechanism has yet to be explained. In this series of papers, I present a detailed study of the origin of spiral activity in simulations in the hope that the mechanism that causes the patterns is also responsible for some of these features galaxies. In this first paper, I use a suite of highly idealized simulations of a linearly stable disk that employ increasing numbers of particles. While the amplitudes of initial non-axisymmetric features scale as the inverse square-root of the number of particles employed, the final amplitude of the patterns is independent of the particle number. I find that the amplitudes of non-axisymmetric disturbances grow in two distinct phases: slow growth occurs when the relative overdensity is below ~2%, but above this level the amplitude rises more rapidly. I show that all features, even of very low amplitude, scatter particles at the inner Lindblad resonance, changing the distribution of particles in the disk in such a way as to foster continued growth. Stronger scattering by larger amplitude waves provokes a vigorous instability that is a true linear mode of the modified disk.Comment: 11 pages, 10 figures, revised after referee's report, accepted to appear ApJ, minor textual revision

Galaxy Formation, Bars and QSOs

A model that accounts for the brief flaring of QSOs in the early stages of galaxy formation is proposed. I argue that a bar must develop early in the life of nearly every galaxy and that gas to create and fuel the QSO is driven into the center of the galaxy by the bar. The QSO lifetime, and the mass of its central engine, are also controlled by large-scale dynamics, since the fuel supply is shut off after a short period by the development of an inner Lindblad resonance. This resonance causes the gas inflow along the bar to stall at a distance of a few hundred parsecs from the center. The ILR develops as a result of previous inflow, making quasar activity self-limiting. The bars are weakened and can be destroyed by the central mass concentration formed in this way.Comment: 4 pages, no figures, to appear in "Galaxy Dynamics", eds Merritt, Sellwood & Vallur

Stability and Evolution of Galactic Discs

In this review, I discuss just three aspects of the stability and evolution of galactic discs. (1) I first review our understanding of the bar instability and how it can be controlled. Disc galaxies in which the orbital speed does not decrease much towards the centre have no difficulty avoiding bars, even when dark matter makes an insignificant contribution to the inner part of the rotation curve. (2) I then briefly discuss interactions between disturbances in the discs of galaxies and the spherical components, which generally exert a damping effect through dynamical friction. The fact that bars in real galaxies appear to rotate quite rapidly, seems to require dark matter halos to have large, low-density cores. (3) In the remainder of the article, I consider the theory of spiral structure. The new development here is that the distribution function for stars in the Solar neighbourhood, as measured by HIPPARCOS, is far less smooth than most theoretical work had previously supposed. The strong variations in the values of the \DF over small ranges in angular momentum have the appearance of having been caused by scattering at Lindblad resonances with spiral patterns. This result, if confirmed when the radial velocity data become available, supports the picture of spiral patterns as dynamical instabilities driven by substructure in the \DF. The details of how decaying patterns might seed conditions for a new instability remain unclear, and deserve fresh attention.Comment: To Appear in "Astrophysical Discs" eds. Sellwood & Goodman 15 pages, 5 figures, Latex needs paspconf.st