# Galactic Dynamics

This is an interactive, online graduate textbook on the astrophysicsof galaxies. Starting out with the basics of gravitational dynamics onthe scale of galaxies, the book contains an in-depth exploration ofthe dynamical and astrophysical processes that shape the formation andevolution of galaxies in the Universe and an exposition of the maintheoretical and observational tools used to study galaxies. Embeddedthroughout the book are interactive examples and animations, and evenPython code examples that you can run without leaving your browser, toexplore the astrophysics of galaxies yourself.

## Galactic Dynamics

The GalacticDynamics Group at the Centerfor Computational Astrophysics (CCA) explores how structures in the universe, suchas dark matter and stellar halos, galaxy disks, and satellite galaxies and streams, areshaped by gravitational interactions and collective dynamics.Our work has a particular focus on dynamical disequilibrium, where we use theory,numerical simulations, and data analysis to studying the impact of mergers andtime-dependent internal dynamical processes on the evolution of galaxies and the MilkyWay.Our group makes heavy use of astrometric and stellar data from the Gaia Mission and theSloan Digital Sky Survey (APOGEE and SDSS-V surveys).

The present paper completes our earlier results on nonlinear stability of stationary solutions of the Vlasov--Poisson system in the stellar dynamics case. By minimizing the energy under a mass-Casimir constraint we construct a large class of isotropic, spherically symmetric steady states and prove their nonlinear stability against general, i. e., not necessarily symmetric perturbations. The class is optimal in a certain sense, in particular, it includes all polytropes of finite mass with decreasing dependence on the particle energy.

gala is an Astropy-affiliated Python package that aims to provide efficienttools for performing common tasks needed in Galactic Dynamics research. Much ofthis code uses Python for flexible, user-friendly interfaces that interact withwrappers around low-level code (primarily C) to enable fast computations.Common operations include gravitational potential and force evaluations, orbit integrations,dynamical coordinate transformations, and computingchaos indicators for nonlinear dynamics. galaheavily uses the units and astronomical coordinate systems defined in theAstropy core package (astropy.units andastropy.coordinates).

"Cosmic rays may help explain aspects of our galaxy from its smallest scales, such as protoplanetary disks and planets, to its largest scales, such as galactic winds," said Alexandre Marcowith, from the University of Montpellier.

Until now, cosmic rays were viewed as being a bit apart within galaxy "ecology." But because instability works well and is stronger than expected around cosmic ray sources, such as supernova remnants and pulsars, these particles likely have far more impacts on galactic dynamics and the star formation cycle than previously known.

Supernova shock waves expanding the interstellar/intergalactic medium "are known to accelerate cosmic rays, and because cosmic rays are streaming away, they may have contributed to generating the magnetic field seeds necessary to explain the actual magnetic field strengths we observe around us," said Marcowith.

Since it was first published in 1987, Galactic Dynamics has become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated edition, James Binney and Scott Tremaine describe the dramatic recent advances in this subject, making Galactic Dynamics the most authoritative introduction to galactic astrophysics available to advanced undergraduate students, graduate students, and researchers. Every part of the book has been thoroughly overhauled, and many sections have been completely rewritten. Many new topics are covered, including N-body simulation methods, black holes in stellar systems, linear stability and response theory, and galaxy formation in the cosmological context. Binney and Tremaine, two of the world's leading astrophysicists, use the tools of theoretical physics to describe how galaxies and other stellar systems work, succinctly and lucidly explaining theoretical principles and their applications to observational phenomena. They provide readers with an understanding of stellar dynamics at the level needed to reach the frontiers of the subject. This new edition of the classic text is the definitive introduction to the field. ?

This unit will provide the student with a broad and thorough understanding of the observed properties of galaxies and the key physical processes affecting their evolution and dynamics. Key topics include (1) galactic structure and morphology; (2) distance indicators; (3) scaling relations; and (4) large scale structures and environmental effects. The content is explored with reference to a range of applications and physical contexts, including a discussion of open problems in galactic dynamics.

Students are able to (1) discuss current research in the field of galaxy evolution, using the language and reasoning at the level of a junior research scientist in the field; (2) critically interpret current state-of-the-art research on the topic; (3) quantify the effect of the environment on galaxy evolution and the key time scales regulating the growth of galaxies; (4) directly analyse astronomical data in the framework of galaxy evolution; and (5) demonstrate a critical understanding of open problems in galactic dynamics.

galpy is a python package for galactic dynamics. It supports orbit integration in a variety of potentials, evaluating and sampling various distribution functions, and the calculation of action-angle coordinates for all static potentials.

Since it was first published in 1987, Galactic Dynamics has become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated edition, James Binney and Scott Tremaine describe the dramatic recent advances in this subject, making Galactic Dynamics the most authoritative introduction to galactic astrophysics available to advanced undergraduate students, graduate students, and researchers.

Every part of the book has been thoroughly overhauled, and many sections have been completely rewritten. Many new topics are covered, including N-body simulation methods, black holes in stellar systems, linear stability and response theory, and galaxy formation in the cosmological context. Binney and Tremaine, two of the world's leading astrophysicists, use the tools of theoretical physics to describe how galaxies and other stellar systems work, succinctly and lucidly explaining theoretical principles and their applications to observational phenomena. They provide readers with an understanding of stellar dynamics at the level needed to reach the frontiers of the subject.

The Department's tradition in stellar and galactic dynamics follows pioneering work by Lyman Spitzer on the dynamical evolution of globular clusters, and by Martin Schwarzschild on collisionless equilibria of galaxies. Jerry Ostriker now studies the dynamics context of cosmology and galaxy formation. David Spergel's recent work in galactic structure has focused on using tidal streams to probe the lumpiness of the Galactic halo. He has also investigated high-velocity clouds, and the dynamics of galactic bars. Jeremy Goodman has current interests in astrophysical fluid dynamics and MHD, especially disk accretion and stellar and planetary tides. Scott Tremaine is interested in a wide range of issues in astrophysical dynamics, including the formation and evolution of planets, the long-term stability of planetary systems, small bodies in the solar system (comets, asteroids, the Kuiper belt, and planetary rings), debris disks and planetesimal disks, binary stars and stellar systems, structure and formation of galaxies, dynamics of dark matter, and black holes and galactic nuclei. Other astrophysical dynamicists in Princeton include Piet Hut of the Institute for Advanced Study (IAS), with interests in dense stellar systems, collisional N-body problems, and dynamical computation; and Edward Belbruno, formerly of Princeton's Program in Applied and Computational Mathematics, with interests in celestial mechanics, astrodynamics, chaos theory. Peter Goldreich, an emeritus professor at the IAS and a frequent visitor, has broad interests in astrophysics and planetary science.

From observations, it appears that the distribution of metals is significantly homogeneous in disk galaxies and in the ISM. For example, the radial metallicity gradient in disk galaxies is appreciably shallow, contrary to the otherwise steep gradient of star formation rate. Moreover, members within each star cluster of various type show high degree of homogeneity in their chemical composition, which has become a foundation for the technique of chemical tagging and galactic archaeology. Therefore, an efficient mechanism to homogenize the distribution of metals is required in galactic disks and in the ISM.

Our understanding of the mechanisms governing the structure and secularevolution galaxies assume nearly integrable Hamiltonians with regular orbits;our perturbation theories are founded on the averaging theorem for isolatedresonances. On the other hand, it is well-known that dynamical systems withmany degrees of freedom are irregular in all but special cases. The bestdeveloped framework for studying the breakdown of regularity and the onset isthe Kolmogorov-Arnold-Moser (KAM) theory. Here, we use a numerical version ofthe KAM procedure to construct regular orbits (tori) and locate irregularorbits (broken tori). Irregular orbits are most often classified inastronomical dynamics by their exponential divergence using Lyapunov exponents.Although their computation is numerically challenging, the procedure isstraightforward and they are often used to estimate the measure of regularity.The numerical KAM approach has several advantages: 1) it provides themorphology of perturbed orbits; 2) its constructive nature allows the tori tobe used as basis for studying secular evolution; 3) for broken tori, clues tothe cause of the irregularity may be found by studying the largest, divergingFourier terms; and 4) it is more likely to detect weak chaos and orbits closeto bifurcation. Conversely, it is not a general technique and works mostcleanly for small perturbations. We develop a perturbation theory that includeschaos by retaining an arbitrary number of interacting terms rather thaneliminating all but one using the averaging theorem. The companion papers showthat models with significant stochasticity seem to be the rule, not theexception. 041b061a72