Oort constantsThe Oort constants (discovered by Jan Oort) and are empirically derived parameters that characterize the local rotational properties of our galaxy, the Milky Way, in the following manner: where and are the rotational velocity and distance to the Galactic Center, respectively, measured at the position of the Sun, and and are the velocities and distances at other positions in our part of the galaxy. As derived below, and depend only on the motions and positions of stars in the solar neighborhood.
Stellar kinematicsIn astronomy, stellar kinematics is the observational study or measurement of the kinematics or motions of stars through space. Stellar kinematics encompasses the measurement of stellar velocities in the Milky Way and its satellites as well as the internal kinematics of more distant galaxies. Measurement of the kinematics of stars in different subcomponents of the Milky Way including the thin disk, the thick disk, the bulge, and the stellar halo provides important information about the formation and evolutionary history of our Galaxy.
Galactic haloA galactic halo is an extended, roughly spherical component of a galaxy which extends beyond the main, visible component. Several distinct components of galaxies comprise the halo: the stellar halo the galactic corona (hot gas, i.e. a plasma) the dark matter halo The distinction between the halo and the main body of the galaxy is clearest in spiral galaxies, where the spherical shape of the halo contrasts with the flat disc. In an elliptical galaxy, there is no sharp transition between the other components of the galaxy and the halo.
Galactic coordinate systemThe galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane. Longitude (symbol l) measures the angular distance of an object eastward along the galactic equator from the Galactic Center.
Bifurcation theoryBifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.
Galaxy rotation curveThe rotation curve of a disc galaxy (also called a velocity curve) is a plot of the orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy's centre. It is typically rendered graphically as a plot, and the data observed from each side of a spiral galaxy are generally asymmetric, so that data from each side are averaged to create the curve. A significant discrepancy exists between the experimental curves observed, and a curve derived by applying gravity theory to the matter observed in a galaxy.
Hopf bifurcationIn the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic solution arises. More accurately, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues—of the linearization around the fixed point—crosses the complex plane imaginary axis as a parameter crosses a threshold value.
Stellar parallaxStellar parallax is the apparent shift of position (parallax) of any nearby star (or other object) against the background of distant stars. By extension, it is a method for determining the distance to the star through trigonometry, the stellar parallax method. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations.
Period-doubling bifurcationIn dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original. With the doubled period, it takes twice as long (or, in a discrete dynamical system, twice as many iterations) for the numerical values visited by the system to repeat themselves. A period-halving bifurcation occurs when a system switches to a new behavior with half the period of the original system.
Galactic discA galactic disc (or galactic disk) is a component of disc galaxies, such as spiral galaxies, lenticular galaxies, and the Milky Way. Galactic discs consist of a stellar component (composed of most of the galaxy's stars) and a gaseous component (mostly composed of cool gas and dust). The stellar population of galactic discs tend to exhibit very little random motion with most of its stars undergoing nearly circular orbits about the galactic center.
Bifurcation diagramIn mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system. It is usual to represent stable values with a solid line and unstable values with a dotted line, although often the unstable points are omitted. Bifurcation diagrams enable the visualization of bifurcation theory.
List of stellar streamsThis is a list of stellar streams. A stellar stream is an association of stars orbiting a galaxy. It was once a globular cluster or dwarf galaxy that has now been torn apart and stretched out along its orbit by tidal forces. An exception in the list about Milky Way streams given below is the Magellanic Stream, composed of gas (mostly hydrogen) although in 2023 a population of some star has been described inside it.
IntegralIn mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration started as a method to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Today integration is used in a wide variety of scientific fields.
Pitchfork bifurcationIn bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points. Pitchfork bifurcations, like Hopf bifurcations, have two types – supercritical and subcritical. In continuous dynamical systems described by ODEs—i.e. flows—pitchfork bifurcations occur generically in systems with symmetry. The normal form of the supercritical pitchfork bifurcation is For , there is one stable equilibrium at .
Hydrogen lineThe hydrogen line, 21 centimeter line, or H I line is a spectral line that is created by a change in the energy state of solitary, electrically neutral hydrogen atoms. It is produced by a spin-flip transition, which means the direction of the electron's spin is reversed relative to the spin of the proton. This is a quantum state change between the two hyperfine levels of the hydrogen 1 s ground state. The electromagnetic radiation producing this line has a frequency of 1420.405751768MHz (1.
Hamiltonian pathIn the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a Hamiltonian cycle, and removing any edge from a Hamiltonian cycle produces a Hamiltonian path.
Hamiltonian mechanicsHamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.
Milky WayThe Milky Way is the galaxy that includes the Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. The term Milky Way is a translation of the Latin via lactea, from the Greek γαλακτικὸς κύκλος (galaktikòs kýklos), meaning "milky circle". From Earth, the Milky Way appears as a band because its disk-shaped structure is viewed from within.
ResonanceResonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system.
Hamiltonian systemA Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory. Informally, a Hamiltonian system is a mathematical formalism developed by Hamilton to describe the evolution equations of a physical system.
