We perform local $N$-body simulations of disk galaxies and investigate the evolution of spiral arms. We calculate the time autocorrelation of the surface density of spiral arms and find that the typical evolution timescale is described by the epicycle period. We investigate the distribution of the orbital elements of stars and find that in spiral arms the epicycle motions of stars are in phase while the spatial distribution of the guiding center is nearly uniform. These facts clearly show that the phase synchronization of the epicycle motion takes place, which is theoretically predicted by the swing amplification.
We study transient spiral structures in an isothermal, thin, galactic disc. We find no instability that can grow everywhere from infinitesimal disturbances, but spiral structure does grow in the disc due to an arbitrarily strong, asymmetric, central source. An initially finite spiral undergoes transient swing amplification as it is gradually wound-up by differential rotation. An independent sequence in negative time describes a leading spiral swinging to a trailing spiral. The dynamical coupling is established between the swinging potential and the arm particles, by ensuring that this potentia…
Using 3D N-body simulations we analyse an onset of the bar in cuspy models, and argue that role of swing amplification is twofold. Amplified shot noise due to disc discreteness hampers bar formation, while induced resonance perturbations allow bar amplitude to overcome shots. A bar pattern speed and a growth rate obtained in N-body simulations agree well with global mode analysis.
We revisit the swing amplification model of galactic spiral arms proposed by Toomre (1981). We describe the derivation of the perturbation equation in detail and investigate the amplification process of stellar spirals. We find that the elementary process of the swing amplification is the phase synchronization of the stellar epicycle motion. Regardless of the initial epicycle phase, the epicycle phases of stars in a spiral are synchronized during the amplification. Based on the phase synchronization, we explain the dependence of the pitch angle of spirals on the epicycle frequency. We find the…
Based on the swing amplification model of Julian and Toomre (1966), we investigate the formation and structure of stellar spirals in disk galaxies. We calculate the pitch angle, wavelengths, and amplification factor of the most amplified mode. We also obtain the fitting formulae of these quantities as a function of the epicycle frequency and Toomre's $Q$. As the epicycle frequency increases, the pitch angle and radial wavelength increases, while the azimuthal wavelength decreases. The pitch angle and radial wavelength increases with $Q$, while the azimuthal wavelength weakly depends on $Q$. Th…
A typical galactic disk is observed to have a finite thickness. Here, we present the study of the physical effect of introduction of finite thickness on the generation of small-scale spiral arms by swing amplification in a differentially rotating galactic disk. The galactic disk is modelled first as a one-fluid system, and then as a gravitationally-coupled two-fluid (stars and gas) system where each fluid is taken as isothermal, and corotating with each other. We derived the equations governing the evolution of growth of the non-axisymmetric perturbations in a sheared frame of reference while …
The origin of galactic spiral arms is one of fundamental problems in astrophysics. Based on the local analysis Toomre (1981) proposed the swing amplification mechanism in which the self-gravity forms spiral arms as leading waves of stars rotate to trailing ones due to galactic shear. The structure of spiral arms is characterized by their number and pitch angle. We perform global $N$-body simulations of spiral galaxies to investigate the dependence of the spiral structure on disk parameters and compare the simulation results with the swing amplification model. We find that the spiral structure …
The principal results of the classic analysis of the shearing sheet and swing amplification by Julian & Toomre (1966) are re-derived in a more accessible way and then used to gain a better quantitative understanding of the dynamics of stellar discs. The axisymmetric limit of the shearing sheet is derived and used to re-derive Kalnajs' 1965 dispersion relation and Toomre's 1964 stability criterion for axisymmetric disturbances. Using the shearing sheet to revisit Toomre's important 1969 paper on the group velocity implied by Lin-Shu-Kalnajs dispersion relation, we discover that two rather than …
Since the discovery that the majority of low-redshift galaxies exhibit some level of spiral structure, a number of theories have been proposed as to why these patterns exist. A popular explanation is a process known as swing amplification, yet there is no observational evidence to prove that such a mechanism is at play. By using a number of measured properties of galaxies, and scaling relations where there are no direct measurements, we model samples of SDSS and S$^4$G spiral galaxies in terms of their relative halo, bulge and disc mass and size. Using these models, we test predictions of swin…
A model based on disk-stability criteria to determine the number of spiral arms of a general disk galaxy with an exponential disk, a bulge and a dark halo described by a Hernquist model is presented. The multifold rotational symmetry of the spiral structure can be evaluated analytically once the structural properties of a galaxy, such as the circular speed curve, and the disk surface brightness, are known. By changing the disk mass, these models are aimed at varying the critical length scale parameter of the disk and lead to a different spiral morphology in agreement with prior models. Previou…
One of the key parameters that characterize spiral arms in disk galaxies is a pitch angle that measures the inclination of a spiral arm to the direction of galactic rotation. The pitch angle differs from galaxy to galaxy, which suggests that the rotation law of galactic disks determines it. In order to investigate the relation between the pitch angle of spiral arms and the shear rate of galactic differential rotation, we perform local $N$-body simulations of pure stellar disks. We find that the pitch angle increases with the epicycle frequency and decreases with the shear rate and obtain the f…
Effects of Resolution and Local Stability on Galactic Disks: I. Multiple Spiral Mode Formation via Swing Amplification
Universität Potsdam, Institut für Physik und Astronomie（波茨坦大学物理与天文学系）；Department of Astronomy and Yonsei University Observatory, Yonsei University（延世大学天文学系及延世大学天文台）
The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is investigated using the inhomogeneous Balescu-Lenard equation expressed in terms of angle-action variables. The matrix method is implemented numerically in order to model the induced gravitational polarization. Special care is taken to account for the amplification of potential fluctuations of mutually resonant orbits and the unwinding of the induced swing amplified transients. Quantitative comparisons with ${N-}$body simulations yield consistent scalings with the number of particles…
Spiral patterns in some disc galaxies have two arms in the centre, and three or more arms on the periphery. The same result is also obtained in numerical simulations of stellar and gaseous discs. We argue that such patterns may occur due to fast cooling of the gas, resulting in formation of giant molecular clouds. The timescale of this process is 50 Myr, the factor of 10 shorter than of ordinary secular instability. The giant molecular clouds give rise to multiarm spirals through the mechanism of swing amplification.
The formation and evolution of galactic spiral arms is not yet clearly understood despite many analytic and numerical work. Recently, a new idea has been proposed that local density enhancements (waklets) arising in the galactic disk connect with each other and make global spiral arms. However, the understanding of this mechanism is not yet sufficient. We analyze the interaction of wakelets by using N-body simulations including perturbing point masses, which are heavier than individual N-body particles and act as the seeds for wakelets. Our simulation facilitates more straightforward interpret…
We investigate the short-term dynamical evolution of stellar grand-design spiral arms in barred spiral galaxies using a three-dimensional (3D) $N$-body/hydrodynamic simulation. Similar to previous numerical simulations of unbarred, multiple-arm spirals, we find that grand-design spiral arms in barred galaxies are not stationary, but rather dynamic. This means that the amplitudes, pitch angles, and rotational frequencies of the spiral arms are not constant, but change within a few hundred million years (i.e. the typical rotational period of a galaxy). We also find that the clear grand-design sp…
The causes of spiral structure in galaxies remain uncertain. Leaving aside the grand bisymmetric spirals with their own well-known complications, here we consider the possibility that multi-armed spiral features originate from density inhomogeneities orbiting within disks. Using high-resolution N-body simulations, we follow the motions of stars under the influence of gravity, and show that mass concentrations with properties similar to those of giant molecular clouds can induce the development of spiral arms through a process termed swing amplification. However, unlike in earlier work, we demo…
Swing amplification is a model of spiral arm formation in disk galaxies. Previous $N$-body simulations show that the epicycle phases of stars in spiral arms are synchronized. However, the elementary process of the phase synchronization is not well understood. In order to investigate phase synchronization, we investigate the orbital evolution of stars due to gravitational scattering by a perturber under the epicycle approximation and its dependence on orbital elements and a disk parameter. We find that gravitational scattering by the perturber can cause phase synchronization of stellar orbits. …
The majority of astrophysics involves the study of spiral galaxies, and stars and planets within them, but how spiral arms in galaxies form and evolve is still a fundamental problem. Major progress in this field was made primarily in the 1960s, and early 1970s, but since then there has been no comprehensive update on the state of the field. In this review, we discuss the progress in theory, and in particular numerical calculations, which unlike in the 1960s and 1970s, are now commonplace, as well as recent observational developments. We set out the current status for different scenarios for sp…
We study the evolution of galactic magnetic fields using 3D smoothed particle magnetohydrodynamics (SPMHD) simulations of galaxies with an imposed spiral potential. We consider the appearance of reversals of the field, and amplification of the field. We find magnetic field reversals occur when the velocity jump across the spiral shock is above $\approx$20km s$^{-1}$, occurring where the velocity change is highest, typically at the inner Lindblad resonance (ILR) in our models. Reversals also occur at corotation, where the direction of the velocity field reverses in the co-rotating frame of a sp…
In order to understand the physical mechanisms underlying non-steady stellar spiral arms in disk galaxies, we analyzed the growing and damping phases of their spiral arms using three-dimensional $N$-body simulations. We confirmed that the spiral arms are formed due to a swing amplification mechanism that reinforces density enhancement as a seeded wake. In the damping phase, the Coriolis force exerted on a portion of the arm surpasses the gravitational force that acts to shrink the portion. Consequently, the stars in the portion escape from the arm, and subsequently they form a new arm at a dif…
Several mechanisms of bar formation in stellar galactic disks are considered, including Toomre swing amplification and normal mode approach. On example of the well-known model of Kuzmin--Toomre using N-body simulations it was shown that the stellar bar is developed as a result of the evolution of an unstable normal mode. The pattern speed and the growth rate found agree well with linear perturbation theory. Nonlinear evolution of the bar is followed. Role of the growing transient spirals in bar formation is discussed.
We propose an explanation of features of spiral galaxies: spiral arms and observed flat rotation curves, without the presence of an exotic form of matter. The formalism is based on Boltzmanns transport equation for the collisional matter and the very-low-velocity post-Newtonian approximation of the general relativity equations expressed in the Maxwell-like form. The Maxwell-like formulation provides the base for the explanation of the above phenomena in the language of dynamically created gravitoelectromagnetic fields by the movement of mass streams in the plane of the galaxy disc. In the mode…
Recent developments in computer hardware and software enable researchers to simulate the self-gravitating evolution of galaxies at a resolution comparable to the actual number of stars. Here we present the results of a series of such simulations. We performed $N$-body simulations of disk galaxies with between 100 and 500 million particles over a wide range of initial conditions. Our calculations include a live bulge, disk, and dark matter halo, each of which is represented by self-gravitating particles in the $N$-body code. The simulations are performed using the gravitational $N$-body tree-co…
Context: The Faraday rotation measure (RM) is often used to study the magnetic field strength and orientation within the ionized medium of the Milky Way. Observations indicate a RM in the spiral arms that exceeds the commonly assumed range. This raises the question of under what conditions spiral arms create such strong RM. Aims: We investigate the effect of spiral arms on Galactic RMs through shock compression of the interstellar medium (ISM). It has recently been suggested that the Sagittarius spiral arm creates a strong peak in RM where the line of sight (LOS) is tangent to the arm, and tha…
Magnetic fields constitute an energetic component of the interstellar medium in galaxies and hence can affect the formation of galactic structures. Sensitive resolved radio continuum observations together with statistical studies in galaxy samples are performed to investigate the origin and the impact of the magnetic fields. The JVLA cloud-scale survey of the local group galaxy, M33, unveils strong tangled magnetic field along the spiral arms and in the galaxy center indicating amplification due to compression and local shear in molecular clouds. Studying a sample of non-cluster, non-interacti…
The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is described using the inhomogeneous Balescu-Lenard equation. Assuming that only tightly wound transient spirals are present in the disc, a WKB approximation provides a simple and tractable quadrature for the corresponding drift and diffusion coefficients. It provides insight into the physical processes at work during the secular diffusion of a self-gravitating discrete disc and makes quantitative predictions on the initial variations of the distribution function in action space. When …
We investigate the build-up of the galactic dynamo and subsequently the origin of a magnetic driven outflow. We use a setup of an isolated disc galaxy with a realistic circum-galactic medium (CGM). We find good agreement of the galactic dynamo with theoretical and observational predictions from the radial and toroidal components of the magnetic field as function of radius and disc scale height. We find several field reversals indicating dipole structure at early times and quadrupole structure at late times. Together with the magnetic pitch angle and the dynamo control parameters $R_α$, $R_ω$ a…
