Corotation Resonance Research Articles

The spatial distribution of pulsars and the spiral structure of the Galaxy

We have looked for and found a possible spatial correlation between the present pulsar distribution and the estimated locations of the spiral arms at earlier epochs. Through a detailed statistical analysis we find a significant correlation between the present distribution of pulsars and the mass distribution (in the spiral arms) expected about 60 Myr ago for a corotation resonance radius of 14kpc. We discuss the implications of this correlation for the minimum mass of the progenitors of pulsars. Interpreting the spread in the locations of pulsars with respect to the past locations of the spiral arms as predominantly due to their space velocities, we derive an average velocity for the pulsar population.

Dynamical friction in disc galaxies

The force of dynamical friction on a softened point mass moving in a circular orbit inside a particle disc is studied theoretically and by means of numerical simulations. We derive an improved analytic estimate of the dynamical friction taking into account the effects of corotation and Lindblad resonances. This estimate is compared with the frictional force measured in numerical experiments where the disturber is constrained to move on a circular orbit. The analytic estimate is in good agreement with the measured force in non-self-gravitating experiments. We then study non-linear and collective effects on the friction by means of experiments involving larger disturber masses and the self-gravity of the disc

A new way to locate corotation resonances in spiral galaxies

Kinematical information over the entire disk of a spiral galaxy can be used in a new way to locate the position of the corotation resonance. The spiral residual velocity field has a global appearance that is distinctly different inside and outside the corotation resonance radius. Inside the corotation radius, the spiral velocity field shows a single spiral feature (that is, a single approaching-receding spiral arm pair). Outside the corotation radius, there are three spiral features (approaching-receding arm pairs). The corotation radius is located where this morphological change occurs. The effect is a consequence of geometric phase. It should apply generally, regardless of the functional form of the velocity perturbation due to a spinal arm, if the spiral structure is wave-based

COROTATION RESONANCE: UGC 2885 AND A NEW METHOD

ABSTRACT Kinematic data on the minor axis of the giant sprial galaxy UGC 2885 show a change in the sign of the raidal velocity across spiral arms. Such a sign change indicates that corotation has been crossed. In fact, two sign changes are seen, implying that there are two spiral patterns. The morphology of the galaxy supports this interpretation. A general method is also presented that can be used to locate the corotation resonance in a grand design spiral galaxy. The method relies on the effects of geometric phase, and assumes only that the spiral flow is wave-based and periodic in azimuth.

H-ALPHA FABRY-PEROT OBSERVATIONS OF THE DENSITY WAVE PATTERN IN M51

ABSTRACT The Maryland-Caltech wide-field Fabry-Perot camera has been used to image H-alpha emission in the grand design spiral galaxy M51. The velocity field of the ionized gas has been determined over most of the optical disk at an angular resolution of 2-8" and a realtive velocity accuracy of 1-2 km s-1 rms. The well-known kinematic perturbations due to density wave streaming are clearly resolved in both arm and interarm regions. Determination of the radius at which the gas and spiral pattern corotate using reversals in the streaming direction, frequently proposed as the preferred method of locating the corotation resonance, is hampered by the observed complexity of the density wave response. Nonetheless, new evidence is presented that supports previous determinations using other methods that corotation of the inner spiral is located near a glactocentric radius of 6 kpc, and that the outer optical arms cannot be part of the same spiral pattern as the inner arms.

Numerical Calculations of the Linear Response of a Gaseous Disk to a Protoplanet

In this paper we present calculations of the linear response of a flat gaseous disk to the presence of an embedded protoplanet. The calculations are numerical and take into account terms neglected by analytic theory and also examine the effects of gradients in surface density and sound speed in the disk. We have also developed a means of rapid calculation of Laplace coefficients for a softened potential (or for a disk of nonzero height). In general, the classical analytic theory is confirmed. However, the magnitude of calculated torque due to the corotation resonance disagrees with previously derived analytical results. The calculated corotation torque is smaller than the analytic value, is much less sensitive to the value of the perturbing potential at corotation, and falls off more rapidly as a function of the azimuthal wavenumber m. It is possible that the rapid variation of the perturbing potential near corotation is responsible for this behavior. We find that the dominant effect of a pressure gradient is to increase the net torque, due to the inward displacement of the Lindblad resonances. The effect countervails the opposing effect of a gradient in disk surface density, in general. We have calculated the inferred orbital evolution timescales for the Earth and outer planets for a variety of model nebulae. In general the orbital evolution timescale for the Earth is on the order of 10 6 years. Timescales for the outer planets are much shorter: 10 3-10 4 years in general. Although the effects of the reaction of the solar nebula to the torques have been neglected in our calculations, the results indicate the importance of the protoplanets for the later stages of nebular evolution.

Nonlinear evolution of spiral density waves generated by the instability of the shear layer in a rotating compressible fluid

In a previous paper we considered the nonlinear stability of a cylindrical mixing layer in an incompressible fluid at large Reynolds numbers. Nonlinear evolution results in the formation of vortex structures in the vicinity of the corotation radius rc. This paper considers the same model but in a compressible fluid. A fundamental difference implied by the presence of compressibility is the possibility of the generation of disturbances which are no longer localized near the shear layer but embrace the entire region. These are acoustic waves generated in the region of corotation resonance and emitted into the periphery. In the r > rc region lines of equal density are trailing spirals. The nonlinear evolution of such disturbances is determined by redistribution of the mean flow inside the critical layer (CL). It is shown that only two possible types of CL, viscous and unsteady, can be realized here. For both types of these regimes, evolution equations describing the dynamics of a spiral density wave amplitude are obtained and their solutions analysed. It appears that at any values (provided that they are small enough) of initial supercriticality of the flow, an explosive growth of amplitude occurs which continues as long as values comparable with background ones are reached.

Bar-disc angular momentum exchange

A model galaxy with an artificial bar is used to explore the angular momentum exchange induced by bar-like (m = 2) perturbations to a disc. An analytic formula is provided for this exchange which predicts to within ∼1 per cent the interaction between a weak bar and a non-self-gravitating disc. The results of N-body experiments are also presented, which suggest that the neglect of disc self-gravity in analytic theory leads to : (i) an underestimate of the slowdown rate of a bar which is dominated by corotation and outer Lindblad resonances; (ii) an overestimate of the spin-up rate of a bar which is dominated by inner Lindblad resonances

Numerical exploration of planetary arc dynamics

Ground-based observations have revealed in 1984 and 1985 the existence of interrupted ring-like structures, or “arcs” around Neptune. Recent observations by the Voyager 2 spacecraft in August 1989 have confirmed the presence of stable, dense arcs, embedded in a faint continuos ring. These structures would be destroyed in a few years if they followed unperturbed Keplerian motions. We study here the stabilizing effect of corotation and Lindblad resonances on planetary arcs, along the lines of previous analytical work by Lissauer ( Nature (London) 318, 1985, 544–545) and Goldreich, Tremaine, and Borderies ( Astron. J. 92, 1986, 490–494). We first describe analytically the responce of a test particle to the combined effects of corotation and Lindblad resonances, caused by Neptunian satellites. The evolution of the particle is shown to be described by two coupled dynamical systems, the coupling depending on collective effects in the arc. This yields a formula for the energy provided by the Lindblad resonance, which is actually used to confine the arc material around the corotation resonance radius. We show in particular that the gradient of the torque density across the arc must be negative for the latter to be stable. This confirms in a general framework the constraints, previously given by Lin, Papaloizou, and Ruden ( Mon. Not. R. Astron. Soc. 227, 1987, 75–95), on the relative positions of the corotation and the Lindblad resonances for the arc to be stable. We test our results with a direct numerical simulation, which takes into account inelastic collisions between identical spherical particles. Two configurations are studied: (1) an arc at a L 4 Lagrange point of a satellite, further perturbed by an isolated Lindblad resonance with a second satellite, and (2) an arc at an isolated corotation resonance with a single satellite on an eccentric orbit. Our main results are: (a) the corotation points alone are unstable against dissipative collisions, (b) a stable arc must be submitted to a negative gradient of torque density, and (c) such a stable arc reaches a limit cycle where the energy provided by the resonant satellite is balanced by the energy dissipated by collisions.

Optical tracers of spiral wave resonances in galaxies - Applications to NGC 1566

view Abstract Citations (54) References (37) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Optical Tracers of Spiral Wave Resonances in Galaxies: Applications to NGC 1566 Elmegreen, Bruce G. ; Elmegreen, Debra Meloy Abstract Likely radii for the inner and outer Lindblad resonances (ILR, OLR), the corotation resonance (CR), the inner 6:1 and 4:1 resonances, and the outer 1:1 resonance in the grand design galaxy NGC 1566 are identified from optical features and from constraints set by plausible rotation curves. In the preferred solution, the OLR is placed where the outer edge of the spiral pattern joins the outer ring, the CR is at the endpoints of the bright star-formation ridges and sharply defined dust lanes, where the main arms bifurcate and a ring of interarm star-formation circles the galaxy, the 6:1 resonance is where two short and faint spurs lie parallel and equally spaced between the main arms in the west, the 4:1 resonance is where a large and bright spur lies midway between the arms in the east and where there is a kink in both arms, and the ILR is at the position of another kink in the spiral at the inner part of the galaxy, near the end of a small bar. The outer ring extends between the OLR and the outer 1:1 resonance. The ratios of these resonance radii to the corotation resonance are shown to be relatively insensitive to the rotation curve, and all of the observed ratios are in good agreement with theory. Other possible solutions for the resonance radii are discussed. Publication: The Astrophysical Journal Pub Date: May 1990 DOI: 10.1086/168740 Bibcode: 1990ApJ...355...52E Keywords: Galactic Structure; Orbital Resonances (Celestial Mechanics); Spiral Galaxies; Corotation; Galactic Rotation; H Ii Regions; Astrophysics; GALAXIES: INDIVIDUAL NGC NUMBER: NGC 1566; GALAXIES: INTERNAL MOTIONS; GALAXIES: STRUCTURE full text sources ADS | data products SIMBAD (4) NED (1) Related Materials (1) Part 2: 1992ApJS...79...37E

Nonaxisymmetric instabilities in thin self-gravitating rings and disks

The stability of geometrically thin self-gravitating rings and disks is studied by computing the eigenvalues and eigenfunctions of linearized normal mode oscillations in these systems. For the vertically averaged incompressible models and models of gaseous and stellar disks with softened gravity, analytic treatment is possible. The existence of oscillatory normal modes is established using a variational principle and infer instability using perturbation theory. Effects due to the Lindblad and corotation resonances are analyzed in detail. The distribution of the ratio of vorticity to surface density is important for determining the stability of the systems.

Neptune's Story

It is conjectured that Triton was captured from a heliocentric orbit as the result of a collision with what was then one of Neptune's regular satellites. The immediate post-capture orbit was highly eccentric with a semimajor axis a approximately 10(3)R(N) and a periapse distance rp that oscillated periodically above a minimum value of about 5R(N). Dissipation due to tides raised by Neptune in Triton caused Triton's orbit to evolve to its present state in less, similar10(9) years. For much of this time Triton was almost entirely molten. While its orbit was evolving, Triton cannibalized most of the regular satellites of Neptune and also perturbed Nereid, thus accounting for that satellite's highly eccentric and inclined orbit. The only regular satellites of Neptune that survived were those that formed well within 5R(N) and they move on inclined orbits as the result of chaotic perturbations forced by Triton. Neptune's arcs are confined around the corotation resonances of one of these inner satellites. The widths and lengths of the arcs imply that the satellite's radius is at least 30/(sin i)(2/3) kilometers for i less, similar 1, where i is the angle of inclination.

Spiral arm amplitude variations and pattern speeds in the grand design galaxies M51, M81, and M100

view Abstract Citations (157) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Spiral-Arm Amplitude Variations and Pattern Speeds in the Grand Design Galaxies M51, M81, and M100 Elmegreen, Bruce G. ; Elmegreen, Debra Meloy ; Seiden, Philip E. Abstract The amplitudes of the spiral arms in M51, M81, and M100 have been found to oscillate smoothly around their mean radial variations with a characteristic wavelength of ~5 kpc and a relative amplitude of 100%. The phases of the spirals and the relative amplitudes of the m = 4 and m = 2 Fourier components oscillate slightly too. The absence of corresponding color variations and the symmetry of the amplitude peaks with respect to the galaxy centers suggest that the oscillations are an intrinsic part of the stellar spiral density wave. ThIs observation confirms predictions of both the modal and stellar dynamical theories of spiral structure. The radial positions of the prominent gaps in the spiral arm amplitudes are compared to the expected positions of various wave resonances. Excellent fits are obtained for M81 and M100 if the gaps are at the 4:1 resonances; then the spirals end at the outer Lindblad resonances, the inner Lindblad resonances are well shielded, and the primary star formation ridges and dust lanes are between the 4:1 and corotation resonances. Prominent interarm features and spurs also occur at the 4:1 and corotation resonances in these galaxies. The situation is similar but more complicated in M51, which requires two spiral systems to cover the disk. The best fit is for an inner spiral mode that has an outer Lindblad resonance at the position of a prominent arm intensity gap, and an outer material spiral that corotates with the companion. Then the average position of the inner Lindblad resonances of the outer material arms occurs at the same radius as the corotation resonances of the inner mode. This conjunction of resonances may explain how the companion to M51 triggered a strong spiral throughout most of the disk. Publication: The Astrophysical Journal Pub Date: August 1989 DOI: 10.1086/167733 Bibcode: 1989ApJ...343..602E Keywords: Andromeda Galaxy; Galactic Structure; Spiral Galaxies; Interstellar Gas; Orbital Resonances (Celestial Mechanics); Star Formation; Astrophysics; GALAXIES: INDIVIDUAL MESSIER NUMBER: M51; GALAXIES: INDIVIDUAL MESSIER NUMBER: M81; GALAXIES: INDIVIDUAL MESSIER NUMBER: M100; GALAXIES: INTERNAL MOTIONS; GALAXIES: STRUCTURE full text sources ADS | data products SIMBAD (4) NED (4)

On the relative frequency of flocculent and grand design spiral structures in barred galaxies

The bars in late-type spiral galaxies (SBbc to SBm and SABbc to SABm) show little correlation with grand design spiral structure, unlike the bars in early-type galaxies. This is further evidence for two different types of bars in the SB morphological class, and two different types of ovals in the SAB class. The weak, short, and exponential-shaped bars that tend to occur in late-type galaxies may end far inside the corotation resonance and be unable to produce large-scale wave patterns in the outer stellar disks. The strong, long, and flat-shaped bars that tend to occur in early-type galaxies may extend closer to the corotation resonance and be able to produce strong and symmetric arms. This difference in bar-spiral correlation is consistent with the theoretical prediction that short-wavelength trailing spirals propagate outward beyond corotation and inward inside corotation. 30 refs.

Tidal friction in early-type stars

The tidal torque on an early-type star is concentrated near the boundary between the convective core and radiative envelope and a train of gravity waves is excited there. The angular momentum which the torque removes from the fluid is transported outward by the gravity waves, which carry negative angular momentum. Before the surface layers are despun to synchronous rotation, the gravity waves propagate to just below the photosphere where they suffer radiative damping and are partially reflected. It is here that the negative angular momentum is deposited and the primary tidal despinning takes place. The surface layers cannot be spun down below synchronous rotation because as a train of gravity waves approaches a corotation resonance its group velocity and wavelength tend to zero, its amplitude diverges, and it is completely absorbed. Thus, tidal despinning to synchronous rotation proceeds from the outside toward the inside of the star. Our picture provides a neat explanation for the otherwise puzzling discovery by Giuricin, Mardirossian, and Mezzetti that Zahn's theory for tidal evolution in early-type close binaries seems to be compatible with the observed rates of orbit circularization while significantly underestimating the observed rates of spin synchronization.

Corotation torques in the solar nebula - The cutoff function

The behavior of high-order corotation resonances in a disk of finite thickness is examined. The torque exerted at an mth-order resonance is determined by employing a vertically averaged disturbing function, and the ratio of this torque to that exerted on a cold, two-dimensional disk is identified as the so-called torque cutoff function. This function is then used to calculate contributions from the corotation torques to eccentricity variations of a perturber's orbit assumed orbiting in the disk.

On disk-planet interactions and orbital eccentricities

The eccentricity evolution from density wave interaction between a planetesimal and a Keplerian disk is studied. While it is known that Lindblad resonances both interior and exterior to the perturber's orbit excite its eccentricity, we show that corotation resonances in these regions become ineffective at eccentricity damping if the object is embedded in a continuous disk without a gap. However, under these conditions another class of Lindblad resonances exists that has not been included in earlier treatments of this problem. These operate on disk material co-orbiting with the perturber and become the most important source of eccentricity damping. We employ a model problem to obtain estimates of the various disk torques and conclude, therefrom, that the eccentricity ultimately suffers decay. The limitations of this model are also discussed, as is the need for further studies.

On the confinement of planetary arcs⋆

The necessary conditions for planetary arc confinement are investigated, concentrating on the limiting case where the arc is marginally confined. It is shown that periodic perturbations due to a discrete Lindblad resonance can induce a secular change of Jacobian energy as well as orbital eccentricity. If the particles are subject to the perturbation of only one inner (outer) Lindblad resonance, the Lindblad resonance's location must be exterior (interior) to that of the corotation resonance if the perturbations are to lead to confinement. The trajectories of particles that are subject to inelastic collisions and pertubations due to corotation and Lindblad resonances are computed, showing that the confinement mechanism can indeed operate provided the perturbation due to the Lindblad resonance is sufficiently strong to balance viscous effects. The possibility that internal nonradial oscillations of Neptune may provide the necessary perturbations for arc confinement is considered.

A Schmidt law for the molecular gas profiles of disk galaxies

An explanation for the observed difference in radial profiles of the atomic and molecular gas components of disk galaxies is proposed which involves GMC formation in local gravitational potential perturbations such as spiral arms. It is assumed that GMC form through binary cloud-cloud collisions within the potential of spiral density perturbations, with progenitors whose radial profile is that of the atomic gas, the rate of collisions being determined by how often a spiral arms is encountered. This model provides a good fit to the overall shape of the molecular gas distribution for disk galaxies where there is believed to be an underlying stationary density wave, with corotation resonance in the outer regions of the disk, as well as for those disk galaxies where the spiral arms are more probably transient. 41 references.

Towards a theory for Neptune's arc rings

It is proposed that the incomplete rings of Neptune consist of a number of short arcs centered on the corotation resonances of a single satellite. The satellite must have a radius of the order of 100 km or more and move on an inclined orbit. Corotation resonances are located at potential maxima. Thus, mechanical energy dissipated by interparticle collisions must be continually replenished to prevent the arcs from spreading. It is shown that each corotation resonance is associated with a nearby Lindblad resonance, which excites the ring particles' orbital eccentricity, thus supplying the energy required to maintain the arc. The ultimate energy reservoir is the satellite's orbital energy. Therefore, interaction with the arcs damps the satellite's orbital inclination. The self-gravity of the arcs limits their contraction and enforces a relation between arc length and mass. The estimated arc masses are so small, of the order of 10^16 g, that the satellite's orbital inclination suffers negligible decay over the age of the solar system. The inferred surface mass densities are comparable to those found in the major rings of Saturn and Uranus.