The shearing sheet and swing amplification revisited

ABSTRACT The principal results of the classic analysis of the shearing sheet and swing amplification by Julian and Toomre (JT) are re-derived in a more accessible way and 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 the Lin–Shu–Kalnajs (LSK) dispersion relation, we discover that two wavepackets emerge inside corotation: one each side of the inner Lindblad resonance. An extended form of the JT equation is used to investigate the impact of there being a deficit or surplus of stars in a narrow range of angular momenta. Swing amplification of leading waves introduced by such a groove gives rise to transient trailing spirals that extend further in radius and live longer at smaller azimuthal wavenumbers. Although the LSK dispersion relation provides useful interpretations of wavepackets, the shearing sheet highlights the limitations of the LSK approach to disc dynamics. Disturbances do not avoid an annulus around corotation, as the LSK dispersion relation implies. While disturbances of the shearing sheet have a limited life in real space, they live on much longer in velocity space, which Gaia allows us to probe extensively. c++ code is provided to facilitate applications of winding spiral waves.

Angle-action variables for orbits trapped at a Lindblad resonance

ABSTRACT The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic Galaxy model. Tori are computed for orbits trapped at both the inner and outer Lindblad resonances of our Galaxy. At the outer Lindblad resonance, orbits are quasi-periodic and can be accurately fitted by torus mapping. At the inner Lindblad resonance, orbits are significantly chaotic although far from ergodic, and each orbit explores a small range of tori obtained by torus mapping.

Stellar bars in counter-rotating dark matter haloes: the role of halo orbit reversals

Disc galaxies can exchange angular momentum and baryons with their host dark matter (DM) haloes. These haloes possess internal spin, λ, which is insignificant rotationally but does affect interactions between the baryonic and DM components. While statistics of prograde and retrograde spinning haloes in galaxies is not available at present, the existence of such haloes is important for galaxy evolution. In the previous works, we analysed dynamical and secular evolution of stellar bars in prograde spinning haloes and the DM response to the bar perturbation, and found that it is modified by the resonant interactions between the bar and the DM halo orbits. In this work, we follow the evolution of stellar bars in retrograde haloes. We find that this evolution differs substantially from evolution in rigid unresponsive haloes, discussed in the literature. First, we confirm that the bar instability is delayed progressively along the retrograde λ sequence. Secondly, the bar evolution in the retrograde haloes differs also from that in the prograde haloes, in that the bars continue to grow substantially over the simulation time of 10 Gyr. The DM response is also substantially weaker compared to this response in the prograde haloes. Thirdly, using orbital spectral analysis of the DM orbital structure, we find a phenomenon we call the orbit reversal – when retrograde DM orbits interact with the stellar bar, reverse their streaming and precession, and become prograde. This process dominates the inner halo region adjacent to the bar and allows these orbits to be trapped by the bar, thus increasing efficiency of angular momentum transfer by the inner Lindblad resonance. We demonstrate this reversal process explicitly in a number of examples.

Bar Formation in Milky Way type Galaxies

Many barred galaxies, possibly including the Milky Way, have cusps in their centers. There is a widespread belief, however, that the usual bar instability, which occurs in bulgeless galaxy models, is impossible for cuspy models because of the presence of the inner Lindblad resonance for any pattern speed. At the same time, there is numerical evidence that the bar instability can form a bar. We analyze this discrepancy by performing accurate and diverse

A SINFONI view of circum-nuclear star-forming rings in spiral galaxies

We present near-infrared (H- and K-band) SINFONI integral-field observations of the circumnuclear star formation rings in five nearby spiral galaxies. We made use of the relative intensities of different emission lines (i.e. [FeII], HeI, Brγ) to age date the stellar clusters present along the rings. This qualitative, yet robust, method allows us to discriminate between two distinct scenarios that describe how star formation progresses along the rings. Our findings favour a model where star formation is triggered predominantly at the intersection between the bar major axis and the inner Lindblad resonance and then passively evolves as the clusters rotate around the ring (‘Pearls on a string’ scenario), although models of stochastically distributed star formation (‘Popcorn’ model) cannot be completely ruled out.

Star Clusters in Galactic Resonance Rings

Resonance rings are intriguing sites of organized star formation in some galaxies. The Hubble Space Telescope Wide Field and Planetary Camera 2 has been used to image several resonance rings at high resolution in order to study the star clusters in the rings. Here I summarize results on inner Lindblad resonance rings in ESO 565–11 and NGC 1326, and on an inner 4:1 resonance ring in the Seyfert 2 galaxy NGC 3081. The latter ring provides one of the strongest cases illustrating the connection between star formation and dynamics in disk galaxies.