We explore a second order Hamiltonian vertical resonance model for X-shaped or peanut-shaped galactic bulges. The X-or peanut-shape is caused by the 2:1 vertical Lindblad resonance with the bar, with two vertical oscillation periods per orbital period in the bar frame. We examine N-body simulations and find that due to the bar slowing down and disk thickening during bar buckling, the resonance and associated peanut-shape moves outward. The peanut-shape is consistent with the location of the 2:1 vertical resonance, independent of whether the bar buckled or not. We estimate the resonance width from the potential m = 4 Fourier component and find that the resonance is narrow, affecting orbits over a narrow range in the angular momentum distribution, dL/L ∼ 0.05. As the resonance moves outward, stars originally in the mid plane are forced out of the mid plane and into orbits just within the resonance separatrix. The height of the separatrix orbits, estimated from the Hamiltonian model, is approximately consistent with the peanut-shape height. The peanut-or X-shape is comprised of stars in the vicinity of the resonance separatrix. The velocity distributions from the simulations illustrate that low inclination orbits are depleted within resonance. Within resonance, the vertical velocity distribution is broad, consistent with resonant heating caused by the passage of the resonance through the disk. In the Milky Way bulge we relate the azimuthally averaged mid-plane mass density near the vertical resonance to the rotation curve and bar pattern speed. At an estimated vertical resonance galactocentric radius of ∼ 1.3 kpc, we confirm a mid-plane density of ∼ 5 × 10 8 M kpc −3 , consistent with recently estimated mass distributions. We find that the rotation curve, bar pattern speed, 2:1 vertical resonance location, X-shape tips, and mid-plane mass density, are all self-consistent in the Milky Way galaxy bulge.

We present Hubble Space Telescope WFC3-IR imaging in the fields of six apparently bright dusty star-forming galaxies (DSFGs) at z = 2 -4 identified by their rest-frame far-infrared colors using the Planck and Herschel space facilities. We detect near-infrared counterparts for all six submillimeter sources, allowing us to undertake strong-lensing analyses. One field in particular stands out for its prominent giant arcs, PLCK G165.7+67.0 (G165). After combining the color and morphological information, we identify 11 sets of image multiplicities in this one field. We construct a strong-lensing model constrained by this lensing evidence, which uncovers a bimodal spatial mass distribution, and from which we measure a mass of (2.6±0.11) × 10 14 M within ∼250 kpc. The bright (S 350 ≈ 750 mJy) DSFG appears as two images: a giant arc with a spatial extent of 4. 5 that is merging with the critical curve, and a lower-magnification counterimage that is detected in our new longer-wavelength groundand space-based imaging data. Using our ground-based spectroscopy, we calculate a dynamical mass of 1.3 +0.04 −0.70 × 10 15 M to the same fixed radius, although this value may be inflated relative to the true value if the velocity distribution is enhanced in the line-of-sight direction. We suggest that the bimodal mass taken in combination with the weak X-ray flux and low SZ decrement may be explained as a pre-merger for which the intracluster gas is diluted along the line of sight, while the integrated surface mass density is supercritical to strong-lensing effects.

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.

We explore the kinematics (both the radial velocity and the proper motion) of the vertical X-shaped feature in the Milky Way with an N-body bar/bulge model. From the solar perspective, the distance distribution of particles is double-peaked in fields passing through the X-shape. The separation and amplitude ratio between the two peaks qualitatively match the observed trends towards the Galactic bulge. We confirm clear signatures of cylindrical rotation in the pattern of mean radial velocity across the bar/bulge region. We also find possible imprints of coherent orbital motion inside the bar structure in the radial velocity distribution along l = 0 • , where the near and far sides of the bar/bulge show excesses of approaching and receding particles. The coherent orbital motion is also reflected in the slight displacement of the zero-velocity-line in the mean radial velocity, and the displacement of the maximum/minimum in the mean longitudinal proper motion across the bulge region. We find some degree of anisotropy in the stellar velocity within the X-shape, but the underlying orbital family of the X-shape cannot be clearly distinguished. Two potential applications of the X-shape in previous literature are tested, i.e., bulge rotation and Galactic center measurements. We find that the proper motion difference between the two sides of the X-shape can be used to estimate the mean azimuthal streaming motion of the bulge, but not the pattern speed of the bar. We also demonstrate that the Galactic center can be located with the X-shape, but the accuracy depends on the fitting scheme, the number of fields, and their latitudinal coverage.

Using the LAMOST-Gaia common stars, we demonstrate that the in-plane velocity field for the nearby young stars are significantly different from that for the old ones. For the young stars, the probably perturbed velocities similar to the old population are mostly removed from the velocity maps in the X-Y plane. The residual velocity field shows that the young stars consistently move along Y with faster v φ at the trailing side of the local arm, while at the leading side, they move slower in azimuth direction. At both sides, the young stars averagely move inward with v R of −5 ∼ −3 km s −1 . The divergence of the velocity in Y direction implies that the young stars are associated with a density wave nearby the local arm. We therefore suggest that the young stars may reflect the formation of the local spiral arm by correlating themselves with a density wave. The range of the age for the young stars is around 2 Gyr, which is sensible since the transient spiral arm can sustain that long. We also point out that alternative explanations of the peculiar velocity field for the young population cannot be ruled out only from this observed data.