Apparent Motion of the Circumstellar Envelope of CQ Tau in Scattered Light

The study of spiral structures in protoplanetary disks is of great importance for understanding the processes in the disks, including planet formation. Bright spiral arms were detected in the disk of young star CQ Tau by Uyama et al. in the H and L bands. The spiral arms are located inside the gap in millimeter-sized dust, discovered earlier using Atacama Large Millimeter/submillimeter Array observations. To explain the gap, Ubeira Gabellini et al. proposed the existence of a planet with the semimajor axis of 20 au. We obtained multi-epoch observations of a spiral feature in the circumstellar envelope of CQ Tau in the I c band using a novel technique of differential speckle polarimetry. The observations covering a period from 2015 to 2021 allow us to estimate the pattern speed of the spiral: −0.°2 ± 1.°1 yr−1 (68% credible interval; positive value indicates counterclockwise rotation), assuming a face-on orientation of the disk. This speed is significantly smaller than expected for a companion-induced spiral, if the perturbing body has a semimajor axis of 20 au. We emphasize that the morphology of the spiral structure is likely to be strongly affected by shadows of a misaligned inner disk detected by Eisner et al.

Identifying resonances of the Galactic bar in Gaia DR2: II. Clues from angle space

The Milky Way disk exhibits intricate orbit substructure of still-debated dynamical origin. The angle variables (θφ, θR)—which are conjugates to the actions (Lz, JR), and describe a star’s location along its orbit—are a powerful diagnostic to identify l:m resonances via the orbit shape relation ΔθR/Δθφ = −m/l. In the past, angle signatures have been hidden by survey selection effects (SEs). Using test particle simulations of a barred galaxy, we demonstrate that Gaia should allow us to identify the Galactic bar’s Outer Lindblad Resonance (l = +1, m = 2, OLR) in angle space. We investigate strategies to overcome SEs. In the angle data of the Gaia DR2 RVS sample, we independently identify four candidates for the OLR and therefore for the pattern speed Ωbar. The strongest candidate, Ωbar ∼ 1.4Ω0, positions the OLR above the ‘Sirius’ moving group, agrees with measurements from the Galactic center, and might be supported by higher-order resonances around the ‘Hercules/Horn’. But it misses the classic orbit orientation flip, as discussed in the companion study on actions. The candidate Ωbar ∼ 1.2Ω0 was also suggested by the action-based study, has the OLR at the ‘Hat’, is consistent with slow bar models, but still affected by SEs. Weaker candidates are Ωbar = 1.6 and 1.74Ω0. In addition, we show that the stellar angles do not support the ‘Hercules/Horn’ being created by the OLR of a fast bar. We conclude that—to resolve if ‘Sirius’ or ‘Hat’ are related to the bar’s OLR—more complex dynamical explanations and more extended data with well-behaved SEs are required.

Morphological and Kinematical Analysis of the Double-barred Galaxy NGC 3504 Using ALMA CO (2–1) Data

We present results obtained from ALMA CO (2–1) data of the double-barred galaxy NGC 3504. With three times higher angular resolution (∼ 0.″8) than previous studies, our observations reveal an inner molecular gas bar, a nuclear ring, and four inner spiral arm-like structures in the central 1 kpc region. Furthermore, the CO emission is clearly aligned with the two dust lanes in the outer bar region, with differences in shape and intensity between them. The total molecular gas mass in the observed region (50″ × 57″) is estimated to be ∼3.1 × 109 M⊙, which is 17 per cent of the stellar mass. We used the Kinemetry package to fit the velocity field and found that circular motion strongly dominates at R = 0.3 − 0.8 kpc, but radial motion becomes important at R < 0.3 kpc and R = 1.0 − 2.5 kpc, which is expected due to the presence of the inner and outer bars. Finally, assuming that the gas moves along the dust lanes in the bar rotating frame, we derived the pattern speed of the outer bar to be 18 ± 5 km s−1 kpc−1, the average streaming velocities on each of the two dust lanes to be 165 and 221 km s−1, and the total mass inflow rate along the dust lanes to be 12 M⊙ yr−1. Our results give a new example of an inner gas bar within a gas-rich double-barred galaxy and suggest that the formation of double-barred galaxies could be associated with the existence of such gas structures.

Galactic seismology: the evolving “phase spiral” after the Sagittarius dwarf impact

In 2018, the ESA Gaia satellite discovered a remarkable spiral pattern (“phase spiral”) in the z − Vz phase plane throughout the solar neighbourhood, where z and Vz are the displacement and velocity of a star perpendicular to the Galactic disc. In response to Binney & Schönrich’s analytic model of a disc-crossing satellite to explain the Gaia data, we carry out a high-resolution, N-body simulation (N ≈ 108 particles) of an impulsive mass (2 × 1010 M⊙) that interacts with a cold stellar disc at a single transit point. The disc response is complex since the impulse triggers a superposition of two distinct bisymmetric (m = 2) modes − a density wave and a corrugated bending wave − that wrap up at different rates. Stars in the faster density wave wrap up with time T according to φD(R, T) = (ΩD(R) + Ωo) T where φD describes the spiral pattern and ΩD = Ω(R) − κ(R)/2, where κ is the epicyclic frequency. While the pattern speed Ωo is small, it is non-zero. The slower bending wave wraps up according to ΩB ≈ ΩD/2 producing a corrugated wave. The bunching effect of the density wave triggers the phase spiral as it rolls up and down on the bending wave (“rollercoaster” model). The phase spiral emerges slowly about ΔT ≈ 400 Myr after impact. It appears to be a long-lived, disc-wide phenomenon that continues to evolve over most of the 2 Gyr simulation. Thus, given Sagittarius’ (Sgr) low total mass today (Mtot ∼ 3 × 108 M⊙ within 10 kpc diameter), we believe the phase spiral was excited by the disc-crossing dwarf some 1 − 2 Gyr before the recent transit. For this to be true, Sgr must be losing mass at 0.5-1 dex per orbit loop.

How the bar properties affect the induced spiral structure

ABSTRACT Stellar bars and spiral arms coexist and co-evolve in most disc galaxies in the local Universe. However, the physical nature of this interaction remains a matter of debate. In this work, we present a set of numerical simulations based on isolated galactic models aimed to explore how the bar properties affect the induced spiral structure. We cover a large combination of bar properties, including the bar length, axial ratio, mass, and rotation rate. We use three galactic models describing galaxies with rising, flat, and declining rotation curves. We found that the pitch angle best correlates with the bar pattern speed and the spiral amplitude with the bar quadrupole moment. Our results suggest that galaxies with declining rotation curves are the most efficient forming grand design spiral structure, evidenced by spirals with larger amplitude and pitch angle. We also test the effects of the velocity ellipsoid in a subset of simulations. We found that as we increase the radial anisotropy, spirals increase their pitch angle but become less coherent with smaller amplitude.

The kinematic richness of star clusters – II. Stability of spherical anisotropic models with rotation

ABSTRACT We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are applied to spherical systems with an initial Plummer density distribution, but modified kinematically in two ways: the velocity distribution is tangentially anisotropic, using results of Dejonghe, and the system is set in rotation by reversing the velocities of a fraction of stars in various regions of phase space, à la Lynden-Bell. The aim of the N-body simulations is first to survey the parameter space, and, using those results, to identify regions of phase space (by radius and orbital inclination) that have the most important influence on the bar instability. The matrix method is then used to identify the resonant interactions in the system that have the greatest effect on the growth rate of a bar. Complementary series of N-body simulations examine these processes in relation to the evolving frequency distribution and the pattern speed. Finally, the results are synthesized with an existing theoretical framework, and used to consider the old question of constructing a stability criterion.

Using Multichannel Singular Spectrum Analysis to Study Galaxy Dynamics

N-body simulations provide most of our insight into the structure and evolution of galaxies, but our analyses of these are often heuristic and from simple statistics. We propose a method that discovers the dynamics in space and time together by finding the most correlated temporal signals in multiple time series of basis function expansion coefficients and any other data fields of interest. The method extracts the dominant trends in the spatial variation of the gravitational field along with any additional data fields through time. The mathematics of this method is known as multichannel singular spectrum analysis (M-SSA). In essence, M-SSA is a principal component analysis of the covariance of time series replicates, each lagged successively by some interval. The dominant principal component represents the trend that contains the largest fraction of the correlated signal. The next principal component is orthogonal to the first and contains the next largest fraction, and so on. Using a suite of previously analysed simulations, we find that M-SSA describes bar formation and evolution, including mode coupling and pattern-speed decay. We also analyse a new simulation tailored to study vertical oscillations of the bar using kinematic data. Additionally, and to our surprise, M-SSA uncovered some new dynamics in previously analysed simulations, underscoring the power of this new approach.

Double X/Peanut Structures in Barred Galaxies – Insights from an N–body Simulation

Boxy, peanut– or X–shaped “bulges” are observed in a large fraction of barred galaxies viewed in, or close to, edge-on projection, as well as in the Milky Way. They are the product of dynamical instabilities occurring in stellar bars, which cause the latter to buckle and thicken vertically. Recent studies have found nearby galaxies that harbour two such features arising at different radial scales, in a nested configuration. In this paper we explore the formation of such double peanuts, using a collisionless N–body simulation of a pure disc evolving in isolation within a live dark matter halo, which we analyse in a completely analogous way to observations of real galaxies. In the simulation we find a stable double configuration consisting of two X/peanut structures associated to the same galactic bar – rotating with the same pattern speed – but with different morphology, formation time, and evolution. The inner, conventional peanut-shaped structure forms early via the buckling of the bar, and experiences little evolution once it stabilises. This feature is consistent in terms of size, strength and morphology, with peanut structures observed in nearby galaxies. The outer structure, however, displays a strong X, or “bow-tie”, morphology. It forms just after the inner peanut, and gradually extends in time (within 1 to 1.5 Gyr) to almost the end of the bar, a radial scale where ansae occur. We conclude that, although both structures form, and are dynamically coupled to, the same bar, they are supported by inherently different mechanisms.

Resonance sweeping by a decelerating Galactic bar

ABSTRACT We provide the first quantitative evidence for the deceleration of the Galactic bar from local stellar kinematics in agreement with dynamical friction by a typical dark matter halo. The kinematic response of the stellar disc to a decelerating bar is studied using secular perturbation theory and test particle simulations. We show that the velocity distribution at any point in the disc affected by a naturally slowing bar is qualitatively different from that perturbed by a steadily rotating bar with the same current pattern speed Ωp and amplitude. When the bar slows down, its resonances sweep through phase space, trapping, and dragging along a portion of previously free orbits. This enhances occupation on resonances, but also changes the distribution of stars within the resonance. Due to the accumulation of orbits near the boundary of the resonance, the decelerating bar model reproduces with its corotation resonance the offset and strength of the Hercules stream in the local vR-vφ plane and the double-peaked structure of mean vR in the Lz–φ plane. At resonances other than the corotation, resonant dragging by a slowing bar is associated with a continuing increase in radial action, leading to multiple resonance ridges in the action plane as identified in the Gaia data. This work shows models using a constant bar pattern speed likely lead to qualitatively wrong conclusions. Most importantly we provide a quantitative estimate of the current slowing rate of the bar $\dot{\Omega }_{\rm p}= (-4.5 \pm 1.4) \, {\rm km}\, {\rm s}^{-1}\, {\rm kpc}^{-1}\, {\rm Gyr}^{-1}$ with additional systematic uncertainty arising from unmodelled impacts of e.g. spiral arms.

Identifying resonances of the Galactic bar in Gaia DR2: I. Clues from action space

ABSTRACT Action space synthesizes the orbital information of stars and is well suited to analyse the rich kinematic substructure of the disc in the second Gaia data release's radial velocity sample. We revisit the strong perturbation induced in the Milky Way disc by an m = 2 bar, using test particle simulations and the actions (JR, Lz, Jz) estimated in an axisymmetric potential. These make three useful diagnostics cleanly visible. (1) We use the well-known characteristic flip from outward to inward motion at the outer Lindblad resonance (OLR; l = +1, m = 2), which occurs along the axisymmetric resonance line (ARL) in (Lz, JR), to identify in the Gaia action data three candidates for the bar’s OLR and pattern speed Ωbar: 1.85Ω0, 1.20Ω0, and 1.63Ω0 (with ∼0.1Ω0 systematic uncertainty). The Gaia data is therefore consistent with both slow and fast bar models in the literature, but disagrees with recent measurements of ∼1.45Ω0. (2) For the first time, we demonstrate that bar resonances – especially the OLR – cause a gradient in vertical action 〈Jz〉 with Lz around the ARL via ‘Jz-sorting’ of stars. This could contribute to the observed coupling of 〈vR〉 and 〈|vz|〉 in the Galactic disc. (3) We confirm prior results that the behaviour of resonant orbits is well approximated by scattering and oscillation in (Lz, JR) along a slope ΔJR/ΔLz = l/m centred on the l:m ARL. Overall, we demonstrate that axisymmetrically estimated actions are a powerful diagnostic tool even in non-axisymmetric systems.