Both the three-dimensional density of red clump giants and the gas kinematics in the inner Galaxy indicate that the pattern speed of the Galactic bar could be much lower than previously estimated. Here, we show that such slow bar models are unable to reproduce the bimodality observed in local stellar velocity space. We do so by computing the response of stars in the Solar neighbourhood to the gravitational potential of slow and fast bars, in terms of their perturbed distribution function in action-angle space up to second order, as well as by identifying resonantly trapped orbits. We also check that the bimodality is unlikely to be produced through perturbations from spiral arms, and conclude that, contrary to gas kinematics, local stellar kinematics still favour a fast bar in the Milky Way, with a pattern speed of the order of almost twice (and no less than 1.8 times) the circular frequency at the Sun's position. This leaves open the question of the nature of the long flat extension of the bar in the Milky Way.
ABSTRACT The oldest stars in the Milky Way (born in the first few billion years) are expected to have a high density in the inner few kpc, spatially overlapping with the Galactic bulge. We use spectroscopic data from the Pristine Inner Galaxy Survey (PIGS) to study the dynamical properties of ancient, metal-poor inner Galaxy stars. We compute distances using starhorse, and orbital properties in a barred Galactic potential. With this paper, we release the spectroscopic AAT/PIGS catalogue (13 235 stars). We find that most PIGS stars have orbits typical for a pressure-supported population. The fraction of stars confined to the inner Galaxy decreases with decreasing metallicity, but many very metal-poor stars (VMP; [Fe/H] <−2.0) stay confined ($\sim 60~{{\ \rm per \, cent}}$ stay within 5 kpc). The azimuthal velocity vϕ also decreases between [Fe/H] = −1.0 and −2.0, but is constant for VMP stars (at ∼+40 km s−1). The carbon-enhanced metal-poor (CEMP) stars in PIGS appear to have similar orbital properties compared to normal VMP stars. Our results suggest a possible transition between two spheroidal components – a more metal-rich, more concentrated, faster rotating component, and a more metal-poor, more extended and slower/non-rotating component. We propose that the former may be connected to pre-disc in-situ stars (or those born in large building blocks), whereas the latter may be dominated by contributions from smaller galaxies. This is an exciting era where large metal-poor samples, such as in this work (as well as upcoming surveys, e.g. 4MOST), shed light on the earliest evolution of our Galaxy.
Starting from an axisymmetric equilibrium distribution function (DF) in action space, representing a Milky Way thin disc stellar population, we use the linearized Boltzmann equation to explicitly compute the response to a three-dimensional spiral potential in terms of the perturbed DF. This DF, valid away from the main resonances, allows us to investigate a snapshot of the velocity distribution at any given point in three-dimensional configuration space. Moreover, the first-order moments of the DF give rise to non-zero radial and vertical bulk flows – namely breathing modes – qualitatively similar to those recently observed in the extended solar neighbourhood. We show that these analytically predicted mean stellar motions are in agreement with the outcome of test-particle simulations. Moreover, we estimate for the first time the reduction factor for the vertical bulk motions of a stellar population compared to the case of a cold fluid. Such an explicit expression for the full perturbed DF of a thin disc stellar population in the presence of spiral arms will be helpful in order to dynamically interpret the detailed information on the Milky Way disc stellar kinematics that will be provided by upcoming large astrometric and spectroscopic surveys of the Galaxy.
We have applied our method for weighing the Galactic disk using phase-space spirals to the Gaia EDR3 proper motion sample. For stars in distant regions of the Galactic disk, the latitudinal proper motion has a close projection with vertical velocity, such that the phase-space spiral in the plane of vertical position and vertical velocity can be observed without requiring that all stars have available radial velocity information. We divided the Galactic plane into 360 separate data samples, each corresponding to an area cell in the Galactic plane in the distance range of 1.4-3.4 kpc, with an approximate cell length of 200-400 pc. Roughly half of our data samples were disqualified altogether due to severe selection effects, especially in the direction of the Galactic centre. In the remainder, we were able to infer the vertical gravitational potential by fitting an analytic model of the phase-space spiral to the data. This work is the first of its kind, in the sense that we are weighing distant regions of the Galactic disk with a high spatial resolution, without relying on the strong assumptions of axisymmetry. Post-inference, we fit a thin disk scale length of $2.2\pm 0.1$ kpc, although this value is sensitive to the considered spatial region. We see surface density variations as a function of azimuth on the order of 10-20 %, which is roughly the size of our estimated sum of potential systematic biases. With this work, we have demonstrated that our method can be used to weigh distant regions of the Galactic disk despite strong selection effects. We expect to reach even greater distances and improve our accuracy with future Gaia data releases and further improvements to our method.
The present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential has previously been computed through perturbation theory within the phase-space coordinates of the unperturbed axisymmetric system. Such an Eulerian linearized treatment, however, leads to singularities at resonances, which prevent quantitative comparisons with data. Here, we manage to capture the behaviour of the distribution function (DF) at a resonance in a Lagrangian approach, by averaging the Hamiltonian over fast angle variables and re-expressing the DF in terms of a new set of canonical actions and angles variables valid in the resonant region. We then follow the prescription of Binney, assigning to the resonant DF the time average along the orbits of the axisymmetric DF expressed in the new set of actions and angles. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits depends only on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data in terms of DFs in action space.
ABSTRACT We study the late-time evolution of the central regions of two Milky Way (MW)-like simulations of galaxies formed in a cosmological context, one hosting a fast bar and the other a slow one. We find that bar length, Rb, measurements fluctuate on a dynamical time-scale by up to 100 per cent, depending on the spiral structure strength and measurement threshold. The bar amplitude oscillates by about 15 per cent, correlating with Rb. The Tremaine–Weinberg method estimates of the bars’ instantaneous pattern speeds show variations around the mean of up to $\sim \!20{{\ \rm per\ cent}}$, typically anticorrelating with the bar length and strength. Through power spectrum analyses, we establish that these bar pulsations, with a period in the range ∼60–200 Myr, result from its interaction with multiple spiral modes, which are coupled with the bar. Because of the presence of odd spiral modes, the two bar halves typically do not connect at exactly the same time to a spiral arm, and their individual lengths can be significantly offset. We estimated that in about 50 per cent of bar measurements in MW-mass external galaxies, the bar lengths of SBab-type galaxies are overestimated by $\sim \!15{{\ \rm per\ cent}}$ and those of SBbc types by $\sim \!55{{\ \rm per\ cent}}$. Consequently, bars longer than their corotation radius reported in the literature, dubbed ‘ultrafast bars’, may simply correspond to the largest biases. Given that the Scutum–Centaurus arm is likely connected to the near half of the MW bar, recent direct measurements may be overestimating its length by 1–1.5 kpc, while its present pattern speed may be 5–10 $\rm km\ s^{-1}\ kpc^{-1}$ smaller than its time-averaged value.
We explore the connections between stellar age, chemistry, and kinematics across a Galactocentric distance of $7.5 < R\,(\mathrm{kpc}) < 9.0$, using a sample of $\sim 12\,000$ intermediate-mass (FGK) turnoff stars observed with the RAdial Velocity Experiment (RAVE) survey. The kinematics of this sample are determined using radial velocity measurements from RAVE, and parallax and proper motion measurements from the Tycho-Gaia Astrometric Solution (TGAS). In addition, ages for RAVE stars are determined using a Bayesian method, taking TGAS parallaxes as a prior. We divide our sample into young ($0 < \tau < 3$ Gyr) and old ($8 < \tau < 13$ Gyr) populations, and then consider different metallicity bins for each of these age groups. We find significant differences in kinematic trends of young and old, metal-poor and metal-rich, stellar populations. In particular, we find a strong metallicity dependence in the mean Galactocentric radial velocity as a function of radius ($\partial {V_{\rm R}}/\partial R$) for young stars, with metal-rich stars having a much steeper gradient than metal-poor stars. For $\partial {V_{\phi}}/\partial R$, young, metal-rich stars significantly lag the LSR with a slightly positive gradient, while metal-poor stars show a negative gradient above the LSR. We interpret these findings as correlations between metallicity and the relative contributions of the non-axisymmetries in the Galactic gravitational potential (the spiral arms and the bar) to perturb stellar orbits.
We investigate the kinematic signatures induced by spiral and bar structure in a set of simulations of Milky Way-sized spiral disc galaxies. The set includes test particle simulations that follow a quasi-stationary density wave-like scenario with rigidly rotating spiral arms, and N-body simulations that host a bar and transient, corotating spiral arms. From a location similar to that of the Sun, we calculate the radial, tangential and line-of-sight peculiar velocity fields of a patch of the disc and quantify the fluctuations by computing the power spectrum from a two-dimensional Fourier transform. We find that the peculiar velocity power spectrum of the simulation with a bar and transient, corotating spiral arms fits very well to that of APOGEE red clump star data, while the quasi-stationary density wave spiral model without a bar does not. We determine that the power spectrum is sensitive to the number of spiral arms, spiral arm pitch angle and position with respect to the spiral arm. However, it is necessary to go beyond the line-of-sight velocity field in order to distinguish fully between the various spiral models with this method. We compute the power spectrum for different regions of the spiral discs, and discuss the application of this analysis technique to external galaxies.
We use data from the Radial Velocity Experiment (RAVE) and the Tycho-Gaia astrometric solution (TGAS) catalogue to compute the velocity fields yielded by the radial (VR), azimuthal (Vϕ),and vertical (Vz) components of associated Galactocentric velocity. We search in particular for variation in all three velocity components with distance above and below the disc mid-plane, as well as how each component of Vz (line-of-sight and tangential velocity projections) modifies the obtained vertical structure. To study the dependence of velocity on proper motion and distance, we use two main samples: a RAVE sample including proper motions from the Tycho-2, PPMXL, and UCAC4 catalogues, and a RAVE–TGAS sample with inferred distances and proper motions from the TGAS and UCAC5 catalogues. In both samples, we identify asymmetries in VR and Vz. Below the plane, we find the largest radial gradient to be ∂VR/∂R = −7.01 ± 0.61 km s−1 kpc−1, in agreement with recent studies. Above the plane, we find a similar gradient with ∂VR/∂R = −9.42 ± 1.77 km s−1 kpc−1. By comparing our results with previous studies, we find that the structure in Vz is strongly dependent on the adopted proper motions. Using the Galaxia Milky Way model, we demonstrate that distance uncertainties can create artificial wave-like patterns. In contrast to previous suggestions of a breathing mode seen in RAVE data, our results support a combination of bending and breathing modes, likely generated by a combination of external or internal and external mechanisms.
We use Gaia DR2 astrometric and line-of-sight velocity information combined with two sets of distances obtained with a Bayesian inference method to study the 3D velocity distribution in the Milky Way disc. We search for variations in all Galactocentric cylindrical velocity components ($V_{\phi}$, $V_R$ and $V_z$) with Galactic radius, azimuth, and distance from the disc mid-plane. We confirm recent work showing that bulk vertical motions in the $R\text{-}z$ plane are consistent with a combination of breathing and bending modes. In the $x\text{-}y$ plane, we show that, although the amplitudes change, the structure produced by these modes is mostly invariant as a function of distance from the plane. Comparing to two different Galactic disc models, we demonstrate that the observed patterns can drastically change in short time intervals, showing the complexity of understanding the origin of vertical perturbations. A strong radial $V_R$ gradient was identified in the inner disc, transitioning smoothly from $16$ km s$^{-1}$ kpc$^{-1}$ at an azimuth of $30^\circ<\phi<45^\circ$ ahead of the Sun-Galactic centre line, to $-16$ km s$^{-1}$ kpc$^{-1}$ at an azimuth of $-45^\circ<\phi<-30^\circ$ lagging the solar azimuth. We use a simulation with no significant recent mergers to show that exactly the opposite trend is expected from a barred potential, but overestimated distances can flip this trend to match the data. Alternatively, using an $N$-body simulation of the Sagittarius dwarf-Milky Way interaction, we demonstrate that a major recent perturbation is necessary to reproduce the observations. Such an impact may have strongly perturbed the existing bar or even triggered its formation in the last $1\text{-}2$ Gyr.