Aims. We propose a new, more realistic description of the perturbed gravitational potential of spiral galaxies, with spiral arms having Gaussian-shaped groove profiles. The aim is to reach a self-consistent description of the spiral structure, that is, one in which an initial potential perturbation generates, by means of the stellar orbits, spiral arms with a profile similar to that of the imposed perturbation. Self-consistency is a condition for having long-lived structures. Methods. Using the new perturbed potential, we investigate the stable stellar orbits in galactic disks for galaxies with no bar or with only a weak bar. The model is applied to our Galaxy by making use of the axisymmetric component of the potential computed from the Galactic rotation curve, in addition to other input parameters similar to those of our Galaxy. The influence of the bulge mass on the stellar orbits in the inner regions of a disk is also investigated. Results. The new description offers the advantage of easy control of the parameters of the Gaussian profile of its potential. We compute the density contrast between arm and inter-arm regions. We find a range of values for the perturbation amplitude from 400 to 800 km 2 s −2 kpc −1 , which implies an approximate maximum ratio of the tangential force to the axisymmetric force between 3% and 6%. Good self-consistency of arm shapes is obtained between the Inner Lindblad resonance (ILR) and the 4:1 resonance. Near the 4:1 resonance the response density starts to deviate from the imposed logarithmic spiral form. This creates bifurcations that appear as short arms. Therefore the deviation from a perfect logarithmic spiral in galaxies can be understood as a natural effect of the 4:1 resonance. Beyond the 4:1 resonance we find closed orbits that have similarities with the arms observed in our Galaxy. In regions near the center, elongated stellar orbits appear naturally, in the presence of a massive bulge, without imposing any bar-shaped potential, but only extending the spiral perturbation a little inward of the ILR. This suggests that a bar is formed with a half-size ∼3 kpc by a mechanism similar to that of the spiral arms. Conclusions. The potential energy perturbation that we adopted represents an important step in the direction of self-consistency, compared to previous sine function descriptions of the potential. In addition, our model produces a realistic description of the spiral structure, which is able to explain several details that were not yet understood.
We present a map of the spiral structure of the Galaxy, as traced by molecular carbon monosulphide (CS) emission associated with IRAS sources which are believed to be compact H ii regions. The CS line velocities are used to determine the kinematic distances of the sources in order to investigate their distribution in the galactic plane. This allows us to use 870 objects to trace the arms, a number larger than that of previous studies based on classical H ii regions. The distance ambiguity of the kinematic distances, when it exists, is solved by different procedures, including the latitude distribution and an analysis of the longitude–velocity diagram. The study of the spiral structure is complemented with other tracers: open clusters, Cepheids, methanol masers and H ii regions. The well‐defined spiral arms are seen to be confined inside the corotation radius, as is often the case in spiral galaxies. We identify a square‐shaped sub‐structure in the CS map with that predicted by stellar orbits at the 4:1 resonance (four epicycle oscillations in one turn around the galactic centre). The sub‐structure is found at the expected radius, based on the known pattern rotation speed and epicycle frequency curve. An inner arm presents an end with strong inwards curvature and intense star formation that we tentatively associate with the region where this arm surrounds the extremity of the bar, as seen in many barred galaxies. Finally, a new arm with concave curvature is found in the Sagitta to Cepheus region of the sky. The observed arms are interpreted in terms of perturbations similar to grooves in the gravitational potential of the disc, produced by crowding of stellar orbits.
In the last few decades many efforts have been made to understand the effect of spiral arms on the gas and stellar dynamics in the Milky Way disc. One of the fundamental parameters of the spiral structure is its angular velocity, or pattern speed Ω p , which determines the location of resonances in the disc and the spirals' radial extent. The most direct method for estimating the pattern speed relies on backward integration techniques, trying to locate the stellar birthplace of open clusters. Here we propose a new method based on the interaction between the spiral arms and the stars in the disc. Using a sample of around 500 open clusters from the New Catalogue of Optically Visible Open Clusters and Candidates, and a sample of 500 giant stars observed by APOGEE, we find Ω p = 23.0 ± 0.5 km s −1 kpc −1 , for a local standard of rest rotation V 0 = 220 km s −1 and solar radius R 0 = 8.0 kpc. Exploring a range in V 0 and R 0 within the acceptable values, 200-240 km s −1 and 7.5-8.5 kpc, respectively, results only in a small change in our estimate of Ω p , that is within the error. Our result is in close agreement with a number of studies which suggest values in the range 20-25 km s −1 kpc −1 . An advantage of our method is that we do not need knowledge of the stellar age, unlike in the case of the birthplace method, which allows us to use data from large Galactic surveys. The precision of our method will be improved once larger samples of disk stars with spectroscopic information will become available thanks to future surveys such as 4MOST.
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