STELLAR KINEMATIC CONSTRAINTS ON GALACTIC STRUCTURE MODELS REVISITED: BAR AND SPIRAL ARM RESONANCES

The study of stellar kinematic groups in the solar neighborhood has a long tradition in Galactic astronomy, going back to the discovery of the Hyades and Ursa Major groups (Proctor 1869). In Antoja et al. (2008) we presented a study of the solar neighborhood kinematic groups using a sample of 24,190 stars. We confirmed the existence of the Sirius, Coma Berenices, Hyades-Pleiades, and Hercules branches (Figure 1(a)). They all have a negative slope of ∼16° in the U–V plane (following the standard definitions of U and V) and a slight curvature.

Zoom In Zoom Out Reset image size

A considerable amount of work has been performed in an attempt to explain the origin of these kinematic groups. External processes like past accretion events (Navarro et al. 2004) and internal disk processes like star formation bursts or secular dynamics have been proposed. Although they were initially considered mutually exclusive, all such mechanisms are natural in current galaxy formation models (Klypin et al. 2008; Romano-Díaz et al. 2008; Ceverino & Klypin 2009). Recently, the hypothesis of the disk-dynamical origin of these structures has gained popularity partially because of the consistency of the Hercules structure with the effects of the Galactic bar resonances (Kalnajs 1991; Dehnen 2000; Fux 2001). In addition, steady or transient spiral arms were proposed to explain the characteristics of some of these stellar groups (Skuljan et al. 1999; De Simone et al. 2004; Famaey et al. 2005; Quillen & Minchev 2005). A more recent study argues that the combined effect of a bar and spiral arms is necessary to accurately reproduce observations in the solar neighborhood (Chakrabarty 2007). In that case, spiral arms at the weaker end of the observational range (with a fractional amplitude of less than 4% of the background disk density) were used. However, in that study the spiral arms seem to contribute only in the fine structure, thus weakening constraints on the Milky Way (MW) spiral structure based on the solar neighborhood kinematics. Previous studies have considered models for the nonaxisymmetric components of the Galaxy motivated by the dynamical point of view, in particular weak spiral arms described by a cosine function and bars described by the quadrupole perturbation. However, it is unclear whether there is any dependence of the induced local solar neighborhood kinematics on the detailed Galactic structure. Moreover, the initial conditions hardly consider the evolution of the MW.

Our contribution improves upon earlier studies. First we investigate the stellar kinematic response to a model that satisfies published observational constraints to the MW structure, in particular to the nonaxisymmetric components. Secondly, we consider for the first time initial conditions and integration times that attempt to represent stars born at different times and with different kinematic conditions, such as those in the solar neighborhood. Lastly, we investigate effects on the local dark matter kinematics, in particular in the disk-like dark matter structure recently predicted by lambda cold dark matter (LCDM) simulations. This issue is important to predict signals in direct dark matter detection experiments.

In order to study the effect of the nonaxisymmetric Galactic structure on the solar neighborhood kinematic distribution, we have performed numerical integrations of test particle orbits on the Galactic plane, adopting the initial conditions discussed in Section 2.2 and the potential described in Section 2.1. Each particle integration time is initialized at a value t = −τ and ended at t = 0, where τ is the time during which the particle is exposed to the nonaxisymmetric potential. The induced kinematic distribution at the end of the simulation is studied by considering the particles inside a circle of radius 500 pc centered at the solar position. Finally, the predicted and the observed distributions are compared. The motion equations were integrated with the Bulirsch–Stoer algorithm of Press et al. (2004), conserving Jacobi's integral within a relative variation of |(E_Ji − E_Jf)/E_Ji| ≈ 10⁻¹¹ for only-arms and only-bar models. The reference frame used for the calculations is the rotation frame of the spiral arms when only this nonaxisymmetric component is considered and the one of the bar in the other cases. In all cases, we check that the number of particles in the final distributions is statistically robust.

2.1. The Galactic Model

2.2. Initial Conditions

Models Using Only Spiral Arms. In this section we present the kinematic structure developed by the self-gravitating spiral arm model. We find that this model produces ample substructure. In particular, assuming low velocity dispersions (IC1), it reproduces a branch at low angular momentum (with V ∼ −40 km s^-1 consistent with the Hercules structure) separated from a central group of substructures. To our knowledge, it is the first time that an unbarred model has produced a similar structure. Figure 1(b) shows the U–V plane for the solar position. Although the shape of the structure at V = −40 km s^-1 is not exactly equal to the Hercules branch, it does show that the spiral arms by themselves crowd the velocity space at these negative V. In particular, the test particles in this kinematic group have a perturbation exposure time of at least ∼1 Gyr. The central part of the distribution seems to be split into two groups or branches, resembling some of the observed central kinematic branches (Figure 1(a)). In order to explore small variations with respect to the configuration of Drimmel & Spergel (2001), given the uncertainty on the exact position of the arms, we also show in Figure 1(c) the U–V plane for a region located at ϕ = −40°, that is at the solar circle but at 40° of the Sun in the counter-clockwise direction. In this case and for a wide range of ϕ, the equivalent to the Hercules structure is also generated. We conclude that the contribution of the spiral arms to the solar neighborhood kinematics may be comparable to that of the bar. The sensitivity of our results to the properties of the arms indicates that local kinematics can be used as one of the constraints to the current observational ambiguities about this nonaxisymmetric component.

Models Using Only a Bar. In agreement with previous studies (e.g., Dehnen 2000), we find that a Galactic model using only a bar can trigger a kinematic group at negative V and U resembling the Hercules branch. However, in our experiments this branch can be populated only under some combinations of model parameters and initial conditions. For example, a bar pattern speed of Ω_b = 60 km s^-1 kpc⁻¹ (R_OLR/R = 0.74) under IC2 produces a branch at an incorrect position (U ⩾ 0). However, if the imaginary solar observer is located at an inner radius R = 6–7 kpc (where R_OLR/R = 0.97) a structure appears at V ∼ −35 km s^-1 and U ⩽ 0, as is shown at the top left of Figure 1(d). A kinematic group at V, U ⩽ 0 also appears if the bar pattern speed is reduced to 45 km s^-1 kpc⁻¹ (Figure 1(e)), although the mean branch velocity V is now slightly smaller: V ∼ −20 km s^-1 (again with R_OLR/R = 0.97). In summary, the Hercules branch at the correct position may be achieved by varying either the model pattern speed, the observer position, or even the initial conditions.

If we consider hotter initial conditions (IC3), arch-shaped structures appear at lower V. These structures appear even if we consider an axisymmetric disk model, as also recently reported by Minchev et al. (2009) who assumed a nonrelaxed model. In our simulations the positions of these kinematic arches are modified when the bar is added to the model. This suggests that both kinematic initial conditions and Galactic structure contribute to create the kinematic groups. For example, differences are observed if we use either Ω_b = 45 km s^-1 kpc⁻¹ (Figure 1(f)) or Ω_b = 60 km s^-1 kpc⁻¹ (Figure 1(g)). The arches developed at V ∼ −40 km s^-1 and −100 km s^-1 for the lower bar pattern speed (not seen when Ω_b = 60 km s^-1 kpc⁻¹) are closer to the Hercules and Arcturus observed structures. ⁴ This result should be considered only as evidence of sensitivity to the model but not necessarily as favoring a particular Ω_b value. Furthermore, these simulations show the important role of the bar in the development of the local kinematic structure.

Combined Models. Here we present the results obtained with the model that includes both the bar and the spiral arm perturbations. This model, with different pattern speeds for the bar and the spirals, is supported by recent studies like Patsis et al. (2009). They reported that the best match between observations and models for the galaxy NGC 3359 is found when different pattern speeds for the bar (39 km s^-1 kpc⁻¹) and for the spiral arms (15 km s^-1 kpc⁻¹) are considered. Now we show examples of how the branches generated by the spiral arms or the bar are maintained when the combined model is used. Figure 1(h) shows the results for the spiral arms plus the bar with Ω_b = 45 km s^-1 kpc⁻¹ used with IC1 near the solar position (ϕ = −40°). In Figure 1(i), we show the case corresponding to spiral arms and a bar with Ω_b = 45 km s^-1 kpc⁻¹ under IC3. Here the arch-shaped structures associated with Hercules and Arcturus are still observed.

The diversity of the initial conditions in our simulations is not extensive. Moreover, the observed velocity field is likely to be the result of the combined action of several Galactic processes. Therefore, comparison between the observed velocity distribution (Figure 1(a)) and the results of test particle simulations is not straightforward. A first approach might be to compare the observed velocity field with the combined model results under IC1 and IC3, where the central branches and the kinematic groups at low angular momentum would appear simultaneously. The next complexity level might require the inclusion of age and kinematic criteria in the definition of the artificial observational sample. We defer such details to a future study, since they do not alter the conclusions of this Letter.

Another unexpected aspect of the bar- and spiral arm-induced phase space structure is the effect on the local dark matter kinematics. Particles in a possible dark matter bar (Colín et al. 2006), dark disk (Bruch et al. 2008; Read et al. 2008), and even in the dark matter halo (Athanassoula 2005) are trapped/scattered in the same resonances as stars are. Ceverino & Klypin (2007) show in their Figures 9 and 11 that different bar-induced resonances can be populated by disk-like and halo particles.

Our study considers only the case of the dark disk. Following Read et al. (2009) we assume that our IC3 initial conditions set also represents the dark particles in the dark thick disk. Thus Figures 1(f), (g), and (i), obtained from IC3, also reproduce the local dark matter kinematics induced by our MW dynamical models. Our results show that these models generate dark matter currents inside the Galactic dark disk. These dark-matter currents would be independent of the Galactic assembly history or the dark substructure abundance. The dynamical history of the Galaxy and its detailed large scale structure may help to establish whether the amplitude of the dark matter kinematic structure is detectable by planned dark matter detection experiments.

The orbital analysis of a MW model consistent with published observational constraints has several unexpected consequences for the local stellar kinematics.

The spiral arm contribution to the resonant structure in the solar neighborhood may be comparable to that of the Galactic bar. The main differences to previous studies are the arm force contrast and force field shape (Pichardo et al. 2003, Figures 5, 8, and 9), as well as the variety in initial conditions. In particular, we find that the Hercules structure may be produced by the spiral arms and not exclusively by bar resonances as traditionally believed. Dehnen (2000) concluded that the Hercules branch is unlikely to have been produced by resonant scattering processes due to spiral arms. His main argument is that spiral arms do not act on stars with epicycles greater than the interarm separation. However, the epicycle amplitude of the stars in the structure created in our simulations⁵ (at U ∼ [ − 30, 30] and V ∼ [ − 45, − 35]) is about 3 kpc. On the other hand, the interarm separation in the different loci of our model is in the range 5.5–7 kpc. This is sufficient to produce the Hercules structure and is still in agreement with Dehnen (2000). Other authors such as Quillen & Minchev (2005) reproduced the Hyades-Pleiades and Coma Berenices branches as ascribed to periodic orbits related to the spiral arm 4:1 ILR, but not the Hercules structure. For some parameter combinations our model reproduces both kinds of structure. Detailed comparison with other authors is not straightforward because many of them used the tight-winding approximation to model the spiral arms, a different simulation strategy, and, in some cases, even a four-armed model (Chakrabarty 2007), while ours includes two arms.

As in previous studies, we confirm that the Hercules structure can also be produced by the Galactic bar under certain combinations of the model parameters and initial conditions. However, we considered a prolate bar (for the detailed force field, see Figure 16 of Pichardo et al. 2004) instead of the widely used cosine bar potential (Dehnen 2000). The study of possible differences in the local kinematic structure generated by each model is postponed for a future study.

A subset of our experiments develops a structure resembling the Arcturus kinematic group. The required condition seems to be a relatively hot stellar disk population similar to the thick disk in kinematics. This kinematic group may have arisen from a past accretion event (Navarro et al. 2004; Villalobos & Helmi 2009). Alternatively Williams et al. (2008) recently discussed a possible disk-dynamical origin of Arcturus based on stellar population evidence, and postulated the bar 6:1 OLR as the triggering mechanism. On the other hand, Minchev et al. (2009) proposed an origin related to nonequilibrium initial conditions. Our results support an internal disk origin and, in addition, we find that the dynamics of the bar have an influence on these low angular momentum kinematic groups as they modify these structures generated in the axisymmetric model. Preliminary results of orbit integration in three dimensions show that the main arches generated in the two-dimensional case are maintained and the Galactic bar significantly takes part in defining their shape. However, the three-dimensional case deserves special attention and is the subject of ongoing studies. The fact that a vrms of 40 km s^-1 is high enough to allow the creation of these arches in our experiments is encouraging, but it is still not sufficient to disentangle the origin of Arcturus. A deeper discussion of this point is beyond of the scope of this Letter, but it is the subject of an upcoming study.

We show that the Galactic nonaxisymmetric potential develops dark kinematic groups in the dark disk predicted in cosmological simulations of galaxy formation. These currents are independent of the halo substructure abundance and may have new consequences for planned dark matter direct detection experiments.

The dependence of the stellar kinematics in the solar neighborhood on the structure, dynamics, and initial conditions of our experiments suggests that kinematic groups may provide a useful constraint on nonaxisymmetric MW models. A systematic scan of the associated parameter space will be required in order to disentangle the origin of the different kinematic groups in the solar neighborhood. We are currently exploring strategies to do so. Studies like the ones discussed in this Letter will derive benefit from upcoming surveys like GAIA and SEGUE2. In summary, the imprints of the nonaxisymmetric Galactic structure on the local stellar kinematics are strong.

We thank G. Lake and D. Ceverino for enlightening discussions about dark matter in the MW, K. Freeman for suggesting the study of Arcturus in our simulations, and J. González, V. Avila-Reese, L. Aguilar, and H. Throop for a careful reading of the manuscript. We also thank the referee for the very helpful comments and suggestions which much improved the first version of this paper. This study was supported by MEC contracts ESP2006-13855-C02-01 and AYA2006-15623-C02-02, grants CONACyT 60354 and 50720, and UNAM PAPIIT IN1 19708. T.A. was supported by the Predoctoral Fellowship of the Generalitat de Catalunya 2008FIC 00121 and by the LENAC mobility program. The simulations were run at the HP CP 4000 cluster (KanBalam) in the DGSCA/UNAM.