Óscar Jiménez-Arranz - Kinematic analysis of the Large Magellanic Cloud

Kinematic analysis of the Large Magellanic Cloud

In the section Large and Small Magellanic Cloud clean samples for Gaia DR3 we explained how we obtained clean Large and Small Magellanic Cloud (LMC and SMC, respectively) samples for Gaia DR3. However, in Jiménez-Arranz+23a we do not only offered the LMC clean samples (with different levels of completeness and purity) but also presented the study of the internal kinematics of the LMC.

To do so, we transform the Gaia heliocentric measurements (𝛼, 𝛿, D, 𝜇𝛼∗, 𝜇𝛿, 𝑣los) to the LMC reference frame coordinates (x', y', z', 𝑣𝑥′, 𝑣𝑦′, 𝑣𝑧′), i.e., we move from the Gaia observables to the LMC in-plane coordinates. It is necessary to know the LMC morphological parameters (inclination angle i and position angle of the line-of-nodes 𝜃) and systemic motion (𝜇𝛼∗,'0, 𝜇𝛿,0, 𝑣los,0). We consider the LMC parameters obtained in Gaia Collaboration, X. Luri et al. 2021b (Section 5, Table 5).

On the other hand, since we do not have reliable information for individual distances because the parallaxes are very small and close to the noise (Gaia Collaboration, X. Luri et al. 2021b; Lindegren et al. 2021c), we assume that all the stars lie on the LMC disc plane, as an approximation. Thus, we impose 𝑧′ to be zero, which leads to a distance of 𝐷𝑧′ =0 (different to the real one) for each star. In Fig. 1, we show a schematic representation of what this assumption implies. We represent the position of a real star in dark gray, while the white star in red solid line is the projection of the real star on the LMC plane. With this strategy all LMC stars are assumed to lie on its plane.

The formalism used allows taking into account line-of-sight velocities. Thus, in this work we deal with two different datasets: the full samples without line-of-sight velocity information and, the sub-samples of stars with individual line-of-sight velocities. For the former, we estimate each star line-of-sight velocity by taking into account its position and proper motion and the global parameters of the LMC plane.

Figure 1. Schematic representation of the reference frames used, all of them centred on the LMC centre (𝛼0, 𝛿0). In red, we show the Cartesian LMC frame, (𝑥′, 𝑦′, 𝑧′). We also show the position of a real star (solid dark gray), its projection in the LMC cartesian frame under the imposition of 𝑧 ′ = 0 (red frame).

Once we have the Cartesian positions (x', y', z') and velocities (𝑣𝑥′, 𝑣𝑦′, 𝑣𝑧′) described in the plane of the LMC, for convenience we can express the velocities in cylindrical coordinates (𝑣R, 𝑣ϕ, 𝑣𝑧′). The radial component 𝑣R indicates the motion towards (negative) as well as away (positive) from the galactic centre, while the residual tangential velocity 𝑣ϕ - mean(𝑣ϕ(R)) is obtained by subtracting the tangential velocity curve to the tangential velocity component, indicating the motion with respect to the tangential curve. The vertical component 𝑣𝑧′ indicates the motion across the galactic plane.

Here, in Fig. 2, we analyse the velocity profiles in the LMC coordinate system:

Figure 2. Velocity profiles for the four LMC samples in the case 𝑉 𝑙𝑜𝑠 is not available (left) and when it is available (right). From top to bottom: Radial, tangential, and vertical velocity profiles. Each curve corresponds to one LMC sample: PM selection (blue), NN complete (orange), NN optimal (green) and NN truncated-optimal (red).

The vertical velocity profile for the four full samples is completely flat and centered at 0 km s−1, which is a consequence of not using the observational 𝑉𝑙𝑜𝑠 in these samples

Now, we analyse the velocity maps in the LMC coordinate system for the four LMC samples:

Figure 3. LMC median radial velocity maps. All maps are shown in the (𝑥′, 𝑦′) Cartesian coordinate system. From top to bottom: PM sample, NN complete, NN optimal, and NN truncated-optimal sample. Left: Line-of-sight velocity not included. Right: Line of sight velocity included. NN truncated-optimal 𝑉𝑙𝑜𝑠 sub-sample map is not shown because it is the same as the NN optimal 𝑉𝑙𝑜𝑠 sub-sample.

Figure 4. Same as in Fig. 3, but for the LMC median residual tangen-tial velocity.

Figure 5. Same as in Fig. 3 for the median vertical velocity of the 𝑉𝑙𝑜𝑠 sub-samples. As in Fig.2, the vertical velocity for all stars in the four full samples is 0 km s−1, which is a consequence of not using the observational 𝑉𝑙𝑜𝑠 in these samples

From these maps we can conclude the following:

In all samples and sub-samples, the dynamics in the inner disc are mainly dominated by the bar. An asymmetry along the bar-major axis is emphasised , especially when mapping the kinematics with the 𝑉𝑙𝑜𝑠 sub-samples.
The kinematics on the spiral arm over-density seem to be dominated by an inward (𝑉𝑅 < 0) motion and a rotation faster than that of the disc (𝑉𝜙 − mean(𝑉𝜙(R)) > 0) in the part of the arm attached to the bar, although 𝑉𝑙𝑜𝑠 sub-samples are not conclusive in this region.
The dynamics seems to change in the part of the arm with lower density or even detached from the main arm after the density break, in the sense that the radial velocity and residual tangential velocity can reverse signs.
The lack of a 𝑉𝑙𝑜𝑠 value for all stars does not substantially impact the kinematic profiles or maps. The approximation used to derive the internal kinematics is accurate.

In this short summary of Jiménez-Arranz+23a we do not enter in many more details. However, just mentioning that in the full article we also analyse the stellar velocity curves (both radial and residual tangential) of the different evolutionary phases, and analyse with animations the variation of the velocity profile and maps with the variation of the LMC morphological parameters and systemic motion to test the robustness of the results. For the latter, we show below few examples, however, all animations can be found here.

Figure 6. Dependence of the LMC kinematic maps with the variation of the inclination angle i with a change of +/- 10º.

Figure 7. Same as in Fig. 6, but for the position angle of the line-of-nodes 𝜃.

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