A second important result is that the TW method is extremely sensitive to the orientation of the x-y frame, and therefore to the way the integrals view the bar perturbation in the disc. The origin of the strong variations with the bar angle, and of the large discrepancy with true values, may be the impact of patterns other than the bar in the TW integrals, like spiral arms in the N-body simulation and the LMC data.
Thus, without agreement among the trends found with the various simulations used in the previous works and our present study, and without an identifiable region of bar orientation where ground-truth and measured pattern speeds agree within simulations, the individual pattern speeds found by the TW method in Fig. 9 cannot be representative of the real LMC bar pattern speed. The agreement of Ω𝑝 found by the LTW method with the value found by the IPTW method for the LMC also indicates that the pattern speed of bars measured by means of the LTW method may likely be only representative of any value stemming from random frame orientations fixed by the position angle of the major axis of discs on the sky plane, but not of a global bar angular frequency.
The pattern speed obtained with the Dehnen method, when applied to the LMC data, it surprisingly results in a bar with null rotation, perhaps slightly counter-rotating with respect to the disc. Peculiar bars with such property exist in numerical simulations (e.g. Collier & Madigan 2023). However, this result does not come without issues. An almost non-rotating LMC bar would indeed not show any corotation within the disc since such Ω𝑝 should never cross the Ω curve. It is not an easy task to imagine how the orbits and the disc structure would respond to this peculiar circumstance. An absence of corotation could allow the bar to increase its length and strength out to the disc outskirts, that is, make the orbits of stars and the LMC stellar gravitational potential very elongated throughout the whole LMC disc. Indeed, nothing could prevent it here from growing significantly owing to the absence of corotation and the expected destructive orbits perpendicular to the bar beyond corotation. We think that the method may be sensitive to dust extinction and completeness effects in the inner LMC region, perhaps more strongly than the other methods.
Assuming that the corotation radius 𝑅𝑐 = 4.20 ± 0.25 kpc measured by the BV model is more representative of the bar properties, it corresponds to a pattern speed of 18.5 +1.2 −1.1 km s−1 kpc-1 . The LTW pattern speed of 30.4 ± 1.3 km s-1 kpc−1 would thus be discrepant by 64% from the one inferred here. When compared to its radius of 2.3 kpc, the LMC stellar bar has 𝑅𝑐 /𝑅1 = 1.8±0.1, thus corresponding to a slow bar, according to numerical methods (Athanassoula 1992). Finally, if we assume that the pattern speed has to be estimated using a velocity curve tracing more closely the circular velocity (the rotation curve of the younger stellar populations in Jiménez-Arranz+23a) than the tangential velocity of the whole sample dominated by older stars (upper panel of Fig. 11), then 𝑅 𝑐 = 4.2 kpc would translate into Ω𝑝 = 20.9 ± 1.1 km s −1 kpc −1, which still compares well with the value found for the whole sample.
For a more extensive discussion of the results obtained using the TW we refer the reader to the full paper.