There are several different lines of evidence which together form a coherent picture: that of a barred galaxy. Moreover, as most disc galaxies are barred, we should expect the same from the Milky Way. The various evidences are:
The observed light distribution (2MASS) shows a left-right assymmetry in brightness and the vertical height. This is explained by the near end of the bar being located on that side.
The observed gas velocities show velocities which are "forbidden" in an axisymmetric or near-axisymmetric (spiral arms only) galaxy. These velocities occur naturally from the orbits of gas in a barred potential
The velocity distribution of stars in the Solar neighbourhood shows some asymmetries and clumping which is most naturally explained by orbital resonance with the bar rotation.
The extent, pattern speed, and orientation of the bar is consistent between all three of these.
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