The observed velocities of the gas in barred galaxies are a combination of the azimuthally-averaged circular velocity and non-circular motions, primarily caused by gas streaming along the bar. These non-circular flows must be accounted for before the observed velocities can be used in mass modeling. In this work, we examine the performance of the tilted-ring method and the DiskFit algorithm for transforming velocity maps of barred spiral galaxies into rotation curves (RCs) using simulated data. We find that the tilted-ring method, which does not account for streaming motions, under/over-estimates the circular motions when the bar is parallel/perpendicular to the projected major axis. DiskFit, which does include streaming motions, is limited to orientations where the bar is not-aligned with either the major or minor axis of the image. Therefore, we propose a method of correcting RCs based on numerical simulations of galaxies. We correct the RC derived from the tilted-ring method based on a numerical simulation of a galaxy with similar properties and projections as the observed galaxy. Using observations of NGC 3319, which has a bar aligned with the major axis, as a test case, we show that the inferred mass models from the uncorrected and corrected RCs are significantly different. These results show the importance of correcting for the non-circular motions and demonstrate that new methods of accounting for these motions are necessary as current methods fail for specific bar alignments.
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