Reliability of the Tremaine-Weinberg Method for Measuring Multiple Pattern Speeds in Barred-Spiral Galaxies

Barred-spiral galaxies possess double patterns: a bar and spiral arms. While their angular speeds play an important role in governing gas dynamical evolution of barred spiral galaxies, there is no direct way to observe them. The Tremaine-Weinberg (TW) method has been one of the most reliable indirect methods to estimate pattern speeds, although it requires a few strict assumptions, notably one that the gas tracer is in a quasi-steady state. In barred-spiral galaxies, however, non-steady gas flows are significant especially when the double patterns have different angular speeds. Using numerical models, we explore the effect of non-steady gas motions on the determination of double pattern speeds based on the TW method. We find that the TW method is accurate within 15% when there is only a single pattern or when double patterns have the same angular speed. When double patterns have different speeds, on the other hand, neglecting the non-steady flows leads to quite large errors (> 30%) in the derived pattern speeds, and severely underestimate the real values for the viewing angle parallel to the bar minor axis. This suggests that one should be cautious when applying the TW method to galaxies with double patterns with different speeds.