Testing the Tremaine-Weinberg Method Applied to Integral-field Spectroscopic Data Using a Simulated Barred Galaxy

Tremaine and Weinberg (TW) proposed a conceptually simple procedure relying on long-slit spectroscopy to measure the pattern speeds of bars ($\Omega_{\rm p}$) in disk galaxies. Using a simulated galaxy, we investigate the potential biases and uncertainties of TW measurements using increasingly popular integral-field spectrographs (IFSs), for which multiple pseudo-slits (and thus independent measurements) can be constructed with a single observation. Most important, to establish the spatial coverage required and ensure the validity of the measurements, the inferred $\Omega_{\rm p}$ must asymptotically converge as the (half-)length of each pseudo-slit used is increased. The requirement for our simulation is to reach $\approx1.3$ times the half-light radius, but this may vary from galaxy to galaxy. Only those slits located within the bar region yield accurate measurements. We confirm that the position angle of the disk is the dominant source of systematic error in TW $\Omega_{\rm p}$ measurements, leading to under/overestimates of tens of percents for inaccuracies of even a few degrees. Recasting the data so that the data grid aligns with the disk major axis leads to slightly reduced uncertainties. Accurate measurements are obtained only for well-defined ranges of the bar angle (relative to the galaxy major axis) $\phi_{\rm bar}$ and the inclination angle $i$, here $10\lesssim\phi_{\rm bar}\lesssim75^{\circ}$ and $105\lesssim\phi_{\rm bar}\lesssim170^{\circ}$ and $15\lesssim i\lesssim70^{\circ}$. The adopted (pseudo-)slit widths, spatial resolution, and (unless extremely aggressive) spatial binning of IFS data have no significant impact on the measurements. Our results thus provide useful guidelines for reliable and accurate direct $\Omega_{\rm p}$ measurements with IFS observations.