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.
