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|a Determining the shape of dwarf irregular (dIrr) galaxies is controversial because if one assumes that these objects are disks and if these disks are randomly distributed over the sky, then their projected minor-to-major axis ratios should follow a particular statistical distribution, which is not observed. Thus, different studies have led to different conclusions. Some believe that the observed distributions can be explained by assuming the dIrrs are thick disks while others have concluded that dIrrs are triaxial. Fortunately, the central stellar velocity dispersion, σ[subscript z,0], combined with maximum rotation speed, V[subscript max], provides a kinematic measure, V[subscript max]/σ[subscript z,0], which gives the three-dimensional shape of a system. In this work, we present the stellar and gas kinematics of DDO 46 and DDO 168 from the Local Irregulars That Trace Luminosity Extremes; The H i Nearby Galaxy Survey (LITTLE THINGS) and determine their respective V[subscript max]/σ[subscript z,0] values. We used the Kitt Peak National Observatory's Mayall 4 m telescope with the Echelle spectrograph as a long-slit spectrograph, which provided a two-dimensional, 3'-long slit. We acquired spectra of DDO 168 along four position angles (PAs) by placing the slit over the morphological major and minor axes and two intermediate PAs. However, due to poor weather conditions during our observing run for DDO 46, we were able to extract only one useful data point from the morphological major axis. We determined a central stellar velocity dispersion perpendicular to the disk, σ[subscript z,0], of 13.5 ± 8 km s[superscript −1] for DDO 46 and ‹σ[subscript z,0› of 10.7 ± 2.9 km s[superscript −1] for DDO 168. We then derived the maximum rotation speed in both galaxies using the LITTLE THINGS H i data. We separated bulk motions from non-circular motions using a double Gaussian decomposition technique and applied a tilted-ring model to the bulk velocity field. We corrected the observed H i rotation speeds for asymmetric drift and found a maximum velocity, V[subscript max], of 77.4 ± 3.7 and 67.4 ± 4.0 for DDO 46 and DDO 168, respectively. Thus, we derived a kinematic measure, V[subscript max]/σ[subscript z,0], of 5.7 ± 0.6 for DDO 46 and 6.3 ± 0.3 for DDO 168. Comparing these values to ones determined for spiral galaxies, we find that DDO 46 and DDO 168 have V[subscript max]/σ[subscript z,0] values indicative of thin disks, which is in contrast to minor-to-major axis ratio studies.
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