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Molecular line observations using a variety of tracers are often used toinvestigate the kinematic structure of molecular clouds. However, measurementsof cloud velocity dispersions with different lines, even in the same region,often yield inconsistent results. The reasons for this disagreement are notentirely clear since molecular line observations are subject to a number ofbiases. In this paper, we untangle and investigate various factors that drivelinewidth measurement biases by constructing syntheticposition-position-velocity cubes for a variety of tracers from a suite ofself-gravitating magnetohydrodynamic simulations of molecular clouds. Wecompare linewidths derived from synthetic observations of these data cubes tothe true values in the simulations. We find that differences in linewidth asmeasured by different tracers are driven by a combination of density-dependentexcitation, whereby tracers that are sensitive to higher densities samplesmaller regions with smaller velocity dispersions, opacity broadening,especially for highly optically thick tracers such as CO, and finite resolutionand sensitivity, which suppress the wings of emission lines. We find that, atfixed signal to noise ratio, three commonly-used tracers, the J=4->3 line ofCO, the J=1->0 line of C^{18}O and the (1,1) inversion transition of NH_3,generally offer the best compromise between these competing biases, and produceestimates of the velocity dispersion that reflect the true kinematics of amolecular cloud to an accuracy of about 10% regardless of the cloud magneticfield strengths, evolutionary state, or orientations of the line of sightrelative to the magnetic field.

Understanding biases in measurements of molecular cloud kinematics using line emission