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Anomalously Narrow Linewidths of Compact Massive Star-Forming Galaxies at z~2.3: A Possible Inclination Bias in the Size-Mass Plane

Compact, massive star forming galaxies at $z\sim2.5$ are thought to be building the central regions of giant elliptical galaxies today. However, a significant fraction of these objects were previously shown to have much smaller H$α$ line widths than expected. A possible interpretation is that H$α$ emission from their central regions, where the highest velocities are expected, is typically obscured by dust. Here we present ALMA observations of the CO(3-2) emission line of three compact, massive galaxies with H$α$ line widths of FWHM(H$α$)$\sim$125-260 km s$^{-1}$ to test this hypothesis. Surprisingly, in all three galaxies, the CO line width is similar to the H$α$ line width: we find FWHM(CO)$\sim$165 km s$^{-1}$ for all three galaxies whereas FWHM(CO)$\sim$450-700 km s$^{-1}$ was expected from a simple virial estimator. These results show that the narrow H$α$ linewidths of many compact massive star-forming galaxies are not due to preferential obscuration of the highest velocity gas. An alternative explanation for the narrow line widths is that the galaxies are disks that are viewed nearly face-on. We suggest that there may be an inclination bias in the size-mass plane, such that the apparent rest-frame optical sizes of face-on galaxies are smaller than those of edge-on galaxies. Although not conclusive, this hypothesis is supported by an observed anti-correlation between the size and axis ratio of massive galaxies.