We examine the self-consistency of laboratory and observational data for potential carriers of the 3.3 $mu$m infrared emission feature (IEF), a member of the ubiquitous family of strong interstellar IEFs at 3.3, 3.4, 6.2, 7.7, 8.6, 11.2, and 12.7 $mu$m. Previous studies have shown that most Galactic sources (reflection nebulae, HII regions, and planetary nebulae) show 3.3 $mu$m IEFs displaying similar central wavelengths, full widths at half maximum, and profiles. Our study is focused on the band profile designated as Class A, the most prevalent of four classes of observed band profiles. In contrast to the observations, laboratory spectra for gas phase polycyclic aromatic hydrocarbons (PAHs), the widely assumed carriers of the IEFs, display central wavelength shifts, widths, and profiles that vary with temperature and PAH size. We present an extrapolation of the laboratory band shifts and widths for smaller PAHs ($le$32 carbon atoms) to the larger PAHs ($>$50 carbon atoms) that are thought to be the IEF carriers. The extrapolation leads to tight constraints on the sizes of the putative PAH carriers. Reconciling the observations with the implications of the laboratory spectra pose a significant challenge to the PAH and other IEF carrier hypotheses.
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