White dwarfs (WDs) with carbon absorption features in their optical spectra are known as DQ WDs. The subclass of peculiar DQ WDs are cool objects (T_eff<6000 K) which show molecular absorption bands that have centroid wavelengths ~100-300 Angstroms shortward of the bandheads of the C_2 Swan bands. These peculiar DQ bands have been attributed to a hydrocarbon such as C_2H. We point out that C_2H does not show strong absorption bands with wavelengths matching those of the peculiar DQ bands and neither does any other simple molecule or ion likely to be present in a cool WD atmosphere. The most straightforward explanation for the peculiar DQ bands is that they are pressure-shifted Swan bands of C_2. While current models of WD atmospheres suggest that, in general, peculiar DQ WDs do not have higher photospheric pressures than normal DQ WDs do, that finding requires confirmation by improved models of WD atmospheres and of the behavior of C_2 at high pressures and temperatures. If it is eventually shown that the peculiar DQ bands cannot be explained as pressure-shifted Swan bands, the only explanation remaining would seem to be that they arise from highly rotationally excited C_2 (J_peak>45). In either case, the absorption band profiles can in principle be used to constrain the pressure and the rotational temperature of C_2 in the line-forming regions of normal and peculiar DQ WD atmospheres, which will be useful for comparison with models. Finally, we note that progress in understanding magnetic DQ WDs may require models which simultaneously consider magnetic fields, high pressures and rotational excitation of C_2.
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