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Constraining the size of the carrier of the $λ$5797.1 diffuse interstellar band

The diffuse interstellar band (DIB) at 5797.1 Å is simulated based on three premises: (1) The carrier of the DIB is polar as concluded by T. Oka et al. from the anomalous spectrum toward Herschel 36. (2) The sharp central feature observed by P. J. Sarre's group is the $Q$-branch of a parallel band of a prolate top. (3) The radiative temperature of the environment is $T_r$=2.73 K. A $^2 Π\leftarrow$ $^2Π$ transition of a linear radical is simulated. Results depend on 10 parameters, with the rotational constant $B$ being the most critical. Comparisons of calculated spectra with observed data constrain $B$, which in turn constrains the number of heavy atoms to 5 $\leq n \leq 7$. Upper limits based on the Her 36 spectrum and lower limits based on stability against photodissociation are also discussed. The latter is based on the assumption that the DIB molecules are produced top-down from the breakdown of dust rather than bottom-up by chemical reactions. A difficulty with this limit is that J. P. Maier's laboratory has observed many molecules within this size range, some of which have been tested astronomically. Candidates are discussed in light of many prolate tops observed by the P. Thaddeus and M. C. McCarthy microwave group.