Claimed detection of PH$_3$ in the clouds of Venus is consistent with mesospheric SO$_2$

The observation of a 266.94 GHz feature in the Venus spectrum has been attributed to PH$_3$ in the Venus clouds, suggesting unexpected geological, chemical or even biological processes. Since both PH$_3$ and SO$_2$ are spectrally active near 266.94 GHz, the contribution to this line from SO$_2$ must be determined before it can be attributed, in whole or part, to PH$_3$. An undetected SO$_2$ reference line, interpreted as an unexpectedly low SO$_2$ abundance, suggested that the 266.94 GHz feature could be attributed primarily to PH$_3$. However, the low SO$_2$ and the inference that PH$_3$ was in the cloud deck posed an apparent contradiction. Here we use a radiative transfer model to analyze the PH$_3$ discovery, and explore the detectability of different vertical distributions of PH$_3$ and SO$_2$. We find that the 266.94 GHz line does not originate in the clouds, but above 80 km in the Venus mesosphere. This level of line formation is inconsistent with chemical modeling that assumes generation of PH$_3$ in the Venus clouds. Given the extremely short chemical lifetime of PH$_3$ in the Venus mesosphere, an implausibly high source flux would be needed to maintain the observed value of 20$pm$10 ppb. We find that typical Venus SO$_2$ vertical distributions and abundances fit the JCMT 266.94 GHz feature, and the resulting SO$_2$ reference line at 267.54 GHz would have remained undetectable in the ALMA data due to line dilution. We conclude that nominal mesospheric SO$_2$ is a more plausible explanation for the JCMT and ALMA data than PH$_3$.