Revised spectroscopic parameters of SH$^+$ from ALMA and IRAM 30 m
  observations
  Hydrides represent the first steps of interstellar chemistry. Sulfanylium
(SH$^+$), in particular, is a key tracer of energetic processes. We used ALMA
and the IRAM 30 m telescope to search for the lowest frequency rotational lines
of SH$^+$ toward the Orion Bar, the prototypical photo-dissociation region
illuminated by a strong UV radiation field. On the basis of previous
$Herschel$/HIFI observations of SH$^+$, we expected to detect emission of the
two SH$^+$ hyperfine structure (HFS) components of the $N_J = 1_0 - 0_1$ fine
structure (FS) component near 346 GHz. While we did not observe any lines at
the frequencies predicted from laboratory data, we detected two emission lines,
each $\sim$15 MHz above the SH$^+$ predictions and with relative intensities
and HFS splitting expected for SH$^+$. The rest frequencies of the two newly
detected lines are more compatible with the remainder of the SH$^+$ laboratory
data than the single line measured in the laboratory near 346 GHz and
previously attributed to SH$^+$. Therefore, we assign these new features to the
two SH$^+$ HFS components of the $N_J = 1_0 - 0_1$ FS component and
re-determine its spectroscopic parameters, which will be useful for future
observations of SH$^+$, in particular if its lowest frequency FS components are
studied. Our observations demonstrate the suitability of these lines for SH$^+$
searches at frequencies easily accessible from the ground.
