Almost 30 years ago, Aller [1970] first proposed that the observed
overabundances of Mn in HgMn stars followed a positive temperature trend.
Since then, her result has been confirmed and extended by, for example,
Adelman [1989] and SD93, who showed that when a large enough sample
of HgMn stars is observed, the trend displays an upper envelope. Our Mn
abundance results confirm in remarkable detail those of SD93 (with
improvements for the double-lined binary stars). In Fig. 10
the dashed line at 
indicates the solar abundance of Mn
(Anders & Grevesse [1989]). For 
Cnc the visible-region data
yielded only an upper limit, hence we plot for that star the UV-derived
abundance of SD93, marked as a cross. The dotted line is the maximum
photospheric abundance of Mn that can be supported in a homogeneous
atmosphere by radiative acceleration (Alecian & Michaud [1981]). We
note the apparent remarkable agreement between the distribution of the
highest abundances as a function of 
and the shape of the
theoretical upper envelope, which is a more important confirmation of a
prediction of diffusion theory than exact vertical agreement (SD93),
because calculations by SD93 showed that the lower values of observed (or
inferred) maximum abundances from homogeneous models could be interpreted
as due to Mn being stratified in relatively thin layers at 
. We also confirm the existence of a class of hot HgMn stars
which exhibit only mild Mn enhancements and other anomalies as described
by Cowley [1980], SD93, and Smith [1993].
Figure 10: Mn abundance versus 
. Solar abundance is given by the
dashed line. The dotted line indicates the maximum supportable
abundance of Mn under the assumption of a homogeneous distribution with
optical depth. The envelope would be lower if Mn were concentrated in a
stratified layer high in the photosphere (SD93). The cross indicates
Cnc, taken from the UV abundance.
The internal agreement of abundances in our results for Mn I and Mn II
over a wide range of 
is remarkable. One might well have expected
some effects of stratification or non-LTE on the ionisation balance, but
the LTE results presented here (based on the assumptions of homogeneous
abundance distributions with optical depth) show a remarkable coherence
between the results from neutral and singly ionised Mn, as well as between
visible-region lines and UV resonance lines. In the absence of a detailed
calculation, we cannot comment on possible non-LTE effects on equivalent
widths other than to predict (on the basis of our results) that they ought
not to be expected to be large. This expectation should be checked by a
detailed calculation, which is beyond the scope of the present paper. It
is possible that non-LTE or stratification effects (or a combination of
both) are responsible for the remaining (0.3 - 0.4 dex) discrepancies
between the hfs-affected lines 
4206, 
4326 and the other
Mn II lines.
The fact that hfs must be having some sort of effect on many atomic
species including the Mn II lines, and should therefore be taken into
account in abundance analyses, was recognised by Booth & Blackwell
[1983] but the present paper is the first abundance analysis of
Mn II in HgMn stars which explicitly attempts to take this into account.
As shown in our previous work on Ga (Dworetsky et al. [1998]), these
hfs effects can be dominant: here they have been shown to be enormous (2-3
dex) for certain strong lines. It is interesting that some Mn II lines
appear to be relatively free of significant hfs broadening. Obviously,
future work on abundance determinations should concentrate on lines like
4478, which are evidently free of significant hfs curve-of-growth
effects. However, while we have accounted for much of the abundance
discrepancy to be found in analyses based on simple equivalent width
calculations, we have not been able to account for all the deduced
abundance differences between 
4206, 4326 and the other,
weaker lines by using our ad hoc hfs models. We suspect that part
of the remaining discrepancies might be eliminated if a laboratory study
of hfs in Mn II were to be made available through laboratory
spectroscopy, and we urge our colleagues in that field to examine this
interesting astrophysical problem.
