The probability of chance coincidence between laboratory and umbral
wavenumbers can be tested by means of the Russell-Bowen formula
(Engvold et al. 1980). In the method of wavelength coincidence, the
procedure of identification is completed as the list of accurate
wavelengths for a particular transition of the selected molecule and
the stellar spectrum are compared for coincidences
(Hansen 1985;
Lambert 1988). The method of coincidence assumes an identification of
the solar line with
a laboratory line if the line is located within 0.05 of the
listed laboratory value. In order to exclude the possibility of
identifying a molecular band by chance, the number of coincidences
found, should exceed the number of chance coincidences. In
addition, the variation of relative line strength with rotational
quantum number J is checked (see Sotirovski 1971).
A quantitative measure of the
significance of the coincidences is performed by using the following formula
(Hansen 1985):
where is in
and N represents successively
all integer numbers between 0 and 40. An example of the resulting plots
of mean residual intensities
for a given band, versus shift in
wavenumber relative to the predicted line positions, is shown in
Fig. 1 (click here). The presence of a molecular band in the umbral spectrum shows up as
a peak above the noise produced by random coincidences. All known FeH
bands
(Phillips et al. 1987) within the spectral range of the present
umbral spectrum were checked with this procedure
(Fawzy 1995). A
slightly different version of this method was developed and used by
Lambert (1988). Figure 1 shows a good example of the coincidence curve
for the transition (1/2-1/2) of the lower (a) energy level of the
-doublet pair for the R-branch of the FeH (0-0) band. We
have searched for all laboratory line positions of the bands (2-0),
(1-0), (2-1), (0-0), (1-1),
and (2-2) within the available range of the
umbral spectrum
Å;
). Figure 2 shows a part of the umbral
spectrum of the studied sunspot with the locations of FeH lines of the
(0-0) band. The laboratory, umbral wavenumbers and their differences
are given in Tables
2-5 with the corresponding transitions
for the identified bands (0-0),
(1-0), (2-0),
and (2-1) respectively. The numbers (1), (2), (3), and
(4) are used for transitions (7/2-7/2),
(5/2-5/2), (3/2-3/2), and
(1/2-1/2), respectively, for either the upper (b), or the lower (a)
energy level of
-doublet pair for both R and P-branches. The
differences between laboratory and umbral wavenumbers of the identified
lines are less than
.
Figure 1: Example of the coincidence curve for the transition
(1/2-1/2)
of the R-branch of the (0-0) band
Figure 2: Part of the umbral spectrum with locations of the FeH lines of
the (0-0) band