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About V I spectral lines with overlay of Zeeman and hyperfine structure
splitting in spectra of sunspot umbra

S.G. Mozharovsky

Ussuriysk Astrophysical Observatory of FEB RAS, Ussuriysk, Russia

sw@newmail.ru

Abstract. In this article we analyzed the number of spectral lines of
neutral vanadium with atomic transitions including levels 3d4(5D)4s a4D1/2
and 3d4(5D)4p y4Do1/2 in the spectra of sunspot umbrae. It is shown that
the hyperfine structure (HFS) for each of these lines consists of two
components or of two groups of close enough components. The distance
between the HFS components is comparable with the distance between the
components of the Zeeman splitting of these lines in the spectrum of
sunspot umbrae. Overlay of components of the different types can allow
obtain the parameters of the magnetic field by the ratio of the component
intensities. HFS parameters found by the line profiles in the sunspot
umbrae differ substantially from those parameters previously known from
theoretical calculations and ground based laboratory data. This fact raises
the issue for the specialists in the field of atomic physics.

Keywords: "hyperfine structure"; "spectral line profiles";
"sunspots";"umbra"; "magnetic field measurements"

Introduction

Observers have long been known the vanadium lines ? 6111 and 6058 å, which
demonstrate an unusual splitting in the spectrum of sunspot umbrae. The
reason for the unusual splitting is not clear until now. The V I ? 6111 å
line has four visible components, while the Zeeman splitting structure
predicts only two, and the V I ? 6058 å line shows five components instead
of four. The structure of Zeeman splitting which follows from the
parameters of the line atomic levels can be seen in Figure 1.
[pic]
Figure 1. The structure of the Zeeman splitting of lines V I ? 6111 and
6058 å. Segments above the X axis mark the positions of ?-components and
below the X axis - ?-components. The length of the segments is proportional
to the relative intensity of the components. Splitting distances plotted
along the X axis. Dotted lines mark the splitting with Lande factor g = ±
1.

If we trace the change of the profiles of these lines in the spectrum along
the slit of the spectrograph from the position of the umbra center to the
penumbra, we can see that the components of each of the lines behave as a
single ensemble (see Figure 2). This gives reason to doubt on the
explanation of the additional component of unknown atomic or molecular
blends. Other lines of V I of the same multiplet number 34 (Moore 1945) do
not have any noticeable anomalies of splitting.
We believe that the most comprehensive and available collection
(compilation) of data on the atomic spectral lines representing
astrophysical interest, the spectral lines table of Kurucz (2009) can be
considered. Texts of the tables can be found on the website (Kurucz 2011).
A thorough search in these tables allowed us to find three more lines with
the same lower atomic level 3d4(5D)4s a4D1/2 that not covered by blends and
have a sufficient intensity. Two of these lines also have abnormal
splitting, though less appreciable. Line V I ? 8144.559 å does not show
abnormal splitting perhaps because its upper level belongs to the other
electron shell. In addition to these three lines the anomalous splitting
was also found for the line V I ? 5646.108 å. Configurations of the atomic
transition of these lines taken at NIST website (Kramida et al, 2013) are
shown in Table 1.
Table 1. Parameters of atomic transition of the studied lines of neutral
vanadium.
| |Lower Level |Upper Level |
| |pixel|GHarv|GTheo|pixel|GHarv|GTheo|
| |s |ey |r |s |ey |r |
|V I |15 |2.07 |1.27 |6 |0.83 |-* |
|6111 | | | | | | |
|V I |24 |3.41 |2.57 |12 |1.70 |0.86 |
|6058 | | | | | | |
|V I |7 |1.25 |0 |- |- |- |
|5626 | | | | | | |
|V I |14 |2.52 |1.76 |7 |1.26 |0.59 |
|5604 | | | | | | |
|V I |14 |2.49 |1.82 |7 |1.24 |0.57 |
|5646 | | | | | | |
|V I |13(ef|1.35 |1.50 |- |- |- |
|8144 |f) | | | | | |
|Ti I |14 |1.99 |1.99 |- |- |- |
|6064 | | | | | | |
|Fe I |20 |2.48 |2.49 |- |- |- |
|6302 | | | | | | |
|Fe I |23 |3.08 |3.00 |- |- |- |
|5250 | | | | | | |


Note. A dash - no data or splitting cannot be measured; * - the only case
where theoretical data does not exist, and there is experimental data;
(eff) - effective value, i.e. the average value for the two components.


HFS as a possible cause of abnormal splitting

In the paper (Baranov & Mozharovsky 2013) have been analyzed the possible
causes of abnormal splitting of the lines V I ? 6058 and 6111 å, such as
anomalous dispersion, a crossover effect, significant deviations from the
LS-coupling of the Zeeman splitting. All of these explanations have been
rejected. Further analysis of the additionally found lines, particularly
the line V I ? 5626 å prompted explanation of the abnormal splitting by the
splitting of hyperfine structure (Hyper Fine Structure - HFS). The line V I
? 5626 å is a singlet in accordance of its Zeeman structure. But in the
spectrum of sunspot umbra we can see three identical unpolarized components
at equal distances from each other. During the transition from umbra to
penumbra change in the distance between the components is not noticeable.
This behavior at change of the magnetic field is typical for components of
HFS splitting. Features of HFS of the spectral lines of the isotope 51V
devoted sufficient number of works; see, for example, the review in the
introduction to the article (LefÕbvre, Garnir, and Biemont 2002). However,
we have not found articles with a particular description of the
experimental data on the HFS for the lines of interest. HFS data can be
found in the tables of the spectral lines Kurucz (2011), where, as we
believe, in a uniform manner gathered all known to date information. These
data for the lines V I ? 6111 and 6058 å are shown in Table 3. All HFS
components for the V I ? 5646 å line merged in the range 1-2 må. For lines
V I ? 5626, 5604 and 8144 å HFS data are not available.





Table 3. Structures of hyperfine splitting for the lines V I ? 6111 and
6058 å, according to (Kurucz, 2011).

|Spectral |Wavelength, å |Relative |
|line | |intensity |
|V I ? 6111 å|6111.622 |0.109 |
| |6111.622 |0.328 |
| |6111.662 |0.328 |
| |6111.662 |0.234 |
|V I ? 6058 å|6058.115 |0.156 |
| |6058.126 |0.164 |
| |6058.126 |0.055 |
| |6058.140 |0.117 |
| |6058.140 |0.164 |
| |6058.157 |0.344 |


Figure 3 shows the results of the calculation of line profiles V I ? 6111
and 6058 å for the model of umbra Stellmacher and Wiehr (1975) for
realistic physical parameters of a large sunspot umbra at the center of the
solar disk (i.e. parameters, roughly corresponding to sunspot that was seen
in the atlas of Harvey (1972)).

[pic]

Figure 3. Calculation of the I/IC and V/IC Stokes profiles for the lines V
I ? 6111 and 6058 å for the model of sunspot umbra Stellmacher - Wiehr
(1975). The magnetic field B=3000 gauss, the angle of the field vector to
the line of sight ?=15œ, the microturbulent velocity Vmi=0. HFS parameters
correspond to the data of the spectral line lists Kurucz (2011), see Table
3.

Comparing Figures 2 and 3 we can see that the parameters of HFS, taken from
tables Kurucz (2011) for the line V I ? 6058 å do not correspond to the
observed profile, since not lead to the appearance of the fifth component.
Calculated HFS components of the line V I ? 6111 å are much closer to each
other than those observed. To analyze this line we used the results of
photometry of our spectral observations of a large sunspot near the center
of the solar disk in May 1985 - see Figure 4.

[pic]

Figure 4. The copy of the original records of the photometric intensity
profiles of the line V I ? 6111 å in neighboring points of the large
sunspot umbra placed near the center of the solar disk. (Neighboring
profiles arbitrary shifted along the Y axis.) Intensity profiles correspond
to the superposition of two Zeeman components for the magnetic field B=2900
gauss and two HFS components with the distance between the intensity peaks
of 63 må.

From the form of intensity profiles, we can conclude that the distance
between the HFS components of the line V I ? 6111 å is about 63 må. Since
the Zeeman structure is symmetric, and the outer of the four components are
formed by different components of HFS then at the intensity peaks we can
see that the right (longer wavelength) HFS component has a greater
intensity. A similar analysis can be done for all the other examined lines,
suggesting that HFS components of each of the lines are placed in two
compact groups (three groups for the line V I ? 5626 å).

By the fitting method we can try to find the parameters of HFS splitting of
the investigated lines. As the samples for fitting we used the intensity
profiles from the spectral atlas of a sunspot umbra (Wallace, Hinkle, and
Livingston 2000). Atlas recorded using Fourier Transform Spectrometer.
Evidently, the spectral lines in the atlas are not recorded simultaneously
and the position of the umbra on the spectrograph slit changed during
recording. Therefore, the angle of inclination and the strength of the
magnetic field and also the effective temperature of the recorded area
varied from line to line, which is reflected in the parameters of our
calculations. Results of the parameter adjusting calculation can be seen in
Figures 5-9, the data obtained are summarized in Table 4. In the
calculations we used the umbra model of Stellmacher and Wiehr (1975)
(hereinafter SW75). Calculation program uses algorithms similar to those
described in the works (Landi Degl'Innocenti 1975) or (Gadun, Sheminova
1988).

[pic]

Figure 5. Fitting of the HFS parameters for the line V I ? 6111 å for the
umbra model (Stellmacher, Wiehr 1975). Parameters of HFS and other
parameters of the calculation giving the best fit to the observed profile
summarized in Table 4. At right plot shows the profile calculated with the
same parameters but without HFS splitting.

[pic]

Figure 6. Fitting of the HFS parameters for the line V I ? 6058 å. See
caption to Figure 5.

[pic]

Figure 7. Fitting of the HFS parameters for the line V I ? 5626 å. See
caption to Figure 5.

[pic]

Figure 8. Fitting of the HFS parameters for the line V I ? 5604 å. See
caption to Figure 5.

[pic]

Figure 9. Fitting of the HFS parameters for the line V I ? 5646 å. See
caption to Figure 5.

Table 4. The results of fitting the parameters of the calculated line
profiles for the model SW75 to their best match to the observed profiles
taken from the atlas of Wallace, Hinkle and Livingston (2000).

Spectral
Line |NHFS |(I:I)HFS |??,
må |B, G |?œ |Vma,
km•s-1 |lg(gf)G-K |?? | |V I ? 6111 å |2 |3:2 |65 |3160 |17 |1.0 |-0.68 |-
0.08 | |V I ? 6058 å |2 |5:4 |90 |2650 |301) |1.2 |-1.36 |-0.20 | |V I ?
5626 å |3 |1:1:1 |49 |- |- |0.6 |-1.20 |-0.24 | |V I ? 5604 å |2 |3:2 |52
|2600 |45 |0.7 |-1.17 |-0.27 | |V I ? 5646 å |2 |3:4 |54 |2650 |50 |0.9 |-
1.10 |-0.25 | |Notation: NHFS - the number of components; (I:I)HFS - the
intensity ratio of the components; ?? - the distance between HFS-
components; Vma - macroturbulent velocity; lg(gf)G-K - oscillator strengths
in the system of Gurtovenko and Kostyk (1979); here ?? - a model parameter
of Unsold (1955) calculated relative to effective temperature of the SW75
model, where ? = 5040/T; parameters of the magnetic field: strength B and
angle of the field vector to the line of sight ?.

1) Note. Unsure definition of value.

As mentioned above, the profiles of the atlas (Wallace, Hinkle, and
Livingston 2000) recorded not simultaneously, therefore apparently belong
to the different areas of spot. This is evidenced by the fact that the
magnetic field strength B, the angle of the field vector with the line of
sight ? and the model parameter ??, which defines the effective temperature
of the model are correlated.

Especially it should be noted the small value of the parameter, which is
named as a value of the macroturbulent speed Vma. In fact it is the
quantity equivalent to the sum of all kinds of a Spectrum smoothing. It is
defined as a function of the sum of the widths of the Gaussian for macro-
and microturbulent velocity of atoms and the width of the instrumental
function of a spectrograph. For explaining such a small value, we can
assume that the magnetic field of a large sunspot suppresses any
turbulence, but what instrumental profile of the spectrograph is so narrow
(less than 12 må for the line V I ? 5626 å) is in doubt. Perhaps the reason
is unaccounted methodical inaccuracy of the calculations. (The calculations
did not take into account the scattering in line and deviations from LTE;
SW75 temperature distribution is not well describes the physical parameters
of sunspot umbra.) Besides the fact that the values found for Vma small,
they do not show the anticorrelation with a field strengths B. However,
this can be explained by assuming that the number of HF component for each
line is much more than two, but the components are assembled into close
groups. Scattering of component wavelength within these groups will
determine the higher measured values Vma for some lines.

Number of the variable parameters in Table 4 is large. Therefore, it may
seem that for the best fit of the observed and calculated profiles we can
find many different combinations of the parameters. However, it is not so.
We show this by analyzing the structure of the split of the line V I ? 6058
å (see Figure 6). If we want to get five observed components from four
Zeeman components (as in the lower graph of Figure 6), we must have exactly
two HFS components or two groups of close placed HFS components. With three
HFS components resulting profile will have either six components, or just
smoothed shape. When the number of HFS component is only two, the distance
between the first and fifth component of the observed profile (~320 må) is
formed of two terms - the distance between the outer components of the
Zeeman splitting plus the distance between the HFS components. If we
substitute in the known formula for the Zeeman splitting ??H=4.67•10-5gB?2
[cm] the wavelength and the Lande factor for the outer components (g =
2.565), then the Zeeman splitting will be 233 må for the magnetic field B =
2650 G and 264 må for B = 3000 G. The distance between the HFS components
will be respectively 87 and 56 må. However, in case of the calculation for
B = 3000 G the positions of second and fourth component are substantially
moved relative to their positions in the observed profile. HFS component
intensity ratio can be estimated from the ratio of intensities of the outer
components of the observed profiles.


Features of the hyperfine splitting of lines with atomic level 3d4(5D)4s
a4D1/2

As we can see from Table 4, HFS components for lines with lower level
3d4(5D)4s a4D1/2 gather in close groups of two, maximum three components
(or simply composed of two or three component), which is unusual for the
typical pattern of HFS splitting. According to paper (Scharf & Gaigalas
2006) theoretical calculations reproduce the experimental data with
accuracy better than 5%. However, the experimentally determined structures
in our study differ from the known data for the lines V I ? 6058, 6111 and
5646 å much more than 5%. This discrepancy may have two explanations:
1) Known laboratory and calculated data for HF splitting for atomic
transitions including level a4D1/2 contain a systematic error and
should be revised.

2) Different physical conditions in the sunspot umbra and in the ground
laboratory measurements of the HFS for these lines lead to different
patterns of splitting.

In any case, it is requiring detailed laboratory study of hyperfine
splitting of these particular lines, as well as analysis of the conditions
of theoretical calculations.


On a possible use for astrophysical measurements overlay and of the
hyperfine and Zeeman splitting

For the investigated lines of V I there is a rare situation when value of
magnetic splitting in the sunspot umbrae comparable to the value of HFS
splitting. In addition, the number of HFS and Zeeman splitting component is
small, which allows observing the interference pattern of two types of
splitting component. The intensity ratio of adjacent maxima and minima of
Stokes profiles must be changed depending on the parameters of the magnetic
field. If so, it becomes possible to measure the sunspot magnetic field in
a new way. We check this presupposed possibility using model calculations.
[pic]
Fig. 10. The dependence of the calculated line profile V I ? 6058 å on the
magnetic field strength. Calculation parameters: HFS as listed in Table 4,
model SW75, model parameter specified relative to SW75 ??=-0.2, angle of
the magnetic field vector with a line of sight ?=30œ, macroturbulent
velocity Vma =1.2 km / s, microturbulent velocity Vmi =0. Oval marks the
region of rapid change in the central component of splitting.

Figure 10 shows the behavior of the line V I ? 6058 å depending on changes
in the magnetic field strength. As can be seen from the figure, clear, well-
marked changes occur only at the central component of the line in the range
of magnetic field strengths 2100 - 2500 G. However, in the areas of sunspot
where there are such strength, i.e. in the penumbra, the line profile is
weakened and is unsuitable for measurement. Also inexpressive line profile
varies with changes in the angle between the magnetic field vector and the
line of sight and with changes in temperature. Thus, the line V I ? 6058 å
despite the extremely large distance between the outer components and
impressive appearance is almost ill-suited for the evaluation of the
magnetic field by interference pattern of the Zeeman and HFS components.

[pic]

Figure 11. The dependence of the calculated line profile V I ? 6111 å (a)
of the magnetic field B and (b) of the angle between the magnetic field
vector and the line of sight ?. Calculation parameters: HFS as listed in
Table 4, model SW75, oscillator strengths lg(gf)=-0.85, macroturbulent
velocity Vma=1.0 km•s-1, microturbulent velocity Vmi=0. For the Figure
11(a) the angle ?=17œ. For the Figure 11(b) magnetic field strength B=3100
G; the difference between the residual intensities at position of the
second and third depressions of the profile marked as d2 and d3 is
correlated with an angle ?.

Figure 11 shows changes in profiles of the line V I ? 6111 å depending on
the parameters of the magnetic field. At Figure 11(a) we can see the merge
of the second and third component of the splitting with decreasing of the
magnetic field strength. Merger leads to rapid changes in intensity of the
central point of the profile in comparison with the intensities of the
first and the fourth component of the splitting, especially near field
strength 2900 G. Also the changes of the profile due to changing the angle
between the magnetic field vector and the line of sight is remarkable see
Figure 11(b). A characteristic detail, depending on the magnitude of this
angle is the ratio of residual intensities in the depression between the
peaks - see details identified as d2 and d3 in Figure 11(b). We should note
that in the Zeeman structure of the line V I ? 6111 å position of ?-
components coincides with the position of the ?-components (a rare kind of
splitting, which, for example, is known also for the line of Fe II 6149 å).
Profile of the line V I ? 6111 å has a sufficient intensity in the sunspot
umbra and penumbra so it is a good means to determine the parameters of the
magnetic field.

[pic]

Figure 12. The dependence of the calculated line profile V I ? 5626 å (a)
of the turbulent velocity Vmi and (b) of the model parameter ??, which
defines the effective temperature of the model. Parameters of calculations:
(common) HFS as listed in Table 4, model SW75, magnetic field - arbitrary;
(a) model parameter ??=-0.24 relative the SW75 model, Vma=0; (b) Vmi=0,
Vma=0.8 km•s-1.

Figure 12 shows the profiles of non-magnetic line V I ? 5626 å depending on
(a) the turbulent velocity and (b) the effective temperature of the model.
It is obviously that the line can be a good tool for evaluating the
turbulent velocity (in the calculations corresponding to Figure 12 line
profiles at the same values of the macroturbulent and microturbulence
velocities are practically coincide). Changes in temperature also cause
significant changes in the profile of the line. Observations of an umbra in
this line would be good to supplement by observations in the non-magnetic
line Fe I ? 5576 å, which has inverse temperature sensitivity.


Conclusion

In this paper it was proposed interpretation of an unusual type of
splitting of the V I lines with atomic transitions which include levels
3d4(5D)4s a4D1/2 and 3d4(5D)4p y4Do1/2. This interpretation is that for
each of these lines proposed a simple structure of HFS splitting, the
magnitude of that is comparable with the value of the Zeeman component
splitting in a sunspot umbra. Since found HFS do not coincide with the
known data for these lines it follows that may need attention from
specialists in atomic spectroscopy to explain the nature of such
differences. Observed in the sunspot umbra splitting structures of these
lines is well reproduced by model calculations with the proposed HFS
splitting parameters. This fact confirms the correctness of these found
parameters.

Detailed knowledge of the structure of the HF splitting of vanadium lines
should allow uses them to estimate the parameters of the magnetic field in
sunspot observations. Quite simple and quick evaluation of the magnetic
field and its angle with the line of sight (by the line V I ? 6111 å), and
the magnitude of the turbulent velocity and the effective temperature of
umbra (by the line V I ? 5626 å) can be made on profiles appearance. Also,
a detailed knowledge of the HFS splitting allows use these lines to the
analysis of the sunspot umbra models by inversion methods.


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