SNSTITUTE OF THEORETICAL ASTROPHYSICS BLINDERN - OSLO

REPORT .No. 35

ISOTOPIC COMPOSITION OF SOME METALS IN THE SUN

by

ØIVIND HAUGE y

UNIVERSITETSFORLAqET • OSLO 1972 Universitetsfc lagets trykningssentral, Oslo

INSTITUTE OF THEORETICAL ASTROPHYSICS BLINDERN - OSLO

REPORT No. 35

ISOTOPIC COMPOSITION OF SOME METALS IN THE SUN

by

ØIVIND HAUGE

UNIVERSITETSFORLAGET • OSLO 1972 Universitetsforlagets tryknlngssentral, Oslo

CONTENTS

Abstract 1

1. Introduction 2

2. Fine structure in spectral lines from atoms 5

1. Isotope shift 5

2. Hyperfine structure 6

3. Applications to atomic lines in photospheric spectrum .... 8

1. Elements with one odd isotope , 9

2. Elements with two odd isotopes 9

3. Elements with one odd and several even isotopes 11

k. Elements with several odd and even isotopes 11 h. Studies of elements in the Sun with two odd isotopes

1. Isotopes of rubidium 12

A. Observations lk

B. Calculations 16

C. The Rb I line at 78OO Å

1. The continuum level 16

2. Line profiles and turbulent velocities 18

3. The asymmetry of the Si I line 19

h. Isotope investigations 21

P. The Rb I line at 79^7 A 28

E. The isotope ratio of rubidium 31

F. The abundance of rubidium 3k

2. Isotopes of antimony 35

A. Spectroscopic data 35

B. The Sb I lines at 3267 and 3722 A 37 3* Isotopes of europium 1*0

A. Observations and methods of analysis ^1

B. Spectroscopic data 1*1

C. Spectral line investigations

1. Investigations of four Eu II lines **3

2. The Eu II lines at Ul29 and U205 k ^6

D. The isotope ratio of europium 50

E. The abundance of europium 51

5. Study of an element in the Sun with one odd and several

even isotopes

1. The upper limit of the solar Sr 87 content 53

A. Observations 5^

B. Spectroscopic data 56

C. Isotope investigations 58

D. The abundance of strontium » 60

6. The isotope ratio of copper in the Sun studied from

Cu I and CuH lines

1. Studies of molecular lines from other elements 62

2, The isotope ratio of copper , 63

7- Summary and final comments 67

Acknowledgements * 70

References ,., ,, 71 - 1 -

Abstract

Information on the isotopic composition of chemical elements in the

Sun may be obtained by analysis of phctospheric and sunspot spectra.

It is shown that besides investigations performed on molecular lines,

information on isotope abundances of some heavier elements may also be

derived from atomic line studies. A discussion of the elements Kb, Sr,

Sb and Eu are described. Studies of the solar isotopic composition of

Cu from analysis of Cu I lines in photospheric spectra and CuH lines in

sunspot spectra are described.

The results obtained are:

Cu65/Cu65 = (70+T)/(30+T)

Rb85/Rbo7 = (73+1*)/(27+1»)

Eul5l/Eul53 - {52+6)/(kQ+6)

Sr87/Sr <_ 0.25

No conclusions could be drawn about isotopes of Sb in the Sun. Although the results may indicate a solar over-abundance of Eu 151 as compared with terrestrial composition, the investigations provide no proof of non-terrestrial isotope ratios in the Sun of any of the elements listed.

The abundances of Kb. Sr and Eu were determined and the results agree closely with previously determined values. 1. INTRODUCTION

Increased knowledge of isotope abundances is of vital importance

for a "better understanding of the processes that led to the formatien

of the chemical elements and to the formation of celestial bodies.

Conclusions about the evolution of different celestial bodies and their

internal relation might easier be dravn when the isotopic composition

cf their constituting elements is knovn. Accordingly large efforts have

been made in order to increase our knowledge of isotopic compositions

in different celestial bodies. During the last few decades our know­

ledge of the composition of bodies belonging to the Solar System has

increased enormously. The composition of the terrestrial crust,

meteorites and surface layers on the Moon are nov well known.

Data on the isotopic composition of elements in the Sun are important

for theories of the creation and the evolution of this» our nearest star

in space. But the methods one can use to determine isotope abundances

in the Sun are not as direct and sensitive as these that can be applied when analysing stone samples. The solar results must therefore he given with considerably larger error limits.

Some information on isotopes in the Sun may be obtained from direct

study of the composition of the solar wind and of solar cosmic rays.

But the results obtained -from such investigations do not always reflect the average composition in the Sun's photosphere. Orbits of ionized particles are perturbed by electromagnetic fields and in cosmic rays,

secondary emmission is mixed up with the primary rays. Moreover, in the

solar wind and cosmic rays the concentration of many elements is too

small to permit investigations. - 3 -

Information on solar isotopic composition is obtained from spectral

line studies. The wavelength of lines from molecules and atoms is

isotope dependent. In order to interprete the observed spectra, the

physical conditions in the line forming region together with various

atomic or molecular data must be known. The isotope displacements are

often very smell and disappear in line broadening due to high temperature

and velocity fields in the region of line formation. In sunspot spectra

also magnetic fields act on the profile.

In molecular bands spectral lines from different isotopic compounds

are often well resolved. But only few elements exist in molecules in

the photosphere. Investigations often have to be undertaken on spectra

from sunspots where the lower temperature leads to an increase in the

number of molecules. It is often necessary to know the direction and

strength of magnetic fields when sunspot spectra are examined. The

setting of the continuum level may he difficult as spectral lines from

spots are very numerous and overlap. Ho undisturbed spectral region may

be found.

In isotope studies of very light elements atomic line spectra are most frequently used. The isotope shifts in spectral lines from light

elements are large enough to affect line profiles. The reason for this is to be found in the mass dependence of the Rydcerg constant. Considering heavier elements, this effect is negligible. But the isotope shifts also depend on other properties of the nuclei, and isotope shifts and hyperfine structure may lead to information on the isotopic composition of heavier elements. These two effects are usually undetectable, but in some cases minor influences on solar line profiles occur. Recent developements in observational technique and new methods to calculate line profiles, however, make it possible to determine the composition of some - It -

heavier elements from observations of atomic line profiles. Vhen recording

the photospheric spectrum using extremely long observing time, the noi Be

in an averaged spectrum is brought down to a very lov limit. And when

spectra are taken with an integrating lens in front of the slit, an average

of the emission from an extended area is recorded. Local variations in

physical conditions in the photosphere do not affect the result.

The number of elements for which information on isotopes in the Sun may be obtained from molecular line studies must be limited, as only few elements exist in molecular compounds. Also atomic line investigations may give information only on a very small number of elements, but it is fortunate that amongst these there are some e3ements which are not expected to exist in molecular compounds.

Solar isotope ratios are always given with large error limits as compared with results obtained from stone sample analysis. Nevertheless, it should be pointed out that the derived isotope ratios may be given with considerably smaller errors than the derived abundance ratios between different elements. Isotopes from the same elements have many physical constants in common and errors in their values or in the model atmosphere do not substantially affect the final result.

In the following the solar isotopic composition of some heavier elements is discussed. A short bibliography referring to results obtained by different authors on other elements was given by Hauge and Engvold (1970). - 5 -

2. FIHE STRUCTURE IN SPECTRAL LINES FROM ATOMS

When spectral lines are examined vith spectrographs of very-

high resolution, it is frequently found that the line is split into

several components lying close together. As an example the fine

structure of a Tb II line is demonstrated in Figure 2-1. The photospheric

spectrum at this wavelength has earlier heen studied by Engvold and Hauge

(1970). The fine structure of the Yb II line can be considered as the

result of two effects- Even isotopes appear as single lines. One odd

isotope haB several, components shoving the hyper fine structure. And, as

seen from Figure 2-ls two odd isotopes may have different hyperfine

structure. The spectroscopic behaviour of even and odd isotopes is

fundamentally different and of vital importance for the discussion given

in Chapter 3-

a,p> -ni Q,b/.,d - 173

Fig. 2-1. Fine structure of the Yb II line at 36*9^ A as determined by

Krebs and Nelkovski (1955).

2.1. Isotope shift

Golovin and Striganov (196*8) have given, an extended survey of experimental results, theoretical interpretations and a comprehensive bibliography of isotope effects in Bpectra from heavy elements. Only a fev characteristic behaviours of the isotope shift are referred in the following. - 6 -

1. The energy of certain levels is more isotope sensitive than other.

The consequences are that different spectral lioes from an element

show quite different isotope shifts. The heavier isotope may he situated

on the red side or on the blue.

2. As seen in Figure 2-1, the wavelength interval between Yb 170 and Yb 172

is larger than the interval between Yb 17^ and Yb 176. The ratio

between these two isotope shifts will closely hold also in other Yb

lines6 although the absolute shift may be different. In other vords:

Different lines from the same element have nearly constant relative

isotope shifts.

3. 'When comparing relative isotope shifts of different elements, the

shifts seem to "be more dependent on the number of neutrons in the

nucleus than on the element. Maxima in the relative isotope shifts

occur at 52, 90 and 130 neutrons in the nucleus.

2.2. Hyperfine structure

Many textbooks deal with the hyperfine structure in atomic lines.

A good exposition of the subject is due to Candler (196*0. The hyperfine structure has some characteristics which are summarized below:

1. The hyperfine structure in atomic lines can be quantitatively explained

when it is assumed that the atomic nucleus possesses an intrinsic spin

with which is associated a magnetic moment.

2. Each isotope has a characteristic nuclear spin represented by a nuclear

spin quantum number denoted by I.

3. The total spin of a wtoole atom including the nuclear spin is a quantized

quantity and is denoted by P. F is the vectorial sum of J and I. - 7 -

U. Atomic energy levels are split into several hyperfine sublevels

of slightly different energy. Each sublevel correspond to a certain

quantum number F.

5. The number of hyperfine levels is limited to 2J •+ 1 (when J < i) c

to £1 + 1 (when J > I).

6. In transitiona "between tvo states only F •+ F ard F -* F + 1 transitions

will occur. 0 •+ 0 transitions are forbidden.

7. For a chosen state, the energy difference between the lyperfine levels

ia almost proportional to the F quantum number.

8. The nuclear magnetic moment is a characteristic quantity for each isotope.

When comparing the hyperfine splitting of energy levels in two isotopes

of the same elements the separations of the hyperfine levels will,

provided the spin quantum numbers are equal, be proportional to the

magnetic moment. - 8 -

3. APPLICATIONS TO ATOMIC LINES IN THE PHOTOSPHERIC SPECTRUM

———~—s=———sg- rs ass!w=Taar=5;s==— _:r.iiii..uTsraS' -^f—rpgg^ e;

The isotope shifts in atomic spectra are usually very small and

will neither affect the observed profile nor the derived abundance. Lic.es

having their origin in elements as Ca, Fe, Ni and Zn certainly always can

be considered as one-component lines. • These elements consist mainly of

even isotopes and the isotope shifts are very small.

Some heavier elementa, especially amongst the rare earths» may have

more prominent isotope shifts which ought to he considered in abundance

determinations.

For isotope ratio determinations analysis of the effect of isotope

shift alone vill nearly always be insufficient. Cne exceptior. of considerable

astrophysical interest may be samarium. In terrestrial material this

element is present with 7 isotopes having atomic masses lkki 1*)7» 1^8,

11*9» 150» 152 and 15U. Sm 152 has 90 neutrons in the nucleus and the

isotope shift between Sm 150 and Sm 152 is about twice the shift between

other even isotopes. In terrestrial material Sm 152 and Sm 15^ compose

about 1*6 per cent of the total abundance. Some spectral lines show double

structure having two components of nearly equal intensity {King» 1935).

One component is due to the two heaviest isotopes and the five remaining isotopes produce the other component. Several samarium isotopes have large neutron capture cross sections and may serve as indicators of neutron flux.

A study of the solar isotopic composition of samarium is in progress at

Institute of Theoretical Astrophysics in Oslo,

The hyperfine splitting of spectral lines from odd isotopes is of considerable interest. The different hyperfine cor ^-,ts may occur within waveler-gth intervals of several hundreds of mA and Heide (i960) has shown how the hyperfine broadening of the lines act on the derived abundance. - 9 -

And, as shown later, the hyperfine "broadening may also lead to information

on isotopic compositions. For the further discussion, the chemical elements

are divided into four groups depending on the isotopes naturally present:

Elercents with:

1. one odd isotope,

2. two odd isotopes,

3- one odd and one or several even isotopes,

U. several odd and even isotopes.

3*3. Element s wi th pne^ odd_ igptopje

Elements such as £c, V, Mn, Ce, Y ard Pr belong to this group.

Spectral lines from these elements often show a considerable hyper fine

broadening* Photospherie lines from these elements may be regular, but

are often asymmetric or may even have a multistructure. The broadening

vill influence the derived abundance arid when abundance determinations

are performed, a procedure of multicomponent calculation is preferable.

The hyperfine structure may also be important for line identifications.

The elements in this group are of cource without any interest for isotopic

investigations.

3.g. Elements with two odd_ i set op_es

Several elements heve two isotopes both with an odd number of r.ucleons

in the nuclei. Many are represented by spectral lines in the photcspheric

spectrum. These elements are listed in Table 3-1. The relative terrestrial

abundance, nuclear spin quantum numbers and nuclear magnetic moments are

given by Weast (1969) and the number of unblended lines in the photocpheric

spectrum were listed by Moore et al., (1966). The eleirent K is also included

in the table as K Uo only contritiite with 0.22 per cent to the total terristrial potassium abundance. - 10 -

TABLE 3-1

Elements with tvo odd isotopes and with unbleided lines in the

photospheric spectrum

Terr Nuclear Nucl. magi*, Ro. of Element Isotope abundances spin moment unblended (T) (v) lines

K 39 93.70 3/2 0.39 19K 10 X" ltl 6.08 3/2 0.21

Cu 63 69.09 3/2 2.23 29°" 19 Cu 65 30.93 3/2 2.38

Ga 69 60. It 3/2 2.02 31Ga 1 Ga 71 39-6 3/2 2.56

Rb 85 72.15 5/2 37M 2 Eb 87 27.65 3/2 2.75

Ag 107 51.02 1/2 - 0.11 It/8 2 Ag 109 1(8.15 1/2 - 0.13

Ir. 113 1(.SB 9/2 5.52 i.9In 1 In 115 95.72 9/2 5.53

Sb 3 21 57.25 5/2 3.36 51Sb 2 Sb 123 1(2.75 7/2 2.55

Eu 151 1(7.82 5/2 3.U6 63^ 13 Eu 153 52.18 5/2 1.53

Ir 191 0.18 lr 37-3 3/2 77 7 Ir 193 62.7 3/2 0.18

Isotopic investigations can he performed using atomic lines when tre tvc isotopee have spectral lines of different hyperi'ine "broadening. Svch

conditions exist when the two isotopes have different nuclear spin quantum

niapber fl) cr if the sisirt quantum numbers ere equal, vhe:.\ the isotopes have - 11 -

different nuclear magnetic moments. With these conditions in mind, the

figures given in Table 3-1 show that three elements, Rb, Eb and Eu, appear

to be of particular interest for a closer examination. The results of

investigations or these elements are given in Chapter k. Chapter f> contains

some comments on atomic lines from Cu I.

3.3. Elements with one odd and several enen isotopes

The demerits Mg, Cr, Sr and Zr are members of this group. Spectral

lii es from thene elements have one component fvom aach even isotope and

several ' i-pe^fine components from the odd isotope. Kany spectral lit.es

have negligible isotope shifts and lires from the even isotopes* coincide

in wavelength. If the relative abundance of the odd isotope is not too

small and if the odd isotope has an extended hyperfine structure, this

isotope will broaden the observed spectral line. From investigations of

these lines one can only obtain information on the contribution fron the

odd isotope as compered with the total abundance cf o?l the r.-vf-n isotopes.

In Chapter 5 one such investigation is carried out. The analysis

of rubidium described in Chapter h shoved that it vas desirable to investigate

the solar Sr 87 content because Eh 8? is radioactive bnd desint egrates into

Er 87 v

3.U. Elements^ with several odd and even isotopes

Tbjse elements will have very complex spectral lines and seem to be

very difficult to examine. One exception may be elements vhere the odd

isotopes have equal I quantum number in addition to nearly equal nuclear

magnetic moment. If the isotope shift in a spectral line also is negligible,

the even isotopes have components coinciding in vavelength. The hyperfine

components from the odd isotopes will cover each other. Then the sum of

the abundances of the odd isotopes may be found as a fraction of the

abundance of the even isotopes. One element of interest in this context may be barium. - 12 -

k. STUDIES OF ELEMENTS IN THE SUN WITH TWO ODD ISOTOPES

lf.1* Isotopes of rubidium

A somewhat shortened presentation of the rubidium investigation

reported "below is given "by Hauge (1972a).

In terrestrial material, rubidium is present with the isotopes:

Eh 85 and Hh 87. The isotope ratio is almost constant in different

terrestrial minerals (Shields et al., 1963) and equals 72.15:27.85. The

same isotopic composition of rubidium was also found in lunar samples

(Compston et al., 1970) and in meteorites (Murthy and Compston, 1965)»

Rb 87 is radioactive and desintegrates by B-decay to Sr 87. The life­ time of Rb 87 is U.7xl0 years according to Wetherill (1966). Considering that Rb 87 is one of the few isotopes^ used for age determinations of geological material, a knowledge of the solar isotopic composition of rubidium is of great interest.

2 2 0 The 5s S - 5p P resonance lines of Rb I are present in the sol .* spectrum. These lines appear at 78OO and 79^7 A. In the photospheric spectrum, the line at 7800 Å is blended with a highly excited Si I line.

The line at 79^7 Å is located in the violet wing of a terrestrial water vapour line.

Rubidium has a very low ionization potential of It. 176 eV. The lines therefore strengthen considerably when spectra are taken from positions near the solar limb and in sunspots.

The solar abundance of rubidium has been investigated by several authors

Goldberg et al. (i960) found loge_,. = 2.1*8 (on the loge„ = 12.00 scale), ' •" no H

Lambert and Mallia (1968) obtained an average of loge_, = 2.63. Stellmacher and Wiehr (1969) determined the ratio lo6(e~/E_ ) from analysis of sunspot spectra and arrived at a value equal to or less than zero.

2 0 2 The energy level 5p P and especially the level 5s S show hyperfine - 13 -

splitting. Rb 85 has a nuclear spin quantum number of 5/2 and a nuclear

magnetic moment of 1.35 nuclear magneton units. The corresponding figures

for Eb 87 are 3/2 and 2.T5 respectively («east, 1969). Kb 87 shows a

more pronounced hyperfine splitting than the other isotope. These lines

appear exceptionally broad in the solar spectrum because of the hyperfine

structure. The broadening, and hence the line profile, depends on the

isotopic composition as shown in Figure it.1-1.

I I I 1 U 7800.20 . .«0 Wavelength in A *

Fig. It. 1-1. Computed limb spectra (u = O.158) of the unblended Rb I line

at 7800 A. Three different isotope ratios have been assumed.

Lambert and Mallia (1968) considered the effect of the hyperfine

splitting in their careful abundance determination. In this connection

they used spectroscopic data given by Johansson (1961). The same data

are used in the present investigation and are listed in Table lt.l-I.

It was assumed by Lambert and Mallia that the solar and the terrestrial

isotopic composition of rubidium were equal. The possibility of determining the solar isotope ratio from line profile investigations was mentioned

and it was suggested that sunspot spectra might be the more suitable for an

isotope investigation. In such spectra the Rb I lines are strong whereas the highly excited Si I line at 7800 Å is faint.

The present investigation is based on photospheric spectra of high

quality. Sunspot spectra of Rb I were excluded for the following reasons: - Ill -

TABLE U.l-I 2 2 0 Bb I resonance lines: 5s S - 5p P

Wavelength Rel. int. of Isotope in air hfs. components

T800.176 Eb 87 0.102 .232 Rb 85 0.303 .293 Rb 85 0.1(25 .321 Rb 87 0.170

79U7.513 Rb 87 0.102 • 565 Rb 85 0.303 .629 Rb 85 0.1*25 .657 iTb 87 0.170

Magnetic fields in sunspots will cause a very complex structure of the lines. The rubidium lines are formed at other levels than the lines which can be used to determine the magnetic field. Hence a considerable uncer­ tainty in the magnetic field strength at the place of origin of the Rb I lines has to be considered. Even a small error in the magnetic field determination may cause a considerable error in the derived isotope ratio.

If.l-A Observations!

The two resonance lines of Rb I were observed with the MeMath Solar

Telescope {Pierce3 I96U) at Kitt Peak National Observatory by the author in April and May 1971- The photoelectric equipment was used in double pass and each spectrum is an average of 200 consecutive scans. The spectral resolution is about 13 mA. The total observing time for each spectrum was approximately 12 minutes.

The spectra were Fourier analysed and filtered for high frequency noise. The instrumental profile was corrected for. The rms error is less - 15 -

than UxlO" of the continuum intensity.

The spectra were plotted on the scales: 1 Å - 20 cm, 1 per cent of

continuum intensity - 1 cm. The intensity vas also printed out and given

with Tour numbers and fcy interpolation at every second mA in wavelength.

1.00 T? RB: j*** "~ ^>X

•.\\ 'if .90

Li = 158

M =,312 .80 \\ // \7 .8 7800.0 Wavelength

Fig. i|.l-2. Observed spectra of the Si I - Rb I blend at 7800 Å at three

different distances from the limb.

Both wavelength regions were observed with the spectrograph slit placed at the solar disk centre and at six different distances from the limb, corresponding to u-values in the range from O.158 to 0.U61. Spectra from the centre of the disk were obtained with an integrating lens in front of* the slit. Thus an average of the emission from an extended area was received.

Both wavelength regions were observed with the Sun at different zenit distances and also with the Sun very close to the horizon in order to detect faint terrestrial lines. The line at 79^7 A, which is blended by a water vapour line, was observed on a very dry day with the Sun at small zenit distances

in order to reduce the intensity of the H20 line. Spectra obtained at the - 16 -

eastern solar limb were examined in order to increase the wavelength

difference between the Rb I and the HgO lines. The atmospheric water

vapour content was checked during the observations by observing alterna­

1 tively the H20 reference line at 69 »3 A and the Rb I lines.

!iiåzIL£^£u^ations The analysis has been carried through using the method of spectrum

synthesizing. A computer program has been developed by 0, Engvold and

0. Kjeldseth Moe for the purpose of calculating synthetic liDe profiles.

The resulting intensity profiles of blended lines are obtained by integrating

the contribution from each component of the blend simultaneously through

the model atmosphere. Numerical integrations were performed at steps of

AlogT = 0.1 in the atmospheric models (T = optical depth).

The atmospheric model of the solar atmosphere given by Holweger (1967)

has been used in the calculations. This model was chosen because it has

been derived from studies of the photospheric absorption line spectrum.

In onr particular case we also used the Harvard Smithsonian Reference

Atmosphere (Gingerich et al., 1971). It turned out that the choice of model atmosphere had a negligible effect on the isotope ratio derived.

The atmospheric model was transformed to the wavelength of the Rb I

lines using the tables of the continuous absorption coefficient given by

Bode (1965).

The partition functions were taken from de Galan et al. (1968).

C_l^ £he„£ontinuum level

The observed spectra cover the wavelength region between 7797-8 and

7&03.3 A. The spectra of this region obtained with the Sun at different

zenit distances of relative air masses ranging from 1.3 to k.5 reveal no traces of terrestrial lines- - 17 -

There appears to he several good continuum windows within this wave­

length region. At several wavelengths the intensity is nearly constant

over hundreds of IQAS. For some region to be regarded as showing the

feontinuum level, one required that the intensity never showed variations

more than 0.1 ;er cent within a wavelength interval of 100 mA. With this

restriction, four "continuum" levels were found. The intensities in these

windows at different distances from the solar limb are tabulated in Table U.l-II.

At several wavelength or u-values the intensity variations were less than

0.05 per cent.

The continuum level was also determined by assuming the residual intensi­

ty in a line wing to be proportional to l/(A-A ) where X is the wavelength

of the line centre. The last line in Table ^.l-II shows the continuum levels

as obtained in this way using the violet wing of the Si I line. It is

expected that the local continuum level is determined within an error limit

of 0.2 per cent.

TABLE Ij.l-II The continuum intensity (100.00) used in the present investigation as

compared with the intensity in neighbouring, undisturbed regions. The last

line shows the intensities obtained when the residual intensity in the Si I

line ving was assumed to follow an inverse square law.

Wavelength - value in Å 0.158 0.222 0.271 0.312 0.380

7T99.6 100.00 100.00 100.00 99.91 99.89

7800.9 99.70 99-82 100.00 100.00 100.00

7801.3 99.79 99. Bh 99.95 99.98 99.88

7802.0 99.66 99.70 99.83 99.90 99.86

Si I wing 99.80 99.914 99.60 99.78 99.85

The continuum level might be assumed to have a slope corresponding to the general trend in the spectral intensity distribution. Such a correction, - 18 -

however, will be very small compared with the error limit quoted above. As will appear from the subsequent discussion, the derived" rubidium isotopic

composition is insensitive to small variations of the continuum level.

A continuum level of constant intensity is therefore used throughout the investigation.

C 2. Line profiles and "frugj^gg^Vgjrggj^gg

When computing faint lines (W < 10 mA) a very good fit to be observed profile can be obtained using a line absorption coefficient represented by a Gaussian function. Stronger lines, however, have to be computed using

Voigt profiles. Gaussian functions are convenient because they lead to shorter computing time. We used Voigt profiles for the Si I line and

Gaussian functions for the Rb I line components. The macro- and micro- turbulent velocities were determined by applying Gaussian functions on an unblended Ti I line at 79^9 Å. This line has an excitation potential of

1.50 eV and an equivalent width of about 10 mA when observed close to the solar limb. At the limb, the Ti I line has a profile which is almost symmetric and a good fit with a synthetic profile may be obtained.

Holweger (1967) determined the macro- and microturbulent velocity distributions by studying the relation between equivalent width and residual intensity for a great number of lines. The macroturbulent velocity was found to be constant at all optical depths and amounted to 0.35 km/s at the limb

(y = 0.3). The microturbulent velocity distribution was given as a function of optical depth. At the limb, the velocity was 1 km/s above logT = -U.0 and

3.0 km/s below logf = -0.3. It was a linear function of logT in the interval between. We adapted a macroturbulent velocity independent of optical depth and a Holweger type of microturbulent velocity function to our spectra. The results are given in Table It.l-III. It was necessary to introduce a micro­ turbulent velocity which differed from that of Holweger. As judged from the computed contribution functions we found that the velocity at the optical depth corresponding to the maximum contribution was about 3.0 km/s, while - 19 -

TABLE U.l - III Data on microturbulent velocities derived from analysis of the Ti I line

at 79W A.

u- value 0.158 0.222 0.271 0.312 0.380

3.8 3.7 3.6 3.6 3.5 v . at logT = -0.3 km/s micro 1.0 1.0 1.0 1.0 1.0 v . at logx - -U.0 km/ s micro -1.3 -1.2 -1.1 -1.0 logr (at max.contr.) -0.95 3.0 3.0 3.0 3.1 3.0 v . at T km/s micro m

Holweger's function gave about 2.5 km/s. Best agreement between computed and

observed line profiles were obtained by neglecting the macroturbulent velocity.

If a macroturbulent velocity of 0.35 km/s as given by Holweger was intro­

duced, our microturbulent velocity came out with a value very close to his.

A small increase in the macroturbulent velocity has very nearly the same

effect on the profiles as a small increase in the microturbulent velocity.

In the spectrum closest to the limb the turbulent velocities have also

been determined from the profile of the Si I line at 7800 A. Within an error

limit of less than 0.1 km/s, we obtained just the same results as reported

above.

Our.results on the microturbulent velocity are in good agreement with

the velocity field given by Waddell (1958). He has given a value of 3-0 km/s

independent of dci^h for the tangential component of the anisotropic velocity

distribution.

C 3. The asy_mmetr^_of_the_Si_I_line

The asymmetry of the Si I line has been discussed by Lambert and Mallia

(1968). The line was found to be considerably more asymmetric in spectra taken at the centre of the solar disk than in spectra obtained at u = 0.3. The present observations verify their results. The high resolution photospheric - 20 -

spectra obtained at Kitt Peak National Observatory clearly reveal an

asymmetric profile in observations from the centre of the solar disk. The

asymmetry is reduced in spectra taken near the limb. Very close to the limb,

the wingB of the Si I line show symmetry. Only very close to the line

centre an asymmetry still exists. Moving from the limb to the centre of the solar disk, the asymmetry becomes more pronounced over a larger part of the line. Xn order to reproduce the symmetric line wings, the wavelength

of the computed line had to be shifted an amount of 3 mA towards the Mue when considering the spectrum taken at the closest distance to the limb

(see Table U.l-V).

Lambert and Mallia (1968) mentioned three different explanations of the asymmetry that will be further discussed below:

1. Isotope effect. Silicon has three stable isotopes, Si 28, Si 29 and

Si 30 with relative terrestrial abundances of 92.2:k.7:3.1 respectively.

Holmes and Hoover (I962) measured isotopic shifts for 11 Si I lines in the ultraviolet wavelength region. No data are available for the Si I line at 7800 Å. But by assuming a terrestrial isotopic composition and the maximum displacement given by Holmes and Hoover (1962), the main outcome of our calculations was a displacement of the line of nearly k mA from the

Si 28 line component (See Figure ^.1-3)- According to this it should be difficult to detect any asymmetry in the profile, only a very small line broadening results.

2. Blend. The intensity of this blend must vary with the distance from the limb in a way that makes the hypothesis rather doubtful.

3. Atmospheric effect. Presently the third explanation appears to be the more plausible; the asymmetry occurs as a result of photospheric inhomogeneities with respect to temperature and motions (de Jager and Neven, 1967).

It seems permissible to use symmetric profiles very close to the limb.

Farther away, symmetric profiles may also be used. The asymmetry is then - 21 -

Wavelength in A

Fig. k.1-3. The Si I line as computed under two different assumptions:

a_) a one component line (dashed curve) and b) a three component spectral line with

isotope shift and terrestrial isotope ratio (full line). The total abundance

is slightly different in the two cases in order to keep the curves slightly

separated, u = 0.15^.

regarded as one of the error sources.

Lambert and Mallia (19-68) pointed out that information on the

asymmetry might be obtained from the Si I line at 5666 Å. This line has an

equivalent width and an excitation potential similar to those of the Si I line

at 7800 Å. At one distance from the limb (u = 0-312) a correction for the

asymmetry was possible. The 5666 Å line was observed at the limb (u = 0.300).

An asymmetric profile was fitted to this line and the result was applied on the Si I line at 78OO Å.

C U. Isotoge_investigation

When investigating the solar isotopic composition of rubidium, a limited wavelength interval was analysed. The extension of this interval was ranging - 22 -

from 260 mA when spectra taken close to the limb (y= O.I58) were used to

210 mA for spectra observed at u - 0.380. Still farther away from the

limb, the asymmetry of the Si I line makes isotopic investigations doubtful.

The red end of the wavelength intervals was fixed at 7800.390 Å. At longer

wavelengths the contribution from rubidium is very small and the profile was

more influenced by observational errors and the selected continuum level than

"by the rubidium isotopic composition. The blue end of the investigated

interval was at a wavelength where the residual intensity was about 5 per cent.

The contribution from Si I then was a factor 5 to 10 times higher than from Rb I.

The residual intensities used are tabulated in Table ^.1-IV. The intensity

is tabulated for steps of 10 mA in wavelength and for 5 different distances

from the limb.

Synthetic profiles of the Si I line were computed by adjusting abundance, wavelength and damping factor (Ross, 1970) so as to obtain the best fit with the observed profile. Great care was excercised in order to reproduce the violet wing far out as well as the steeper parts of both wings with a high degree of accuracy. Some discrepancies were allowed to occur near the line centre. A computed intensity that never differed by more than 0.1 per cent from that observed was always obtainable at intensity levels higher than

90 per cent. The results are given in Table ^.1-V.

In the reduction procedure, the rubidium abundance and isotopic compo­ sition as well as the redshift were treated as unknown quantities. The observed residual intensity was integrated over the investigated wavelength interval

(see Figure U.l-l*). Using the data reported on the Si I line and different values of the unknown rubidium parameters, synthetic profiles were computed.

With a given rubidium isotopic composition and redshift, the rubidium abundance was varied until agreement was obtained with the integral of the observed intensity. Some data on the rubidium line are given in Table l+.l-VI. The differences in intensity between the observed and the computed profiles were - 23 -

TABLE ll.l-IV

Observed residual intensity at the Rb I T8O0 A line. The intensity

is given in per cent of the continuum intensity and at five distances

from the limb.

Wavelength u - value in Å 0.158 0.222 0.271 0.312 0.380

7800.Il40 5.11 .150 "t. 51 .160 U.0*1 It.90 .170 3.70 U.U9 It.88 .180 3.1i9 It.20 lt.lt9 It.76 .190 3.38 U.01 k.sk it.lt9 5.00 .200 3.38 3.91 It.10 It.33 It. 78 .210 3.1*6 3.89 It.07 It.26 It.63 .220 3.59 3.93 It.11 It.25 It.55 .230 3.75 1».00 U. 19 It.30 It.52 .21(0 3.91 It. 09 It.26 It.36 It.52 .250 It.06 It.19 It.31 It. 1)2 lt.51! .260 It.19 It. 27 lt.3lt l*.l»T It.55 .270 It.28 It.33 It.32 U.U8 !t.5lt .280 It.32 It.35 It.28 It.ltS It.50 .290 It.31 It.32 It.21 It.38 U.lt-3 .300 It. 25 It.23 It.12 It.26 It.31 .310 It.13 It.07 3.99 It.09 It.lit .320 3.95 3.86 3.82 3.87 3.93 • 330 3.71 3.58 3.60 3.61 3.68 .3U0 3.tt0 3.26 3.33 3.31 3.U0 .350 3.05 2.91 3.01 2.98 3.09 .360 2.67 2.55 2.66 2.63 2.76 .370 2.27 2.19 2.29 2.29 2.U3 .380 1.87 1.85 1.93 1.95 2.10 .390 1.50 1.5lt 1.59 1.61t 1.79 -2k -

TABLE k.l-V

Data on the Si I line at 7800 Å as derived from observations at five

different distances from the limb.

Asymm. Symmetric S: I line line

VI -value 0.158 0,222 0.271 0.312 0.380 0.312

log gfesi 6.75 6.78 6.80 6.78 6.79 6.75 Wavelength (X) 7800.005 0.006 0.006 0.006 0.009 0.003

Damping factor 1.1(5 1.50 1.50 1.50 1.60 1.1(5

Wavelength in Å -

Fig. 4,1-U, Observed (solid line) and computed profiles of the Si I-Eh I blend at 7900 Å. The line centres of the components are shown together with the unblended profile of each component, p = 0.158. Within the investigated interval the composite spectrum does not deviate more than

0.05 % from that observed. - as -

calculated for steps of 10 mA in wavelength. In Figure l(.l-5 these

differences are shown as a function of wavelomgth. The spectrum in the

example was observed at u = 0.158. In this case the rubidium isotopic

TABLE li.l-VT

Data on the Eb I line at 7800 Å. Equivalent widths are total equivalent

widths of the Kb I line under the assumption that it is unblended.

The rms values are given in units of 10 of the continuum intensity

Asymm. Symmetric Si I line line

\i- value 0.158 0.22S 0.2T1 0.312 0.380 0.312

log gfeKb 2.758 2.727 2.715 2.731 2.730 z.isk

W(Bb),unblended (mA) 7.1(70 7.103 6.922 7.131» 7.010 7.038

Hel. redshift at best fit (mA) 16 13 13 11 9 16

ras at best fit 31 25 73 51 69 1(6

Fig. lj.l-5. Differences "between observed and computed intensities given as a function of the wavelength. Tfr • isotopic composition of rubidium is assumed to he terrestrial. AA is a measure of the relative redshift of the Kb I line as described in the text. -26-

composition equals the terrestrial one. The free parameter is the relative redshift, i.e. the wavelength shift of the Rb I line relative to the Si I line. The laboratory wavelength of the Si I line is 78OG.OO8 Å according to Striganov and Sventitskii £1968).

Figure U.l-6 shows the differences between observed and computed intensities as calculated for different isotope ratios. The distance from the limb is the same as in the previous example and the relative redshift is 16 mA. From Figures It.1-5 and U.l-6 it is seen that the best fit between calculated and observed profiles is obtained with a relative redshift of about 16 mA and a isotopic composition not far from the terrestrial , one.

As two parameters e.re varied (redshift and isotopic composition), the results may be presented in a redshift - isotope ratio diagram. For a

.150 7800.200 .250 .300 .350 .4C0 Wave leng In in A »-

Fig. U.l-6. Difference between observed and computed intensities shown

as a function of wavelength for different Rb87/Rb85+87 ratios. The

relative redshift is 16 mÅ. - 27 -

Relative redshift in mÅ »•

Fig. ^4-.1—7- Rms values of the differences between observed and computed

intensities at 10 mÅ intervals plotted in a relative redshift - isotope

ratio diagram. The numbers are in uaits of 10 of the continuum intensity.

Continuous lines are drawn through points of equal rms values, u = 0.158.

Relative redshi:t in mA »

Fig. U.l-8. Figure corresponding to Fig. h.l-Jt but constructed for a different distance from the limb, u = 0.222, - 28 -

selected set of relative redshifts and isotope ratios the rms values of

the differences between observed and computed profiles are found. This

is shown in Figure U.1-7.In this redshift - isotope ratio diagram lines are drawn

connecting points of equal rms values. The minimum at l6 mA and for a

terrestrial isotope ratio is now easily seen. Similar diagrams were

constructed using spectra from all five positions on the Sun. Figure

H.l-8 shows the results obtained for u = 0.222. At this distance from

the limb, the relative redshift has decreased, but the isotope ratio found

confirms the results obtained closer to the limb.

The analysis of the spectrum obtained at p = 0.271 gives a somewhat higher Rb 87 content. But studying the observed intensities given in

Table ^.1-IV, a deviation from the general trend is easily seen in the wavelength interval 7800.270 - .310 Å. The observed intensities in this region which correspond to the wavelength where Rb 85 has its maximum are too small. We believe that this is an observational defect.

Farther away from the limb, the asymmetry of the Si I line makes the results more uncertain. This clearly appears when we introduce an asymmetric

Si I line at u = 0.312. It is also demonstrated by the minimum rms values obtained at different distances from the limb (Table lt.l-Vl).

Figure U.l-9 shows the isotope ratio obtained from spectra observed at different U - values. The length of the bars cover the isotope ratio where the rms value is less than ^2 times the minimum value. The length of the bars indicate to some extent the uncertainty of the different results.

As mentioned previously the Rb I line at 79U7 Å is located in the violet wing of a terrestrial vater vapour line. The spectrum observed from the centre of the solar disk in this wavelength region is reproduced in

Figure 1*.1-10. Observations were made at several distances from the limb 29

Fig.14.1-9. Derived values of

Rb8T/Rb85 + 87 for different values

of y. The bars at different

u-values show the isotope ratio

interval within which the rras

values are less than times

the minimum rms value.. In the

case of the double bar at

\s = 0.312 correction has been

made for the asymmetry of the

Si I line.

and with the Sun at different altitudes. The humidity was very low at the

time of observations. The minimum intensity at the centre of the H-0 line

was down to 6 per cent below the continuum level. In the observed spectra

a nearly linear relationship exists between the central intensity of the

HO line and the relative air mass. By extrapolation to zero air mass a

rest intensity of 2 + 0.5 per cent was derived. This is indicated by the

bar in Figure U.1-10. The rest intensity is smaller than what is expected to be caused by the Rb I line. Hence it is probable that an additional line is present in the red wing of the Rb I line. This conclusion is supported by the

fact that a high intensity is obtained on the red side of the H20 line when one attempts to remove the latter. But it should be born in mind that elimination of the terrestrial line in the observed spectrum is subject to - 30 -

1.00

.96 -

L .94 H20

7947400 J .600 -800 79^8.000 Wavelength in A >•

Fig. i|.l-10. The observed photospheric spectrum from the centre of the solar

disk at 79^7 Å. The Rb I line is expected to occur within the two dashed

curves. The bar at the centre of the H„0 line shows the intensity at this wavelength when the water vapour line is removed. The Rb I line must be blended by several other lines.

appreciable uncertainties. One reason for this is that the width of the line depends on the altitude where it is formed in the atmosphere.

The Rb I line may be predicted to occur within the two dashed lines in

Figure U.l-10. This prediction is based on the abundance derived from the

7800 A region and the oscillator strengths with error limits as given by

Link {1966). The dotted line shows a computed Rb I line when a slightly higher abundance is assumed. The wavelength of the Rb I line is the laboratory wavelength published by Johansson (1961). A redshift of 10 - 20 mÅ

must be expected and uhe Rb I line should therefore be shifted toward the red. However, one cannot account for the profile in the violet wing using any reasonable assumptions as regards abundance, isotope ratio or shift of the line. The slope of the wing is too small to be caused by Rb I only. - 31 -

Moreover in this region unknown lines appear to contribute to the profile.

The unknown component seems to increase in intensity toward the limb.

U.l-E. The isotope ratio of rubidium

It- is evident from the results reported here that only the wavelength

region around 7800 Å could be used for the isotope investigation.

As seen from Figure ^.l-ls the isotopic composition of rubidium has

only a small influence on the line profile. Hence spectra of very high

quality are needed for isotope investigations. In Figures ^.1-5 and U.1—6

there still remains a difference between observed and computed intensities

even at the best fit. The differences appear as a periodic function of the

wavelength. The amplitude in the variation is of the same order of

magnitude as the observational rms error. The deviations may be regarded

as a periodic signal which has different phases and periods in spectra

taken at different distances from the limb. In the spectrum taken at y = 0.222, this signal nearly disappears. Therefore» the signal cannot

be caused by faint blends, but has its origin in the observations or in the filtering process applied afterwards. At y = 0.158 the Rb I line has a width of approximately twice the width of one period in the error signal and the error should be more or less canceled out. It is believed that the periodic signal does not introduce an error of importance in the derived isotope ratio.

One may estimate the error in the derived isotope ratio. The asymmetry in the Si I line is shown to have a negligible influence on the results derived from spectra taken near the limb. When analysing spectra at limb distances corresponding to y = 0.158 and y ~ 0.222 one certainly does not introduce serious errors by assuming that the Si I line is symmetric. Farther away from the limb a symmetric Si I line would give too low intensity in the blue end of the investigated interval. This error would give a higher -32­

Kb 87 content, in agreement with the general trend in Figure k.1-9. In

addition, the Rb I line is displaced toward the blue, as shown when correction

is made for asymmetry.

Close to the limb, the best fit between observed and computed profiles

is obtained with a relative redshift of 16 ml. This may be a surprising result

since vertical motions of cooler and hotter matter in the solar atmosphere

should not introduce a relative displacement between the Si I and Rb I

lines. Pierce (1971) has measured the wavelength of the Si I line at the

centre of the solar disk and arrived at a value of 7800.005 Å. In the

chromosphere (Pierce, I968) he found a value of 7800.007 A. Since the

chromospheric spectrum also shows a small blueshift of the Si I line, one may most easily explain this result by assuming that the laboratory

determination of the wavelength is in error. Another possibility is that the solar atmospheric convection can not only be regarded as occuring vertical convection tubes.

The influences of an incorrect setting of the continuum level and variation of the turbulent velocity have also been examined. In both cases figures similar to Figure k.l-f have been constructed. The resulting isotope ratio turns out to be insensitive to the setting of the continuum level, but a wavelength displacement of the Rb I line occurs. A change of the continuum level from ICO,00 to 100.20 introduces a displacement of the Rb I line of about 3 mÅ towards the red. This may be explained in the following way: When one adjusts the continuum level to a higher value, the abundance and the damping factor of the Si I line must be increased in order to obtain a good fit with the observed profile. Then the increase of the Rb I contribution in the blue part of the investigated interval is considerably smaller than in the red part. This causes a vavelength displacement towards the red. In addition, one also obtains a smaller increase in the rubidium abundance. This increase corresponds to an increase in the Rb I line with in such a way that the isotope ratio remains - 33 -

constant. If the Rb I line had been unblended, one would have

expected that a change in the continuum level would have caused a change

in the derived isotope ratio, but not in the wavelength.

Variations of the turbulent velocity causes only a small wavelength

displacement of the Rb I line, but a pronounced change in the derived

isotope ratio. The results of the present investigation are very sensitive

to the choice of turbulent velocity.

The error in the turbulent velocity can be regarded as a sum of two

contributing factors. First comes the observational errors in the profiles

of the Ti I and Si I lines. Close to the limb, the profiles are sy-nmttric

and the turbulent velocity can be determined with a high degree of

precission. But farther away from the limb, the Ti I line is also assymetric

and the determination of the turbulent velocity is more difficult. The

second error is connected with the fact that the different lines are formed

at different optical depths and one may introduce an error by applying the

results from the Ti 1 and Si I lines to the Rb I line. Ey computing the

contribution function one is able to take this effect into account. As mentioned earlier, just the same microturbulent velocity function was

obtained from the Si I line as from the Ti I line. It was therefore assumed that the applied microturbulent function was a good approximation to the real velocity fields. Anyhow, when examining the contribution functions, one has to assume an error in the velocity of 0.2 km/s for the two spectra observed at the closest distance to the limb. This figure gives an error limit in the derived Rb 87 content of 3-0 per cent. Other sources of error may intrcd-^ce appreciably smaller uncertainties in the results than given by this figure. It seems quite safe to claim that the total error does not exceed k per cent. Consequently the investigation leads to the following value-of *~he solar isotopic composition of rubidium: RVRV8T " "-2T ± 0.04 - 3U -

The terrestrial value is 0.278 and is well within the limits derived

above.

The result is valid provided there is no influence of faint unknown

lines. Certainly, very faint lines could alter the result considerably.

Moreover the tvo isotopes are supposed to have equal transition probabilities.

This assumption should be tested by experiments.

U.l-F. The abundance of rubidium

In Table U.i-VI, the derived log gfeRh values obtained from spectra

taken at different distances from the limb are tabulated. For reasons given

in the previous discussion, it is believed that the asymmetry of the Si I

line has resulted in too high log gfe«t values at y = 0.312 and at y = 0.380, while observational errors led to too low a value at u = 0.271.

When this is taken into account, the log gfeR-u values seem to decrease

slightly from the limb toward the solar centre, an effect certainly caused by the atmosphere model. The best value is estimated to be:

log gfeRb = 2.73.

Using the oscillator strength given by Link (1966), the solar rubidium abundance becomes

logeR>i - 2.60

.00 sc

Noise fluctuations of the observed signal and the uncertainty of the value of the oscillator strength are expected to introduce an error of about Aloge - 0,05 in the result. One should be aware that non LTE effects have been neglected in the above discussion. Such effects may introduce systematic errors in the result, especially when resonance lines are treated.

The rubidium abundance obtained i - in good agreement with earlier results and coincides remarkably well with f.he value loge_. = 2-61+ obtained no - 35 -

by Lambert and Mallia (1968) from spectra taken close to the limb in the

7800 Å region.

k.2 Isotopes of antimony

Antimony has two stable isotopes: Sb 121 and Sb 123. The terrestrial

isotopic composition is: Sbl2l/Sbl23 = 57.25/^2.75. The tvo isotopes

have different spin quantum ivumbers I and different magnetic moments which make a closer examination of this element desirable.

According to Moore et_ al. (1966) antimony is present in the photospheric

spectrum with two unblended lines; the Sbi lines at 3232 and 3267 Æ.

*w2-A_ Spectroscopic data

Spectroscopic data on Sb I lines are given by several authors. Some

information on the hyperfine structure of the two lines mentioned and on

some other lines which may be present in the photospheric spectrum has been given by Badami (1932). The Sb I line at 3232 Å has a rather small hyperfine broadening and is without interest for a study of the isotope ratio. The Sb I line at 3267 A has a distinct broadening and an examination of this wavelength region is undertaken in the following. In addition, the wavelength region at 3722 Å is considered. At this wavelength an

Sb I line with pronounced hyperfine broadening may occur.

The relative intensities of the hyperfine components are calculated

(Candler, 196k) and given in Tables It.2-1 and U.2-TT. The isotope ratio is considered to be the same as the terrestrial value. The wavelengths are given on the assumption that no isotope shift exists; i.e. both isotopes have a common centre of gravity. The absolute wavelength are calculated from Atomic Energy Levels (Moore, 1952). The gravitational redshift is taken into account. - 36 -

I ABLE It.2-1

Spectroscopic data for the Sb I line at 3267 A.

Wavelength Sb Hel. in Å isotope intensity

3267. >( 61 121 6.0 Mh 123 U.T

.U80 121 21.2

.1*88 123 lU.l

.510 123 lU.l

.512 121 21.2

.52*4 123 9.9

.531 121 8.8

TABLE U.2-II

Spectroscopic data for the Sb I line at 3722 A

Wavelength Sb Eel. in A isotope intensity

3722-7U0 121 18.6

.755 123 lH.O

•775 121 5.3

.776 123 U.7

.806 123 10.0

.806 121 lit. 8

.827 123 l'l.O

.81(1 121 18.6 - 37 -

1K2-B The Sb I lines at 3267_and_3722_A

3267 Å. The observed spectrum at 3267 A is shown in Figure I*. 2-1. The

profile certainly reflects the hyperfine structure of the line. However,

a determination of the solar isotopic composition of antimony from this

wavelength region is not to be recommended. Some of the reasons for this

are the following*.

Fig.It.2-1. Spectrum at 3267 A observed at the centre of the solar disk.

The hyperfine components of both antimony isotopes are indicated.

a. As is seen from the observed spectrum, some contribution from an unknown line must be present on the red side of the Sb I line. The

intensity, width and wavelength of this line will modify the apparent

contribution from Sb I. This influence mainly occurs on the part of the Sb I line where a rather strong Sb 121 component is situated. b. The strong line on the violet side of the Sb I line is unidentified - 38 -

(Moore et al., 1966) and when atomic- or molecular weight, ionization- and

excitation or dissociation potentials are unknown quantities, a computed

profile must be rather uncertain. According to Pierce (1971) the line

centre is at 3267.^25 A.

c. A discrepancy in the reported wavelength of the Sb I line exists. The

wavelength difference between the value given in MIT Wavelength Tables

(1969) and the value reported above amounts to 12 mA. The computed profile

of the blend is sensitive to the wavelength of the Sb I line,

_d. The two strongest hyperfine components from both isotopes are situated

at closely spaced wavelengths. The profile is therefore rather insensitive

for variations in the isotopic composition.

e. Informations on the isotopic composition will most easily be extracted

from the wings of the Sb I line where the unknown blends are found. In

addition a change in the isotopic composition will act on the width of the

line and the same effect is obtained when the turbulent velocities in

the model atmosphere are altered.

Fig.2-2. Spectrum observed from the

centre of the solar disk in the 3722 A

region. The hyperfine components of

the antimory isotopes are indicated.

.iV \ f

\ Mil Fel / \ Til / - 39 -

3722 A. The Sb I line at 3722 A is situated in the red wing of a very

strong Fe I line which is blended by Ti I. According to Moore et al. (1966)

a fainter Fe I line is also expected to occur close to the Sb I line. The

observed spectrum from the centre of the solar disk is shown in Figure It.2-2.

Judging from the oscillator strengths given by Corliss and Bozman (1962),

the Sb I line at 3722 A is considerably fainter than the Sb I line at

3267 A. The hyperfine splitting, however, is more pronounced and the

presence of Sb I may be seen in the observed spectrum where the double

structure of the Sb I line perhaps may be present. The wavelength interval

between the two Sb T maxima is rather sensitive to the isotopic composition.

But as is easily seen from the figure, this wavelength region is unsuitable

for isotope studies of solar antimony.

The conclusion must therefore be that information on the solar isotopic conposition of antimony hardly can be obtained from atomic line analysis. - ko -

U.3 . iBOtpTjes of europium A somewhat shortened presentation of the europium investigation

reported in the following is given by Hauge (1972c),

The solar abundance of europitim has earlier been investigated by-

several authors: Grevesse and Blanquet (1969) derived the value

logEEu = °'^9 * °*1^ ^in the logeH = 12,0° SCftle)> Wallerstein (1966) fixed the abundance at 0.8, while Righini and Rigutti (196*6) and Bachmann et al. (1970) found values of O.96 and 1.0 respectively.

From at study of the photospheric spectrum of the Eu II line at

1+129 A Grevesse and Blanquet (1969) derived an abundance of loge^ - 1-12.

This figure is about 0.6 dex higher than the values oK'-ined by the same

authors from other Eu II lines and they concluded that the kX29 Å line must be blended. This line was therefore omitted in the isotope investi­

gation undertaken by Hauge (1970). Later, Bachmann et al. (1970) studied

••"he 1*129 Å wavelength region using photospheric and sunspot spectra.

In both cases an abundance of loge- = 1.0 was obtained. This» together with ot^er evidence led the authors to conclude that the Eu II line is

unblended. The europium abundance given by Bachmann et al. (1970) was

derived from this Eu II line only.

The Eu II line at 1»129 A is, provided it is unblended, v&ry

favourable for isotopic investigations. Therefore this line, together with the five other En II lines previously investigated by Hauge (1970), have been reexamined using high resolution spectra.

Europium has two stable isotopes: Eu 151 and Eu 153. The terrestrial isotope ratio is: Eul53/Eul51 = 52.2/^7.8 (or as given in a logarithmic

scale: loS£Euiq^/EEui5i = O.OU). As the two isotopes are present in almost the same concentration and have different hyperfine broadening, europium is favourable for isotopic investigations. - Ul -

hlJZA' Observations and method of analysis

The six Eu II wavelength regions were observed by the author with

the McMath Solar Telescope at Kitt Peak National Observatory during the

spring of 1971. Each spectrum is an average of 100 consecutive scans, and

the spectral resolution is about 7 m&. All regions were observed with

the spectrograph slit placed at the centre of the solar disk and at a

position near the limb corresponding to p - 0.3.

The analysis has been carried out using the method of spectrum

synthesizing. The resulting intensity of various lines and hyperfine

components are obtained by numerical integration of the contribution from

each component of the blend through the model atmosphere.

The atmospheric model given by Holweger (1967) has been used.

As demonstrated in Chapter U.l» isotope investigations are not sensitive

to the choice of atmospheric model.

The macro- and microturbulent velocities were determined by fitting

synthetic profiles to unblended lines occuring on the same records as

the europium lines. Ho isotope shift or hyperfine broadening was expected

to be present in the unblended lines which vere selected. Rest fit to

the observed profile from the centre of the solar disk was obtained by

neglecting macroturbulence and by assuming the following behaviour of

the microturbulent velocity as a function of optical depth:

1 km/s above logT = 2.3, 2.9 km/s below logr = 0.3 and a linear function

of logr in the interval between. The partition functions of europium were taken from Corliss and Bozman (1962).

U^3-B Spectroscopic data

Laboratory data on the six Eu II lines have been published by Krebs and Winkler (i960). The transitions are between levels having quantum numbers J equal to 3 or k. For both europium isotopes the nuclear angular - 1*2 -

momentum quantum number I equals 5/2. The number of hyperfine levels in each

state is therefore limited by the I quantum number and is equal to 6.

The relative intensities of the hyperfine components may be computed,

(e.g. Candler, 196U). In J+J transitions each isotope has l6 hyperfine

components, while in J-»-J±l transitions the number is 15. The intensities

of the hyperfine components of the Eu II line at 1*129 Å are shown in

Table U.3-I.

TABLE U.3-I

Intensities of the hyperfine components of the Eu II line at hl29 Å given

in per cent of the total intensity. Both isotopes have the same relative

intensity distribution.

1 F 13/2 11/2 9/2 7/2 5/2 3/2

13/2 23.92 2.00 25.92 (7)

11/2 2.00 IT. 16 3-07 22.23 (6)

9/2 3.07 12.12 3.33 18.52 (5)

7/2 3.33 8.57 2.91 111.81 (It)

5/2 2.91 6.35 1.85 11.11 (3)

3/2 1.85 5.56 7.U1 (2)

The hyperfine splittings in the lower S- and 's^ states are considerable larger than in the upper ones. Then» transitions between a lower hyperfine level with quantum number F (total angular momentum of the atom) and upper levels having quantum numbers F - 1, P and F + 1 give three hyperfine components at rather closely spaced wavelengths. In the present investigation the intensiti es of these three components are added (see last colomn in

Table if-3-l). The hyperfine structure is considered to consist of 6 main - 43 -

components which represent transitions from the 6 hyperfine levels in the

lover states. The intensity ratio between these main components is calculated

to be 6:5:^:3:2:1 for the Eu II lines at 3930, 3972 and M35 A. The ratio

is 7:6:5:^:3:2 for the lines at 3725» ^129 and 1*205 A.

The energy differences between the hyperfine levels of Eu 151 are

approximately 2.25 times the corresponding differences in Eu 153. Eu 151

has a total hyperfine splitting ranging from 1^0 to 238 mA for the six

lines investigated.

^3-C _Sgectral line investigations

C 1. Investigations of four Eu II lines

The four spectral lines listed in Table ^.3-11 were previously examined by Hauge (1970). The analysis was performed using spectra recorded on photographic emulsion and obtained at Oslo Solar Observatory. The previous and nev results are given in Table ^.3-11.

Some comments on the figures presented in Table 1+ .3—11 are given below:

TABLE U.3-II

Solar isotope ratio of europium determined from four Eu II lines

Eu II line logeEul53/'eEul51

at (A) Hauge (1970) Present work

3725 0.00 ± 0.06 -0.05 t 0.15

3930 0.18 ± 0.20 <0.00

3972 0.03 ± 0.08 -0.05 ± 0.10

1(1*35 -0.09 ± 0.20 -0.25 ± 0.10 - hk -

3725 A. The observed spectrum could not be satisfactorily reproduced for

any assumed isotopic composition of europium. Best fit was obtained when

another line was introduced at 372^.90 Å. The line may be an Sm II line

which is expected to occur at this wavelength. Calculations show that

the line has an equivalent width of 5 mA, in good agreement with what may

be predicted using the gf-value given by Corliss and Bozman (1962).

The Sm II line was not taken into consideration by Hauge (1970). In

the present analysis the isotope ratio is computed on the assumption that

the Sm II line neither shows isotope shift nor hyperfine broadening. The

observed and computed spectrum at best fit are shown in Figure U.3-1.

W^S

.8 3725.0 3972.0 .1

Fig. it.3-1. Photospheric spectra observed at the centre of the solar disk covering three different Eu lines. The hyperfine ccunponents of the

Eu-isotopes are indicated. The dots represent computed spectra. - Ii5 -

3930 Å. This line is situated in the violet ving of the Fraunhofer K line

and in the red wing of a strong Fe I line. In the observed spectrum

the Eu II line is very narrow at the line centre, even more narrow than

a pure Eu 153 line. A computed spectrum with a pure Eu 153 line is

shown in Figure U.3-1. A faint blend must exist at the centre of the

Eu II line. This blend was not considered by Hauge (1970).

3972 Å. This line is in the red wing of the Fraunhofer H line between

a Fe I line and a Ni I line. The different figures of the isotope

ratio given in Table 4.3-II is expected to he caused by the difficulties

involved in determining the local continuum level.

Fig. *t.3-2. Observed photospheric spectrum at UU35 A.

l4l>35 A. The Eu II hyperfine structure extends over a wavelength interval of 238 mA. 'fhe strongest Eu 151 hyperfine components is situated in the violet end of the Eu II line and coincides in wavelength with the unidentified lins at W35.UUI A (Moore et al., 1966). The main Eu II line is severely blended Dy Ca I. The isotope ratio is obtained on the assumption that the unidentified line is entirely due to Eu 151. This hypothesis is possibly incorrect as the abundance obtained is very high

(see Table 1(.3-III). - 1*6 -

A spectrum observed at ^129 Å from the centre of the solar disk is

shown in Figure fc.3-3a. The Eu II line has a profile which is very different

from that of other lines, and the observed spectrum certainly reflects the

hyperfine broadening of the line. As shown in the figure, the observed

profile may very well be reproduced by a synthetic profile. Best fit, however,

is obtained with a logarithmic isotope ratio (^oSE^ie^/E-Esjcn ) °^ -0-25-

For comparison a synthetic profile computed with a terrestrial isotope ratio

is shown by a dashed line. This result may lead to the conclusion that the

solar isotopic composition deviates from the terrestrial one. Limb spectra

of this wavelength region are also best reproduced by the same non-terrestrial

ratio as shown in Figure U.3-k.

Fig. lj.3-3. £•_ Observed spectrum from the centre of the sclar disk. The hyper­ fine components of both europium isotopes are indicated. Dots show the computed spectrum when a non-terrestrial isotope ratio is assumed. The dashed line

shows the spectrum for a terrestrial ratio. b_^_ Laboratory spectrum of the

Eu II line. - UT -

Fig. H.3-U- Observed spectrum at the

limb (u = 0.30) at 4129 A. The dots

show the computed spectrum when a non-

terrestrial Eu-isotope ratio is assumed.

The dashed line shows the spectrum for

a terrestrial isotope ratio-

The Eu II line at U205 Å is severely blended, as shown in Figure i(.3-5ai on the violet side by CH and Y II and close to the line centre by a V II line {Moore et al., 1966). It is possible to fit a synthetic profile to the observed spectrum by using a logarithmic isotope ratio of 0.30

(dotted line). The blend just on the violet side of the V II line is then considered to be caused by europium only. When Corliss and Bozman's (1962) gf-values are applied on the two Eu II lines at 4129 and 4205 Å it is quite surprising to find that the total abundances obtained are O.98 and O.97 while the logarithmic isotope ratios derived are -0.25 and 0.30 respectively.

The occurence of almost identical abundances but different isotope ratios may be explained in three different ways: a. The relative gf-values are incorrect and the contribution from one of the Eu II lines is overestimated. b. In certain transitions the two isotopes lave different transition probabilities.

g_L Both lines are blended.

Ad a» The two lines have the lower energy level in common and the intensity - 1*8 -

4205.0

Fig. U.3-5- fi±_ Observed and computed spectra from the centre of the solar disk in the 1*205 Å region. The dots represent the computed spectrum for a non-terrestrial Eu-isotope ratio, the dashed line shows the spectrum for a terrestrial ratio. b^_ Laboratory spectrum of the Fa II line.

ratio of the lines measured from laboratory spectra should then be equal to the gf-ratio. Laboratory spectra were obtained at Oslo Solar Observatory using a Westinghouse hollow cathode tube. The two spectra are reproduced in Figures l*.3-3b and k.3-5b. Integrations of the observed profiles give the intensity ratio ^oos^ltlPQ = 1*21, This result is in good agreement with the intensity ratio 1.2 obtained from measurements by King (1939)»

It leads to a difference in the log gjT values of 0.08 while a difference of

0.23 is found from the data given by Corliss and Bozman (1962). One may thus conclude that in the U205 Å region the Eu II contribution is overestimated. - k9 -

Au In solar abundance determinations the different isotopes of an element are all supposed to have equal transition probabilities. This assumption is

certainly valid for many elements, but may not always be correct. In

particular we have in mind isotopes with large nuclear magnetic moment and

transitions between levels showing a pronounced hyperfine splitting. The

different isotope ratios derived above lead to consideration of this problem.

The laboratory spectra of the two Eu II lines give some information

on the relative oscillator strengths of the two isotopes. Although

the different hyperfine components are unresolved, the observed profiles

correspond closely to what can be expected when both isotopes have equal

transition probabilities. Small differences in the gf-values may exist,

but they are not so large as to explain the discrepancy mentioned above.

Ad c. The high Eu 151 abundance obtained from the 1*129 Å region and the

high Eu 153 abundance obtained at 1*205 Å must be caused by blends. Spectral

lines from Eu 151 are considerably broader than Eu 153 lines. The Eu 151

abundance derived from the wings of the Eu lines are not very sensitive

to the chosen Eu 153 abundance. Thus, the Eu 151 abundance obtained from

the 1*205 region is assumed valid also for the 1*129 A line. The upper

limit of the Eu 153 abundance is derived and the logarithmic isotope ratio

becomes - 0.03. This result is obtained by assuming both isotopes to have

the same transition probabilities and by using the relative oscillator

strengths reported above. In order to fit a synthetic spectrum to the observations at 1*129 A, two unknown lines must be introduced within the wavelength region of the europium hyperfine components, one at

U129.6U5 A and the other at 1(129.773 A. The equivalent widths of both lines are computed to be about 5 mA. We are unable to identify these lines, but the lines may possibly have their origin in the R-branches of the CW molecular band, blue system. - 50 -

U.3-D* Tfae__isotoge ratio_of_eurogium.

According to the above discussion, the isotope ratio obtained from

the UU35 Å region ought to be neglected. The results obtained from the

Eu II lines at 3930 and 3972 Å must also be given less weight as both

wavelength regions occur within strong Praunhofer lines. The isotope ratio

obtained from the Ul29 and U205 Å regions is expected to the most reliaWe

although the result depends on the choice of continuum level in two

wavelength regions.

Compared with the terrestrial ratio, all reported results show an

overabundance of solar Eu 151. But one should point out that the present

investigation provides no proof of a non-terrestrial isotopic composition of

europium on the Sun.

Variations of the turbuler.t velocity will cause a change in the

derived isotope ratio. Spectral lines from europium, however, have an

extended hyperfine broadening. Thus the resulting isotope ratio is

relatively intensitive to changes in turbulent velocities. In the case

of rubidium, the isotope ratio depends more critically on the turbulent

velocities. In both cases errors introduced by the uncertainty in turbulent

velocity has been taken into account.

In order to reduce the error limits in the results, well determined

oscillators strengths are needed. Then the abundance of each isotope

obtained from different lines can be compared and conclusions about blends may more easily be reached.

The isotope ratio of europium in the Sun obtained from the present investigation is found to be

logEEul53/eEaL51 = -°-<* * °-10 or given in per cents

Eul53/Eul51 = (U8 i 6)/<52 + 6) - 51 -

1*^3^E. The_abundance of europium

A summary of abundances obtained by different authors from ipectral

synthesizing is given in Table I4.3-III. All results are obtained by using

oscillator strengths given by Corliss and Boznan (1962), the only exception

being the present result from the 1)129 and 1)205 A regions which was derived

by using our experimentally determined relative oscillator strengths

normalized to the average value of Corliss and Bozman's absolute values.

Intensity measurements of the laboratory lines at 3930 and 3972 Å

indicate that the difference in the gf-values between these two lines as

given by Corliss and Bozman is overestimated. The good agreement between

the tabulated abundances may be by chance.

The abundance derived from the 1)1)35 Å region is expected to be

overestimated as the isotope ratio derived also deviates from that other­

wise obtained. If both isotopes are equally abundant, the total abundance

derived from 1,he 1)1)35 Å region is about 0.9.

TABLE 1).3-IH

Solar abundance of europium derived froui different Eu II lines.

Eu II line logEu

at (A) Grevesse & Bachmann Present Blanquet et al. work (1969) (1970)

3725 0.1)l)x 0.56 3930 0.52 3972 0.32 0.56 1)129 1.12 1.0 1)205 { 0.85 1)1)35 1.21

'Average of two values. - 52 -

The abundance values presented indicate to some extent the relative

errors in the oscillator strengths. Nev measurements of oscillator strengths

are needed before the solar europium abundance can be more accurately

specified.

Talcing into consideration that two lines are severely blended by Ca II lines, the best abundance value derived from the present selection of Eu II lines is estimated to be: - 53 -

5. STUDY OF AN ELEMENT IN THE SUN WITH ONE ODD AND SEVERAL EVEN ISOTOPES

5.1 The upper limit of the sola.- Sr Bj content

In Chapter h the results of an investigation of the solar isotopic

composition of rubidium is reported. As Rb 87 is radioactive and desintegrates

into Sr 8Tj it is of considerable interest to determine the solar Sr 87 content. An investigation of the solar Sr 87 content has been reported by Hauge (1972b).

Strontium has four stable isotopes, Sr 8U, Sr 86, Sr 87 and Sr 88 with relative terrestrial abundances of 0.56, 9.86, 7-02 and 82.56 respectively (Weast, 1969). No molecular lines from strontium compounds have been identified in the solar spectrum. The present investigation therefore i3 based on observations of atomic lines. Atomic lines from the even isotopes Sr 81*, Sr 86 and Sr 88 appear as single lines because the isotope shifts are very small (e.g. Golovin and Striganov, 1968).

But the isotope Sr 87 shows hyperfine splitting of the energy levels.

Sr 87 has a nuclear moment of -1.1 nm units and a nuclear spin quantum number I that equals 9/2.

For some transitions the hyperfine splitting of Sr 87 may cause a detectable broadening of solar absorption lines. The; more favourable lines for an isotope investigation of Sr 87 seems to be the lines of

Multiplet No. 3 of Sr I which occur at 6791, 6878 and 7070 A. These are faint lines. Only the strongest one (at 7070 Å) was tabulated by Moore et al. (1966) and given an equivalent width of 1 mA. Faint lines, however, are favourable for isotope investigations. In strong lines the effect of the small line broadening caused by hyperfine splitting cannot be detected because it is masked by broadening due to other mechanisms. - 5* -

5.1-A _Observations

The wavelength regions around 6791» 6878 and 7070 Å were observed

photoelectrieally "by the author with the McMath spectrograph at

Kitt Peak National Observatory in May 1971• Observations were performed

both with the slit in positions close to the solar limb (\i = 0.3) and

in the centre of the solar disk. In order to separate solar and terrestrial

lines the Sun was observed at different zenit distances. Each spectrum

was an average of 200 consecutive scans and the observing time was

approximately 12 minutes. The grating was UBed in third order and the

resolution was about 11 mA. The spectra were subjected to Fourier analysis

and filtered for high frequency noise. Corrections for the effect of

the instrumental profile were made. Figure 5.1-1 shows observed spectra

from the centre of the solar disk. The observational rms noise fluctuations -k were about 2x10 of the continuum intensity.

All three lines were certainly present in the photospheric spectrum.

The lines at 6791 and 7070 Å were unblended by terrestrial lines, while the

line at 6878 Å was seriously blended by terrestrial lines, which Moore

et al. (1966) have identified as 0 lines. The two spectra of this wave­

length region shown in Figure 5.1-1 were obtained with the Sun at different

zenit distances. One can easily see that in addition to the 0„ line,

a solar line contributes to the observed profile. The presence of the

Sr I line is most easily detected in the spectra observed with the slit in a position close to the limb. Here this line is considerably broadened.

But the wavelength region around 6878 Å is still not suitable for an isotope

Study of Sr 87. When the terrestrial contribution to the profile is removed,

errors may be introduced that make an investigation very uncertain. One is therefore limited to investigate the very faint line at 6791 Å and the

somewhat stronger line at 7070 A. - 55 -

1.00c, Sri

1.00 • 2 f\° /V( 2 °2 r \°

.98 r - o2

o2 \ .8 6678.0 .2

1.00 H,0

.98 h

Fig. 5.1-1. Observed photospheric spectra at wavelengths of the Sr I triplet of Multiplet No 3. The two spectra of the 6878 Å region were obtained with the Sun at two different zenit distances corresponding to relative airmasses of 1.23 and I.85 respectively. - 56-

5_.1-B_ Spectroscopic data 3 0 3 The transitions in question occur between the levels 5s5p P - 5s6s S_.

Spectroscopic data given "by Heyden and Kopfermann (1938) are used in the '

present work. Their analysis cover the two lines at 6791 and 6878 A. Data

on the third line at 7070 Å are not found. Figure 5.1-2 shows the transitions

and the hyperfine splitting of the levels of Sr 87. No spectroscopic analysis

of the P level for which J - 2 is known. But this level must have

2J + I, i.e. 5 hyperfine levels, and the hyperfine quantum number of each

level must be as given in Figure 5.1-2.

3P„

Fig. 5-1-2. Energy diagram of the hyperfine splitting of the Sr 87 levels in Multiplet No. 3 of Sr I.

The isotope shifts between the even isotopes of strontium are very small.

The shift between Sr 86 and Sr 88 was measured by Hughes (1957) to be less than

1 mA in the line at 7070 A. Thus one can quite safely conclude that no error is introduced by neglecting isotope shifts between even isotopes. - 57 -

The energy diagram in Figure 5.1-2 shows three hyperfine components

in the 6791 A line. The intensity ratio between these components can be

determined theoretically (Candler, 19610. The wavelength of each component

is determined assuming no isotope shift between Sr 87 and the other strontium

isotopes i i.e. all isotopes have a common centre of gravity. Spectroscopic data on the Sr I line at 6791 Å are given in Table 5.1-1.

3 The P„ level has five hyperfine Bublevels as shown in Figure 5.1-2 and the 7070 Å line of Sr 87 contains nine hyperfine components. The relative intensity of each component is calculated and given in Table 5.1-II. Although the energy difference between the hyperfine levels are unknown, their ratios are known to be proportional to the F quantum numbers (7:9:11:13). In the present work the absolute splitting is treated as a variable parameter.

TABLE 5.1-1

Spectroscopic data on the Sr I line at 6791 Å

(Wavelength Isotope Rel. int.

• 6791-003 Sr 87 11 .01*1 Sr 87 15 .050 Even .087 Sr 87 18

TABLE 5.1-II Intensities of the hyperfine components of Sr 87 at 7070 A given in per cents of the total intensity.

3 Pr2 F 13/2 11/2 9/2 7/2 5/2

11/2 3^.56 8.93 1.98 1*5. >»7 9/2 12.89 11-75 5.65 30.29 7/2 It.Ut 8.89 10.91 3U.56 21.82 18.17 ll».5& 10.81 100.00 - 58 -

If we introduce

we find A = 0.1*8 for J=l. When 3-2 this ratio in unknown, but theoretical estimates can be made. A value of A equal to 0.5 or somewhat smaller seems plausible. But an accurate determination of A can only be done by spectroscopic measurements in the laboratory. It turns out that minimum line broadening

(when J=2) occurs at a value of A of about 0,5 which then gives a maximum value of the solar Sr 87 content.

5.1-C Isotoge investigations

The Sr I line at 6791 and 7070 Å were investigated using the synthetic line profile competing program earlier mentioned. Holweger's (1967) model of the solar atmosphere was used. The macro- and microturbulent velocities were determined by fatting synthetic profiles to the Pe I line at 6793.27 Å.

At he centre of the disk, the best fit was obtained by neglecting the macroturbulent velocity and by assuming thfc following behaviour of the microturbulent velocity as a function of optical depth:

1 km/s above logT = -2.3, 2.9 km/s below logT = 0.3 and a linear function of logT in the interval between. This velocity distribution is in agreement with the results obtained in the U000 Å region reported in the europium investigation in Chapter k.

The log gfe values were adjusted so as to obtain the observed equivalent width. Synthetic profiles vere computed assuming different

Sr 87 contents but keeping the total al>undance constant. At steps of 10 mA in wavelength, the difference between the observed and the computed intensity was found and the rms value of these differences was calculated.

The broadening of solar Sr I lines is very small for small con sent rat ions of Sr 87- In the present investigation only an upper limit - 59 -

to the solar Sr 87 content was obcained. Spectra from the centre of the

solar disk gave the best isotope determination. At the limb the lines

were more broadened by other effects. In addition other faint lines made

the determination of the continuum level more uncertain near the limb. -In

Figure 5.1-3 the rms values of the differences between the observed and the

computed intensities are given as a function of the Sr 87/Sr ratio.

Permitting rms values up to få times the minimum value, the Sr 87 content

may be less than 2*) per cent as found from the 6791 A line and less than

25 per cent as found from the other line. Consequently the investigation

leadB to the following value of the upper limit of the relative Sr 87 content:

Sr 87/Sr < 1/1*

Errors in the continuum level and in turbulent velocities may affect

this figure. However, the terrestrial value is in the range of 0.07c - 0.075

corresponding to different radiogenic contributions. The result given above

render conclusions about the solar radiogenic Sr 87 content impossible.

0 .10 .29 30 Ao

Kg. 5-1-3. Ems values of the difference between observed and computed intensities as a function of the relative Sr 87 content. - 6o -

5.1-D The abundance of strontium

Some resent values of the solar strontium abundance are tabulated in

Table 5.1-III.

The oscillator strengths of the two lines of Multiplet No. 3 of Sr I have been measured and calculated by several authors. A review of this work and a discussion of the results is given by Brinkmann (1969) who measured f-values by the zero field level crossing technique. His results were in good agreement with values given by Corliss and Bozman (1962). Theoretical f-values given by Gruzdev (1967) are also in good agreement with recent experimental results and it is now thought that the f-values are very well known. Oscillator strengths computed using the Coulomb approximation method seem to lead to too- high abundances for the two lines under consideration.

Table 5.1-IV shows the solar strontium abundances obtained from the two lineB of Multiplet Mo. 3 when f-values taken from a *ew different sources are used.

TABLE 5.1-III

Recent results on the solar strontium abundance

1CM5e No. of lines Sr Authors

2.72 1 Sr I Grevesse (1966)

3.00 1 Sr II Grevesse (1966)

3.02 1 Sr I, 1 Sr II Muller (1968)

2.82 ISrI.lt Sr II Eambert and Warner (1968)

3.00 2 Sr II, chromosp. Pecker and Pottasch (1969)

2.90 2 Sr I Present work - 6l -

TABLE 5.1-IV Equivalent widths, log gf£„ -values and derived abundances.

Wavel. Equiy. log gfeSr Sr abundances obtained with f-values from: width Coulomb Corliss Penkin Gruzdev & & A ml approx. Bozman Shabanova (1962) (1962) (1967)

7070 1.188 2.75 3.10 2.93 2.87 2.90

6791 0.287 2.lit 3.12 £.86 2.88 2.99

From the values listed in Table 5.1-IY, the solar strontium abundance

appears to be:

logEgr = 2.90

in the logEj, = 12.00 scale.

With reference to the solar rubidium abundance reported in Chapter k,

the following rubidium-strontium ratio is obtained:

ERb^Sr = °-5 ± "-1

This value is considerably higher than the value of 0.1 given by Cameron

(1968) in a compilation of cosmic abundances based on carbonaceous chondrite

data. The value is also higher than that expected for the bulk composition

of the earth. The ratio is not the same in different carbonaceous chondrites, but it is almost always less than the value obtained above. As rubidium is a

Volatile element the present result may show that even the carbonaceous chondrites which are the richest in rubidium, have lost a fraction of rubidium.

The ionization potential of rubidium is very low (U.I76 eV), According to the theory of Alfvén (195*0 rubidium should be easily trapped in the magnetic field of the protosun and thus may be more abundant farther out in the planetary system. - 62 -

6. TEE ISOTOPE RATIO OF COPPER IN THE SUN STUDIED FROM Cu I AND CuH LINES

6,1 Studies of molecular lines from other elements

The isotope effects in molecular spectra are described in detail in

several textbooks. Here only reference ia made to the classical work by

Herzberg (1950). A short survey, useful as an introduction, is given by

Asundi (1970).

Several authors have investigated the isotopic composition of elements

in the Sun using molecular lines. Such work has mostly been performed for

lighter elements as C and N. In many light elements one isotope is by

far the most abundant, and frequently only an upper limit of the abundance

of the rare isotope is found.

Amongst elements with atom number exceeding 10, only Mg and Ti have been subject to isotopic studies by other authors.

Four different papers are dealing with the solar isotopic composition of Mg. Mallia (1968) derived from MgH lins analysis an isotopic composition

Mg2i+/Mg/25Mg/26 = 80/10/10 which is very close to the terrestrial composition.

Kumar (1969) obtained the values 6U/I8/18 and Branch (1970) found 60/20/20.

Recently Boyer et al. (1971) also derived the values 80/10/10. They discussed the results obtained by other authors and explained the different results to be caused by an underestimation of the contribution from stray light. There seems to be good reasons to believe that no difference in solar and terrestrial composition exists.

Herbig (19U9) searched for isotopes of Ti in late type stars. From

TiO molecular band investigations no evidence was found for the suggestion that the relative abundance of the Ti isotopes differed appreciably from the terrestrial value. Recently 'jambert and Mallia (1972) investigated the solar isotopic composition using TiO molecular lines in sunspot spectra.

Their conclusion was that the solar composition is equal to the terrestrial - 63 -

one within an error limit of 30 per cent.

6.2 _ The jLsotope ratio of copper

The presence of CuH lines in the sunspot spectrum has been discussed

by Wohl (1971) who concluded that its presence vas questionable. Hauge (1971)

shoved that R and P branches of the 'E-x'£(0,0) band exist in sunspot

spectra. He also discussed the possibility of determining the solar isotope

ratio from molecular and atomic lines. According to the spectroscopic work

by Heimer and Heimer (1933), the isotope shifts in the CuH 'E-x'EfO.O) band

are quite small for lines having small J-valueL. None of the molecular lines

investigated were found to be suitable for a determination of the isotope

ratio. Observed profiles of P(l6), P(19) and P(20) indicated the presence

of both isotopes, the Cu63H appeared to be stronger than the Cu6?H lines.

But the lines were to weak and blended for any accurate isotope ratio determination.

Hauge (1971) pointed out that some information regarding the isotope ratio may be obtained from neutral lines of copper in the photospheric spectrum. The Cu I lines at 5105, 5700 and 5782 Å have an isotope shift of about 20 mA in addition to a pronounced hyperfine structure (Fischer, 1961).

Synthetic line profile calculations show these lines to be asymmetric.

A large change in the isotope ratio, however, produces only minor changes in the asymmetric profile and would hardly be detectable. On the other hand, line displacement caused by isotope shift is a more pronounced effect.

When the isotope ratio is changed from the terrestrial value of 2.2^ to

1.00, the line position is changed by 5 mA* From a preliminary investigation of the Cu I lines at 5105 and 5782 A (the line at 5700 A is blended) Hauge

(1971) derived the isotope ratio Cu63/Cu6"5 = 2 + 1.

These three Cu I lines have been reinvestigated using photoelectrically recorded spectra obtained at Kitt Peak National Observatory by the author in 1971. The high resolution spectra show the Cu I line at 5782 A to have - €h -

a profile which cannot be explained by isotopes of copper only. The

line must be blended on the violet side, very close to the line Centre.

The Cu I line at 5105 Å is unblended, but the isotope displacement in this

line is somewhat smaller than in the 5782 A line, and the result obtained

by Hauge (1971) may be luore uncertain than previously expected.

The Cu I line at 5700 Å is blended on the violet side by a Sc I line.

Synthetic spectrum calculations show that the resulting profile of two

neighbouring lines is very sensitive to variations of the vavelength interval

between the two lines. Such a blend should therefore be favourable

for accurate wavelength determination and then for determination of the

copper isotopic composition. In this case, however, we may expect

the Sc I line to have hyperfine broadening. No data on this broadening

is found, and without information on this broadening, analysis of the

blend will be of no value.

In order to obtain better information on the isotopic composition of copper, the molecular 'E-X'EfOjO) and (0,l) bands have been examined in sunspot spectra at wavelengths corresponding to higher J values. The spectra were obtained by Pierce at Kitt Peak National Observatory in

January 1968. A very large and regular spot vas observed and the spectra

are of excellent quality. In the (0,1) band the laboratory lines from

Cu63H and Cu65H are veil resolved in both branches. But the new sunspot spectrum analysis verified the result earlier obtained by Hauge (1971) i.e.: the presence of this band is questional0

CuH lines, however, were found at highe. alues in the P branch of the (0,0) band and observed spertra at P(29), P(30) and P(3l) are shown in Figure 6-1. Other lines in t ranch suitable for isotopic investigations are situated at wavelengths were noe traces of CuH is expected to be seen.

These three wavelength regions are examined using two photographic -65 -

P(29) P(30)

1.0 +

0.9 r

I / / •• Cu H nn4- / 63 ob

8 4543.0

Fig. 6-1. Sunspot spectra observed P(31) at wavelengths of P(29), P(30) and 1.0- P(31) in the CuH'Z-x'EfO.O) band.

Photospheric spectra are shown above. 0.9

Cu H 65 Cu63H 0.S

4557.4

plates, one covering P(29) and P(30) and the other P(30) and P(3l). As is

seen from Figure 6-1, Cu65H is severely blended at P{29) and is therefore

omitted from the investigation.

The isotope ratio may he deduced in a very simple way. From the

expression for the equivalent width (Equation III, k) given by Schadee (196U),

one easily sees that the ratio of the equivalent widths of two weak lines

from two isotopes of an element is equal to the abundance ratio. In weak

lines the residual intensity is proportional to the equivalent width. Therefore,

the isotope ratio is equal to the ratio of the residual intensities. Errors - 66 -

in transition probabilities or ccher molecular parameters do not affect the result. In an expression for the isotope ratio, these quantities are

cancelled out. The sunspot model will not affect the result as both isotopes have equal contribution functions. This method of isotope ratio determination, however, cannot be applied on stronger lines where saturation effects exist. And as easily understood, the method is only applicable on elements where the isotopes have abundances of the same order of magnitude.

From two P(30) spectra and one spectrum of P(3l) the Cu63/Cu65 ratio was found to 2.k ± 1.0, 1,9 ± 0.8 and 2.7 ± 1.9 respectively. The most likely value is estimated to be

or given in per cents

fiag3Zfiug5_5Jloj.I.l^X3Q±-Il

The terrestrial ratio is 69.1/30.9 and is well within the limits given above. -67-

7. SUMtARY AND FINAL COMMENTS

The results of the present investigations are summarized in Table

7-1. No conclusion could "be drawn about the solar isotopic composition

of Sb. Although the results given in the table may indicate a solar

over-rabundance of Eu 151 as compared with the terrestrial composition, it

TABLE 7-1

Isotopic composition of some metals in the Sun

Isotopes Terr- isotope Solar isotope ratio ratio

Cu63/Cu65 69.09/30.91 (70 i 7)/(30 + 7)

Rb85/Rb87 72.15/27.85 (73 - M/(27 + h)

Eul51/Eul53 U7.82/52.18 (52 - 6)/{k8 + 6)

Sr87/Sr 0.0702 ~ 0.25

has not been possible to prove that this is the case. In no case a non-

terrestrial isotope ratio has been found.

A great number of spectral lines are still unidentified in the

photospherie and sunspot spectra. A large fraction of these lines is

expected to be of molecular origin and new information on solar isotopic

compositions may be expected from molecular line analysis. In this field

quite a lot remains to be done concerning theoretical studies, laboratory measurements and analysis cl' spectra.

Mo.lecular compounds of Ca and Ni have been reported to be present

in the sunspot spectrum, but these elements have so far not been subject to isotope studies.

CaH-lines have been identified in spot spectra by Tanaka et al. (1939)»

Webber (1970), Engvold (1971) and Wohl (1971). NiH haj been identified - 68 -

by Wohl (19TD.

In terrestrial material, Ca Uo accoonts for about 97 per cent of

the total Ca abundance. The other isotope will be difficult to detect on

the Sun if the molecular lines are not very strong or the solar isotopic

composition is very different from the terrestrial one.

The NiH lines are very faint, but as Ni 58 accounts for 67 and Ni 60 for 27 per cents of the total terrestrial abundance, this element should also be subject for closer studies.

Several molecules may be put in a class termed: "presence doubtful".

These may be found by some authors, but not by others. The elements Ba,

Fe, La, Si and Zr belong to this group.

New information may also be expected from atomic line studies, especially when better physical data and improved experimental methods have been developed. For further progress in isotope studies using atomic lines, several important problems have to be tackled. Some of these are briefly mentioned in the following.

The asymmetry of solar spectral lines has been investigated by many authors, but interest has mainly been devoted to stronger lines.

As isotope studies are most favourably performed on vet k lines, a better knowledge of weak line asymmetry is of interest, especially far out in the wings. It seems also clear that a one-component atmospheric model is insufficient.

The width and shape of synthetic line profiles are very sensitive to the macro- and micro-turbulent velocity functions used. Although much work has been done in this field, the turbulent velocities must be considered with particular care. The results on velocity distributions obtained lyy other authors cannot be applied without further examination.

The observing technique with long integration time may give other velocity - 69 -

functions than for spectra recorded during fractions of a second. Spectra

from different observatories may give different distributions as, for

instance, the line "broadening due to incorrect instrumental profile

corrections easily may appear as a velocity effect. The derived velocity

functions will also to some extent depend on the setting of the continuum

level. Spectral lines used for velocity investigations must have the

continuum level defined in the same way as the lines otherwise used.

The fine structure in atomic lines is only known for a very limited

number of lines. Spectroscopic investigations in the laboratory have to

be performed in addition to the solar spectrum examination. Laboratory

investigations, however, must be done with spectrographs of very high

resolution. The laboratory investigations are also important for fixing

the accurate wavelength of lines in the solar spectrum.

The present survey shows that the chemical elements rubidium and

europium are suitable for photospheric atomic line studies. Both elements

are of special astrophysical interest. Rb 87 is radioactive and Eu 151

has a large neutron capture cross section and can serve as a neutron flux indicator. Considering the advanced technique with which stellar spectra now are recorded, isotope studies of these elements in stellar atmospheres

should "be possible.

Detailed spectral studies, such as those reported in this paper, are very labourious and often require long computing times. But the importance of the problems which are solved in this way may outweigh the efforts. - 70 -

ACKOWLEDGEMENTS

The author is indepted to the Director and the Staff of Kitt Peak

National Observatory for making the excellent facilities of the observatory-

available. He is also very grateful to Dr. A.K. Pierce for permission

to use his excellent sunspot spectra and to all staff members of

the Solar Division who assisted with the observations.

An expression of gratitude is due to Prof. E. Jen3en for his

encouraging inspiration throughout this work. It is a pleasure to thank

0. Engvold for his continuous interest useful discussions and valuable

assistance with the computer program and laboratory measurements and

Dr. 0. Elgaroy for reading the manuscript.

This research has been sponsered in part by the Air Force Cambridge

Eesearch Laboratories, United States Air Force under Grant AFOSR 72-229**.

(Manuscript received, September 1^. 1972) - Tl -

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mm

INSTITUTE OE THEORETICAL ASTROPHYSICS

< : Reports : , i No. 16 (1965) Øystein Elgarøy: Solar Radio Noise Registrations at the Oslo Solar Observatory, 1960-64. No. 17 (1966) Oddbjørn Engvald: Measurements of the Center-Limb Variations in the H- and K-Lines of Ca II in Undisturbed and Active Regions on the Sun. No. 18 (1966) HansKr.Eckhoff: On Some Properties of Solaj Storm Bursts in the 200 Mc/s '?• Region. No. 19 (1966) Einar Haugen: A Test cjf the Method of Evans and Michard for Measurements of Absorption Line Displacement. No. 20 (1967) Einar Haugen: An Isophotometrical Study of Wiggles in the Solar Iron Lines. ' No. 21 (1967) Odd Gimse: The Lifetime of Ha-structures in Active Regions on the *iun. No. 22(1967) RolfBrahde: A Computer Program for"Almanakk for Norge". :No. 23 (1967) RolfBrahde: The Tower Telescope of the Oslo Solar Observatory, Harestua. 'ff^ '4i.No. 24 (1967) Oddbjørn Engvold: Simultaneous Observations; of Ha and the K-line of Call in the Solar Spectrum. No. 25 (1968) EinarHaugen: On Coordinate Systems for Describing the Position of Solar ,,'i Atmospheric Features. '•' * No. 26 (1968)-, Jan-Erik Solheim and Rolf Stabell: A Program for Determination of Absorption In Cosmological Important Areas. . No. 27 (1968) Olav Kjeldseth Moe: Instrumental Polarization in the Solar Tower Telescope at . " Oslo Solar Observatory. : "'.No. 28 (1968) Papers Presented at the Nordic Astronomical Meeting in Oslo June 15.-16. 1968. No. 2? (1970) RolfStabell: Absence of Discrete Absoiption Clouds Below the Galactic Plane in ' - the Galaxy Cluster Area 0024+ 1654.

= -No. 30 (1970) KnutMessell: The 1970 Mercury Transit Used as a Test of the Correction Method for Scattered Light. , ' ':. No.31 (1970) 0. Hauge and O. Engvold: The Chemical Composition of the Solar Atmosphere. No. 32 (1971) Ove Havnes: On the Apparent Connection between Space Velocity and Rbtatiorial ! l , Velocity in Early Type Stars..

Npf33. (1972) PerMaltby and Lars Stoveland: On the Correction of Observed Penumbral ". - Intensities for Scattered Light. No. 34 (1972) Svein Sivertsen: UBV-system for a 12 Inch Telescope No. 35 (1972) ØivindHauge: Tsotopic Composition of some Metals in the Sun