Solar and meteoritic abundance of silicon

Cm< hrmro 8

i’l Cosmochmmo Acru Vol. 44. pp, 2145 to 2149 Ltd 1980 Prmted m Great Britain

Pergamon Press

NOTE

Solar and meteoritic abundance of silicon U. BECKER,* P. ZIMMERMANN Institut fur Strahlungs- und Kemphysik,

Technische Universitat Berlin. Rondellstrasse 5, D-1000 Berlin 37, West Germany

and H. H~LWEGER Institut fir Theoretische Physik und Sternwarte, Universitlt

Kiel,

D-2300 Kiel, West Germany (Received 10 April 1980; accepted in reuisrdform

30 July 1980)

Abstract-Recent lifetime measurements on excited electronic states of neutral silicon (BECKER et al.. PI7y.x Lrrr. In press, 1980) lead to a reassessment of widely used experimental transition probabilities (GARZ, Astron. Astrophys., 26471-477, 1973) of Si I lines. This translates into a 25% downward revision of the Si abundance determined from the solar spectrum. A solar atomic ratio, Si/Ca = 15.5 is inferred. This value coincides with that found in carbonaceous chondrites, but contrasts with ordinary and enstatite chondrites.

INTRODLICTION COMPARINGSOLARand meteoritic elemental abundances requires a common reference element, a role which is generally allotted to silicon. From the point of view of solar spectroscopy this choice may be considered problematic if such a comparison is aimed towards resolving compositional details in the 20% range as required to discriminate among various types of chondrites, Rather than solar spectrum analysis, what causes problems here is the atomic transition probabilities that enter into the solar abundance determination. Accessible Fraunhofer lines of neutral silicon are all high-excitation transitions difficult to reproduce in the laboratory. Furthermore, reliable quantummechanical calculation of Si If-values is hampered by general occurrence of severe configuration mixing. Current solar Si abundance values reflect this problem. The widely used Ross-Aller compilation (Ross and ALLER, 1976) adopts the value log es, = 7.65 (on the scale log en = 12.00) from HOLWEGER’S(1973) solar analysis which, in turn, is based on experimental flvalues of GARZ (1973). These f-values entered also into the rediscussion of photospheric abundances by LAMBERT and LUCK (1978). In Holweger’s study it was noted that the two accessible Si II lines, whose quantum-mechanical treatment is claimed to be less problematic than that of neutral Si, yielded abundance * Present address: Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California. Berkeley, CA 94720, U.S.A.

values 0.1-0.15 logarithmic units lower than those of neutral silicon. Nevertheless it was felt at that time that the numerous neutral lines together with the new transition probabilities formed a safer base. However, neutral silicon also provided evidence for a lower value. Similar to LAMBERT and WARNER (1968). HOLWEGER (1979) arrived at a value log E = 7.56 i 0.08 by selecting only those ten transitions showing negligible configuration mixing or cancellation. GREVESSE and SWIIQGS(1972) inferred an even lower value, 7.50, from a faint, heavily perturbed forbidden Si I line. These discrepancies, though not drastic, are unsatisfactory in the case of a reference element and major constituent of most meteorites. We wish to point out here that recent lifetime measurements (BECKER et al., 1980) covering different Si I states, and using selective laser excitation lead to a reassessment of the GARZ (1973) fLvalue scale by some 25% which resolves the solar abundance problem. As a consequence, ordinary chondrites no longer match the solar Si/Ca ratio.

TRANSITION PROBABILITIES A critical survey of experimentally determined atomic transition probabilities of Si I shows that the absolute scale of all relative measurements including those of GARZ (1973) are based on the lifetime of the 3~4s ‘P state which has been measured by SAVAGE and LAWRENCE (1966) and MAREK and RICHTER (1973) using the phase shift method. Both lifetime

2146

Notes

measurements are in agreement. However, recent experience with other methods such as level crossing has shown that mutual agreement of phase-shift results does not guarantee that they are accurate. Some phase-shift lifetime results in the 5 nsec range tend to be too large, in the case of collisional excitation due to cascading problems (see, for example. Sn 1. HOLMGRFN and SVANBERG 1973). Clearly a redetermination of the Si I 3~4s 3P lifetime by an independent method was needed to establish a reliable absolute scale for GAR~‘s (1973) set of,f-values. New lifetime measurements of the Si I 3~4s 3P state and additional Si I states have been performed recently and independently by BASHKIN et cd. (1980) and by BECKERet (I/. (I 980). BASHKIK et al. (1980) used the beam foil method to measure the mean lives of excited levels in Si I-Si IV. BECKER ef rrl. (1980) recorded the direct decay curve of the resonance fluorescence by the delayed coincidence method after pulsed dye laser excitation from atomic states of neutral silicon which have been populated by collisional dissociation of evaporated silicon molecules. This method yields lifetimes unaffected by blends and cascades and is only limited to smaller lifetimes by the laser pulse length of about 2.5 nsec. The results of both experiments are in excellent agreement for the 3~4s ‘P and 3p3d ‘P states. Only the results of the 3~4s ‘P state are at variance. BASHKIN rt al. (1980) yield a value of 5.9 nsec in good agreement with the results of SAVAGEand LAWRENCE (1966) and MAREK and RICHTER (1973). But they have pointed out that the strongest line of the investigated 3p2 ‘Pp3p4s 3P multiplet at 251.6 nm coincides with a Si IV transition at 251.X nm. Since the fractions of Si I and Si IV depend on the beam velocity they found different lifetimes at different beam energies for this transition. The 3P state served mainly to test the time calibration of their apparatus and their result for this state seems to be much less reliable than their other beam foil lifetimes. The Becker et al. experiment, which is free of cascading and blend problems, yielded 4.5 nsec for the 3~4s 3P state, about 25% less than the Table

1. Absolute

transition

old phase-shift results, requiring a corresponding raise of Garz’ absolute ~&value scale. Lifetimes of the 3~4s ‘P, and 3p3d ‘P, states determined in both experiments also necessitate an increase in the absolute ,dlvalue scale by the same 25%. The precise reestablishment of this scale requires reliable branching ratios as well as lifetimes. These branching ratios have been determined experimentally only for the 3~4s ‘P and 3P states, and theoretical results are partly at variance with the experimental values and each other. Table I shows the branching ratios deduced from various intensity measurements and &value calculations. The most reliable branching ratios probably are those based on the &values of GARZ (1973). The difference between these and other experimental values by CORLISS and BOZMAN (1962) and MEGGERS et al. (1975) affects the transition probabilities of the strongest transition from the 3~4s 3P and ‘P states by less than & I and +5x, respectively. The results of LAWRENCE (1967), extensively used in the compilation of WISE rt ~1. (1969), are based upon intermediate-coupling calculations as far as their angular parts are concerned, and upon radial integrals determined empirically from the lifetimes of SAVAGEand LAWRENCE(1966). The good agreement of these values with those of GARZ (1973) shows that this method, which assumes independence of the transition radial integrals from the energy of the lower level, works satisfactorily in the case of Si I. Other semiempirical methods based only on the positions of the energy levels like the Coulomb approximation and the Thomas Fermi Method give partly unreliable branching ratios although the absolute yf-value scale of the scaled ThomassFermi-Dirac (STFD) calculations by Warner (1968) and Kurucz and Peytremann (1975) is reasonably correct. In the case of the 3p3d ‘P, state where no experimental data exist and which is not included in Lawrence’s (1966) list. we prefer branching ratios calculated in LScoupling over those of WARNER (1968) and KURU~Z and PEYTREMANN (1975). As WARNER (1968) has pointed out the results of his calculations for the

probabilities and oscillator strengths derived from the lifetime measurements (11.(1980) and selected values of branching ratios Branching

Upper

level

3p4s ‘P, 40991.9 cm- ’ 7 = 4. I (4) nsec

Wavelength (nm)

Lower

243.9-245.2 288.16 390.55

3p2 3P0.,,2 I& ‘SO

1.0 1.0 0.0624 0.0573 0.385 0.485 1.0 1.0 0.0005

level

3p4s jPz 39955.1 cm-’ r = 4.4 (4) nsec

250.69 251.61 297.04

3pZ 3P, ‘P2 ‘DZ

3p3d ‘P, 53387.3 cm 1 r = X.1 (5) nsec

187.3-188.1 212.30 263.13

3p* JP,,,.2 ‘D2 ‘SO

G

CB

S

ratios

A,,:A,,

log Ilf

M

KP

Calc.

Best values

0.0573

0.006 1.0 0.140

0.0114 1.0 0.0801

0.011 1.0 0.064

0.349 0.471 1.0 1.0

by BF,~KERct

A,, (IO”sec-

This ‘) work

Garz

0.025 2.27 (23) 0.145

2.17 IO.07 -0.15 - 1.oo - 1.09

0.330 0.337 0.40 1.o 1.0 I .o 0.0003 0.0002 0.0004

0.65 118) I .62 122) 0.0007

PO.52 -0.66 ~0.12 -0.24 - 3.33 ~ 3.44

0.049 0.341 1.0

0.006 0.107 1.12 (20)

~ 3.05 ~ 1.67 ~ 0.46 ~ 0.52

0.005 0.095 1.0

0.005 0.095 1.o

G = GARZ (1973); CB = CORLISS and BOZMAN (1962); S = SLAVENAS (1964); M = MrC;(jl;Rs (jr (I/. (1075); KP = KUKUU

and PFYTREMANN(1975).

Notes

3p2-3p3d transitions are reliable only for lines having large f-values. For the 3~‘~3p4s transitions, intermediate-coupling line intensities agree with the values for LS-coupling. For the same reasons the contribution of the spinforbidden transition has been assumed to be in the same order as those of the corresponding pz-ps transitions. We estimate an uncertainty of 207: for the &values of the strongest transition from the 3p3d ‘P, state. The adopted branching ratios (Table 1) represent mean values of all data listed excluding those of KURUCZ and PEYTREMANN(1975). In this manner we determine the absolute transition probabilities and & values of the nine strongest downward transitions arising from our three states (Table 1). The quoted mean error of these transition probabilities is the sum of the branching ratio and lifetime value uncertainties, Six of these lines are in common with Garz’ list. As to be expected the difference between both sets is quite uniform, with a mean relation log Elf (this work) log d (Garz) = 0.10 _t 0.03. Combination of GARZ (1973) valuable set of relative f-values with the new lifetimes by BECKER et al. (1980) is thus simply achieved by increasing all log &values in the Garz’ list by 0.10. The other Si I lifetime results of BASHKIN et nl. (1980) (3p3d ‘D, ‘F and 3p3 3D) support an increase of the absolute dvalue scale. Although no direct comparison with Garz can be made and no reliable branching ratios are available, they can be compared with the emission data of HOFMANN (1969) who has normalized his results also by means of the old 3~4s 3P lifetime value. The lifetimes following from the emission data of HOFMANN (1969) are about 40% larger than the beam foil results of BASHKIN et al. (1980). The difference between this figure and our 25% simply retlects the lack of reliable branching ratios for transitions from these states. Table

2147 THE SOLAR

ABUNDANCE

The new Si I j-values can be incorporated into the solar abundance analysis of HOLWEGER (1973) in a straightforward manner without further model-atmosphere comp~ltations. Since line formation depends on ,f-value and abundance only via the product. trfi, the overall increase of the former requires a corresponding decrease of log E by 0.10 if the fit to the observed solar spectrum is to remain unchanged. In this way, the sample of 19 Si I lines in Table 1 of Holweger leads to a silicon abundance, log t = 7.55. Just the same value follows from the two ion lines if all sources of Si II f-values are admitted uncritically. We prefer, however, to exclude the (older) Si II arc emission measurements and to rely solely on the quantum-mechanical results of FROESE-FISCHER(I 968) and the beam-foil experiments by BERRY et al. (1971) and BASHKINet ai. (1980). This changes.the Si II result into log E = 7.53. The final result is based on both Si I and Si II, the solar silicon abundance becoming loge,, = 7.55 It O.OS(SD) on the usual astrophysical scale log +r = 12. The small standard deviation of individual lines attests to the accuracy of the GARZ (1973) relative measurements. Furthermore, the new BECKER et ai. (1980) SiI lifetimes remove the solar Si I/Si II discrepancy and render experimental and quantum-mechanical Si I results concordant. THE SOLAR

AND METEORITIC

Si:Ca RATIO The revised silicon abundance combined with the solar abundance of calcium log eta = 6.36 (Hoi_WEGER, 1972). leads to a solar (atomic) ratio Si/Ca = 15.5,

2. Summary of chondritic and solar Si/Ca atomic ratios and Ca abundances

Group

Carbonaceous Carbonaceous Carbonaceous Carbonaceous Bronzite Hy~rsthene Amphoterite Enstatite

(Cl) (C2) (CO) (CV (H) (L) (LL) (E4-E6)

Sun (this work) Sun (previous value)

1 -VON MICHAELISei u(. (1969);

OF

SILICON

Si/Ca

Ca abundance (Si = 106)

16.1

62200

14.4 14.0

69400 71400 84700 49600 48500 46400 35600

2 2 3 2

64500 51300

(4)

11.X 20.2 20.6 21.5 28.1

15.5 19.5

Ref,

I I I 1

MCCARTHY and AHRENS (1972);

KALLEMEVN and WASSON

(1980). ~~-VON MICHAELISrt ul. (1969). finds excluded 3 -MASON (1971). 4pHOLWEGER (1972, 1973).

from average.

Notes

2148

Ba determined relative to Ca ~HOLWEGI-.R. 1979). More specifically, Cl turns out to fit the sun in all six cases. The sample now covers a considerable range of condensation and ionization properties. Not precluding anomalies of minor constituents there is now substantial evidence that the bulk of the matter of Cl chondrites is a well-preserved condensate from a gas of solar composition. Condensation apparently has been a~omplished without s~gnitic~~rlt plasma-gassolid fractionation.

_E”

4ckffC)lt’fPdyeMellt.s-We arc grateful to J. T. WASSO~; and G. W. KALLCMEYN for critical comments and for communicating their results on carbonaceous chondrites prior to publication. REFERENCES

-1

Fig. I. Comparison of solar and chondritic Si/Ca ratios. 0 (ordinary) stands for the mean of groups H, L. and LL. A typical spread of &4”/, has been assigned to the meteorite data.

with an estimated overall uncertainty of + 20%. Error limits include solar model uncertainties; the ratio changes by less than 10% if the VERNAZZA et 4. (1976) solar model is employed instead of the HolwegerMiiller model. The quoted model dependence is probably an upper limit since the Vernazza et ul. model turned out to be only marginally acceptable (AYRES, 1977; LAMBERTand LWK, 1978; HOLWEGER, 1979). Carbonaceous chondrite abundances were derived by combining the recent Ca/Mg data of KALLEMEYN and WASSON (1979, 1980) with the detailed MgjSi determinations by MCCARTHY and AHRENS (1972) and VON MICHAELIS et al. (1969). Meteoritic and solar data are summarized in Table 2 and Fig. 1.

CONCLUSIONS Obviously the solar Si/Ca ratio matches the carbonaceous chondrite groups Cl, C2, and Ornans but not the Vigarano group, and is definitely different from that found in ordinary and enstatite chondrites. The coincidence of the old solar value with that for ordinary chondrites was fallacious. The same conclusion follows from other spectroscopically favourable elements like Na, Mg, Al, S, and

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Notes I..Ahmkn

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2149

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probabilities-II.

Sodium through

calcium,

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