A N O T E O N T H E S Y S T E M A T I C S O F N O B L E G AS A B U N D A N C E R A T I O S

IN THE SOLAR SYSTEM

YU. A. SHUKOLYUKOV

Vernadsky Institute of Geochemistry and Analytical Chemistry, Kosygin Str. 19, 117957 Moscow, USSR

(Received 20 July, 1990)

Elemental noble gas ratios vary g rea t ly - and, at first glance, i rregularly- from planet to planet (Table 1). A number of interesting hypotheses have been suggested in order to explain the observed elemental gas ratios: It was proposed that

- they may have resulted from selective loss of noble gases from the initial atmo- spheres of the terrestrial planets or their planetesimais, or

- they may be the due to solar wind irradiation of the planets and their small precursor bodies, or

- the noble gases were imported by carrier grains with their peculiar abundance ratio already fixed.

The aim of this article is to demonstrate that there is indeed a general regularity in all noble gas elemental patterns in the atmospheres of the planets, and to judge which of the above models fits best to this regularity.

In order to characterize the elemental abundance of noble gases, often one uses the ratio of the whole gas inventory in the atmosphere to the planetary mass. However, since the degree of degassing of the planets could differ, This ratio may not be relevant. This is why we prefer to investigate relative fractionation factors FMx/My , which are defined as

FM~,/My = ( CMx/ CMy)planetary body/(CMx/CMy)solar, (1)

where M x and My are the atomic masses of the noble gases. Figure 1 shows that the F- values correlate with the mass ratios My/M x for Venus, Earth, Mars, and the carbonaceous chondrites. No matter what element is taken for normalization, the logarithm of the fractionation coefficient depends linearly on the inverse atomic mass ratios. Thus, the first rule of noble gas abundances on planets is that the fractionation coefficient of two noble gases is an exponential function of the inverse atomic mass ratio:

FMx/M r = exp [2.3.aMy(1 -- My/Mx)] (2)

It is probably not a mere coincidence that noble gas fractionation by absorption, as determined in a laboratory study by Yang and Anders (1982), follows the very same

Space Science Reviews 56: 37-41, 1991. �9 1991 Kluwer Academic Publishers. Printed in Belgium.

38 YU.A. SHUKOLYUKOV

VENUS ~ i i i ~ i i I

0 el, My=130

a_x _4.i,,, I , , , I 0 4. 8

~ ~ , I i /

2 My:36

-2 �9

0 1 2

II,, 1 0 2 4.

J i i , I , ' i i [ |

i I ~ 4 . . My=20

0 0.5 1 My/Mx

MARS i , , I ' i i I

3~

x I ~ 1 ~ 1

u_ 0 4. 8 O3

0 2 4.

0

EARTH iI < I l 1 l i I i ] l~ilt I t< :130_ 0 84

LIII x _/4Ilt , I [ , I I I I I I I I

0 4. 8 0 2 4- t I i I 36

/ r I I I

0 1 2 f l ~ ; i I i i i r I

0 0.5 1 My/Mx

CARBONACEOUS CHONDRITES CT ....... i 121-- .....

~ ' - - 4 . I - 1 , 1 I ~I IOI I _ I , , " l " i i, 0 4. 8 4.0 2 4. o ) i I!II.IL .... io < L

My:36 ~ ] 2 = 36

2 0 0.5 1 0 1 2 My/Mx

ii ~ ' E , , I i , , ,

0~, , ~ , i , , , i 1

0 0.5 My/Mx

Fig. 1. Relative fractionation factors of the noble gases calculated from the in-situ measured inventories given by Pollack and Black (1982).

rule, as shown in Figure 2. Thus, fractionation by low-temperature gas sorption on solid particles in the protoplanetary cloud could have been the dominant process to form the elemental noble gas ratios of planets.

Now we shall do the next step and analyse variations, not of different elemental ratios on one planet, but variations of the ratios from planet to planet, i.e. their variation with heliocentric distance. We again include in the analysis CI carbonaceous chondfites and suppose that they stem from the asteroid belt at 2.8 AU. Figure 3 shows that the proportionality coefficients ay in Eqn. (2) are a smooth function of the heliocentric distances r of planetary bodies:

x Ii uzr) O

0

-2

-4

NOTE ON THE SYSTEMATICS OF NOBLE GAS ABUNDANCE RATIOS

carbon (sugar)

I I I I r F f

2 4 6 My/Mx

YANG +ANDERS, 1982

] > I I I I > " ~ I I I

x carbon x FeCr film I i LL

t~ (paper) t~ 1st anal. o o 2nd anal.

-1 -1

-2 -2

I I I P I I J I I I I I I I 1 I F

8 0 2 4 6 8 0 2 4 6 8 My/Nx My/Mx

39

Fig. 2. Experimentally determined fractionation factors of noble gases (after Yang and Anders, 1982).

ay = qy exp (ny/r) (3)

Thus, the second rule of relative noble gas abundance on planets is that the logarithm of the fractionation coefficient of any two noble gases in planets is an expo-

ay

6

I I I t I I I

~- C L-

03 ~ LO ~ C_)

y=20

y= 36

~ y=84 �9 y=130

I

0 1 2 3

Fig. 3. The dependence of the fractionation parameter ay from the heliocentric distance.

40 YU. A. SHUKOLYUKOV

TABLE I

Summary of elemental ratios of the noble gases in the solar system from measurements (modified from Pollack and Black, 1982) and predictions based on Eqn. 4.

Object

Sun Mercury Venus Earth Mars Chondrites Iupiter ~aturn

Distance from the

Sun (AU)

0 0.39 0.72

1 1.5

(2.8) 5.2 9.5

2ONe/36Ar

35 9,6

0.15 + 0.04 0.57

0.43 (0.15 - 1.0) 0.27 0.05 O.025

36KAr/84Kr

2,500 865

50 - 1,200 48

31 (10 -90 ) 109 75

100

84Kr/13ox e

66 81

>17 179

58 (13-230) 7 25 4

nential function of the inverse orbital radius of these planets. From the graphs ln(ay) versus 1/r for each noble gas, a set of qy, ny-pairs are

obtained. It then turns out that the logarithms of the qy are proportional to the square roots of the noble gas masses (ln qy = 2.83 - 0.229,,/y) and that the ny are proportional to the inverse of the masses (ny = 11.1/y - 0.856).

By combining Equations (2) and (3), the following empirical formula is obtained which is valid for all noble gases and holds at least for the terrestrial planets:

In Fx/y = 38.97.(1 - My/Mx)-exp[-0.229-My'~ + ( l l .1 /My - 0.856)/r1

(4)

Data about the noble gas abundances on terrestrial planets are still inexact (Table I). This leads inevitably to deviations which had to be smoothed. Notwithstanding that fractionation coefficients calculated according to the general formula (Eqn. 4), in certain cases can differ up to several times from observed ones, the overall agreement is striking (Fig.4).

Eqn. 4 allows us to rather confidently predict the elemental noble gas composition for Mercury for which experimental data are absent. The resulting values are given in Table I. Of yet unknown significance is the similarity of the 36Ar/13~ ratio predicted (70,000; cf. Table 1) and the ratio determined by Crabb and Anders (1981) in the FA-5 chondrite South Oman for a subsolar noble gas component which is 15,700 _ (36Ar/130Xe)sub_solar <_ 30,300.

The predictions for the noble gas abundances in the outer planets (Table I) are less justified since, e.g., possible variations of the gas/dust-ratio between the early inner and outer solar system may have strongly influenced the noble gas composition.

NOTE ON THE SYSTEMATICS OF NOBLE GAS ABUNDANCE RATIOS 41

4

2 E 0~

u2 0 O'3 0 -2

-4

-6

- I I [ I I I

I

-6

�9 0 ~ 0 "

�9

I I I / t I I I I I I -/+ -2 0 2 4 6

log Fexper.

Fig. 4. Comparison of fractionation factors which were determined experimentally (cf. Fig. 1) and calculated using Eqn. 4.

Contrary to the predictions for Mercury, however, the predicted values for Jupiter and Saturn may be tested by upcoming space missions.

We stress that the observed systematics do not pretend to explain any fine structures of the noble gas abundances on planets, but rather to reveal general trends in a semi- quantitative analytical way. Even so, previously puzzling apparent noble gas abundance irregularities disappear. Differences in the abundance ratios of various gases on the planets can now be related to the mass-dependent affinity of the gases for absorption on solid protoplanetary dust particles. Then the ratio variations of the elemental abundances of any pair of noble gases on different planets can be explained by different sorption conditions in the protoplanetary cloud at different distances from the Sun.

References

Crabb, J. and Anders, E.: 1981, Geochim. Cosmochim. Acta 45, 2433-2464. Pollack, J.B. and Black, D.C.: 1982, Icarus 51, 169-198. Yang, J. and Anders, E.: 1982, Geochim. Cosmochim Acta 46, 877-892.