PImet. Spcw Sci.. Vol. 27. pp. 951-957.
Pergamon Press Ltd.. 1979. Printed in Northem kehnd
A DUST RING AROUND
V. A. KRASNOPOLSKY and A. A. KRYSKO Space Research Institute, Academy of Sciences, U.S.S.R., Profsojusnaja 88, 117810, (Received
in find form 21 December 1978)
Ahstrati-Four surveys in which the geometrical parameters were suitable for observations on weak scattering objects were carried out by the Venera 9, 10 orbiters using 3000-8000A spectrometers. The results of one survey can be explained by a dust layer at the height of sighting h = 100-700 km. Its absence in other sessions suggests a ring structure. The spectrum of dust scattering is a power function of the wavelength with the index varying from -2.1 at 1OOkm to -1.3 at 500km. A method is proposed for obtaining the optical thickness, density and size distributionof dust particles from the
scattering spectra. For m > lo-l4 g the number of dust particles with a mass higher than m is proportional to m-*J . The radial optical thickness T is 0.7 x lo-’ at 5000 8, assumingthe geometric thickness S to be 100 km. The maximum optical thicknessalong the normal to the plane of the ring is T,,=4X 10P6. The mass of the ring is 20 tons or 5 X 10m3 g err-’ per unit circumference length; the
maximum mass in a column normal to the ring plane is 10-‘“gcm-2; the maximum density (for 6 = 100 km) is 10-l’ g ~m-~. A satellite of Venus gradually destroyed by temperature effects and by meteorite streams and plasma fluxes is suggested as the source of dust in the ring. One of 1 km radius could sustain such a ring for a billion years. The zodiacal light intensity near Venus is estimated.
Spectrometers for the range 3000-8000 A with a spectral resolution of 20 8, on-board Venera 9, 10 orbiters investigated the nightglow of Venus. The sensitivity threshold of the Venera 9 spectrometer was 1.5 R_.&-’ at 5000 8, for 20°C and 7.5 R A-’ for 7O”C, 3 and 13 R A-’ respectively for Venera 10 (at A = 5000 A near Venus one Rayleigh per Angstrijm is equal to a brightness coefficient R = 7rI/I,-2.5 lo+ or -25OSlO (stars of the tenth magnitude for square degree). The instrument temperature was 15°C on the orbits at the end of October 1975 and about 60°C in December. The temperature increase was caused by the changing relative position of the Sun. Earth and Venus. The dynamic range of the spectrometer (the ratio of the maximum-to-minimum registered brightness) is 3 x lo”, the field of view is 12’X 3.5”. Nightglow spectra representing the second system of Herzberg bands OZ. the height profiles of the glow and the data on its diurnal variations were obtained in the experiments. The experiments and their interpretation are described in detail by Krasnopolsky et al. (1976). THE RESULTSOF OBSERVATIONS OF THE DUm COMPDM
We made an attempt to measure the twilight airglow of the Venusian atmosphere. The vehicle was oriented to obtain a suitable geometry for the observations (Fig. 1). The limb of the planet almost 951
Mde~faringmd on orbit plane
The figure shows the orbit lying in the drawing plane, the direction of the optical axis, the shadow line (dashed) and orbiter positions at the moments of limb crossing, for a height of sighting h and for the entry in shadow. A point of limb crossing A, a height of sighting h, a height of shadow h,, its minimum value h,, and the real height for the object of observation h, are indicated and should be corrected by 80 km.
coincided with the morning terminator, the optical axis of the spectrometer appeared from the shadow at h, = 90 km when the height of sighting h was equal to that of screening -80 km, the air mass was close to maximum and the orbiter itself was in the solar shadow which ensured the absence of stray light. The observations were carried out on Venera 10 on 30 December 1975; the results of the measurements were rather unexpected. The atmospheric spectrum was found to be similar to that of the Sun,
V. A. Ka~.~ororsx~
and A. A. KRYSKO
I I -a2
/ / as
-03 CicgX) I
I I 0.8
HE1GH’l-S OF SIGHTLNG.
Every spectrum is plotted over 600 measured points. ‘Ihe straight lines- the approximation of spectra by power functions using the least squares method. indicating non-selective forms of scattering, gas or aerosol. The wavelength dependences of the brightness coefficient R = d/IO for five spectra obtained at the sighting heights h = 120-490 km are shown in Fig. 2. Each spectrum was recorded for 2.5 s; corresponding to 11 km-variation of h. These spectra will be considered in greater detail below. Dependences of R on h for wavelengths of 3300, 5000 and 6500 8, are given in Fig. 3. Bach curve is based on 65 data points. The measured values of brightness for h < 5.50 km were considerably higher than threshold values. Let us analyse how the curves change in the upward direction though in reality the vehicle moved downwards. If the instrument is pointed towards the dark disk of Venus, it records only its nightglow. As it approaches the limb, the optical axis enters the region with a much narrower solar depression angle and the sunlight scattered in the atmosphere and in the cloud layer, rapidly increases its intensity. The increase should be most sharp near the planet’s limb where the rate of the decrease of solar depression angle has its maximum. The brightness maximum should correspond to the sighting height at which the slant
optical depth is equal to unity, i.e. at 80 km (Krasnopolsky et al., 1976). Indeed, the real time of observation of the maximum in Fig. 3 differs from the calculated time for h =8Okm by about 5 s which corresponds to a mis~i~ent of the optical axis of 12.5 angular min from the assumed direction. This is considerably better than the assumed accuracy of the instrument mounting, in spite of the fact that it was obtained without taking into account the errors in the data on the satellite orbit and orientation. After passing rstant= 1 the brightuess should decrease with the sighting height h according to UT(~) dependence, where w is the single scattering albedo. In this case the scale height for OT should be of the order of some kilometers and just near the maximum the slope curve is determined by the size of the field of view (equal to 20 km). Fmthe~ore, in case of any minor contribution from the aerosol component, the observed scale height should be equal to the true value averaged over the field of (Marov and Ryabov, 1974; view, i.e. -4km O’Leary, 1975). The real variations of brightness are quite different; they point to the presence of
Venera 9,10: is there a dust ring around Venus
COEFFICIENT RG. 3. BRIGH~NF.S~ HEXGHT OF SIGHTING
geometry, i.e. when the satellite was in the shadow and the instrument optical axis entered the sunlit atmosphere at a comparatively low height. The orientation data for these sessions are summarized in the table. In all these sessions the larger side of the spectrometer slit was in the direction tangential to the disk of the planet and its optical axis was in the orbital plane. In two sessions the signal was lower than the sensitivity threshold and in one it exceeded the threshold (the instrument on Venera 9 was more sensitive). In all three sessions the signal was more than three orders of magnitude lower than in the last session. Such a difference cannot be caused by either the scattering indicatrix or smaller air mass in the former sessions. Consequently, the dust object discovered on 30 December, was not observed in these sessions. The most natural explanation, which has astronomic analogs, is the assumption of a ring structure of this dust layer. In the session on 30 December 1975, the optical axis passed through the sunlit node of the planes of the satellite orbit and the ring.
scale of brightness in numbers of stars of the tenth magnitude per square degree is also given on the abscissa. The sensitivity threshold is 3000 S 10 at 5000 8, and - lo4 S 10 at 3300 and 6500 A.
considerable amounts of aerosol along the spoctrometer optical axis. It should be mentioned that this effect could not be caused by the instrument contour which was tested in the laboratory and showed a decrease of sensitivity by a factor of 3000 for 0.5” displacement of the source (53 km in our case, i.e. for a distance of 6000 km to the sighting point) relative to the optical axis. Neither can parts of the satellite, nor dust or gas released from it, produce such an effect, as the satellite was in Venus’s shadow and there were no foreign bodies in the field of view of the instrument. The effect of very bright stars, asteroids or Mercury can be excluded by astronomic data and by the type of radiation spectrum. Therefore, the results obtained yield the brightness of the circumplanetary dust. With the increase of the sighting height, it decreased and above 700 km became impossible to measure due to the satellite leaving the shadow of the planet. This was observed by a sharp enhancement of stray light. We have dwelt on these problems to show the conformity between the results and the observation geometry. Having obtained such unusual data of the circumplanetary dust scattering, we analysed the observations from other sessions with similar
Independence of the signal on the session of 29 November on the sighting height points to its source being the zodiacal light. Similar assumptions can be made for the session of 30 December at heights of 600-700 km, for which the brightness curves (Fig. 3) are rather flat. The measured brightness can be compared with the results of observations of the zodiacal light usually described by a number of stars of the tenth magnitude per square degree n SlO = I,,, nil.2 10e9 erg x cm-2s-I sr-l A-.‘. The intensity of the zodiacal light depends on elongation E and inclination i which was less than 5” during the sessions of 29 November and 30 December. For comparison, rocket observations of Leinert et al. (1974) can be used for E = 15.21, 30” and i [email protected]
For E < 15” these data should be extrapolated parallel to other measurements (Leinert, 1975). Then on 29 November I = 1.8X 10e3 SlO (our data) and 2.3X TABLE Date 18.11.1975 27.11.1975 29.11.1975 30.12.1975
v-10 V-10 V-9 V-10
R 5000 A
35.5” 32“ 27.5” 8”
17” 14” 18” 6”
159km 132 161 89
510~” S10-8 1.8. 10-s see Fig. 3
E is the elongation, p is solar depression angle for A (Fig. 11, h, is the minimum height of the optical axis going out from the shadow.
lO’SlO according to data of observations near the Earth; on 30 December 1=2.3x 10“ SlO and 3 x 10” SlO respectively. Observations by Helios A space probe (Link er al., 1976) showed that the zodiacal light brightness near Venus’s orbit is about twice that near the Earth. Consequently our data on the zodiacal light intensity is 2.5 times lower than that from the above observations (Helios A data are given in relative values). However, the angular dis~bution (the ratio of brightnesses for the session of 29 November and 30 December) is in agreement with the observations near the Earth. According to our data, the zodiacal light spectral distribution does not depend on the wavelength for h. ~450OA and is characterized by a IS-fold increase to 33OOA. Due to the high temperature of the spectrometer, the signat level in short and longwave parts of the spectrum, where the instrument sensitivity is considerably less than at 5000 A, has been close to the sensitivity threshold that makes our spectral data on the zodiacal light les, reliable. Most ground-based and rocket measurement show the zodiacal light brightness does not depend on wavelength, although there are data suggesting such a dependence (see Leinert, 1975). It is possible, however, that near Venus’s orbit the spectrum is somewhat different from that near the Earth. THE DUST RING SPECMWM
Generally speaking, the spectrum is determined by the size distribution of particles, optical properties of their material, their form and the scattering angle E. For small E the dependence on the form can be disregarded (see Leinert, 1975) and calculations can be carried out for spherical particles by the Mie theory. Such calculations were done by Shifrin and Zelmanovich (1968) for different scatindices and tering angles, complex refractive parameters x = 2?rrfh, where r is the particle radius and we shall use their numerical results. In their tables the values i, f i,, which determine the intensity of light scattered by a particle, have been calculated I =&(i,+i,),
where D is the distance to the particle and A is the wavelength in cm. As in investigations of cosmic dust and micrometeorites the size distribution of particles may be assumed to be n = am--,
and A.A. KRYSKO where n is the number of particles per unit volume with a mass higher than m. For the density of the dust material we take 2.4 g cme3, which is close to the density of stone meteorites. Then m = IOr’ and it is not difficult to obtain the value of the brightness coefficient for a unit-thickness layer dR -=dl
3 c~alo-* ~ (2T)3ah-3a+2 sin cp
x -3a-‘(i, + i,) dx,
where cp is the angle formed by the optical axis with the layer plane. Hence the R(A) dependence for the assumed size distribution should be a power function with index y = 3cu - 2 giving OLthe parameter of distribution. This, in particular, suggests that for the interplanetary dust responsible for the zodiacal light, a = 213, as R does not depend on A. The averaged results of direct observations of micrometeorites at distances more than 1000 km from the Earth (Nazarova et al., 1976) give a =0.57, consistent with the value obtained from the scattering spectrum. The description of dust scattering spectra by a power function is valid for Xindependent complex refractive indices (in this case the integral in equation (2) is A-independent too). Such a wavelength dependence has been taken into account by Roeser and Staude (1978). Their calculations show that the spectra are not very sensitive to properties of material in most cases. To obtain the parameters of size distribution, the R dependence on A in log-coordinates was approximated by a straight line by the least squares method (Fig. 2). The dis~ibution index y = 3a! - 2 varied from 2.1 at h = 120 km to 1.3 at 490 km, i.e. a = 1.37 - 1.1. This can be compared with direct observations of micrometeorites near the Earth at 100-400 km, which give (Y = 1.3 (Nazarova et al., 1976). Therefore the size distributions of cosmic dust in the near-Earth cloud and in Venus’s ring are similar. 7’he region at 300 km is characterized by a sharp increase of the spectrum to the red end. This layer thickness is about SO km. Five spectra have been obtained during its passing. The increase considerabIy exceeds the error. The type of spectrum makes it possible to assume that the su~~sition of the distribution typical of our data, with y = 1.7, i.e. average between spectra at 210 and 410 km, and another distribution with a negative value of y is observed. The values of a < 0 or y < -2 are physically not allowed. Figure 2 demonstrates the spectrum approximation by R = AA-‘.’ + BA*. The term
Venera 9, 10: is there a dust ring around Venus with A2 corresponds to the size distribution of particles where the main dust mass is concentrated in dust particles with radius r > 10 pm. In the spectra of Fig. 2 there are a number of significant features, the most striking of which is the minimum at 3900 A. A sharp decrease of intensity in the solar spectrum is also observed at the same wavelength. At this wavelength the spectrometer sensitivity varies rather strongly. All this can be the source of systematic error. However, the minimum depth somewhat exceeds its expected level. It is possible that this minimum is caused by some excess over the assumed distribution of particles with r = lam, which should have the ditfraction minimum for the scattering angle 8” at wavelengths of about 4000 A. MA.%, DENSITY
The problem in describing mass distribution of particles by a power function is that it gives a divergent integral in the density calculation. For OL> 1, as in our case, the divergence is observed for r + 0 and in order to avoid it, the distribution should be limited by some minimum mass mti. Let us assume that mlnin= lo-r4 g or r&= O.lpm. For r
P= -----am a-l
For our case, OL= 1.3. An order of magnitude error in the choice of mminleads to a factor of 2 error in the density determination. To calculate the density it is necessary to find a from the measured values of R by means of (2). The integral in (2) was computed with the aid of the tables of Shifrin and Zelmanovich (1968), assuming the complex refractive index of the dust to be 1.5 + 0.065i which is close to the mean for zodiacal light (Leinert, 1975). The result is rather insensitive to the assumed index. For the scattering angle E = 8” and OL= 1. l1.5 it is found that dR -ZZ dl
and hence (5) for A = 0.5 10e4 cm. It is necessary to know the angle cp between the optical axis and the plane of the ring to deduce the dust density in the ring. To make an estimate, let us assume sin cp= 0.2 (for details see below). If we use R from Fig. 3 in equation (5) instead of dR/dl, we obtain the ring mass per column in the direction normal to its plane about 10-‘“gcm-2 for h = 150 km. For the ring thickness S = 100 km [the rings of Saturn are about 10 km wide, see Bobrov (1970)] its density is about lo-“g crC3, i.e. some 3 x 10’ times higher than the density of the interplanetary dust giving the zodiacal light. Using cgz R dh in equation (5) the ring mass of 2.3 x 10W3gcm-’ per unit circumference length was obtained. The total mass of the part of the ring viewed by the instrument is 10 tons. It is not known what part of the dust ring was observed by our instrument and what part was concealed from it by the Venus limb. The presence of a flat zone at minimum heights of sighting makes it possible to assume that its density here is maximum. If its total mass is the same on the upper and lower branches the derived value should be doubled. For comparative purposes, a similar calculation was carried out on the assumption that the dust shell had a spherical structure. The solution of Abel’s integral equation leads to a dust density of 3 x lo-‘*g cm3 at 150 km, a vertical column density of 5 X 6 lo-“g cm2 and total mass of the dust shell of 270 tons. For the known dust density and size distribution it is easy to calculate the ring optical thickness in the radial direction (T) and in the direction normal to its plane, assuming an approximation that the scattering cross-section is equal to the doubled geometric cross-section of a particle. It then follows that for the visible part of the ring r = 0.7 lo-’ for S = 100 km and T =706-l for arbitrary 6 in cm. The optical thickness in the direction normal to the ring plane is equal to r,, = 0.45R,, (5000 A) according to the calculation, i.e. to about half the brightness coefficient at 5OOOA reduced to the normal (the data of Fig. 3 decreased by a factor of l/sin cp= 5). The observed intensity for the scattering angle 8” is 8 times that for an isotropically and conservatively scattering layer of the same optical thickness. The ring position in space cannot be determined simply by the results of the one session on which it
was observed. Nevertheless, the data on the instrument orientation in this session can be useful. These data can be directly given by the observation time at OOU.T. on 30 December 1975, by the coordinates of a point A (Fig. 1): the declination (latitude) 28”S, the right ascension 256”, the direction of the optical axis: the declination 1.3”N, the right ascension 175”. The orbit plane of Venera 10 had a precession velocity of 3.5” per month and was at an angle of 28” to the equator. If this precession is neglected during our observations (18 November-30 December) it can be deduced that the ring is either at a height of about 1000 km or more than 8000 km. As the instrument optical axis passes almost parallel to the plane of the equator at the latitude 28”S, the inclination of the ring plane to the equator should exceed this value. Although most satellites of planets and, in particular, the rings of Saturn and Uranus (Elliot et al., 1977), are in the plane of the equator, many satellites, nevertheless, have large inclinations. Apparently it is not so important for Venus with its very low angular momentum.
OF THE DUST RING
dust ring of micron particles cannot exist long enough if there is no mechanism providing a steady influx of new material which compensates a gradual deceleration of particles, the lowering of their orbits and a precipitation to the planet. The life-time of a particle in a satellite orbit is (Solodov, 1969) The
where pA is the atmospheric density; H is its scale height, m and s are the mass and cross-section of a particle, t.~is the product of the planet mass and the gravitation constant. The calculation for heights of about 1000 km using the atmospheric models of Marov and Ryabov (1974), gives t = 1 year for micron particles. In this case the rate of dust formation must be about 20 tons a year. In our opinion the most probable source of the dust is a small satellite of Venus. The conditions for ground-based observations of small satellites of Venus are considerably worse than in the case, for instance, of Mars. The data of Goody and McCord (1968) on the upper limit of the nightglow intensity can be used
and A. A.
for evaluating the size of a minimum detectable satellite. Observations were carried out by a 5 m telescope when the phase was about 90” and the distance was 90x lo6 km, which is close to the optimum conditions, as there is a possibility of carrying out measurements late in the evening when the background of the Earth’s atmosphere is similar to the night background. Nevertheless, the bright crescent gives considerable stray light and the threshold of detectability greatly depends on the distance of the satellite from the planet. Recalculation of the derived limit for the nightglow, taking into account the air mass and the phase curve, gives the size of the smallest detectable satellite r = 10 km for a distance of some thousands of kilometers, i.e. like Phobos. Kuiper (1962) gave the upper limit r = 6 km for near-by satellites, without giving accurate distances to the planet. The best opportunities for the detection of satellites of Venus are provided by photography from spacecraft near the planet. During Mariner 10’s fly-by, the space resolution of images obtained close to the planet was about 100m (Murray et al., 1974). However, only a small part of the planet was photographed with such a high resolution and the mosaic images of the full disk had a resolution from 2 to 130 km depending on the distance. It can be assumed that the source of the dust ring could be a satellite of r - 1 km. For density of 3 g cmm3, its mass will be adequate for a billion years with a consumption of 20 tons a year. Its life-time in an orbit of 1000 km is similar. If this satellite is lower than the Roche limit R < 18,000 km, it remains as a whole only due to tensile strength. Gradual destruction of its surface, caused by temperature differences under changing conditions of illumination by the Sun and the planet and also under the effect of micrometeorites and the solar wind, should supply dust into its orbit plane; this has, in fact, been observed. It is quite probable that the satellite orbit passes at heights of sighting of about 300 km (Fig. 3), where a considerable excess of large particles was observed. We appreciate that our explanation of the experimental results is somewhat exotic and we have presented it in the absence of other likely hypothesis. Observation of the dust ring and the planet satellite generating it, is a formidable task. However it can be carried out with the U.V. spectrometer and the TV camera on board the Pioneer-Venus orbiter.
Acknowledgements-We would like to Galperin for helpful discussions.
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