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Dust particles beyond the asteroid belt—a study based on recent results of the Ulysses dust experiment
Planet. Space Sci., Vol. 43, No. 6, pp. 827-832, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain, All rights reserved 0032-0633/95 $9.50 + 0.00
Pergamon
0032-0633(95)00073-9
Dust particles beyond the asteroid belt-a of the Ulysses dust experiment Ingrid Mann’
and Eberhard
’ Max-Planck-Institut ’ Max-Planck-Institute
study based on recent results
Griin’
fur Aeronomie, Postfach 20, D 37189 Katlenburg-Lindau, F.R.G. fur Kernphysik, Postfach 103980, D 69029 Heidelberg, F.R.G.
Received 3 August 1993 ; revised 19 April 1994; accepted 5 May 1995
1. Introduction The general shape of the interplanetary dust cloud is made up of particles on Keplerian orbits approaching the sun by decelerating forces of Poynting-Robertson effect (see for instance Wyatt and Whipple, 1950). It is concentrated to the ecliptic plane and rotational symmetric with respect to an axis through the solar pole. Aside from this general structure, there are local phenomena like dust rings and cometary dust tails, which will not be discussed in this context. The Ulysses space probe, carrying a dust detector (Grtin et al., 1992a), drew renewed attention to the part of the dust cloud that is beyond the asteroid belt. An influence from the local interstellar medium was expected and has been recently observed with UZysses for this region (see Grtin et al., 1993). A review about the dust measurements beyond the asteroid belt is given elsewhere (Grtin, 1994). We concentrate the present study on a discussion of possible sources of dust in the context of the UZysses results and we attempt a comparison to observations of the Zodiacal light. We present the general distribution of dust in the solar system as derived from Zodiacal light observations (Section 2) and then in contrary the UZysses dust flux data (Section 3). In Section 4 we discuss the dust emission from comets and the orbital evolution of cometary dust particles and finally study the influence of these outer dust components on the Zodiacal light brightness (Section 5).
2. Spatial
Correspondence to : I. Mann
distribution
of dust from Zodiacal
light data
Zodiacal light data from ground based observations in the visual range by Levasseur-Regourd and Dumont (1980) were mainly confirmed by measurements of the Helios photometric experiment (Leinert et al., 198 1). Data about interplanetary dust thermal emission were given by the IRAS satellite at elongations, E, 60” < E < 120” (see
828
Hauser et al., 1984) and by rocket borne photometry which covers solar elongation angles, E, 22” < E < 180” and ecliptic latitudes, /?,, -60” < /ILos < 90” (Murdock and Price, 1985). Usually, the brightness is strongly influenced by the inner dust cloud at small solar distances, however, in the case of the thermal emissions, the relative contribution from different regions varies also with the observed wavelength. As far as the size distribution is concerned, the Zodiacal light is produced by particles in a size range from 1 to 100 pm (Grtin et al., 1985), smaller particles, as for instance measured with impact detectors, although their number density in the interplanetary dust cloud is much higher, give only a small contribution. Particles in both size ranges can be compared, since at least in the inner solar system they are both produced from a similar collisional evolution (Mann and Grtin, 1992). The inversion of the Zodiacal light brightness, as described elsewhere (Giese et al., 1986), gives different models of the spatial distribution. These are related to the local flux rates of orbiting grains. As their number density n(v, /&) = n(r) f(/&) is assumed to be separated between the in-ecliptic n(r) and the out-of-ecliptic fraction f(PJ, inversion of the dynamical structure leads to a separation between the orbital distribution densities d(a, e) of eccentricity, e, and semi major axis, a, and the distribution d(i) of inclinations i. Models of the radial slope in the dust cloud are given with an n(r) = r-” power law. The Poynting-Robertson drift of particles and their final sublimation in the solar vicinity show the need for sources of dust to explain a stable dust cloud. A collisional balance was discussed in order to explain an exponent v = 1.3 in the radial slope of number density, that was derived from Helios photometric results (cf. Leinert et al., 1981 ; Grtin et al., 1985). Later studies, based on an analysis of both, thermal emission and scattered light from brightness data point to the combination of two effects, an increase of number density and an increase of albedo with decreasing solar distance, to explain the slope of the visual Zodiacal light. They are in agreement with a simple l/r law for the number density (see Levasseur-Regourd et al., 1991), which is already explained by PoyntingRobertson drift of particles on circular orbits. Eccentricities between 0 < e < 0.3, as found to be predominant in the inner solar system, have only small deviations from the distribution of circular orbits. These eccentricities are consistent with a l/r power law in the spatial distribution and thus with recent Zodiacal light analysis. A discrepancy of the out-of-ecliptic distributions in different Zodiacal cloud models led to the assumption of a bimodal description proposed by Kneirjel and Mann (1991), which fits to the data within 10%. The main component is concentrated to the ecliptic and has a radial dependence of the VSF (i.e. volume scattering function, the average scattering cross section of particles per volume element) with l/r, whereas the second component has a spherical shape and increases with a power law with exponent v = 1.5-2 towards the sun. This approach gives the distribution of the number density folded with the optical efficiency and the original idea was, to explain this radial slope with a variation of particle properties. However, we will show, that also dynamical effects can
I. Mann and E. Griin : Dust particles beyond the asteroid belt cause a component in the dust cloud, with steeply increasing number density (and thus VSF) towards the sun.
3. Detected dust fluxes Present Zodiacal cloud models are in acceptable agreement with previous dust flux measurements in the inner solar system and also dust fluxes detected onboard UZysses in the inner solar system are best explained by particles in low inclined, low eccentricity orbits. Fluxes detected at increasing solar distance show an increasing amount of unbound and highly inclined orbits. Deviant from Zodiacal cloud models the dust detector observed an impact rate, that is significantly higher than would be expected from a radially decreasing distribution expected for particles in nearly circular orbits (Grtin et al., 1993). An attempt by Divine (1994) to describe the interplanetary meteoroid environment includes a so-called halo component with randomly inclined orbits, which sets in beyond solar distances r, r M 2.5 AU to take these detected flux rates into account (see Grtin et al., 1992b), however, so far without any physical explanations. No mechanism is yet proposed to explain the cutoff of this component at 2.5 AU and also other assumptions of the dust flux distribution could give a sufficient explanation of the so far rare data. Also the Pioneer 10 and 11 penetration sensors (Humes, 1980) detected fluxes, deviant from the distribution in the inner solar system, however in a different size range. The Pioneer 10 results for instance were explained by Humes (1980) with particles on orbits with eccentricity e = 0.99, semi major axis a x 10 AU and randomly distributed inclinations i (i.e. n(i) E sin i). To sum up, dust fluxes in the outer solar system are distinctly different from the inner parts. This is not only due to the interstellar flux but includes also a component which is not related to the interstellar flux directions.
4. Dust ejected from comets Comets entering the inner solar system start their activity already far away from the sun and are most likely the main interplanetary source for dust beyond the asteroid belt. Long period comets are assumed to have eccentricities e > 0.98 and random inclinations (Rahe, 1981), whereas the average inclination of short period comets is (i) = 15” and their average eccentricity is (e) = 0.56 (Allen, 1983). We regard the evolution of particles with initial long period or short period comet orbits under deceleration from Poynting-Robertson effect discussed as an example by the two cases of initial eccentricity e = 0.99 and 0.6.
4.1. Dust ejection The dust ejection from comets has already been discussed by many authors and detailed studies can be found in Kresak (1976) and Mukai et al. (1989). For our purpose we regard simply the conditions for the orbits of parent
1. Mann and E. Griin : Dust particles beyond the asteroid belt
829
bodies and the influence of radiation pressure, not including the effect of the emission velocity, which in special cases can be significant. Dynamics of dust particles is initially determined by the orbital elements of their parent bodies. The deceleration from Poynting-Robertson effect reduces the orbital parameters semi major axis, a, and eccentricity, e.
4.2. Radiation pressure When emitted from a comet, the increase of radiation pressure in comparison to gravity for the smaller fragments reduces the gravitational attraction of the sun and small particles with a strong influence from radiation pressure will be ejected from the solar system in unbound orbits. The condition for an unbound orbit depends on the p-value defined as the ratio of the force of radiation pressure to the force of gravity on the particles. Calculations of the p-value taking into account particle’s material and size (Schwehm, 1976) show a maximum value of 0.8 for water ice and a maximum value of 0.5 for andesite and obsidian. This however is based on assumptions for spherical particles.
We apply a simple model of dust emission or fragmentation close to the perihelion of parent bodies to estimate under which conditions produced particles are still on bound orbits around the sun (cf. Dohnanyi, 1978). This approach still uses the properties of compact spherical grains. Irregular shaped particles of very loose structure will even be more affected by radiation pressure (e.g. Mukai et al., 1992). Also the exact conditions of ejection are, not taken into account. When regarding these orbital parameters, the condition for a particle to stay still in bound orbits is when emitted in the perihel of the parent bodies’ orbit :
and when emitted
(1)
in the aphel : P d l/2(1 fe,).
0.1 PR -lifetime
(2)
Assuming that a particle is ejected in the perihel (which is the “worse case”) from initial eccentricity e = 0.99 (i.e. the orbit of the parent body) and bulk density 3.5 g cmp3 it will go into unbound orbit for sizes s < 40 pm. For a parent eccentricity of e = 0.9 particles with size s < 3 pm will be in unbound orbits. We can expect that submicron particles emitted from long period comets will be in unbound orbits and thus only contribute to the interplanetary dust cloud during a part of its orbit before leaving the solar system. This component cannot be the source of the main ecliptic concentrated dust cloud observed in the inner solar system. Conditions are different for short period comets with lower eccentricity of orbits. We assume an initial value (i.e. value of the parent body) of e = 0.6 and again a bulk density 3.5 g cme3.
1 T /rgcs
Fig. 1. Time z(e) a particle with initial eccentricity e, spends in
orbits with eccentricity > e when applying j3 = 0.2. The time z(e) is given in terms of the total Poynting-Robertson lifetime zpR, discussed in the text
In this case particles with m > lo-” respectively, stay in bound orbits.
4.3. Conditions for unbound orbits
P < l/2(1 -eo)
0.01
g or s > 0.9 ,um,
4.4. Evolution of dust releasedfrom comets The deceleration of particles due to Poynting-Robertson effect goes along with a reduction of orbital eccentricity. The Poynting-Robertson lifetime r(e) of a particle of initial eccentricity e,, is shown in Fig. 1. The value z(e) is given in terms of the total Poynting-Robertson lifetime r(e). A particle of initial eccentricity 0.99 and initial semi major axis a, = 10 AU (as proposed by Humes to explain the Pioneer dust flux rate) will stay 90% of its lifetime in orbits with eccentricity e > 0.75. For a particle with initial eccentricity 0.6 and initial semi major axis a,, = 10 AU the reduction of eccentricity is much faster, it has already an eccentricity of about e = 0.15 after 90% of its lifetime. It should be noted, that comparing particles of the same mass, the total Poynting-Robertson lifetime of a high eccentricity orbit particle (in our case mentioned above, it amounts to IO4 years) is significantly smaller than the lifetime of a moderate eccentricity orbit particle (in our case this amounts to 8 x IO5 years) with the same initial semi major axis a,, (see Wyatt and Whipple, 1950). As can be seen in Fig. 2, particles with initial eccentricity e = 0.6 at a, = 10 AU, have eccentricities e < 0.3 from 4 AU inward. Particles with initial eccentricity e = 0.99, on the other hand, will keep on in high eccentricity orbits e > 0.8 up to 0.5 AU inward towards the sun and are still far from circular orbits in the solar corona. Consequently, particles emitted from short period comets and asteroids make up a l/r dependent radial slope of number density. Particles emitted from long period comets make up a steep radial slope of number density, even in the inner solar system.
I. Mann and E. Grtin : Dust particles
830
beyond
the asteroid
belt
sity and scattering cross section) is smaller than that of the general Zodiacal cloud. Since the VSF is given as a product of average number density, average albedo and average geometric cross section, the two latter values have to be reduced, if this component has a higher number density. Assuming the number density of the background component to be one order of magnitude higher than the Zodiacal component and the albedo to be 5% this results in an average particle size of S = 15 pm. Such a constant background component is of minor influence at small solar distances, thus a proof of a sudden break up, as claimed by Divine (1994) is not possible.
5.2. Comparison
semimajor
axis
a
Fig. 2. Eccentricity
e of a particle with initial eccentricity e0 in an orbit with semimajor axis a. The initial semimajor axis is a, = 10 AU, as was proposed to explain previous data
4.5. Comparison
ofparticles
of different size
As a further result we conclude, that in the outer solar system, i.e. close to their sources, the particles of different size are not directly comparable. For the Ulysses data, this means that, even if they would be available, we could not directly compare derived flux densities to the brightness observations dominated by larger dust particles. If typical size distributions of dust ejected from comets (see for instance McDonnell et al., 1987) are still valid in the outer solar system, we can also conclude, that most probably the detected flux is connected to a further component of larger particles.
of relative brightness proJles
Further information about the shape of the dust cloud is given by the relative slope of the brightness. We test how the brightness profiles can show whether we have a continuous decrease of number density n(r), n(r) x r-l or whether there remains a larger background component. We regard the ratio of out-of-ecliptic brightness to ecliptic brightness at a line of sight elongation of 90”. We calculate this ratio first for a sombrero type Zodiacal cloud model and then assume a constant isotropic background component. In Fig. 3 this is shown as a comparison to the values Z(/3r,os)/Z(Oo) derived from observational data by Levasseur-Regourd and Dumont (1980) (crosses). The solid line gives calculations according to the optimum sombrero model discussed in Giese et al. (1986). The dashed line shows the values, when applying an additional isotropic background component. We see a clear deviation for this additional component, but even for the optimum sombrero model, which has only a small average deviation from observations, the regarded ratio of brightness values is not in best agreement with the observations in all parts. This shows, that even visual brightness models are still limited in their description of the out-of-ecliptic parts.
5. Influence of the outer dust cloud on the Zodiacal light brightness 5.1. Comparison
Although impact detection gives the most direct information about dust fluxes, its validity is restricted to a very small spatial and temporal interval. On the other hand, brightness data give the possibility for a comparison to the general dust distribution. As was discussed by Giese et al. (1986) the contribution to the visual Zodiacal light brightness observed in the symmetry plane of the Zodiacal light from Earth, respectively r = 1 AU decreases to 1% at a solar distance of 4 AU. This of course is based on common models of the Zodiacal cloud and is different, if the concentration of dust particles is higher in the outer solar system. We test the influence of an enhanced outer dust cloud on the brightness. The approach is a simple sombrero model (see Giese et al., 1986) with an additional isotropic background component. This gives a deviation of less than 20% from the Zodiacal light if its volume scattering function (VSF, i.e. the product of number den-
A = 0.55
1
of absolute brightness data
urn
0.8
OL
0
15
30
45
60
75
90
B ['I Fig. 3.
Relative brightness profile Z(BLos)/Z(Oo)at I = 0.55 pm derived from observational data (crosses) in comparison to cal-
culations with the optimum sombrero model (solid line) and with calculations applying an isotropic background component (dashed line)
831
I. Mann and E. Grtin : Dust particles beyond the asteroid belt
and detailed observational wide spectral ranges.
studies of the IR brightness in
6. Discussion
0.2
t
0 0
I
I
I
I
I
15
30
4s
60
75
I
90
B [“I Fig. 4. Relative brightness profile Z&,s)/Z(O”)
at n = 12 pm
In Figs 4 and 5 we present a similar modelling for the thermal emission, the observational values derived from IRAS data given by flauser et al. (1984) are given as crosses (the brightness profiles according to the rocketborne observation by Murdock and Price (1985) could not be explained). The solid line gives the calculation of an optimum sombrero model with blackbody temperature at 2 = 12 pm in Fig. 4 and 1 = 25 pm in Fig. 5. Additional calculations for empirical temperature profiles discussed by Levasseur-Regourd et al. (1991) gave similar results and are therefore not presented in the figures. Again the dashed lines present calculations with an isotropic background component and in this case a significant difference between the two regarded wavelengths can be seen. Whereas the relative slope keeps the same in the case of the a = 12 pm brightness it changes in the case of the i = 25 pm brightness. We explain this with the different temperatures and emission profiles in the inner part of the dust cloud and in the outer region. Dust in the inner solar system has the maximum in its thermal emission according to the Planck function at wavelength A = 12 pm and shorter. In this wavelength range the thermal emission from the colder background component is still in the low emission part of the Planck curve and its contribution to the brightness negligible. These model calculations show, that indeed a further analysis of the outer dust cloud can be achieved by studying the brightness data, but needs sufficiently good models 1
h = 25 urn
0.6 6
g
0.6
\
c iG
0.4
Fig. 5. Relative brightness profile Z(&,s)/Z(O”)
at R = 25 pm
The conditions of cometary dust emission can partly explain dust fluxes detected by Ulysses in the outer solar system and we can show the general structure of the dust cloud, to result from decelerated particles drifting inward the solar system. The majority of submicron sized particles emitted from long period comets will mainly be in unbound orbits and thus will not contribute significantly to the inner dust cloud. Larger fragments, on the other hand will stay coupled to the solar system. This means, that different from the inner solar system, dust particle distributions in different size intervals cannot directly be compared. The increase in the relative amount of high eccentricity orbits and of unbound orbits when going to greater solar distances, can be explained by dust ejection from long period comets. Previous attempts to describe the Zodiacal light from the superposition of two components are consistent with the dust production from long period comets and would mean, that these components are different not only in their properties but also in their orbital distributions. The influence of the outer dust cloud on the Zodiacal light brightness is only small. Thus an observational proof of the results is not yet possible. But future infrared observations on this topic are especially worthwhile, when regarding different wavelengths of infrared thermal emission. Acknowledgement. Thanks are due to T. Mukai and J. A. M. McDonnell for critical and helpful discussion. This work was supported by the Bundesministerium fiir Forschung und Technologie BMFT (Contract 50 ON 9101).
References Allen, C. W., Astrophysical Quantities, 3rd Edn. The Athlone Press, London, 1983. Divine, N., Five populations of interplanetary meteroids. J. geophys. Res. 98(E9), 17029-17048, 1994. Dolmanyi, J. S., Particle dynamics, in Cosmic Dust (edited by J. A. M. McDonnell), pp. 527-587. Wiley, New York, 1978. Glese, R. H., Kneiel, B. and Rittich, U., Three dimensional models of the Zodiacal dust cloud : a comparative study. Icarus 68,395-411,1986. Grlin, E., Dust measurements in the outer solar system, in Asteroids, Comets, Meteors 1993 (edited by A. Milani et al.), pp. 367-380. IAU, The Netherlands, 1994. Proc. of the 1993 ACM Meeting, in preparation, 1994. Griin, E., Zook, H. A., Fechtig, H. and Giese, R. H., Collisional balance of the meteoritic complex. Icarus 62,244-272, 1985. Grlln, E,, Fechtig, H., Giese, R. H., Kissel, J., Linker& D., Maas, D., McDonnell, J, A. DA., MorCll, G. E., Schwehm, G. and Zook, H. A., The ULYSSES dust experiment. Astron. Astrophys. Suppl. Ser. 92,41 l-423, 1992a. Grlln, E., Zook, H. A., Bag&l, M., Fechtig, H., Hauner, M. S., Klssel, J., Lindblad, B.-A., Linker& D., Liukert, G., Mann, I., McDonnell, J. A. EM.,Moffill, G. E., Phillips, J. L., Polanskey,
832 C., Riemann, R., Schwehm, G. and Siddique, N., Dust measurements: from Venus to Jupiter. Geophys. Res. Lett. 19, 1311-1314, 1992b. Grim, E., Zook, H. A., Bagnhl, M., Balogh, A., Bame, S. J.,
Fechtig, H., Forsyth, R., Hauuer, M. S., Horanyi, M., Kissel, J., Liudblad, B.-A., Linker& D., Linker& G., Mann, I., McDonnell, J. A. M., Moriill, G. E., Phillips, J. L,, Polanskey, C., Schwehm, G., Siddique, N., Staubach, P., Svestka, J. and Taylor, A., Discovery of Jovian dust streams and interstellar grains by the ULYSSES spacecraft. Nature 362, 428-430, 1993. Hauser, M. G., Glllett, F. C., Low, F. J., Gautier, T. N., Beichman, C. A., Neugebauer, G., Aumann, H. H., Baud, B., Boggess, N., Emerson, J. P., Houck, J. R., Soifer, B. T. and Walker, R. G., IRAS observations of the diffuse infrared background. Astrophys. J. 278, L15-L18, 1984. Hmues, D. H., Results of PIONEER 10 and 11 meteoroid experiments : interplanetary and near Saturn. J. geophys. Res. 85, 5841-5852, 1980. Kneillel, B. and Mann, I., Spatial distribution and orbital properties of Zodiacal dust, in Origin andEvolution of Interplanetary Dust (edited by A. C. Levasseur-Regourd and H. Hasegawa),
pp. 139-146. Kluwer, Dordrecht, 1991. Kresak, L., Orbital evolution of the dust streams released from comets. Bull. Astron. Inst. Czech. 27, 35-46, 1976. Leinert, C., Richter, I., Pitz, E. and Planck, B., The Zodiacal light, from 1,O to 0,3 AU as observed by the HELIOS space probes. Astron. Astrophys. 103, 177-188, 1981. Levasseur-Regourd, A. C. and Dumont, R., Absolute photometry of the Zodiacal light. Astron. Astrophys. 84,277-279, 1980.
I. Mann and E. Grtin : Dust particles beyond the asteroid belt Levassenr-Regourd, A. C., Reuard, J. B. and Dumont, R., The Zodiacal dust complex, in Origin and Evolution of Interplanetary Dust (edited by A. C. Levasseur-Regourd and H. Hasegawa), pp. 131-138. Kluwer, Dordrecht, 1991. McDonnell, J. A. M., Alexander, W. M., Burton, W. M., et el., The dust distribution within the inner coma of Comet P/Halley : encounter by Giotto’s impact detectors. Astron. Astrophys. 187,719-741, 1987. Mann, I. and Griiu, E., The dynamics
of interplanetary dust derived from observations of the Zodiacal light in relation to the dust experiments onboard ULYSSES and Galileo, in Hypervelocity Impacts in Space (edited by J. A. M. McDonnell), pp. 200-204. The Unit for Space Science, The University of Kent at Canterbury, 1992. Mukai, T., Fechtig, H., Grim, E. and Giese, R. H., Icy particles from comets. Icarus 80,254266, 1989. Mtiai, T., Ishimoto, H., Kozasa, T., Blum, J. and Greenberg, J. M., Radiation pressure forces of fluffy porous grains. Astron. Astrophys. 262,315-320, 1992. Murdock, T. L. and Price, S. D., Infrared measurements of the Zodiacal light, Astron. J. 90, 375-386, 1985. Rahe, J., Comets, in Landolt-Biirnstein, Bd. 2, Astronomie und Astrophysik, pp. 202-227. Springer, Berlin, 198 1. Schwehm, G., Radiation pressure on interplanetary dust particles, in Interplanetary Dust and Zodiacal Light (edited
by H. Elsasser and H. Fechtig), Lecture Notes in Physics, Vol. 48, pp. 459-463. Springer, Heidelberg, 1976. Wyatt, S. P. and Whipple, F. L., The Poynting-Robertson effect on meteo orbits. Astrophys. J. 111, 134-141, 1950.
Pergamon
0032-0633(95)00073-9
Dust particles beyond the asteroid belt-a of the Ulysses dust experiment Ingrid Mann’
and Eberhard
’ Max-Planck-Institut ’ Max-Planck-Institute
study based on recent results
Griin’
fur Aeronomie, Postfach 20, D 37189 Katlenburg-Lindau, F.R.G. fur Kernphysik, Postfach 103980, D 69029 Heidelberg, F.R.G.
Received 3 August 1993 ; revised 19 April 1994; accepted 5 May 1995
1. Introduction The general shape of the interplanetary dust cloud is made up of particles on Keplerian orbits approaching the sun by decelerating forces of Poynting-Robertson effect (see for instance Wyatt and Whipple, 1950). It is concentrated to the ecliptic plane and rotational symmetric with respect to an axis through the solar pole. Aside from this general structure, there are local phenomena like dust rings and cometary dust tails, which will not be discussed in this context. The Ulysses space probe, carrying a dust detector (Grtin et al., 1992a), drew renewed attention to the part of the dust cloud that is beyond the asteroid belt. An influence from the local interstellar medium was expected and has been recently observed with UZysses for this region (see Grtin et al., 1993). A review about the dust measurements beyond the asteroid belt is given elsewhere (Grtin, 1994). We concentrate the present study on a discussion of possible sources of dust in the context of the UZysses results and we attempt a comparison to observations of the Zodiacal light. We present the general distribution of dust in the solar system as derived from Zodiacal light observations (Section 2) and then in contrary the UZysses dust flux data (Section 3). In Section 4 we discuss the dust emission from comets and the orbital evolution of cometary dust particles and finally study the influence of these outer dust components on the Zodiacal light brightness (Section 5).
2. Spatial
Correspondence to : I. Mann
distribution
of dust from Zodiacal
light data
Zodiacal light data from ground based observations in the visual range by Levasseur-Regourd and Dumont (1980) were mainly confirmed by measurements of the Helios photometric experiment (Leinert et al., 198 1). Data about interplanetary dust thermal emission were given by the IRAS satellite at elongations, E, 60” < E < 120” (see
828
Hauser et al., 1984) and by rocket borne photometry which covers solar elongation angles, E, 22” < E < 180” and ecliptic latitudes, /?,, -60” < /ILos < 90” (Murdock and Price, 1985). Usually, the brightness is strongly influenced by the inner dust cloud at small solar distances, however, in the case of the thermal emissions, the relative contribution from different regions varies also with the observed wavelength. As far as the size distribution is concerned, the Zodiacal light is produced by particles in a size range from 1 to 100 pm (Grtin et al., 1985), smaller particles, as for instance measured with impact detectors, although their number density in the interplanetary dust cloud is much higher, give only a small contribution. Particles in both size ranges can be compared, since at least in the inner solar system they are both produced from a similar collisional evolution (Mann and Grtin, 1992). The inversion of the Zodiacal light brightness, as described elsewhere (Giese et al., 1986), gives different models of the spatial distribution. These are related to the local flux rates of orbiting grains. As their number density n(v, /&) = n(r) f(/&) is assumed to be separated between the in-ecliptic n(r) and the out-of-ecliptic fraction f(PJ, inversion of the dynamical structure leads to a separation between the orbital distribution densities d(a, e) of eccentricity, e, and semi major axis, a, and the distribution d(i) of inclinations i. Models of the radial slope in the dust cloud are given with an n(r) = r-” power law. The Poynting-Robertson drift of particles and their final sublimation in the solar vicinity show the need for sources of dust to explain a stable dust cloud. A collisional balance was discussed in order to explain an exponent v = 1.3 in the radial slope of number density, that was derived from Helios photometric results (cf. Leinert et al., 1981 ; Grtin et al., 1985). Later studies, based on an analysis of both, thermal emission and scattered light from brightness data point to the combination of two effects, an increase of number density and an increase of albedo with decreasing solar distance, to explain the slope of the visual Zodiacal light. They are in agreement with a simple l/r law for the number density (see Levasseur-Regourd et al., 1991), which is already explained by PoyntingRobertson drift of particles on circular orbits. Eccentricities between 0 < e < 0.3, as found to be predominant in the inner solar system, have only small deviations from the distribution of circular orbits. These eccentricities are consistent with a l/r power law in the spatial distribution and thus with recent Zodiacal light analysis. A discrepancy of the out-of-ecliptic distributions in different Zodiacal cloud models led to the assumption of a bimodal description proposed by Kneirjel and Mann (1991), which fits to the data within 10%. The main component is concentrated to the ecliptic and has a radial dependence of the VSF (i.e. volume scattering function, the average scattering cross section of particles per volume element) with l/r, whereas the second component has a spherical shape and increases with a power law with exponent v = 1.5-2 towards the sun. This approach gives the distribution of the number density folded with the optical efficiency and the original idea was, to explain this radial slope with a variation of particle properties. However, we will show, that also dynamical effects can
I. Mann and E. Griin : Dust particles beyond the asteroid belt cause a component in the dust cloud, with steeply increasing number density (and thus VSF) towards the sun.
3. Detected dust fluxes Present Zodiacal cloud models are in acceptable agreement with previous dust flux measurements in the inner solar system and also dust fluxes detected onboard UZysses in the inner solar system are best explained by particles in low inclined, low eccentricity orbits. Fluxes detected at increasing solar distance show an increasing amount of unbound and highly inclined orbits. Deviant from Zodiacal cloud models the dust detector observed an impact rate, that is significantly higher than would be expected from a radially decreasing distribution expected for particles in nearly circular orbits (Grtin et al., 1993). An attempt by Divine (1994) to describe the interplanetary meteoroid environment includes a so-called halo component with randomly inclined orbits, which sets in beyond solar distances r, r M 2.5 AU to take these detected flux rates into account (see Grtin et al., 1992b), however, so far without any physical explanations. No mechanism is yet proposed to explain the cutoff of this component at 2.5 AU and also other assumptions of the dust flux distribution could give a sufficient explanation of the so far rare data. Also the Pioneer 10 and 11 penetration sensors (Humes, 1980) detected fluxes, deviant from the distribution in the inner solar system, however in a different size range. The Pioneer 10 results for instance were explained by Humes (1980) with particles on orbits with eccentricity e = 0.99, semi major axis a x 10 AU and randomly distributed inclinations i (i.e. n(i) E sin i). To sum up, dust fluxes in the outer solar system are distinctly different from the inner parts. This is not only due to the interstellar flux but includes also a component which is not related to the interstellar flux directions.
4. Dust ejected from comets Comets entering the inner solar system start their activity already far away from the sun and are most likely the main interplanetary source for dust beyond the asteroid belt. Long period comets are assumed to have eccentricities e > 0.98 and random inclinations (Rahe, 1981), whereas the average inclination of short period comets is (i) = 15” and their average eccentricity is (e) = 0.56 (Allen, 1983). We regard the evolution of particles with initial long period or short period comet orbits under deceleration from Poynting-Robertson effect discussed as an example by the two cases of initial eccentricity e = 0.99 and 0.6.
4.1. Dust ejection The dust ejection from comets has already been discussed by many authors and detailed studies can be found in Kresak (1976) and Mukai et al. (1989). For our purpose we regard simply the conditions for the orbits of parent
1. Mann and E. Griin : Dust particles beyond the asteroid belt
829
bodies and the influence of radiation pressure, not including the effect of the emission velocity, which in special cases can be significant. Dynamics of dust particles is initially determined by the orbital elements of their parent bodies. The deceleration from Poynting-Robertson effect reduces the orbital parameters semi major axis, a, and eccentricity, e.
4.2. Radiation pressure When emitted from a comet, the increase of radiation pressure in comparison to gravity for the smaller fragments reduces the gravitational attraction of the sun and small particles with a strong influence from radiation pressure will be ejected from the solar system in unbound orbits. The condition for an unbound orbit depends on the p-value defined as the ratio of the force of radiation pressure to the force of gravity on the particles. Calculations of the p-value taking into account particle’s material and size (Schwehm, 1976) show a maximum value of 0.8 for water ice and a maximum value of 0.5 for andesite and obsidian. This however is based on assumptions for spherical particles.
We apply a simple model of dust emission or fragmentation close to the perihelion of parent bodies to estimate under which conditions produced particles are still on bound orbits around the sun (cf. Dohnanyi, 1978). This approach still uses the properties of compact spherical grains. Irregular shaped particles of very loose structure will even be more affected by radiation pressure (e.g. Mukai et al., 1992). Also the exact conditions of ejection are, not taken into account. When regarding these orbital parameters, the condition for a particle to stay still in bound orbits is when emitted in the perihel of the parent bodies’ orbit :
and when emitted
(1)
in the aphel : P d l/2(1 fe,).
0.1 PR -lifetime
(2)
Assuming that a particle is ejected in the perihel (which is the “worse case”) from initial eccentricity e = 0.99 (i.e. the orbit of the parent body) and bulk density 3.5 g cmp3 it will go into unbound orbit for sizes s < 40 pm. For a parent eccentricity of e = 0.9 particles with size s < 3 pm will be in unbound orbits. We can expect that submicron particles emitted from long period comets will be in unbound orbits and thus only contribute to the interplanetary dust cloud during a part of its orbit before leaving the solar system. This component cannot be the source of the main ecliptic concentrated dust cloud observed in the inner solar system. Conditions are different for short period comets with lower eccentricity of orbits. We assume an initial value (i.e. value of the parent body) of e = 0.6 and again a bulk density 3.5 g cme3.
1 T /rgcs
Fig. 1. Time z(e) a particle with initial eccentricity e, spends in
orbits with eccentricity > e when applying j3 = 0.2. The time z(e) is given in terms of the total Poynting-Robertson lifetime zpR, discussed in the text
In this case particles with m > lo-” respectively, stay in bound orbits.
4.3. Conditions for unbound orbits
P < l/2(1 -eo)
0.01
g or s > 0.9 ,um,
4.4. Evolution of dust releasedfrom comets The deceleration of particles due to Poynting-Robertson effect goes along with a reduction of orbital eccentricity. The Poynting-Robertson lifetime r(e) of a particle of initial eccentricity e,, is shown in Fig. 1. The value z(e) is given in terms of the total Poynting-Robertson lifetime r(e). A particle of initial eccentricity 0.99 and initial semi major axis a, = 10 AU (as proposed by Humes to explain the Pioneer dust flux rate) will stay 90% of its lifetime in orbits with eccentricity e > 0.75. For a particle with initial eccentricity 0.6 and initial semi major axis a,, = 10 AU the reduction of eccentricity is much faster, it has already an eccentricity of about e = 0.15 after 90% of its lifetime. It should be noted, that comparing particles of the same mass, the total Poynting-Robertson lifetime of a high eccentricity orbit particle (in our case mentioned above, it amounts to IO4 years) is significantly smaller than the lifetime of a moderate eccentricity orbit particle (in our case this amounts to 8 x IO5 years) with the same initial semi major axis a,, (see Wyatt and Whipple, 1950). As can be seen in Fig. 2, particles with initial eccentricity e = 0.6 at a, = 10 AU, have eccentricities e < 0.3 from 4 AU inward. Particles with initial eccentricity e = 0.99, on the other hand, will keep on in high eccentricity orbits e > 0.8 up to 0.5 AU inward towards the sun and are still far from circular orbits in the solar corona. Consequently, particles emitted from short period comets and asteroids make up a l/r dependent radial slope of number density. Particles emitted from long period comets make up a steep radial slope of number density, even in the inner solar system.
I. Mann and E. Grtin : Dust particles
830
beyond
the asteroid
belt
sity and scattering cross section) is smaller than that of the general Zodiacal cloud. Since the VSF is given as a product of average number density, average albedo and average geometric cross section, the two latter values have to be reduced, if this component has a higher number density. Assuming the number density of the background component to be one order of magnitude higher than the Zodiacal component and the albedo to be 5% this results in an average particle size of S = 15 pm. Such a constant background component is of minor influence at small solar distances, thus a proof of a sudden break up, as claimed by Divine (1994) is not possible.
5.2. Comparison
semimajor
axis
a
Fig. 2. Eccentricity
e of a particle with initial eccentricity e0 in an orbit with semimajor axis a. The initial semimajor axis is a, = 10 AU, as was proposed to explain previous data
4.5. Comparison
ofparticles
of different size
As a further result we conclude, that in the outer solar system, i.e. close to their sources, the particles of different size are not directly comparable. For the Ulysses data, this means that, even if they would be available, we could not directly compare derived flux densities to the brightness observations dominated by larger dust particles. If typical size distributions of dust ejected from comets (see for instance McDonnell et al., 1987) are still valid in the outer solar system, we can also conclude, that most probably the detected flux is connected to a further component of larger particles.
of relative brightness proJles
Further information about the shape of the dust cloud is given by the relative slope of the brightness. We test how the brightness profiles can show whether we have a continuous decrease of number density n(r), n(r) x r-l or whether there remains a larger background component. We regard the ratio of out-of-ecliptic brightness to ecliptic brightness at a line of sight elongation of 90”. We calculate this ratio first for a sombrero type Zodiacal cloud model and then assume a constant isotropic background component. In Fig. 3 this is shown as a comparison to the values Z(/3r,os)/Z(Oo) derived from observational data by Levasseur-Regourd and Dumont (1980) (crosses). The solid line gives calculations according to the optimum sombrero model discussed in Giese et al. (1986). The dashed line shows the values, when applying an additional isotropic background component. We see a clear deviation for this additional component, but even for the optimum sombrero model, which has only a small average deviation from observations, the regarded ratio of brightness values is not in best agreement with the observations in all parts. This shows, that even visual brightness models are still limited in their description of the out-of-ecliptic parts.
5. Influence of the outer dust cloud on the Zodiacal light brightness 5.1. Comparison
Although impact detection gives the most direct information about dust fluxes, its validity is restricted to a very small spatial and temporal interval. On the other hand, brightness data give the possibility for a comparison to the general dust distribution. As was discussed by Giese et al. (1986) the contribution to the visual Zodiacal light brightness observed in the symmetry plane of the Zodiacal light from Earth, respectively r = 1 AU decreases to 1% at a solar distance of 4 AU. This of course is based on common models of the Zodiacal cloud and is different, if the concentration of dust particles is higher in the outer solar system. We test the influence of an enhanced outer dust cloud on the brightness. The approach is a simple sombrero model (see Giese et al., 1986) with an additional isotropic background component. This gives a deviation of less than 20% from the Zodiacal light if its volume scattering function (VSF, i.e. the product of number den-
A = 0.55
1
of absolute brightness data
urn
0.8
OL
0
15
30
45
60
75
90
B ['I Fig. 3.
Relative brightness profile Z(BLos)/Z(Oo)at I = 0.55 pm derived from observational data (crosses) in comparison to cal-
culations with the optimum sombrero model (solid line) and with calculations applying an isotropic background component (dashed line)
831
I. Mann and E. Grtin : Dust particles beyond the asteroid belt
and detailed observational wide spectral ranges.
studies of the IR brightness in
6. Discussion
0.2
t
0 0
I
I
I
I
I
15
30
4s
60
75
I
90
B [“I Fig. 4. Relative brightness profile Z&,s)/Z(O”)
at n = 12 pm
In Figs 4 and 5 we present a similar modelling for the thermal emission, the observational values derived from IRAS data given by flauser et al. (1984) are given as crosses (the brightness profiles according to the rocketborne observation by Murdock and Price (1985) could not be explained). The solid line gives the calculation of an optimum sombrero model with blackbody temperature at 2 = 12 pm in Fig. 4 and 1 = 25 pm in Fig. 5. Additional calculations for empirical temperature profiles discussed by Levasseur-Regourd et al. (1991) gave similar results and are therefore not presented in the figures. Again the dashed lines present calculations with an isotropic background component and in this case a significant difference between the two regarded wavelengths can be seen. Whereas the relative slope keeps the same in the case of the a = 12 pm brightness it changes in the case of the i = 25 pm brightness. We explain this with the different temperatures and emission profiles in the inner part of the dust cloud and in the outer region. Dust in the inner solar system has the maximum in its thermal emission according to the Planck function at wavelength A = 12 pm and shorter. In this wavelength range the thermal emission from the colder background component is still in the low emission part of the Planck curve and its contribution to the brightness negligible. These model calculations show, that indeed a further analysis of the outer dust cloud can be achieved by studying the brightness data, but needs sufficiently good models 1
h = 25 urn
0.6 6
g
0.6
\
c iG
0.4
Fig. 5. Relative brightness profile Z(&,s)/Z(O”)
at R = 25 pm
The conditions of cometary dust emission can partly explain dust fluxes detected by Ulysses in the outer solar system and we can show the general structure of the dust cloud, to result from decelerated particles drifting inward the solar system. The majority of submicron sized particles emitted from long period comets will mainly be in unbound orbits and thus will not contribute significantly to the inner dust cloud. Larger fragments, on the other hand will stay coupled to the solar system. This means, that different from the inner solar system, dust particle distributions in different size intervals cannot directly be compared. The increase in the relative amount of high eccentricity orbits and of unbound orbits when going to greater solar distances, can be explained by dust ejection from long period comets. Previous attempts to describe the Zodiacal light from the superposition of two components are consistent with the dust production from long period comets and would mean, that these components are different not only in their properties but also in their orbital distributions. The influence of the outer dust cloud on the Zodiacal light brightness is only small. Thus an observational proof of the results is not yet possible. But future infrared observations on this topic are especially worthwhile, when regarding different wavelengths of infrared thermal emission. Acknowledgement. Thanks are due to T. Mukai and J. A. M. McDonnell for critical and helpful discussion. This work was supported by the Bundesministerium fiir Forschung und Technologie BMFT (Contract 50 ON 9101).
References Allen, C. W., Astrophysical Quantities, 3rd Edn. The Athlone Press, London, 1983. Divine, N., Five populations of interplanetary meteroids. J. geophys. Res. 98(E9), 17029-17048, 1994. Dolmanyi, J. S., Particle dynamics, in Cosmic Dust (edited by J. A. M. McDonnell), pp. 527-587. Wiley, New York, 1978. Glese, R. H., Kneiel, B. and Rittich, U., Three dimensional models of the Zodiacal dust cloud : a comparative study. Icarus 68,395-411,1986. Grlin, E., Dust measurements in the outer solar system, in Asteroids, Comets, Meteors 1993 (edited by A. Milani et al.), pp. 367-380. IAU, The Netherlands, 1994. Proc. of the 1993 ACM Meeting, in preparation, 1994. Griin, E., Zook, H. A., Fechtig, H. and Giese, R. H., Collisional balance of the meteoritic complex. Icarus 62,244-272, 1985. Grlln, E,, Fechtig, H., Giese, R. H., Kissel, J., Linker& D., Maas, D., McDonnell, J, A. DA., MorCll, G. E., Schwehm, G. and Zook, H. A., The ULYSSES dust experiment. Astron. Astrophys. Suppl. Ser. 92,41 l-423, 1992a. Grlln, E., Zook, H. A., Bag&l, M., Fechtig, H., Hauner, M. S., Klssel, J., Lindblad, B.-A., Linker& D., Liukert, G., Mann, I., McDonnell, J. A. EM.,Moffill, G. E., Phillips, J. L., Polanskey,
832 C., Riemann, R., Schwehm, G. and Siddique, N., Dust measurements: from Venus to Jupiter. Geophys. Res. Lett. 19, 1311-1314, 1992b. Grim, E., Zook, H. A., Bagnhl, M., Balogh, A., Bame, S. J.,
Fechtig, H., Forsyth, R., Hauuer, M. S., Horanyi, M., Kissel, J., Liudblad, B.-A., Linker& D., Linker& G., Mann, I., McDonnell, J. A. M., Moriill, G. E., Phillips, J. L,, Polanskey, C., Schwehm, G., Siddique, N., Staubach, P., Svestka, J. and Taylor, A., Discovery of Jovian dust streams and interstellar grains by the ULYSSES spacecraft. Nature 362, 428-430, 1993. Hauser, M. G., Glllett, F. C., Low, F. J., Gautier, T. N., Beichman, C. A., Neugebauer, G., Aumann, H. H., Baud, B., Boggess, N., Emerson, J. P., Houck, J. R., Soifer, B. T. and Walker, R. G., IRAS observations of the diffuse infrared background. Astrophys. J. 278, L15-L18, 1984. Hmues, D. H., Results of PIONEER 10 and 11 meteoroid experiments : interplanetary and near Saturn. J. geophys. Res. 85, 5841-5852, 1980. Kneillel, B. and Mann, I., Spatial distribution and orbital properties of Zodiacal dust, in Origin andEvolution of Interplanetary Dust (edited by A. C. Levasseur-Regourd and H. Hasegawa),
pp. 139-146. Kluwer, Dordrecht, 1991. Kresak, L., Orbital evolution of the dust streams released from comets. Bull. Astron. Inst. Czech. 27, 35-46, 1976. Leinert, C., Richter, I., Pitz, E. and Planck, B., The Zodiacal light, from 1,O to 0,3 AU as observed by the HELIOS space probes. Astron. Astrophys. 103, 177-188, 1981. Levasseur-Regourd, A. C. and Dumont, R., Absolute photometry of the Zodiacal light. Astron. Astrophys. 84,277-279, 1980.
I. Mann and E. Grtin : Dust particles beyond the asteroid belt Levassenr-Regourd, A. C., Reuard, J. B. and Dumont, R., The Zodiacal dust complex, in Origin and Evolution of Interplanetary Dust (edited by A. C. Levasseur-Regourd and H. Hasegawa), pp. 131-138. Kluwer, Dordrecht, 1991. McDonnell, J. A. M., Alexander, W. M., Burton, W. M., et el., The dust distribution within the inner coma of Comet P/Halley : encounter by Giotto’s impact detectors. Astron. Astrophys. 187,719-741, 1987. Mann, I. and Griiu, E., The dynamics
of interplanetary dust derived from observations of the Zodiacal light in relation to the dust experiments onboard ULYSSES and Galileo, in Hypervelocity Impacts in Space (edited by J. A. M. McDonnell), pp. 200-204. The Unit for Space Science, The University of Kent at Canterbury, 1992. Mukai, T., Fechtig, H., Grim, E. and Giese, R. H., Icy particles from comets. Icarus 80,254266, 1989. Mtiai, T., Ishimoto, H., Kozasa, T., Blum, J. and Greenberg, J. M., Radiation pressure forces of fluffy porous grains. Astron. Astrophys. 262,315-320, 1992. Murdock, T. L. and Price, S. D., Infrared measurements of the Zodiacal light, Astron. J. 90, 375-386, 1985. Rahe, J., Comets, in Landolt-Biirnstein, Bd. 2, Astronomie und Astrophysik, pp. 202-227. Springer, Berlin, 198 1. Schwehm, G., Radiation pressure on interplanetary dust particles, in Interplanetary Dust and Zodiacal Light (edited
by H. Elsasser and H. Fechtig), Lecture Notes in Physics, Vol. 48, pp. 459-463. Springer, Heidelberg, 1976. Wyatt, S. P. and Whipple, F. L., The Poynting-Robertson effect on meteo orbits. Astrophys. J. 111, 134-141, 1950.