Light Scattering Properties Of Interplanetary Dust

The faint cone of zodiacal light, seldom visible with the naked eye in the night sky, results from the scattering of solar light on interplanetary dust. Its shape indicates that the dust cloud spatial density increases towards the Sun and towards the ecliptic plane. Numerous quantitative observations have been performed from Earth or space observatories during the second half of the XXth century (e.g [1,2,3]). Although ground-based observations suffer from the atmospheric airglow contamination, CCD imaging techniques (e.g. [4,5]) have recently been successfully applied to studies of the interplanetary dust cloud.

Zodiacal light has a solar type spectrum, at least from the near ultraviolet to the near infrared, and is linearly polarised, as expected for solar light scattered by an optically thin medium. The polarisation values can immediately be used to compare, without any normalization to a constant distance to the Sun and to the observer, data obtained for different locations and directions.

2.1. Observations

From the Earth and the Earth's orbit, the scattering properties mainly depend upon the direction of observation, defined by the ecliptic latitude (P) and the helio-ecliptic (A-A0) longitude. For a given direction, small temporal fluctuations are pointed out, which originate in the slight inclination of the symmetry surface upon the ecliptic, in the eccentricity of the Earth's orbit, and possibly in local heterogeneities of the cloud (e.g. dust trails, meteor streams).

Tables providing at 1 AU the line-of-sight integrated brightness and polarisation are available (see e.g. [6,7]). They are given as a function of the latitude above the symmetry plane and of the angle between the direction of the Sun and that of the projection of the line-of-sight on the symmetry plane. The brightness is either indicated in magnitude related units, or in SI units at a given wavelength. The polarisation is a ratio, smaller than one in absolute value. Although the direction of polarisation (electric field vector) is usually perpendicular the scattering plane (Sun, observer, line of sight), it may be parallel to it, leading then to a negative value of the polarisation in the gegenschein (backscattering) region. Deep space measurements have been performed from Helios 1/2 [3] and from Pioneer 10/11 [8,9] space probes, providing observations from 0.3 AU to the outer edge of the asteroid belt. For measurements performed towards a constant direction, the brightness decreases with increasing solar distance (r) of the observer, approximately as r"2 45 ±015, and the polarisation increases approximately as r+0 3. This latter result demonstrates that the properties of the dust change with the solar distance. Although it is difficult to compare data retrieved line of sight data along different directions and from different locations, a slight decrease of the polarisation with increasing wavelength is suspected, at least in the near infrared domain [7], An extensive review on the observations and on their interpretation can be found in [10].

2.2. Local values

The scattering takes place along a significant part of the line of sight, on which each point corresponds to a specific region of the dust cloud, and to a different phase (a) or scattering (0 = n - a) angle. Inversion methods are thus required, to provide local bulk information about the dust properties. Since rigorous inversions are only feasible tangentially to the direction of motion of the Earth or of a moving probe, and for the section of the line of sight where the observer is located, some assumptions need to be done.

Taking into account the above-mentioned change in polarisation, the dust properties cannot be assumed to be the same everywhere. Mathematical methods have thus been developed to retrieve local information in remote regions. Results have mainly been obtained in the symmetry plane, for instance from the nodes of lesser uncertainty method (e.g. [11,12]), or from the kernel of Voltera integral method [13]. The results provided by these two methods, applied to two different data sets, are remarkably consistent.

The solar distance (R) dependence of the local properties is determined between about 0.3 and 1.5 AU. From the nodes of lesser uncertainty method, the local polarisation at 90° phase angle, P{90°), is found to slowly increase with increasing solar distance, while the mean local albedo at 90°, A(90°), decreases with solar distance, and the local dust density varies approximately as 1/7?. For a wavelength of about 0.5 |xm:

Similarly, from the kernel of Voltera integral method, the local polarisation is found to be higher at 1 AU than at 0.3 AU, at least for phase angles above 30°. In other words, when the particles get closer to the Sun under Poynting-Robertson drag, that is to say when they get warmer and older, their polarisation gets smaller and their albedo gets higher.

The dependence of the local polarisation upon the phase angle is also derived. The phase curves, obtained at 0.3, 1.0, and 1.5 AU, are found to be smooth, with a slight negative branch in the backscattering region, and a wide positive branch with a near 90° maximum. Near 1.5 AU, the transition from the negative to the positive branch, so-called the inversion region, takes places at (15 ± 5)° phase angle, and the slope at inversion is of about 0.2 percent per degree.

These smooth polarisation phase curves, which can be described by functions such as:

have shapes similar to those obtained for cometary dust and asteroidal regoliths [14,15], as well as for circumplanetary dust and some atmospheric aerosols. The smoothness of the polarisation phase curves strongly suggests that the scattering dust is built up of irregularly shaped compact particles or aggregates, the size of which is greater than the wavelength.

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