Phase angle dependency of the dust cross section in a cometary coma

Abstract

Rosetta/OSIRIS made optical measurements of the intensity of scattered light from the 67P/Churyumov-Gerasimenko coma over a wide range of phase angles. These data have been used to measure the phase angle dependent radiance profile of the dust coma. In order to derive dust properties such as the dust scattering phase function from these measurements, we need to understand the phase angle dependence of the optical thickness of the coma. This can be measured as the column area density, which is the total solid angle fraction covered by all dust particles within a given field of view. We present a simple numerical model that allows us to study the phase angle dependence of the column area density in a cometary coma.

Method

We consider a spherical nucleus with a given initial position and velocity relative to the Sun. From this nucleus we eject a large number of spherical dust particles at random positions and times. The acting forces considered by the model are the gravitational pull and the radiation pressure of the Sun. The neglect of other forces such as gas drag or nucleus gravity is justified for distances greater than about 10 km from the nucleus.

Since our model cannot describe the dust behavior close to the comet, we emit the dust particles from an imaginary sphere with a radius of 10 km around the nucleus. The initial velocity of the dust particles relative to the nucleus points radially away from the nucleus. The magnitude of the initial velocity is determined by the dust radius according to values found in the literature, with larger particles being emitted at lower velocities.

Since the activity of the comet is not constant across its surface, we need to implement a non-uniform dust production rate.We do this by adding a weighting factor to each dust particle released, based on its initial position. The weighting factor is determined by the angle between the particle, the nucleus center, and the subsolar point. We compare several weighting functions, the simplest being a cosine function that has its maximum at the subsolar point and decreases toward the terminator, being zero on the night side of the nucleus. The parameters used in the model correspond roughly to the properties of 67P/Churyumov-Gerasimenko, but the results are expected to be qualitatively valid for other comets as well.

All calculations are performed in an inertial frame of reference. To evaluate the column area density as seen from Rosetta, we then transform back to the spacecraft frame. The column area density is then calculated by summing the solid angle covered by all dust particles within a given field of view as seen from the spacecraft. This allows us to study the phase angle dependence of the column area density in a cometary coma. The model presented here can be easily adapted to parameters of other comets or to more realistic activity distributions.

Results

We find that the observed phase angle dependence of the column area density is largely independent of the position of the spacecraft in the terminator plane. For the case of a cosine activity distribution on the day side of the nucleus, we find that the column area density reaches plateaus at low and high phase angles, with the column area density being about two orders of magnitude larger at high phase angles. The increase occurs between 45° and 135° and appears to be symmetric around the terminator (90°). The dust radius has no effect on the phase angle dependence of the column area density. The activity distribution however proves to have a strong impact on the dust column area phase function. For models with no or almost no activity on the night side of the nucleus, the column area density remains about 2 orders of magnitude lower at low phase angles compared to the high phase angles. Activity distributions with higher night side activity lead to a smaller difference between low and high phase angles as well as deviations from the two plateau structure described above.

Conclusion

The results of this study show that the u-shaped phase function measured by Rosetta/OSIRIS cannot correspond to the single particle scattering phase function of the dust particles in the coma unless the activity distribution is isotropic. Attempts to infer the dust scattering phase function have to debias for the here measured dust column area density.