Sub-millimetre/millimetre extinction of real protoplanetary matter derived from Rosetta/MIRO observations on comet 67P

Introduction

Optical properties are required information for correct models of the early solar system and protoplanetary disks. To this day the properties used in the models are mostly provided by laboratory studies of primitive analogs. Comets provide us with a closer analog to the protoplanetary material but have been, until recently, difficult to observe. Rosetta has given us the unique opportunity to observe with unprecedented accuracy.

The Microwave Instrument for the Rosetta Orbiter (MIRO) (Gulkis et al. 2007) measured the thermal radiation emitted from the subsurface of comet 67P/Churyumov-Gerasimenko (hereafter 67P). MIRO operated at millimetre (hereafter MM) and sub-millimetre (hereafter SMM) wavelengths with corresponding frequencies of 188.2 GHz (1.594 mm) and 562.8 GHz (0.533 mm), respectively.

The thermal radiation received by MIRO is strongly dependant on the sub-surface material properties, mainly its temperature and optical constants. Our aim is to derive from these observations the complex refractive index of the material of comet 67P's subsurface. To achieve this, we match the brightness temperatures measured by MIRO with synthetic values derived from a one-dimensional thermal model of the subsurface combined with radiative transfer models.

MIRO data selection

MIRO data used in this study are taken from the ESA Planetary Science Archive. We selected only those measurements where the orbiter was close to the surface of the nucleus, to minimise the MIRO beam size on the nucleus and, thus, to be able to focus on specific areas of the comet. Additionally, we set our focus on flat areas, which allows us to use a one-dimensional thermal model.

Just before equinox in March 2016, the Rosetta orbiter was 11 km from the surface of 67P, observing the relatively flat region Imhotep (Auger et al. 2015). This region is located on the bottom of the big lobe and consists of four sub-regions, a,b,c and d (Thomas et al. 2018). We analysed MIRO measurements in sub-region 'a', as it is the smoothest and closest to the equator (Thomas et al. 2018). Fig. 1 illustrates the location of sub-region 'a' on the nucleus.

Fig. 2 shows the brightness temperatures MIRO measured in Imhotep's sub-region 'a' in March 2016 plotted against the effective local solar hour on the nucleus of comet 67P. Here, only measurements that are made at distances smaller than 20 km and with low emission angles were selected.

For the comparison with synthetic brightness temperatures, we filtered those measurements in sub-region 'a' that were made close to 67P's equator (see white line in Fig. 1) and, thus, experience similar illumination conditions. The three suitable temperature sets we found, two at night and one at day, are highlighted in Fig. 2 with darker colours.

 

Thermophysical simulation

The one-dimensional thermal model described in Gundlach et al. 2020 is based on a homogeneous medium and solves the heat transfer equation using the Crank-Nicolson method. We simulated 1000 cometary days, using as input parameters 67P's precise heliocentric distance and the illumination angle of the analysed area on the surface. The last simulated day refers to the day of the selected MIRO measurement. The output of the thermal model is a temperature profile with depth, which serves as input for the raytracing and radiative transfer models.

We modelled both, a homogeneous and a inhomogeneous medium (the inhomogeneous medium was built using pebble radii ranging from 3 mm to 6 mm). While for the former only heat conduction is relevant, the latter requires heat transfer by conduction and radiation. 

Raytracing

The thermal emission of the comet measured by MIRO is modelled by raytracing, applying geometric optics through a three-dimensional structure of spherical pebbles, packed randomly at a volume filling factor of ∼0.58, close to a value of 0.55 expected for random loose packing (Onoda and Liniger 1990). Rays are traced backwards, from MIRO down to the comet, where they are reflected or absorbed. The complex refractive index of the pebble material is varied in a range n = 1.0 ... 1.4 for the real part and k = 0.001 ... 0.02 for the imaginary part. For the larger wavelength, the decrease rate of the number of rays with depth in the comet has been compared to attenuation coefficients calculated by waveoptics (FDTD, for pebble radii 3mm to 6mm, n = 1.2, k = 0.001, 0.003) and have been found to be similar. For the smaller wavelength, geometric optics then should be valid as well. The raytracing returns a depth profile e(x) of the starting points of rays contributing to the thermal emission and the directional-hemispherical reflectivity R_dh from which, after Kirchhoff's law (Hapke 1993), the emissivity of the cometary surface results.

Synthetic temperatures

The raytracing's emission profile e(x) is convolved with the intensity profile B_ν(T(x)), where B_ν is Planck's function, to get the temperature dependent emission profile. Integration over depth considering reflectivity R_dh yields the total comet's intensity. The additional reflected 3K cosmic background radiation can be neglected. Thus, the synthetic temperature T_ν is given by:

T_v = B_v^-1 ( (1 - R_dh) ∫ B_vT(x)e(x) dx )

Conclusion

By using a one-dimensional thermal model combined with both a raytracing and radiative-transfer model, we were able to derive constraints on the subsurface material properties, namely its optical properties (real and imaginary part of the index of refraction) down to around 10 cm beneath the surface. We will present the models in detail as well as the optical properties we derived from this study. Reliable optical data are important as they provide the community with values of optical constants representative of the early solar system, protoplanetary disks and debris disks.

Acknowledgements

This study was performed as part of the DFG Research Unit ''Debris Disks in Planetary Systems". 

References

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Gulkis S., et al., 2007, Space Sci. Rev., 128, 561
Gundlach B., et al., 2020, MNRAS, 493, 3690
Hapke, B., 1993, Cambridge University Press, Chapter 13.D
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Thomas N., et al., 2018, Planet. Space Sci., 164, 19