The dust-to-gas ratio, size distribution, and dust fall-back fraction of comet 67P/Churyumov-Gerasimenko

Abstract

<p>The European Space Agency's (ESA) Rosetta mission escorted comet 67P/Churyumov-Gerasimenko (hereafter 67P) from August 2014 to September 2016 along its orbit through the inner Solar System. It watched as the comet's activity started to develop at large heliocentric distances, come to its culmination at perihelion, and decline as the comet travelled out towards Jupiter's orbit. This long-term continuous monitoring of the comet's activity has provided an unprecedented wealth of data on this comet and its activity.</p><p>The observations revealed a complex bi-lobate shape [1, 2] and diverse morphology [3]. As a comet approaches the Sun it is heated and the ices start sublimating and ripping with them dust particles. Thus one of the important questions to be answered was what the bulk of the comet was made of i.e. what the bulk refractory-to-volatile ratio is. In the simplified view where any ejected material is lost to space two measurements are sufficient to determine this ratio. First, the total mass loss during one apparition measured by the Radio Science Investigation (RSI) [4]. Second, the total volatile mass loss which can be indirectly determined by the in-situ measurements of the gas density [5, 6, 7] or remote sensing data [8, 9, 10, 11]. In this simple case, the refractory-to-volatile ratio can be immediately inferred from those two measurements. But the complex surface morphology has revealed large dust deposits [12] that indicate that possibly a large fraction of the ejected dust is re-deposited [13]. If that is indeed the case, then the two above mentioned quantities cannot constrain the total dust mass ejected but rather only the dust mass escaping the nucleus gravity. Further, the process of dust fall-back obscures the emitted dust-to-gas ratio.</p><p>In this work, we present results that simultaneously constrain the dust size distribution, dust-to-gas ratio, fraction of dust re-deposition, and total mass production rates for comet 67P. We use a 3D Direct Simulation Monte Carlo (DSMC) gas dynamics code to simulate the inner gas coma of the comet for the duration of the Rosetta mission. The gas model is constrained by ROSINA/COPS data. Further, we simulate for different epochs the inner dust coma using a 3D dust dynamics code including gas drag and the nucleus' gravity. Using advanced dust scattering properties these results are used to produce synthetic images that can be compared to the OSIRIS data set. These simulations allow us to constrain the properties of the dust coma and the total gas and dust production rates.</p><p>In particular, we show how the dust-to-gas mass production rate ratio, the power-law exponent of the dust size distribution, the fraction of dust fall back, and the scattering properties of the dust are inter-related and constrain each other. Because these parameters are not independent they need to be fit simultaneously. E.g. the lowest mass needed to match the brightness of the dust coma as observed by OSIRIS is achieved with power-law distributions with exponents between 4 and 4.5. Using the constraint of the total mass loss of the comet during the 2015 apparition we will show that only a narrow parameter set fits all observations. </p><p>We determined a total volatile mass loss of (6.1 ± 1.5)·10<sup>9 </sup>kg during the 2015 apparition. Further, we found that power-laws with q=3.7<sup>+0.57</sup><sub>-0.078</sub> are consistent with the data. This results in a total of 5.1<sup>+6.0</sup><sub>-4.9 </sub>·10<sup>9 </sup>kg of dust being ejected from the nucleus surface, of which 4.4<sup>+4.9</sup><sub>-4.2</sub>·10<sup>9 </sup>kg escape to space and 6.8<sup>+11</sup><sub>-6.8</sub>·10<sup>8</sup>kg (or an equivalent of 14<sup>+22</sup><sub>-14 </sub>cm over the smooth regions) is re-deposited on the surface. This leads to a dust-to-gas ratio of 0.73<sup>+1.3</sup><sub>-0.70</sub> for the escaping material and 0.84<sup>+1.6</sup><sub>-0.81</sub> for the ejected material. We have further found that the smallest dust size must be strictly smaller than ~30 μm and nominally even smaller than ~12 μm.</p><p> </p><p><strong>Acknowledgements<br></strong>We thank Frank Preusker and Frank Scholten for providing us the comet shape model SHAP7 [2] used in this work.<br>We thank Vladimir Zakharov for providing valuable comments on the section of the analytical solution.<br>We acknowledge the personnel at ESA's European Space Operations Center (ESOC) in Darmstadt, Germany, European Space Astronomy Center (ESAC) in Spain, and at ESA for the making the Rosetta mission possible. Furthermore, we thank the OSIRS and ROSINA instrument and science teams for their hard work. We thank Martin Rubin and Kathrin Altwegg for giving us access and support to/for the ROSINA/COPS data.</p><p><strong>References<br></strong>[1] Sierks, H., Barbieri, C., Lamy, P. L., Rodrigo, R., Koschny, D., Rickman, H., et al. 2015, Science, 347, 1044<br>[2] Preusker, F., Scholten, F., Matz, K.-D., et al. 2017, A&A, 607, L1.<br>[3] Thomas, N., Davidsson, B., El-Maarry, M. R., Fornasier, S., Giacomini, L., Gracia-Berna, A. G., et al. 2015. A&A 583, A17<br>[4] Pätzold, M., Andert, T. P., Hahn, M., Barriot, J.-P., Asmar, S. W., Häusler, B., et al. 2019, MNRAS, 483, 2337–2346.<br>[5] Fougere, N., Altwegg, K., Berthelier, J. J., et al. 2016, A&A, 588, A134.<br>[6] Läuter, M., Kramer, T., Rubin, M., and Altwegg, K., 2018, MNRAS, 483, 852–861<br>[7] Combi, M., Shou, Y., Fougere, N., Tenishev, V., Altwegg, K., Rubin, M., et al., 2020, Icarus 335, 113421<br>[8] Migliorini, A., Piccioni, G., Capaccioni, F., Filacchione, G., Bockelée-Morvan, D., Erard, S., et al., 2016, A&A 589, A45.<br>[9] Bockelée-Morvan, D., Crovisier, J., Erard, S., Capaccioni, F., Leyrat, C., Filacchione, G., et al., 2016, MNRAS, 462 S170–S183<br>[10] Marshall, D. W., Hartogh, P., Rezac, L., von Allmen, P., Biver, N., Bockelée-Morvan, D., et al., 2017, A&A, 603, A87<br>[11] Biver, N., Bockelée-Morvan, D., Hofstadter, M., Lellouch, E., Choukroun, M., Gulkis, S., et al. 2019, A&A, 630, A19<br>[12] Thomas, N., El Maarry, M. R., Theologou, P., Preusker, F., Scholten, F., Jorda, L., et al., 2018, PSS, 164, 19–36<br>[13] Thomas, N., Sierks, H., Barbieri, C., Lamy, P. L., Rodrigo, R., Rickman, H., et al., 2015. Science, 347, 440</p>

Modelling the water and carbon dioxide production rates of Comet 67P/Churyumov–Gerasimenko

“…They find that the dust-to-gas mass ratio changed over time (i. e., A#4 is not strictly valid). However, during the period 200 days pre-perihelion to 100 days post-perihelion (when most of the gas and dust are being produced), the dust-to-gas mass ratio is still rather stable: Marschall et al (2020) find that it is 0.5 ± 0.25, except for a brief period around 100 days pre-perihelion when the dust-to-gas mass ratio increased to ∼ 1.3. Considering that the production rate changed by orders of magnitude in this period, the fact that their ratio remained quasi-constant to within ±50 per cent for most of the time shows that A#4 is a reasonable approximation.…”

“…We find 𝐹 = 1.05 with our method, suggesting that the escaping mass of refractories is very similar to the escaping mass of water vapour. This can be compared to measured values obtained using different instruments and techniques: 𝐹 = 0.64 (Hansen et al 2016), 𝐹 = 0.72 (Marschall et al 2020), 𝐹 = 1.06 (Läuter et al 2019), 𝐹 = 1.14 (Combi et al 2020), 𝐹 = 1.63 (Läuter et al 2020), and 𝐹 = 3.4 (Biver et al 2019), i. e, a mean and standard deviation of 𝐹 = 1.4 ± 1.…”

“…We note that ℎ = 0.87 m, estimated by Davidsson et al ( 2021) through mass transfer calculations, is consistent with the deposition of 1.4 ± 0.8 m in Hapi (Cambianica et al 2020) and 0.7 ± 0.3 m in Ma'at (Cambianica et al 2021), based on measurements of boulder shadow lengths and their temporal changes. Marschall et al (2020) estimated a deposition of 0.14 +0.22 −0.14 m. Applying ℎ = 2.2 m (the upper limit according to Cambianica et al 2020) instead of ℎ = 0.87 m would increase the peak contribution from the extended source from 8 to 18 per cent. The fraction of the nucleus surface being responsible for chunk ejection would increase from 4 to 11 per cent.…”

“…Hansen et al (2016) point out that the coma brightness determined by groundbased telescopes is highly correlated with the water production rate that has been inferred from the ROSINA measurements. A careful reconstruction of both the dust production rate and the water production rate was made by Marschall et al (2020). They find that the dust-to-gas mass ratio changed over time (i. e., A#4 is not strictly valid).…”

“…Given the factor 2-3 dispersion in measured water production rates, a factor 0.82 reduction of the nominal production rate that we try to match (remembering that in principle should reproduce the contribution from the nucleus, not the full measured 𝑄 H2O that also includes the extended source) has a negligible impact on our results. A smaller ℎ value, as suggested by Marschall et al (2020) would further motivate our decision of using 𝐺 (𝑡) = 1.…”