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In this work, we present results that simultaneously constrain the dust size distribution, dust-togas ratio, fraction of dust re-deposition, and total mass production rates for comet 67P/Churyumov-Gerasimenko. 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. We determined a total volatile mass loss of (6.1 ± 1.5) • 10 9 kg during the 2015 apparition. Further, we found that power-laws with q = 3.7 +0.57 −0.078 are consistent with the data. This results in a total of 5.1 +6.0 −4.9 •10 9 kg of dust being ejected from the nucleus surface, of which 4.4 +4.9 −4.2 • 10 9 kg escape to space and 6.8 +11 −6.8 • 10 8 kg (or an equivalent of 14 +22 −14 cm over the smooth regions) is re-deposited on the surface. This leads to a dust-togas ratio of 0.73 +1.3 −0.70 for the escaping material and 0.84 +1.6 −0.81 for the ejected material. We have further found that the smallest dust size must be strictly smaller than ∼ 30µm and nominally even smaller than ∼ 12µm.

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<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>