Analysis of MIRO/Rosetta Data

Analysis of MIRO/Rosetta Data Dissertation zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades “Doctor rerum naturalium” der Georg-August-Universität Göttingen im Promotionsprogramm PROPHYS der Georg-August University School of Science (GAUSS) vorgelegt von David Marshall aus Norwich, Vereinigtes Königreich Göttingen, 2018 Betreuungsausschuss Dr. Paul Hartogh Max-Planck-Institut für Sonnensystemforschung, Göttingen Prof. Dr. Stefan Dreizler Institut für Astrophysik, Georg-August-Universität Göttingen Mitglieder der Prüfungskommision Referent: Dr. Paul Hartogh Max-Planck-Institut für Sonnensystemforschung, Göttingen Korreferent: Prof. Dr. Stefan Dreizler Institut für Astrophysik, Georg-August-Universität Göttingen Weitere Mitglieder der Prüfungskommission: Prof. Dr. Ulrich Christensen Max-Planck-Institut für Sonnensystemforschung, Göttingen Prof. Dr. Ariane Frey II. Physikalisches Institut, Georg-August-Universität Göttingen Prof. Dr. Thorsten Hohage Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttin- gen Prof. Dr. Andreas Pack Geowissenschaftliches Zentrum, Georg-August-Universität Göttingen Tag der mündlichen Prüfung: 19.12.2018 Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar. ISBN 978-3-944072-65-4 uni-edition GmbH 2019 http://www.uni-edition.de c David Marshall This work is distributed under a Creative Commons Attribution 3.0 License Printed in Germany Contents Summary9 Zusammenfassung 11 1 Introduction 13 1.1 Comets................................... 13 1.2 Observational history: from the stone age to the space age........ 16 1.3 The Rosetta mission............................. 21 1.4 67P/Churyumov-Gerasimenko....................... 24 1.5 The Microwave Instrument for the Rosetta orbiter............. 28 1.6 MIRO aims, results and spectra....................... 32 1.7 Thesis aims................................. 36 2 Theoretical concepts 37 2.1 Haser model................................. 37 2.2 A two level atom.............................. 37 2.3 Optical depth................................ 39 2.4 Radiative transfer equation......................... 41 2.5 LTE vs. non-LTE.............................. 42 2.6 Inversion methods.............................. 44 3 Paper I - Spatially resolved water evolution 47 3.1 Summary.................................. 47 3.2 Introduction................................. 48 3.3 MIRO observations............................. 49 3.4 Method................................... 49 3.4.1 Water absorption lines....................... 50 3.4.2 Generating the lookup tables.................... 51 3.4.3 Thermal sublimation model.................... 54 3.5 Results.................................... 55 3.5.1 Water production rate........................ 55 3.5.2 Behaviour with heliocentric distance................ 58 3.5.3 Regional variations......................... 61 3.6 Conclusions................................. 63 5 Contents 4 Paper II - Interpretation of water production rates 67 4.1 Summary.................................. 67 4.2 Introduction................................. 68 4.3 Sublimation model............................. 69 4.4 Results.................................... 71 4.4.1 Effect of comet shape and obliquity................ 71 4.4.2 Effect of activity distributions................... 72 4.4.3 Effects of obliquity and Φ ..................... 75 4.5 Conclusions................................. 76 5 Paper III - Thermal inertia and roughness 79 5.1 Summary.................................. 79 5.2 Introduction................................. 80 5.3 Instruments................................. 81 5.4 Methods................................... 83 5.4.1 Observational overlap....................... 83 5.4.2 Thermal model........................... 84 5.4.3 Radiative transfer model for MIRO data.............. 85 5.4.4 Radiance model for VIRTIS data.................. 88 5.4.5 Importance of roughness...................... 89 5.5 Results.................................... 90 5.5.1 MIRO results............................ 90 5.5.2 VIRTIS results........................... 91 5.6 Discussion and conclusions......................... 97 5.6.1 Thermal inertia........................... 97 5.6.2 Roughness............................. 99 6 Future work 101 6.1 Introduction................................. 101 6.2 Method................................... 102 6.2.1 Creating the a priori profiles.................... 102 6.2.2 Creating K, S a and S e ....................... 105 6.2.3 Optimal estimation inversion.................... 106 6.3 Application................................. 106 6.3.1 Synthetic case study........................ 107 6.3.2 MIRO case study.......................... 109 6.4 Discussion.................................. 111 7 Discussion 113 Bibliography 117 A Derivation of radiative transfer equation 131 Publications 133 Acknowledgements 135 6 Contents Curriculum vitae 137 7 Summary In August 2014, the Rosetta spacecraft completed its ten year journey when it arrived at its target destination, the comet 67P/Churyumov-Gerasimenko. The Rosetta mission was a flagship endeavour for the European Space Agency as it was the first time that any spacecraft had rendezvoused with a small solar system body for long period of time (two years) and also the first time that a lander had been placed onto the surface of a comet. In September 2016, the mission came to an end when Rosetta descended onto the surface for one final close up look at the surface. This thesis uses data from one of the instruments on this ground-breaking mission: the Microwave Instrument for the Rosetta Orbiter (MIRO). MIRO was a spectrometer operating at millimetre and submillimetre frequencies and enabled the detection of several volatile species including water. Using the spectroscopic observations of the water lines, I investigated the behaviour of comet 67P/Churyumov-Gerasimenko relating to the gas coma, mass loss, spatial outgassing and the nucleus surface. Since comets are thought to be pristine building blocks left over from the formation of the solar system, we hope that by studying them, we can learn about the conditions from which other solar system bodies originate. 16 18 Firstly, I used the line areas of the H2 O and H2 O spectral lines to measure the change in the local water production rate from August 2014 to April 2016. Lookup tables made from a Haser model show how the measured Doppler shift velocity, the continuum temperature and the line area ratio can give the column density for each observation and thus the water production rate. The maximum production rate calculated from the MIRO observations was (1.42±0.51)×1028 molec/s, found on August 29, 2015, and integrating under all the data points gave a total water mass loss of (2.4 ± 1.1)×109 kg for this ap- parition. By making assumptions about the dust-to-gas ratio and the comet mass, the total mass loss was estimated to be (1.2 ± 0.6)×1010 kg, or 0.12 ± 0.06 %. The spatial resolution of MIRO allowed for each measurement to be assigned to a region on the nucleus. The regions on the southern hemisphere appeared to be the origins of the highest production rates, in particular the regions Neith, Wosret and Bes. Finally, the data show that the production rate peak is offset by 22-46 days after perihelion and that the pre- and −3:8±0:2 −4:3±0:2 post-perihelion slopes followed power laws of Q / rh and Q / rh , respectively. Following this, I performed numerical modelling to investigate how nucleus shape, spin axis orientation and activity distribution affect the water production rate curves. I found that it is impossible to disentangle these effects from each other by only looking at the change in the production rate and that the pre- and post-perihelion slopes are also functions of heliocentric distance. It is therefore difficult to derive quantitative constraints on surface area ice fraction and active regions from the water production rate curve unless the shape, orientation and activity of the nucleus are well established. In addition, it may 9 Summary not be meaningful to compare the water production rate curves of different comets at different heliocentric distances. I used the measured continuum temperatures from MIRO to derive properties of the nucleus in the third part of this work. I utilised an insolation driven thermal model to derive the temperature gradient in the upper layers of the comet surface and a radiative transfer model to reproduce the MIRO continuum measurements. In conclusion, a low value was derived for the thermal inertia in the surface layers of 67P with an upper bound +80 −1 −2 −0:5 estimated to be 80−40 JK m s for most of the MIRO measurements. A low value for the average thermal inertia over the entire surface would be consistent with the majority of reported calculated values for 67P. In the future, the retrieval of coma parameters from the MIRO spectra will become an important avenue of investigation. Using inverse methods, the behaviour of the gas temperature, expansion velocity and molecular number density profiles can be extracted from the spectral lines. This will be important for assessing and characterising the activity around the nucleus which is observed but not so well understood. In addition, we may learn more about the physics of the coma from the inversion solutions, such as

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