tokens: Acknowledgements We thank Hiroshi Kimura for providing the optical constants for glassy silicates, and for the discussions about the DDE mechanism. We also thank Rik van Lieshout for the useful discussion concerning sublimation processes. We acknowledgethe financial support from the Programme National de Planétologie (PNP) of CNRS-INSU co-funded by the CNES. Our code uses the NumPy ( Oliphant 2006 ) and the Matplotlib libraries ( Hunter 2007 ). This work has made use of data from the European Space Agency (ESA) mission Gaia ( https://www.cosmos.esa.int/gaia ), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium ). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.
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