tokens: objects, the models were applied to the set of Spitzer , Herschel , and ALMA fluxes. We used the Spitzer and Herschel /PACS flux values as published in Lim et al. (2010) , but updated the Herschel /SPIRE fluxes, accounting for (i) a new reduction pipeline (HIPE version 8.2) and destriping methods ( Fornasier et al. 2013 ) and (ii) the availability of new Makemake observations from June 2010, in addition to the Nov./Dec. 2009 data presented in Lim et al. (2010) . Averaging the two epochs, the new SPIRE fluxes are 12.5 1.3 mJy, 9.5 1.3 mJy, and 4.7 1.5 mJy at 250, 350 and 500 m, respectively. In the first model (“Makemake-alone”), a standard NEATM fit was performed on the 3-band Herschel /PACS and the Spitzer 71.42 m fluxes, ignoring the Spitzer 23.68 m flux, with as the only free parameter. As before, the model was then applied to other wavelengths to determine the corresponding spectral emissivities. The best fit solution, shown in the left panel of Fig. 7 , has 9, but even though the diameter and geometric albedos are fixed, the error bar on is large (; see Table 5 ), a consequence of the strong effect of the phase integral uncertainty for a bright object. Our ALMA flux measurements then imply a 1.03 relative mm emissivity. In a second model (“Makemake + moon”), the two Spitzer and the three Herschel /PACS measurements were fit with the sum of emission from Makemake and its moon. This model had initially four parameters, and (, and ) for its moon, for which we adopted 0.3 (to allow for possible light curve variation). However, the system was somehow degenerate and best fit solutions tended to call for very large values of (3–4), while values larger than 2.7 are unphysical (see e.g., Fig. 4 of Lellouch et al. 2013 ). was then fixed at a maximum value of 2.64. Even then, the problem remained somewhat under-constrained, leading to broad ranges for (, and ) of the moon (Table 5 ). More worryingly but consistent with the previous studies ( Lim et al. 2010 ; Parker et al. 2016 ), the solution range of remained unphysical (0.34) suggesting that Makemake’s moon alone might not entirely explain the 24-m flux. Since the temperatures scale as (), a possible way to alleviate the problem would be to invoke a bolometric emissivity much lower than 1 for Makemake’s moon, but we note that restoring physically reasonable values of (say ) would then require . In any case, with this “Makemake + moon” model, we infer a 1.05 relative mm emissivity for the system. In a third model, the 24 m flux excess from Makemake’s system was attributed to dust emission. For this we adopted the dust absorption coefficients of Li Draine (2001) , giving, for example, m kg at 23.68 m, and specified a dust grain temperature of 54.6 K, which corresponds to the instantaneous equilibrium of a sun-facing surface with zero albedo at Makemake’s 52 AU distance. This choice is somewhat arbitrary as small grains could be poor radiators (hence warmer than the above value), and/or radiating
ner_tags: O O O O O O O O O B-Telescope O B-Telescope O O B-Observatory O O O O B-Telescope O B-Telescope B-Instrument O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Telescope B-Instrument O O O O O O O O B-Software B-Identifier I-Identifier O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Instrument O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O B-Model O O B-Model I-Model O O O O O B-Telescope B-Instrument O O B-Telescope B-Wavelength I-Wavelength O O O B-Telescope B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O B-Model I-Model I-Model O O B-Telescope O O O B-Telescope B-Instrument O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O B-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O O O B-CelestialObject O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O