Thermal Properties of Large Main-Belt Asteroids Observed by Herschel

Home , 19 Fortuna, 423 Diotima, 511 Davida, 88 Thisbe

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T. , rs ohi h iil n h thermal the and visible the in both orts, ∼ %cnitn ihwa ol eepce ie h absolute the given expected be would what with consistent 5% uehe l 01 iknok tal. et Viikinkoski 2011; al. et Durech ˇ µ aucitn.pacs_accepted_arxiv no. manuscript )adsaeo-h-r hp oesdrvdfo adaptive from derived models shape state-of-the-art and m) nski ´ 5 .Marciniak A. , 1 .Kiss C. , 2 , 3 eshlPACS Herschel .Szakáts R. , uehe al. et Durech uehe al. et Durech ˇ ˇ 5 .Podlewska-Gaca E. , eprtr)a temperature) . dbfr,wihcniust iespott h ointhat notion the to support give to continues which before, ed ebcsrse1 54 acig Germany Garching, 85748 1, senbachstrasse ftemladpyia rpriso seodsrae pr surfaces asteroid of properties physical and thermal of s cades agt eurdlre esaigt erdc h Rdata IR the reproduce to re-scaling larger required targets cated remi-etatris eas oeldpeiul well previously modelled also We asteroids. main-belt arge ubet osri ieadtemlietaadnttosens too not and inertia thermal and size constrain to luable ewvlntsa hc ASosre r ogad fteem the of longwards are observed PACS which at wavelengths he ABSTRACT as- t rtia, i hropyia oes eue calibration-programm used We models. thermo-physical via ikeizUiest,Soeza3,6-8 Pozna 60-286 36, Słoneczna University, Mickiewicz . srnmas Astronomía a epeaiehwdi how examine help R) he yPtrstn 1 sétány Péter ny s, éáy1 sétány r tn ecmrs sn h cl safe aaee,ms t most parameter, free a as scale the Using benchmarks. rtant e - - l 2 .Marton G. , hSine,KnoyTeeMkó t1-7 -11Budapest H-1121 15-17, út Miklós Thege Konkoly Sciences, th ülre l 07 admne l 08 and 2006; 2018) al. al. et et Emery Landsman 2004; 2017; al. Blommaert et & Müller Müller tar- 2002; facilitie 2018, space-based Müller and to of ground- Up th from provided collection (WISE). observations or geted those Explorer AKARI, large Survey (IRAS), like a Infrared Satellite catalogues Wide-field Astronomical of several Infrared use the from by make data IR readily thermal can we increase, therein). references and 2015, al. et Benner 05 atzk&Dudzi & Bartczak 2015; 04 oii ta.21;Hnše l 05 06 ahe al. model et to Bach used 2016; been 2015, had 2018) al. et al. Hanuš et al Marciniak 2014; et 2017; Alí-Lagoa al. 2009; et Tanga Rozitis & Delbo’ 2014; (e.g. surveys IR thermal radar, occultations, (e.g. stellar observations on optics also adaptive based and models of dozens ( SR- n h tcm ag Millimiter Large Atacama data Hersch the for (PACS) and Programme ASTRO-F Preparatory Spectrometer Asteroid the and during Hersc taken Camera with (MBAs) Array asteroids Photodetector largest main-belt single of the characterisation now 100 another are of inertias. data thermal addition asteroid WISE of recent source 2018b), the al. With et (Hanuš TPMs. with teroids uehe l 07 ülre l 07,adteeaenow are there and 2017), al. et Müller 2017; al. et Durech ˇ eaysystems netary ff steaalblt fatri hp oescniusto continues models shape asteroid of availability the As u i nti oki opoieathermo-physical a provide to is work this in aim Our / c u nepeaino h results. the of interpretation our ect ,H11 uaet Hungary Budapest, H-1117 A, / ,108Gaaa Spain Granada, 18008 n, 5 / 2 ,H11 uaet Hungary Budapest, H-1117 A, .Du R. , , ff 3 .Farkas-Takács A. , rn auso h xoetue o cln the scaling for used exponent the of values erent otc bevtosand observations -optics airto ro as hscntttsagood a constitutes This bars. error calibration ff ard 6 si21) vntemlI data IR thermal even 2018), nski .Santos-Sanz P. , ´ 2 , 4 .Bartczak P. , / ril ubr ae1o 28 of 1 page number, Article rotcllgtcurves light optical or ,Poland. n, ´ eotie low obtained We . 6 vddteshape the ovided uehe l 2015; al. et Durech ˇ n .L Ortiz L. 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5 c M. , S 2020 ESO argets ission y ∼ 0 as- 100 , (e.g. s hel 6 el, e . A&A proofs: manuscript no. pacs_accepted_arxiv ray (Müller et al. 2005a). Onlya fractionof this data set has been provide all relevant details about the production of the IRDB4, exploited so far, for example in the context of absolute infrared including the colour correction approach, sources and references flux calibration using well-characterised asteroids (Müller et al. of each catalogue, and useful auxiliary quantities such as ob- 2014), or in studies of specific targets (e.g. O’Rourke et al. 2012; servation geometry, and light-travel time. For completeness, Ta- Marsset et al. 2017). The PACS data are important not only in ble B.1 provides all previously unpublished PACS observations terms of quality and additional wavelength coverage, but be- used in this work. cause their combination with AKARI and IRAS data allows us to bring the number of large MBAs analysed via a TPM closer to completeness1. 3. Thermo-physical model implementation This work was possible thanks to (i) the availability of a set of new shape models derived using the All-Data Aster- Our TPM implementation is the one used by (Alí-Lagoa et al. oid Modelling (ADAM) (Viikinkoski et al. 2015) and the Shap- 2015) based on that of Delbo’ et al. (2007) and Delbo’ & Tanga ing Asteroids with Genetic Evolution (SAGE) (Bartczak et al. (2009). Said version was upgraded to account for the effects 2014; Bartczak & Dudzinski´ 2018) algorithms and (ii) the of shadowing, but global self-heating was neglected for this expert-reduced data products submitted to the Herschel Science work (see e.g. the discussion about average view factors by Archive, which include some targets for which a non-standard Rozitis & Green 2013). Below we provide only a brief sum- 2 data reduction approach was required . Such data reduction mary of the technique that we use and the approximations that and the creation of a large database featuring IRAS, AKARI, we make. Our methodology was described in more length in and WISE data (Szakáts et al. 2020) have been carried out in Marciniak et al. (2018) and Marciniak et al. (2019). There, de- the framework of the “Small Bodies: Near and Far” (SBNAF) tails about the thermo-physical modelling of each target were project (Müller et al. 2018), funded by the European Commis- provided in separate sections. Here, we only present some rele- sion. SBNAF aimed at exploiting synergies between different vant plots in the main text and include all TPM-related plots and small-body modelling techniques that use a wide range of data additional comments in Appendix A. types from ground and space observatories (stellar occultations, We take a shape model as input for our TPM (see Table 1) visible and thermal infrared photometry, etc.) to produce physi- with the main goal of modelling the surface temperature distri- cal models of the selected targets, which range from near-Earth bution at epochs at which we have thermal IR observations and asteroids to trans-Neptunian objects. constrain the target’s diameter, thermal inertia and, whenever In Sect. 2 we briefly describe the IR data set and in Sect. 3 possible, surface roughness. From the known geometry of ob- the TPM approach and simplifying assumptions. In Sect. 4 we servation we identify which surface elements (usually triangular present our results and in Sect. 5 we provide further discussion facets) were visible to the observer at each epoch and compute and comments. Appendix A contains plots relevant to the TPM the model fluxes from the surface temperature distribution. analysis and Appendix B a table with all the Herschel PACS data used in this work. To account for heat conduction towards the subsurface, we solve the 1D heat diffusion equation for each facet and we use the Lagerros approximation when modelling the surface roughness via hemispherical craters of different depth coveraging 2. Data 0.6 of the area of each facet (Lagerros 1996, Lagerros 1998, In this section we give a brief summary of the IR data. Further Müller & Lagerros 1998, Müller 2002). We also consider the details of the Herschel PACS (Pilbratt et al. 2010; Poglitsch et al. spectral emissivity to be 0.9 regardless of the wavelength (see 2010) catalogue of asteroid observations (Müller et al. 2005b) e.g. Delbo et al. 2015). can be found in Müller et al. (2014), who already published the For each target, we estimated the Bond albedo (necessary in- PACS data of (1) Ceres, (2) Pallas, (4) Vesta, and (21) Lutetia, put) as the average value obtained from the different radiometric which were used as IR calibrators in that work. In addition, in- diameters available from AKARI and/orWISE (Usui et al.2011; formation about the more specialised data reduction approach Alí-Lagoa et al. 2018; Mainzer et al. 2016), and all available H- required for some PACS measurements is already available from G, H-G12, and H-G1-G2 values from the Minor Planet Center, the User Provided Data Products release note of the main-belt Oszkiewicz et al. (2011), or Vereš et al. (2015). asteroid expert-reduced data products submitted to the Herschel This approach leaves us with two free parameters, the scale Science Archive by Kiss, Müller and Farkas-Takács2. of the shape (interchangeably called the diameter, D) and the We also used whatever data was available from the IRAS and thermal inertia (Γ). The diameters and other relevant information Midcourse Space Experiment (MSX) (Tedesco et al. 2002b,a), related to the TPM analyses of our targets are provided in Table AKARI Infrared Camera (Murakami et al. 2007; Takita et al. 2. Whenever the data are too few to provide realistic error bar 2012; Usui et al. 2011; Hasegawa et al. 2013), and WISE cat- estimates, we report the best fitting diameter so that the models alogues (W3 and W4 data; Mainzer et al. 2011; Masiero et al. can be scaled and compared to the scaling given by the occulta- 2011; Wright et al. 2010) 3. We used all colour-corrected flux tions. On the other hand, if we have multiple good-quality ther- densities and absolute calibration error bars compiled in the SB- mal data (with absolute calibration errors below 10%) then this NAF thermal infrared database (IRDB). Szakáts et al. (2020) typically translates to a size accuracyof around5% as long as the shape is not too extreme and the spin vector is reasonably well 1 Large MBAs were too bright for WISE and their partially saturated established. This rule of thumb certainly works for large MBAs fluxes might not be optimal for thermo-physical modelling. On the like the Gaia mass targets. We do not consider the errors intro- other hand, partial saturation can be corrected for and reasonably suited duced by the pole orientation uncertainties or the shapes (see for thermal modelling purposes (e.g. Masiero et al. 2011; Mainzer et al. 2015). Hanuš et al. 2015 and Bartczak & Dudzinski´ 2019), so our TPM 2 http://archives.esac.esa.int/hsa/legacy/UPDP/SBNAF_MBA/SBNAF_MBA_Release_Note.pdferror bars estimates are lower values. 3 For (21) Lutetia (see Sect. A.4), we also included most of the data analysed in O’Rourke et al. (2012). 4 https://ird.konkoly.hu/

Article number, page 2 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

Table 1. Origin and references for the shape models. pole-on views. In this particular case, this could also explain the lower thermal inertia needed to fit the data when we kept the Asteroid Model Reference scale fixed, because the data taken at higher phase angles were (1) Ceres Dawn Park et al. (2019)a coincidentally the ones taken at non-equatorial sub-observer lat- (2) Pallas ADAM Hanuš et al. (2017)b ffi (3) Juno ADAM Viikinkoski et al. (2015)b itudes, which makes it more di cult for the shape model to re- (3) Juno SAGE Podlewska-Gaca et al. (2020)c produce the thermal phase curve (see Fig. 4). (4) Vesta Dawn Gaskelld We found formally good fits and thermal properties within (8) Flora ADAM Hanuš et al. (2017)b the expected range for the two targets with SAGE models avail- (10) Hygiea ADAM Vernazza et al. (2019) able for our study as well, albeit with slightly higher error bars. (18) Melpomene ADAM Hanuš et al. (2017)b Additional SAGE models scaled using stellar occultation chords (19) Fortuna ADAM Hanuš et al. (2017)b and further discussion are provided by Podlewska-Gaca et al. (20) Massalia SAGE 1, 2 Podlewska-Gaca et al. (2020)c (2020). It is worth mentioning that the TPM did not help us to (21) Lutetia Rosetta Jorda (Farnham 2013) favour any of the two mirror shape solutions of (20) Massalia. (29) Amphitrite ADAM Hanuš et al. (2017)b b For each shape model, we also fitted the data using spheres (52) Europa ADAM Hanuš et al. (2017) with the corresponding rotational parameters with the aim of (54) Alexandra ADAM Hanuš et al. (2017)b (65) Cybele ADAM Viikinkoski et al. (2017)b comparing the resulting thermo-physical parameters (see Table (88) Thisbe ADAM Hanuš et al. (2017)b 2). On the one hand, this approximation seems to provide rea- (93) Minerva ADAM Hanuš et al. (2017)b sonable estimates for the diameters that would be expected for (423) Diotima ADAM Hanuš et al. (2018a)b large objects with relatively low-amplitude light curves. On the (511) Davida ADAM Viikinkoski et al. (2017)b other hand, spheres lead to scales ∼5% largeron average than the ADAM shapes, and several of the thermal inertia values were up Notes. (a) Downloaded from the PDS. https://pds.nasa.gov/ to an order of magnitude higher than those of the correspond- (b) Downloaded from the DAMIT database ing shape models. With the current sample we could not identify https://astro.troja.mff.cuni.cz/projects/damit/ any single cause that should lead to such systematic effects, but (c) (Durechˇ et al. 2010) Available from the ISAM service perhaps a future larger sample could help explore this further. http://isam.astro.amu.edu.pl (see Marciniak et al. 2012, Also, this could be used to create a reliable benchmark to esti- for details). (d) Downloaded from the Dawn Public Data site http://dawndata.igpp.ucla.edu/tw.jsp?section=geometry/ShapeModelsmate thermal inertias of objects with more limited shape models.

4.1. Thermal inertia, pole-on views, and rotational variability 4. Results Only those asteroids with highly oblique rotational axes (or al- ternatively, unusually high orbital inclinations) can be seen with Table 2 summarises the thermophysical properties obtained for aspect angles close to pole-on, that is, 0 or 180 degrees for the each target in our sample. For comparison, we also include the north and the south pole. In these cases, seasonal effects on the results for the spheres with the same rotational properties as the surface temperature distribution are expected, since the depth at shape models. All plots produced during the modelling and fur- which the heat wave penetrates is higher at close to pole-on illu- ther details about some selected targets are providedin Appendix minations. In principle, data taken in such circumstances could A. In this section we provide a summary of the results and focus require a model accounting for thermal inertia variation with on several aspects relevant to the sample and/or a larger cata- depth (such as those used for the Moon; Hayne et al. 2017), but logue of thermo-physical properties retrieved from the literature. our OMR versus aspect angle plots do not suggest problems in For example, the thermal inertia versus size plot (Fig. 1) shows fitting data taken at close to pole-on views (e.g. see Fig. 2). We that our new thermal inertias fall within the same range of those did not find any correlation between Γ and the pole ecliptic lat- of other large MBAs found in previous works. itude either. The vast majority of OMR versus rotational phase Most ADAM shape models only required a small re-scaling plots suggest that the shape models and the assumption of ho- 2 of the size to fit the data with lowχ ¯min , which we take as an mogeneous thermal properties throughout the surface can still additional confirmation of their high quality. However, in the reproduce the IR data well (see Figs. A.1–A.20, third panel from cases of (65) Cybele, (18) Melpomene, and (54) Alexandra, we the top). required re-scalings of the order of 10% to fit the data, which are larger than expected for the available high-quality thermal data and shape models (e.g. Delbo et al. 2015). Thus, regard- 4.2. Constant thermal inertia with temperature less of their quality, it is still worthwhile keeping the scale as Given the dependence of conductivity on temperature, thermal a free parameter when performing thermo-physical modelling inertia obtained from IR data taken at an average heliocentric using already-scaled shape models in order to check potential is- distance r needs to be normalised to some reference heliocentric sues. For example, the ADAM shape of Pallas with a fixed scale distance (i.e. temperature), usually 1 au, following could not reproduce well PACS data taken closer to pole-on, as α illustrated in Figs. 2 and 3. The first one shows the observation- Γ1au = Γ(r)r , (1) to-model ratios (OMR) versus aspect angle for our best fit, that is Γ = 30Jm−2 s−1/2K−1and a re-scaling of +3%. The second where α = −0.75 if we consider a radiative conduction term in one shows the best fit obtained with a fixed scale, which led to the thermal conductivity κ. Marsset et al. (2017) analysed ther- Γ = 8Jm−2 s−1/2K−1. Although this fit is also formally accept- mal IR data of asteroid (6) Hebe taken at a wide range of helio- able, the OMRs are only close to one at equatorial views (aspect centric distances and found indications that higher thermal in- angles around 90 degrees). No other combination of thermal inertias fitted low-r data better. However, even though our sample ertia and roughness could bring the other ratios closer to unity, includes some highly eccentric asteroids, our OMR versus helio- which suggests that the shape model could be less accurate at centric distance plots show no systematics or biases due to the

Article number, page 3 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv

160

/K) ADAM fixed scale (only PACS data) 3

1/2 1.4 10 140 /s 2 120 2 1.2 10 100

1 80 101 Obs/Mod 60

0.8 Wavelength (micron) Our new values (1σ error bars). 40 100 Compilation (Delbo’ et al. 2015) 0.6 20

Thermal inertia at 1 au (J/m 1 10 100 1000 0 20 40 60 80 100 120 140 160 180 Diameter (km) Aspect angle (north pole-view at 0 degress) Fig. 1. Thermal inertia normalised at 1 au versus size. The PACS targets Fig. 3. Same as Fig. 2 but for the case when we kept the scale of (black symbols) follow the trend in the compilation by Delbo’ et al. and the ADAM model ﬁxed. Here, the best-ﬁtting thermal inertia was 8 Hanuš et al. (2018b). J m−2 s−1/2K−1(cf. 30 J m−2 s−1/2K−1), but the data taken with a sub- 160 observer point far from the equator could not be reproduced equally ADAM (only PACS data) well. 1.4 140

120 160 1.2 ADAM fixed scale (only PACS data) 1.4 100 140

1 80 120 1.2 Obs/Mod 60 100

0.8 Wavelength (micron) 1 40 80 Obs/Mod 0.6 20 60 0.8 Wavelength (micron) 40 0 20 40 60 80 100 120 140 160 180 Aspect angle (north pole-view at 0 degress) 0.6 20 Fig. 2. Observation to model ratios vs. aspect angle for the best fitting TPM model to the PACS data of (2) Pallas. The best fit was obtained by -40 -30 -20 -10 0 10 20 30 40 Γ= 30 J m−2 s−1/2K−1and a re-scaling of 1.03 (see Table 2). Phase angle (degree) Fig. 4. Observation to model ratios vs. phase angle for the best fit to PACS data of (2) Pallas keeping the scale of the shape model fixed. A Γ assumption that Γ = constant (see e.g. Fig. 5), so it seems that lower fitted the data better than when the scale was optimised (cf. Fig. A.2, lower panel). the temperaturerange coveredby most MBAs might be such that this effect is not critical. Rozitis et al. (2018) studied three highly eccentric near-Earth On the one hand, α = −0.75 (Fig. 6) leads to the conclusion objects observed by WISE at widely different r and fitted the that most D > 10-km asteroids (i.e. the green, brown and yel- exponent α separately for each case. This work clearly showed low symbols) have thermal inertias at 1 au between 10 and 250 that the physical interpretation of thermal inertia and the com- Jm−2 s−1/2K−1(dotted line), whereas those of most sub-km ob- parison between different objects and populations without good jects (pink symbols) lie between ∼200 and 1000 Jm−2 s−1/2K−1. constraints for α is quite complicated. Here we propose a graphic On the other hand, with α = −2.2 (Fig. 7), we would conclude approach to analyse a large catalogue of thermal inertias with the that there is a much higher degree of thermal inertia variability necessary assumption that all asteroids can be modelled using a amongst D > 10 km asteroids, since Γ1au spans the range < 50– single value of α, which is arguable. The aim, nonetheless is to 2000 Jm−2 s−1/2K−1. further explore the impact of the value of this parameter on our Finally, we also examined plots like Figs. 6 and 7 but us- interpretation of the thermal inertias with a larger catalogue of ing the rotational period instead of size in the colour axis: they values (see also Szakáts et al. 2020). do not show any appreciable excess of slow rotators in the re- Instead of normalising the Γ-values to 1 au, we can plot the gions of higher Γ1au or, conversely, fast rotators in the regions thermal inertias compiled in Delbo et al. (2015) plus those in with lower Γ1au, regardless of the value of α. This is consistent Hanuš et al. (2015), Hanuš et al. (2018a), Hanuš et al. (2018b), with the conclusions of Marciniak et al. (2019), whose sample Marciniak et al. (2018), and Marciniak et al. (2019) as a func- shows that slow rotators do not always present higher thermal in- tion of heliocentric distance and compare them with different ertias (cf. Marciniak et al. 2018, who had a smaller sample, and curves with Γ1au = 10, 50,..., 2000 and a given value of α using Harris & Drube 2016 based on an empirical relation between Eq. 1. With such a plot, we can visually estimate Γ1au for each thermal inertia and the infrared beaming parameter η used in the asteroid as the curve going through its corresponding point. near-Earth asteroid thermal model of Harris 1998).

Article number, page 4 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

160 Finally, we note that our thermal inertias for Ceres and Pal- ADAM (all data) 1.4 las are higher than previous values (Müller & Lagerros 1998; 140 see also Secs.A.1 and A.2). Thermo-physical modelling of Ura- 120 nian satellites by Detre et al. (submitted to Astronomy & Astro- 1.2 physics) suggests this could be a small systematic trend: the ra- 100 diometric diameters are 3-5% larger than the ones derived from

1 direct methods. We have not identified a clear unique cause for 80 such an offset, but it could be related to the absolute flux cali- Obs/Mod 60 bration of the PACS data. On the other hand, we obtained only

0.8 Wavelength (micron) slightly higher values than O’Rourke et al. (2012) for Lutetia 40 and Capria et al. (2014) for Vesta. Another source of error might be the assumption of a constant emissivity of 0.9, but the need 0.6 20 for much lower thermal emissivities has so far been pointed out at significantly longer wavelengths (Müller & Lagerros 1998, 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Heliocentric distance (au) Müller & Barnes 2007, Müller et al. 2014). Fig. 5. Observation-to-model ratios vs. heliocentric distance for (3) Juno using the ADAM model. Although there is a slight curvature in 6. Conclusions the plot, it shows that with reasonable accuracy we can fit data taken at different temperatures with a constant thermal inertia. The more scat- In this work we derive thermo-physical properties of 18 large tered points at about 2.2 au are IRAS data, which did not have a strong main-belt asteroids, 12 of which did not have any previous con- weight on the fit given their significantly larger error bars. Section A.3 straints on thermal inertia. This was enabled by previously un- provides further discussion. published Herschel PACS data (Table B) and recently available state-of-the art non-convex shape models (the term also includes the rotational properties). Most of our targets’ shape models (see 5. Discussion Table 1) were derived from a combination of adaptive optics, occultation and optical light-curve data using the ADAM algorithm One of the original motivations for this work within the frame- (Viikinkoski et al. 2015);three of them,which we used as bench- work of the SBNAF project was to test how the TPM could be marks, from direct images from spacecraft, and two of them used to evaluate the quality of shape models. While the compar- from only optical light curves via SAGE (Bartczak & Dudzinski´ ison of the results with those obtained for a sphere is always a 2018). useful benchmark for discussion of bad or borderline acceptable We find that the ADAM shapes can reproduce the thermal fits, we found a relatively small systematic offset of the equiv- IR data in spite of the usual simplifying assumptions of the alent diameters obtained for the spherical models. However, af- thermo-physical modelling – constant properties over the surface, and thermal inertia also independent of depth and temper- ter a thorough examination of each individual case, we failed to 5 identify any cause that could explain why the spheres would oc- ature – even in the case of (10) Hygiea, which has been recently casionally provide good approximations of the thermal inertia, shown to have a variable albedo over the surface (Vernazza et al. while being up to an order of magnitude higher in other cases. 2019). We optimised the scale of the shape models (i.e. the scale Neither the irregularity of the shape nor the particular orientation was a free parameter in our thermo-physical model, as usual) of the spin axis seem to produceworse results, at least within our and found that most cases required an average re-scaling of 5%, sample. which serves as a cross-validation. Nonetheless, there were notable exceptions, especially (65) Cybele (see Table 2), that re- We fully neglect the uncertainties in the shape models even quire ∼10% scaling, which means these targets are interesting though they would certainly contribute to the final error bars of for follow-up observations and modelling. our TPM parameters (see Hanuš et al. 2015). In this sense, our From the example of (2) Pallas, a target extensively observed error bars are lower limits. One of the reasons for this limita- at a wide range of aspect angles due to the high obliquity of its tion is that the methods to estimate errors in the shape are ei- rotation axis, we also examined how potential inaccuracies in the ther labour intensive, computationally costly, or both, but there shape can bias the results of thermo-physicalmodellingwhen the are already some works that explore this direction. Hanus et al. scale of the shape model is not allowed to vary, so we suggest (2015) proposed a way to assess the effects of shape uncertainty that results from both approaches (fixed and fitted scale) should in TPM modelling by bootstrapping the visible data used to ob- always be compared and a careful examination of the modelling tain a shape model from light-curve inversion and producing a results should be performed on a case-by-case basis. Also, more set of shape models, each one of which is in turn modelledwith a work is needed to quantify and parameterise shape model errors TPM to provide statistics for the inferred TPM parameters. More (Hanuš et al. 2015; Bartczak & Dudzinski´ 2019) so that they can recently Bartczak & Dudzinski´ (2019) used an approach featur- be propagated into the thermo-physical properties derived from ing millions of slightly perturbed shape clones to examine how them in a practical way. the uncertainties and inaccuracies of the inversion models map In addition, we found relatively low thermal inertias in the over the whole surface. As the number of shape models deter- same range as previousresults (Delbo et al. 2015, and references mined from adaptive optics observations and stellar occultations therein) for similarly-sized asteroids, which continues to support continues to rise, we could reach a point where we have suffi- the notion that these bodies are covered by fine regolith. This, cient ground-truth information about the shapes to have a more rather than composition, is the dominant effect governing the empirical estimate of the errors of thermal inertia and diameter. thermal emission of the large asteroids. Although the peak of Podlewska-Gaca et al. (2020) provide a larger sample of SAGE models scaled with stellar occultation chords and, whenever pos- 5 A discussion of the case of (6) Hebe can be found in Marsset et al. sible, thermo-physical modelling. (2017)

Article number, page 5 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv

104 3.5 α=−0.75 (classical), Γ = 10 SI u α Γ1 au =−0.75 (classical), 1 au = 50 SI u 3 α=−0.75 (classical), Γ = 250 SI u α Γ1 au =−0.75 (classical), 1 au = 500 SI u ) 2.5 3 α=−0.75 (classical), Γ = 1000 SI u −1 10 1 au K 2 −1/2 s

−2 1.5

102 1 (diameter)

0.5 10 log 0 101 Thermal inertia (Jm −0.5

−1

100 −1.5 1 2 3 4 5 6 Mid helioc. distance of the observations (au)

Fig. 6. Thermal inertia vs. average heliocentric distance. We include values compiled from the literature (references given in the text). The lines correspond to Eq. 1 using diﬀerent values of Γ1 au and the classically assumed α = −0.75. 104 3.5 α=−2.2 (R18), Γ = 10 SI u α Γ1 au =−2.2 (R18), 1 au = 50 SI u 3 α=−2.2 (R18), Γ = 150 SI u α Γ1 au =−2.2 (R18), 1 au = 500 SI u ) 2.5 3 α=−2.2 (R18), Γ = 1000 SI u −1 10 α Γ1 au K =−2.2 (R18), = 2000 SI u 1 au 2 −1/2 s

−2 1.5

102 1 (diameter)

0.5 10 log 0 101 Thermal inertia (Jm −0.5

−1

100 −1.5 1 2 3 4 5 6 Mid helioc. distance of the observations (au)

Fig. 7. Same as Fig. 6 but α = −2.2, which was found for near-Earth asteroid (1036) Ganymed by Rozitis et al. (2018). the emission of main-belt asteroids is closer to the 10-micron re- especially beneﬁt from the fact that surface roughness is not as gion of the spectrum, high-quality data at longer wavelengths dominant as thermal inertia at this wavelength range. like PACS data are also extremely useful to determine good- Acknowledgements. The research leading to these results has received funding quality sizes and thermal inertias; objects with large data sets from the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement number 687378 (SBNAF). C.K., R.S., A.F-T., and G.M.

Article number, page 6 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data ), we took the au 1 Γ ed in the IR red at 1 au ( Γ plot λ ect? Γ ff e level unless otherwise stated. For more T Γ plot plot plot. North. Hemisph. not sampled σ ∝ λ Γ 3000 facets) with the same spin axis. The λ λ Γ ∼ Γ Γ plot plot. IR insensitive to albedo variegation plot. Southern hemisph. not sampled Γ λ λ λ , perhaps because shape is elongated Γ m data from analysis higher µ despite irregular shape . Requires 8% rescaling → Γ - 2 m χ D , but too high ot constrained at the 1 2 m χ , despite large dataset. level. Few data but low pole obliquity 2 m χ 9. Possible rotational phase shift (see Sect.A.4) and similar σ . minimum, slope in the OMR-vs-wavelength plot 0 2 m 2 χ < χ but unrealistically high , formally acceptable fit too, but significantly higher Γ 2 2 m rms 0.2 at 3 χ χ 5% larger than ADAM < > too high, although in agreement with the SAGE results ∼ 4 2 m . D Comments Modelled PACS data only Similar conclusion but larger errorAKARI bars data show a small slope in the OMR vs. Feature in the OMR-vs-aspect angleFormally plot acceptable fit, consistent thermalFormally properties acceptable fit, consistent thermalShallow properties Formally acceptable fit IRAS data: slope in theLow OMR vs. IRAS data: slope in theVirtually OMR the vs. same results Shallow and asymmetric Similar fit, but only smallrms rescaling required (2%) Lower No mirror solution can beχ rejected. Very low roughness favou 0 Spherical approximation fails IRAS data: strong slope inFormally the acceptable OMR fit vs. but significantlyVery higher shallow Sphere greatly overestimates diameter and Few data, Southern hemisphere notFormally well acceptable sampled fit, in but the inconsistent IRRequired data 12% rescaling. Southern hemisphereFormally not acceptable well fit, sampl size inIRAS better data: agreement slight with slope ADAM inVery the low OMR vs. Removed MSX and IRAS 12- Sphere gets lower IRAS data: slope in theBad OMR fit vs. IRAS data: slight slope inLow the OMR vs. au ce roughness (rms) of the corresponding model. To normalise 1 147 pe models. Spherical model refers to a sphere ( Γ (SI units) (au) 2.802.95 43 2.70 67 126 2.362.20 66 3.02 90 2.35 114 2.45 95 2.40 78 2.40 67 2.55 20 3.05 50 2.60 23 3.30 20 3.00 73 3.01 137 3.07 57 3.35 93 87 ¯ r 3 2 2 2 m χ 1.1 0.5 0.9 0.2 0.6 1.0 0.3 1.1 0.8 1.1 0.5 0.5 0.6 > > > 0.65 1 0.2 1 0.5 1 0.3 1 1.27 0.4 0.4 0.9 0.6 0.4 0.4 0.5 0.5 0.3 0.2 0.9 0.3 0.2 0.5 0.5 0.4 0.6 0.7 0.9 0.8 0.2 0.45 0.65 0.4 0.50 0.5 0.45 0.7 0.45 0.6 ∼ ∼ ∼ ∼ (rms) ¯ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ρ which the data were taken. The surface roughness (rms) were n 40 40 40 50 10 40 80 50 70 45 15 10 15 15 15 15 25 20 20 30 35 30 20 25 25 25 15 44 30 40 30 15 45 5 10 13 25 10 22 10 30 45 10 15 20 15 15 25 15 35 30 10 30 20 15 17 10 2 35 10 55 23 30 40 25 10 + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − Γ 70 25 30 50 60 80 50 50 55 50 80 40 20 25 10 10 75 30 50 60 60 25 40 35 10 25 35 70 35 120 100 100 120 9 7 5 5 3 4 2 3 3 3 2 2 2 1 7 4 5 6 4 1 2 1 3 2 2 9 3 2 3 3 4 3 2 2 4 3 4 2 5 6 2 2 3 2 3 3 2 2 3 4 7 4 3 4 2 2 21 9 20 13 12 6 10 7 1 1 + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − D 146104 35 60 342 200 1.6 205 150 98 (km) (SI units) 951 536 545 252 255 254 142 147 441 445 135 143 219 219 147 202 208 317 153 161 277 292 221 219 167 162 200 307 949 520 520 328 denote the best-fitting diameter, thermal inertia and surfa ρ 0 D (km) is the sphere-equivalent diameter of the ADAM or in-situ sha ) and 1 0 − D K 2 / 1 − s 2 − J m = Spherical model Spherical modelSpherical – modelSAGE – Spherical modelSpherical – model – Spherical – modelSpherical – modelSpherical – modelSpherical – modelSpherical – model Spherical model Spherical modelSpherical – modelSpherical – model Spherical model Spherical model Spherical model Spherical model (SI units ) between the shortest and longest heliocentric distance at Γ r , Summary of TPM results. D Asteroid(1) Ceres Model (2) Pallas Dawn(3) SPC Juno ADAM(4) 939.5 Vesta ADAM(8) Flora 520 Gaskell(10) Hygiea 248 (18) ADAM Melpomene ADAM ADAM(19) Fortuna 522 (20) Massalia 143 ADAM 433.6 146 (21) Lutetia SAGE1(29) Amphitrite Jorda 212 ADAM(52) Europa – (54) Alexandra ADAM 205.5 ADAM 98.15 (65) Cybele(88) Thisbe ADAM 313.7 (93) 143. Minerva ADAM(423) Diotima ADAM 313.3 (511) Davida ADAM 220 ADAM 160 209 313 symbols Table 2. mid-point (¯ information we refer to Appendix A and Table A.1.

Article number, page 7 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv have been supported by the K-125015 and GINOP-2.3.2-15-2016-0000 grants Müller, T. G. & Barnes, P. J. 2007, A&A, 467, 737 of the National Research, Development and Innovation Office (NKFIH), Hun- Müller, T. G. & Blommaert, J. A. D. L. 2004, A&A, 418, 347 gary. P. Santos-Sanz acknowledges financial support by the Spanish grant AYA- Müller, T. G., Herschel Calibration Steering Group, & ASTRO-F Calibration RTI2018-098657-J-I00 (MCIU/AEI/FEDER, UE). R. Duffard and P. Santos- Team. 2005a, in ESA Special Publication, Vol. 577, ESA Special Publication, Sanz acknowledge financial support from the State Agency for Research of the ed. A. Wilson, 471–472 Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the Müller, T. G. & Lagerros, J. S. V. 1998, A&A, 338, 340 Instituto de Astrofíica de Andalucía (SEV-2017-0709); they also acknowledge Müller, T. G., Marciniak, A., Kiss, C., et al. 2018, Advances in Space Research, financial support by the Spanish grant AYA-2017-84637-R and the Proyecto de 62, 2326 Excelencia de la Junta de Andalucía J.A. 2012-FQM1776. Müller, T. G., Sekiguchi, T., Kaasalainen, M., Abe, M., & Hasegawa, S. 2005b, A&A, 443, 347 Müller, T. G., Durech,ˇ J., Ishiguro, M., et al. 2017, A&A, 599, A103 Murakami, H., Baba, H., Barthel, P., et al. 2007, PASJ, 59, S369 References Nielbock, M., Müller, T., Klaas, U., et al. 2013, Experimental Astronomy, 36, 631 Alí-Lagoa, V., Delbo’, M., & Libourel, G. 2015, ApJ, 810, L22 O’Rourke, L., Müller, T., Valtchanov, I., et al. 2012, Planet. Space Sci., 66, 192 Alí-Lagoa, V., Lionni, L., Delbo, M., et al. 2014, A&A, 561, A45 Oszkiewicz, D. A., Muinonen, K., Bowell, E., et al. 2011, Alí-Lagoa, V., Müller, T. G., Usui, F., & Hasegawa, S. 2018, A&A, 612, A85 J. Quant. Spectr. Rad. Transf., 112, 1919 Bach, Y. P., Ishiguro, M., & Usui, F. 2017, AJ, 154, 202 Park, R. S., Vaughan, A. 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Article number, page 8 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

Appendix A: Thermo-physical model analysis approach we use. Nonetheless, we leave it to future work to re- visit the data with additional observations and better constraints In this section we provide all observation-to-modelratio (OMR) on spectral emissivity. plots to help further examine the fits. Table A.1 links each target to its corresponding plots. Some targets warrant a short subsec- tion with relevant comments in addition to those of Table 2. Appendix A.2: (2) Pallas The ADAM shape fits the 80 PACS data with a very lowχ ¯2 Table A.1. List of targets and references to the corresponding figures. min (lower than 0.1) with extremely high roughness and a thermal inertia of 30 Jm−2 s−1/2K−1. Nevertheless, we find indications Target OMR plots of small shape model inaccuracies given it cannot reproduce all data equally well when we fix the scale (see the main text). (1)Ceres Fig.A.1 (2)Pallas Fig.A.2 (3)Juno Figs.A.3andA.4 Appendix A.3: (3) Juno (4) Vesta Fig. A.5 The OMR plots present systematics within the 10% error mar- (8)Flora Fig.A.6 gins. From the aspect angle plot, we infer that the northern (10)Hygiea Fig.A.7 hemisphere part of the shape model could have an artefact, and (18) Melpomene Fig. A.8 the wavelength plot shows a slight "convex up" curvature. The (19)Fortuna Fig.A.9 SAGE model provides a borderline formally acceptable fit and (20)Massalia Fig.A.10 shows more scatter in the OMR plots and larger parameter error (21)Lutetia Fig.A.12 bars, which means the shape is not optimal (the rotational pa- (29)Amphitrite Fig. A.13 rametersare virtually the same). The trends in the OMR plots are (52)Europa Fig.A.14 slightly blurred to the eye due to the higher scatter. Nonetheless, (54)Alexandra Fig.A.15 the best-fitting values of size and gamma are fully compatible (65)Cybele Fig.A.16 within the error bars, but the ADAM ones are still better con- (88)Thisbe Fig.A.17 strained. The same can be said about the scatter in the plots cor- (93)Minerva Fig.A.18 responding to the sphere (which does slightly better than SAGE (423)Diotima Fig.A.19 in terms of χ2, but not statistically significantly). (511)Davida Fig.A.20

Appendix A.4: (21) Lutetia For this target we incorporated most of the data featured in O’Rourke et al. (2012) in our analysis, for example Spitzer In- Appendix A.1: (1) Ceres frared Array Camera (IRAC) fluxes, with the notable exception 2 of Herschel SPIRE fluxes, which we did not model in this work. The 180 PACS data points are fitted with a very lowχ ¯min −2 −1/2 −1 As expected, our results for Lutetia are fully consistent with the of 0.2 with Γ = 25Jm s K , an extremely high rough- previous work. O’Rourke et al. suggest that a localised inaccu- ness of rms∼1, and a rescaling of about +2% of the original racy in the shape model, which is after all based on data that did ADAM shape. This thermal inertia is higher than but com- not cover 100% of Lutetia’s surface, is responsible for the inabil- patible within the error bars with classical TPM results (10 ± ity of the TPM model to fully reproduce the October 17 IRAC 10Jm−2 s−1/2K−1; Müller & Lagerros 1998) and Dawn-based −2 −1/2 −1 thermal light curve (see their Fig. 4). Here we also considered an analyses (< 20Jm s K ; Rognini 2018). If we fit the data offset in the rotational zero-phase as a possible explanation, so while keeping the Dawn stereo-photoclinometry (SPC) shape +9 −2 −1/2 −1 we repeated the analysis with a delay of 20 degrees.As Fig. A.11 fixed, we obtain a lower thermal inertia of 6−6 Jm s K and shows, the maxima and minima of the model were better aligned roughness values lower than rms∼0.35 are rejected at the 3σ with both IRAC light curves but the overall flux levels of the Oc- level. tober 17 one were still not matched. Nevertheless, this mismatch We find systematically higher thermal inertias when we is small, on average 5% (pink OMRs at aspect angle close to 40 model only PACS data and optimise the diameter, although the degreesin the fourth panel of Fig. A.12), and a possible localised results are not statistically significantly different (1-σ regions in inaccuracy in the shape-model still cannot be ruled out. the χ2 vs. Γ plots overlap). Actually, for targets with such a rich PACS data set as Ceres, we can fit data from the three PACS fil- ters separately. We found Γ= 35, 40, and 50 Jm−2 s−1/2K−1with Appendix B: Herschel PACS observations the 70, 100, and 160 µm data. Although the trend is not statistically significant – our χ2 minima still overlap within the We refer the reader to the caption of Table B.1. ranges of formally acceptable fits – it could be caused by the fact that the longer wavelengths probe deeper and perhaps more compacted layers of the subsurface. However, it could also be an artefact related to our assumption of a constant emissivity of 0.9 if the (spectral) emissivity at the PACS wavelengths was lower, but previous work by Müller (2002) suggests that the effect should only be significant at wavelengths much longer than that of PACS. Indeed, Müller et al. (2014) were able to reproduce even Herschel Spectral and Photometric Imaging Receiver (SPIRE) data at 250, 350 and 500 µm with the same modelling

Article number, page 9 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv

180 180 SPC (only PACS data) ADAM (only PACS data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 10 100 10 100 Wavelength (micron) Wavelength (micron) 160 160 SPC (only PACS data) ADAM (only PACS data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 2.6 2.8 3 3.2 3.4 3.6 Heliocentric distance (au) Heliocentric distance (au) 180 180 SPC (only PACS data) ADAM (only PACS data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase 160 160 SPC (only PACS data) ADAM (only PACS data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degrees) Aspect angle (north pole-view at 0 degress) 160 160 SPC (only PACS data) ADAM (only PACS data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

-40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degrees) Phase angle (degree) Fig. A.1. (1) Ceres: From top to bottom, observation-to-model ratios Fig. A.2. (2) Pallas. See the caption in Fig. A.1. vs. wavelength, heliocentric distance, rotational phase, and phase angle. The colour bar corresponds either to the aspect angle or to the wavelength at which each observation was taken.

Article number, page 10 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

180 180 ADAM (all data) SAGE (all data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 10 100 10 100 Wavelength (micron) Wavelength (micron) 160 160 ADAM (all data) SAGE (all data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

2 2.2 2.4 2.6 2.8 3 3.2 3.4 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Heliocentric distance (au) Heliocentric distance (au) 180 180 ADAM (all data) SAGE (all data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase 160 160 ADAM (all data) SAGE (all data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) Aspect angle (North=0 degress) 160 160 ADAM (all data) SAGE (all data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

-40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Phase angle (degree) Fig. A.3. (3) Juno (ADAM model). See the caption in Fig. A.1. Fig. A.4. (3) Juno (SAGE model). See the caption in Fig. A.1.

Article number, page 11 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv

180 2 180 Gaskell (PACS) ADAM (all data) 1.4 160 160

140 140 1.5 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod Aspect angle (deg.) 60 60 Aspect angle (deg.) 0.8 0.5 40 40

0.6 20 20

0 0 0 10 100 10 100 Wavelength (micron) Wavelength (micron)

160 2 160 Gaskell (PACS) ADAM (all data) 1.4 140 140

120 1.5 120 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) 0.8 Wavelength (micron) 0.5 40 40

0.6 20 20

0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 Heliocentric distance (au) Heliocentric distance (au)

180 2 180 Gaskell (PACS) ADAM (all data) 1.4 160 160

140 140 1.5 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod Aspect angle (deg.) 60 60 Aspect angle (deg.) 0.8 0.5 40 40

0.6 20 20

0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase

160 2 160 Gaskell (PACS) ADAM (all data) 1.4 140 140

120 1.5 120 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) 0.8 Wavelength (micron) 0.5 40 40

0.6 20 20

0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degrees) Aspect angle (North=0 degress)

160 2 160 Gaskell (PACS) ADAM (all data) 1.4 140 140

120 1.5 120 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) 0.8 Wavelength (micron) 0.5 40 40

0.6 20 20

0 -40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degrees) Phase angle (degree) Fig. A.5. (4) Vesta. See the caption in Fig. A.1. Fig. A.6. (8) Flora. See the caption in Fig. A.1.

Article number, page 12 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

2 180 180 ADAM (all data) ADAM (all data) 160 1.4 160

140 140 1.5 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.5 40 40

20 0.6 20

0 0 0 10 100 10 100 Wavelength (micron) Wavelength (micron) 2 160 160 ADAM (all data) ADAM (all data) 1.4 140 140

1.5 120 120 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

Wavelength (micron) 0.8 Wavelength (micron) 0.5 40 40

20 0.6 20

0 2.6 2.8 3 3.2 3.4 3.6 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Heliocentric distance (au) Heliocentric distance (au) 2 180 180 ADAM (all data) ADAM (all data) 160 1.4 160

140 140 1.5 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.5 40 40

20 0.6 20

0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase 2 160 160 ADAM (all data) ADAM (all data) 1.4 140 140

1.5 120 120 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

Wavelength (micron) 0.8 Wavelength (micron) 0.5 40 40

20 0.6 20

0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) Aspect angle (North=0 degress) 2 160 160 ADAM (all data) ADAM (all data) 1.4 140 140

1.5 120 120 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

Wavelength (micron) 0.8 Wavelength (micron) 0.5 40 40

20 0.6 20

0 -40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Phase angle (degree) Fig. A.7. (10) Hygiea. See the caption in Fig. A.1. Fig. A.8. (18) Melpomene. See the caption in Fig. A.1.

Article number, page 13 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv

180 180 ADAM (all data) SAGE 1 (excluded IRAS data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 10 100 10 100 Wavelength (micron) Wavelength (micron) 160 160 ADAM (all data) SAGE 1 (excluded IRAS data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Heliocentric distance (au) Heliocentric distance (au) 180 180 ADAM (all data) SAGE 1 (excluded IRAS data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase 160 160 ADAM (all data) SAGE 1 (excluded IRAS data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) Aspect angle (North=0 degress) 160 160 ADAM (all data) SAGE 1 (excluded IRAS data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

-40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Phase angle (degree) Fig. A.9. (19) Fortuna. See the caption in Fig. A.1. Fig. A.10. (20) Massalia (SAGE model 1). Similar plots were obtained for the second mirror solution.

Article number, page 14 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

8 2 180 IRAC data (MDJ=54391) Jorda (Farnham et al. 2013) IRAC data (MDJ=54771) 7.5 Shifted rot. zero point 160 140 7 1.5 120 6.5 100 6 1 80 Obs/Mod Flux (Jy) 5.5

60 Aspect angle (deg.) 5 0.5 40

4.5 20

4 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 100 Rotational phase Wavelength (micron) 2 100 Fig. A.11. Spitzer IRAC thermal light curve of (21) Lutetia (λ = 7.872 Jorda (Farnham et al. 2013) 90 µm) and our best-fitting model fluxes. O’Rourke et al. (2012) provide 80 details of the observations. MDJ is the modified Julian date, the first 1.5 one (crosses) corresponding to October 17 2007 15:13 UT, the second 70 one (empty squares) to October 31 2008 19:58 UT. 60 1 50 Obs/Mod 40 Wavelength (micron) 0.5 30 20

10 0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Heliocentric distance (au) 2 180 Jorda (Farnham et al. 2013) 160

140 1.5 120

100 1 80 Obs/Mod

60 Aspect angle (deg.) 0.5 40

0 0 0 0.2 0.4 0.6 0.8 1 Rotational phase 2 160 Jorda (Farnham et al. 2013) 140

1.5 120

100

1 80 Obs/Mod 60 Wavelength (micron) 0.5 40

0 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) 2 160 Jorda (Farnham et al. 2013) 140

1.5 120

100

1 80 Obs/Mod 60 Wavelength (micron) 0.5 40

0 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Fig. A.12. (21) Lutetia. See the caption in Fig. A.1.

Article number, page 15 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv

180 180 ADAM (all data) ADAM (all data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 10 100 10 100 Wavelength (micron) Wavelength (micron) 160 160 ADAM (all data) ADAM (all data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

2.35 2.4 2.45 2.5 2.55 2.6 2.65 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 Heliocentric distance (au) Heliocentric distance (au) 180 180 ADAM (all data) ADAM (all data) 1.4 160 1.4 160

140 140 1.2 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.8 40 40

0.6 20 0.6 20

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase 160 160 ADAM (all data) ADAM (all data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) Aspect angle (North=0 degress) 160 160 ADAM (all data) ADAM (all data) 1.4 1.4 140 140

120 120 1.2 1.2 100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60

0.8 Wavelength (micron) 0.8 Wavelength (micron) 40 40

0.6 20 0.6 20

-40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Phase angle (degree) Fig. A.13. (29) Amphitrite. See the caption in Fig. A.1. Fig. A.14. (52) Europa. See the caption in Fig. A.1.

Article number, page 16 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

180 2 180 ADAM (all data) ADAM (all data) 1.4 160 160

140 140 1.5 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.5 40 40

0.6 20 20

0 0 0 10 100 10 100 Wavelength (micron) Wavelength (micron) 160 2 100 ADAM (all data) ADAM (all data) 1.4 140 90 80 120 1.5 1.2 70 100 60 1 1 80 50 Obs/Mod Obs/Mod 60 40

0.8 Wavelength (micron) Wavelength (micron) 0.5 30 40 20 0.6 20 10 0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 2.6 2.8 3 3.2 3.4 3.6 Heliocentric distance (au) Heliocentric distance (au) 180 2 180 ADAM (all data) ADAM (all data) 1.4 160 160

140 140 1.5 1.2 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod

60 Aspect angle (deg.) 60 Aspect angle (deg.) 0.8 0.5 40 40

0.6 20 20

0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase 160 2 100 ADAM (all data) ADAM (all data) 1.4 140 90 80 120 1.5 1.2 70 100 60 1 1 80 50 Obs/Mod Obs/Mod 60 40

0.8 Wavelength (micron) Wavelength (micron) 0.5 30 40 20 0.6 20 10 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) Aspect angle (North=0 degress) 160 2 100 ADAM (all data) ADAM (all data) 1.4 140 90 80 120 1.5 1.2 70 100 60 1 1 80 50 Obs/Mod Obs/Mod 60 40

0.8 Wavelength (micron) Wavelength (micron) 0.5 30 40 20 0.6 20 10 0 -40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Phase angle (degree) Fig. A.15. (54) Alexandra. See the caption in Fig. A.1. Fig. A.16. (65) Cybele. See the caption in Fig. A.1.

Article number, page 17 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv

2 180 2 180 ADAM (all data) ADAM (O02) 160 160

140 140 1.5 1.5 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod Aspect angle (deg.) 60 Aspect angle (deg.) 60 0.5 0.5 40 40

20 20

0 0 0 0 10 100 10 100 Wavelength (micron) Wavelength (micron)

2 160 2 160 ADAM (all data) ADAM (O02) 140 140

1.5 120 1.5 120

100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) Wavelength (micron) 0.5 0.5 40 40

20 20

0 0 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 2.9 2.95 3 3.05 3.1 3.15 Heliocentric distance (au) Heliocentric distance (au)

2 180 2 180 ADAM (all data) ADAM (O02) 160 160

140 140 1.5 1.5 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod Aspect angle (deg.) 60 Aspect angle (deg.) 60 0.5 0.5 40 40

20 20

0 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase

2 160 2 160 ADAM (all data) ADAM (O02) 140 140

1.5 120 1.5 120

100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) Wavelength (micron) 0.5 0.5 40 40

20 20

0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) Aspect angle (North=0 degress)

2 160 2 160 ADAM (all data) ADAM (O02) 140 140

1.5 120 1.5 120

100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) Wavelength (micron) 0.5 0.5 40 40

20 20

0 0 -40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Phase angle (degree) Fig. A.17. (88) Thisbe. See the caption in Fig. A.1. Fig. A.18. (93) Minerva. See the caption in Fig. A.1. Here, O02 is an in- ternal code referring to the best-ﬁtting model to a subset of data. In this case, all MSX observations and 12-micron IRAS data were not modelled because they could not be approximated by any model and they led to extremely high values of thermal inertia and surface roughness.

Article number, page 18 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data

2 180 2 180 ADAM (all data) ADAM (all data) 160 160

140 140 1.5 1.5 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod Aspect angle (deg.) 60 Aspect angle (deg.) 60 0.5 0.5 40 40

20 20

0 0 0 0 10 100 10 100 Wavelength (micron) Wavelength (micron)

2 160 2 160 ADAM (all data) ADAM (all data) 140 140

1.5 120 1.5 120

100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) Wavelength (micron) 0.5 0.5 40 40

20 20

0 0 2.95 3 3.05 3.1 3.15 3.2 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Heliocentric distance (au) Heliocentric distance (au)

2 180 2 180 ADAM (all data) ADAM (all data) 160 160

140 140 1.5 1.5 120 120

100 100 1 1 80 80 Obs/Mod Obs/Mod Aspect angle (deg.) 60 Aspect angle (deg.) 60 0.5 0.5 40 40

20 20

0 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Rotational phase Rotational phase

2 160 2 160 ADAM (all data) ADAM (all data) 140 140

1.5 120 1.5 120

100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) Wavelength (micron) 0.5 0.5 40 40

20 20

0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Aspect angle (North=0 degress) Aspect angle (North=0 degress)

2 160 2 160 ADAM (all data) ADAM (all data) 140 140

1.5 120 1.5 120

100 100

1 80 1 80 Obs/Mod Obs/Mod 60 60 Wavelength (micron) Wavelength (micron) 0.5 0.5 40 40

20 20

0 0 -40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 Phase angle (degree) Phase angle (degree) Fig. A.19. (423) Diotima. See the caption in Fig. A.1. Fig. A.20. (511) Davida. See the caption in Fig. A.1.

Article number, page 19 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv (deg.) α be retrievable (au) ∆ is the reference wavelength the distance to the observer, λ ∆ , (au) e t r and s t (Jy) λ f σ (Jy) λ f the heliocentric distance, r m) et al. (2014), and Müller et al. (2014) for details on the data µ ( λ nd the observer. egies for a subset of the observations. These fluxes will also s of the observations are denoted by error (Jy) λ i f h the absolute calibration error, λ (Jy) f λ i σ f h lue 51.7010reen 29.5331lue 0.5174 52.2075 0.2960lue 51.9514reen 0.5221 70 29.0989 100 51.444reen 0.5195 28.813 2.673 28.6849 0.2910reen 1.497 70 2.037 17.1489 51.948 0.2869reen 2.037 1.765 70 2.699 16.7354 1.765 100 51.693 0.1727reen -29.2 28.389 2.037 -29.2 2.686 16.5611 100 0.1674lue 1.765 1.475 27.985 2.037 100 29.6065 0.1657lue 2.037 -29.2 1.765 1.454 16.731 1.765 100 28.8168lue 2.037 -29.2 0.2968 0.870 16.327 -29.2 1.765 100 28.7475lue 2.579 0.2882 0.848 16.157 -29.2 2.249 18.8670lue 2.579 0.2875 0.840 70 22.4 2.249 29.459 18.5508lue 2.579 0.1898 70 1.531 22.4 2.249 28.673 18.3362reen 0.1856 70 2.579 1.490 10.8492 22.4 28.605reen 0.1834 2.249 70 2.579 1.486 10.6099 18.773 0.1103reen 22.4 2.249 70 2.579 0.976 10.6425 18.459 0.1062reen 22.4 2.249 70 2.962 0.959 100 18.245 6.4966 0.1065reen 22.4 2.637 10.585 2.962 0.948 100 6.3771reen -20.0 0.0680 2.637 0.550 10.351 2.962 100 6.3012lue 2.962 -20.0 0.0640 2.637 0.538 10.383 2.637 10.8593lue 100 2.962 -20.0 0.0632 0.539 -20.0 2.637 6.338 10.7859 100 2.962 0.1106 -20.0 0.330 2.638 6.222 100 0.1079 3.327 -20.0 0.323 6.147 3.386 70 3.327 0.320 10.805 17.0 3.386 70 3.327 0.562 10.732 17.0 3.386 3.327 0.558 17.0 3.386 3.327 17.0 3.386 17.0 eded 13.3162ed 13.1645 0.1430ed 13.3157 0.1415ed 13.2663 160 0.1338 12.562ed 13.2155 160 0.1333 0.655 12.419ed 13.2325 160 0.1328 2.037 0.647 12.562ed 1.765 160 7.6438 0.1330 2.037 0.653 12.515ed -29.2 1.765 160 7.6058 2.037 0.0924 0.650 12.467ed -29.2 1.765 160 7.5155 2.037 0.0772 0.648 12.483ed -29.2 1.765 7.4187 160 2.037 0.0763 0.649ed -29.2 1.765 7.211 7.4678 160 2.037 0.0906ed -29.2 0.378 1.765 7.175 7.3943 160 0.0758 2.579ed -29.2 0.373 7.090 4.9989 160 0.0751 2.249 2.579ed 0.369 6.999 5.0019 160 22.4 0.0721 2.249 2.579ed 0.367 7.045 4.9581 160 22.4 0.0517 2.249 2.579ed 0.366 6.976 4.9059 160 22.4 0.0513 2.249 2.579ed 0.363 4.716 4.9400 160 22.4 0.0715 2.249 2.579ed 0.250 4.719 4.9384 160 22.4 0.0511 2.249 2.962ed 0.245 4.678 2.6352 160 22.4 0.0511 2.637 2.962ed 0.243 4.628 2.9479 160 -20.0 0.0583 2.637 2.962ed 0.245 4.660 2.9349 160 -20.0 0.0322 2.637 2.962 0.242 4.659 2.5795 160 -20.0 0.0321 2.637 2.962 0.242 2.486 160 -20.0 0.0580 2.637 2.962 0.138 2.781 160 -20.0 2.638 3.327 0.145 2.769 160 -20.0 3.386 3.327 0.144 2.433 17.0 3.386 3.327 0.136 17.0 3.386 3.327 17.0 3.386 17.0 (JD) Band e ork. See Müller et al. (2005b), Nielbock et al. (2013),Balog t the colour-corrected flux density, vector product between versors from the asteroid to the Sun a λ f the reduction approach, which required non-standard strat ther data and all relevant references. The start and end time (JD) s t the calibrated in-band flux and its error, λ i f h σ and λ i f h Herschel Space Observatory PACS observations used in this w phase angle. The sign of the phase angle is given by that of the Target(3) Juno Obs. ID 1342188358 ChopNod Obs. mode 2455186.74250 2455186.74297 b (3) Juno(3) Juno(3) Juno(3) Juno(3) Juno 1342188358(3) Juno 1342188359 ChopNod(3) Juno 1342188359 ChopNod(3) Juno 2455186.74250 1342188360 ChopNod(3) Juno 2455186.74510 2455186.74297 1342188360 Scanmap(3) Juno 2455186.74510 2455186.74557 1342188361 Scanmap r (3) Juno 2455186.74776 2455186.74557 1342188361 Scanmap g (3) Juno 2455186.74776 1342188362 Scanmap 2455186.75040 r (3) Juno 2455186.75143 1342188362 Scanmap 2455186.75040 b (3) Juno 2455186.75143 1342188363 Scanmap 2455186.75407 r (3) Juno 2455186.75510 1342188363 Scanmap 2455186.75407 b (3) Juno 2455186.75510 1342211811 Scanmap 2455186.75774 r (3) Juno 2455186.75877 1342211811 ChopNod 2455186.75774 g (3) Juno 2455186.75877 1342211812 ChopNod 2455186.76140 r (3) Juno 2455558.62998 1342211812 Scanmap 2455186.76140 g (3) Juno 2455558.62998 2455558.63045 1342211813 Scanmap r (3) Juno 2455558.63263 2455558.63045 1342211813 Scanmap g (3) Juno 2455558.63263 1342211814 Scanmap 2455558.63564 r (3) Juno 2455558.63667 1342211814 ChopNod 2455558.63564 g (3) Juno 2455558.63667 1342211815 ChopNod 2455558.63968 r (3) Juno 2455558.64066 1342211815 Scanmap 2455558.63968 g (3) Juno 2455558.64066 2455558.64113 1342211816 Scanmap r (3) Juno 2455558.64332 2455558.64113 1342211816 Scanmap b (3) Juno 2455558.64332 1342221855 Scanmap 2455558.64632 r (3) Juno 2455558.64736 1342221855 ChopNod 2455558.64632 b (3) Juno 2455558.64736 1342221856 ChopNod 2455558.65036 r (3) Juno 2455710.81815 1342221856 Scanmap 2455558.65036 b (3) Juno 2455710.81815 2455710.81862 1342221857 Scanmap r (3) Juno 2455710.82081 2455710.81862 1342221857 Scanmap b (3) Juno 2455710.82081 1342221858 Scanmap 2455710.82381 r (3) Juno 2455710.82484 1342221858 ChopNod 2455710.82381 b (3) Juno 2455710.82484 1342221859 ChopNod 2455710.82785 r (3) Juno 2455710.82883 1342221859 Scanmap 2455710.82785 b (3) Juno 2455710.82883 2455710.82930 1342221860 Scanmap r (3) Juno 2455710.83149 2455710.82930 1342221860 g Scanmap(3) Juno 2455710.83149 1342238893 2455710.83450 r Scanmap(3) Juno 2455710.83553 1342238893 ChopNod 2455710.83450 g (3) Juno 2455710.83553 1342238894 ChopNod 2455710.83854 r (3) Juno 2455967.40681 1342238894 Scanmap 2455710.83854 g (3) Juno 2455967.40681 2455967.40728 1342238895 Scanmap r 2455967.40946 2455967.40728 1342238895 Scanmap g 2455967.40946 1342238896 Scanmap 2455967.41247 r 2455967.41350 1342238896 ChopNod 2455967.41247 g 2455967.41350 1342238897 ChopNod 2455967.41651 r 2455967.41749 Scanmap 2455967.41651 g 2455967.41749 2455967.41796 r 2455967.42015 2455967.41796 b 2455967.42315 r b α and of the band, set and observing modes (Obs.from mode), the and SBNAF Kiss database (Szakáts et et al. al. (2014) 2020) on along with the o Table B.1.

Article number, page 20 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h lue 10.8523reen 7.9154reen 0.1086 7.9117reen 0.0816 7.8602lue 0.0793 70 10.798 13.5514lue 100 0.0788 0.561 7.722 13.6383lue 100 0.1371 3.327 0.402 7.719 13.6492lue 100 0.1364 3.386 3.324 0.401 7.668 16.2571lue 17.0 0.1366 3.078 70 3.324 0.399 13.484 15.9759lue -17.8 0.1639 3.078 70 3.324 0.701 13.570 15.8407reen -17.8 0.1598 3.078 70 3.324 0.705 13.581 9.2570reen -17.8 0.1585 3.078 70 3.324 0.706 16.176 9.0867reen -17.8 0.0947 3.079 70 3.324 0.841 15.896 9.0288 -17.8 0.0910 3.079 70 2.981 0.826 15.762 100 -17.8 0.0904 3.120 2.981 0.819 9.031 100 18.9 3.120 2.981 0.470 8.865 100 18.9 3.120 2.981 0.461 8.809 18.9 3.120 2.981 0.458 18.9 3.120 2.981 18.9 3.120 18.9 eded 2.9490ed 2.9314 0.0322ed 3.2891 0.0321ed 3.6666 160 0.0615ed 2.782 3.6610 160 0.0389ed 0.145 2.765 3.4365 160 0.0388 3.327ed 0.144 3.103 3.7076 160 0.0623 3.386 3.327ed 0.169 3.459 3.6961 160 17.0 0.0393 3.386 3.324ed 0.180 3.454 4.3142 160 17.0 0.0392 3.078 3.324ed 0.180 3.242 4.2627 160 -17.8 0.0676 3.078 3.324ed 0.175 3.498 4.2638 160 -17.8 0.0446 3.078 3.324ed 0.182 3.487 4.3432 160 -17.8 0.0446 3.078 3.324ed 0.182 4.070 4.2364 160 -17.8 0.0678 3.079 3.324 0.217 4.021 4.2200 160 -17.8 0.0443 3.079 2.981 0.209 4.022 160 -17.8 0.0442 3.120 2.981 0.209 4.097 160 18.9 3.120 2.981 0.218 3.997 160 18.9 3.120 2.981 0.208 3.981 18.9 3.120 2.981 0.207 18.9 3.120 2.981 18.9 3.120 18.9 blueredblue 6.1766red 1.6713blue 6.1504 0.0652red 1.6385blue 0.0546 6.1592 0.0650red 1.6594blue 0.0545 6.1750 0.0651 70red 1.7095 160blue 0.0546 6.1962 6.146 0.0652 70red 1.577 1.7046 160blue 0.0547 0.320 6.2185 6.120 0.0654 70red 0.096 1.546 1.7498 160blue 2.514 0.0547 0.319 6.2339 6.129 0.0656 2.514 70red 0.094 2.754 1.565 1.7314 160blue 2.514 0.0549 2.754 0.319 6.2627 6.144 0.0658 2.514 70red -21.7 0.095 2.754 1.613 1.6933 160 2.514blue -21.7 0.0548 2.754 0.320 6.2397 6.165 0.0661 2.514 70red -21.7 0.097 2.754 1.608 1.7033 160 2.514blue -21.7 0.0547 2.754 0.321 6.2860 6.188 0.0658 2.514 70red -21.7 0.097 2.754 1.651 1.7061 160 2.514 -21.7 0.0547 2.754 0.322 6.3377 6.203 0.0663 2.514 70 -21.7 0.099 2.754 1.633 1.6343 160 2.514 -21.7 0.0547 2.754 0.323 6.231 0.0668 2.514 70 -21.7 0.098 2.754 1.597 160 2.514 -21.7 0.0545 2.754 0.325 6.209 2.514 70 -21.7 0.096 2.754 1.607 160 2.514 -21.7 2.754 0.323 6.255 2.514 70 -21.7 0.097 2.754 1.609 160 2.514 -21.7 2.754 0.326 6.306 2.514 -21.7 0.097 2.754 1.542 2.514 -21.7 2.754 0.328 2.514 -21.7 0.094 2.754 2.514 -21.7 2.754 2.514 -21.7 2.754 -21.7 2.754 -21.7 -21.7 (JD) Band e t (JD) s t continued. Target(3) Juno Obs. ID 1342238897 Scanmap Obs. mode 2455967.42015 2455967.42315 r (3) Juno(3) Juno(3) Juno(3) Juno(3) Juno 1342238898(3) Juno 1342238898 Scanmap(3) Juno 1342249295 Scanmap(3) Juno 2455967.42419 1342249295 ChopNod(3) Juno 2455967.42419 1342249296 ChopNod 2455967.42719(3) Juno 2456149.60314 1342249296 Scanmap 2455967.42719 b (3) Juno 2456149.60314 2456149.60361 1342249297 Scanmap r (3) Juno 2456149.60579 2456149.60361 1342249297 Scanmap g (3) Juno 2456149.60579 1342249298 Scanmap 2456149.60880 r (3) Juno 2456149.60983 1342249298 ChopNod 2456149.60880 g (3) Juno 2456149.60983 1342249299 ChopNod 2456149.61284 r (3) Juno 2456149.61382 1342249299 Scanmap 2456149.61284 g (3) Juno 2456149.61382 2456149.61429 1342249300 Scanmap r (3) Juno 2456149.61648 2456149.61429 1342249300 Scanmap b (3) Juno 2456149.61648 1342269819 Scanmap 2456149.61948 r (3) Juno 2456149.62052 1342269819 ChopNod 2456149.61948 b (3) Juno 2456149.62052 1342269820 ChopNod 2456149.62352 r (3) Juno 2456393.13257 1342269820 Scanmap 2456149.62352 b (3) Juno 2456393.13257 2456393.13304 1342269821 Scanmap r (3) Juno 2456393.13523 2456393.13304 1342269821 Scanmap b (3) Juno 2456393.13523 1342269822 Scanmap 2456393.13823 r (3) Juno 2456393.13927 1342269822 ChopNod 2456393.13823 b (8) Flora 2456393.13927 1342269823 ChopNod 2456393.14227 r (8) Flora 2456393.14325 1342269823 Scanmap 2456393.14227 b (8) Flora 2456393.14325 2456393.14372 1342269824 Scanmap r (8) Flora 2456393.14591 2456393.14372 1342269824 Scanmap g (8) Flora 1342182740 2456393.14591 Scanmap 2456393.14892 r (8) Flora 1342182740 2456393.14995 ChopNod 2456393.14892 g (8) Flora 1342182740 2456393.14995 ChopNod 2456393.15296 r (8) 2455066.93796 Flora 1342182740 ChopNod 2456393.15296 g (8) 2455066.93796 Flora 2455066.93844 1342182740 ChopNod r (8) 2455066.94178 Flora 2455066.93844 1342182740 ChopNod(8) 2455066.94178 Flora 2455066.94226 1342182740 ChopNod(8) 2455066.94560 Flora 2455066.94226 1342182740 ChopNod(8) 2455066.94560 Flora 2455066.94607 1342182740 ChopNod(8) 2455066.94942 Flora 2455066.94607 1342182740 ChopNod(8) 2455066.94942 Flora 2455066.94989 1342182740 ChopNod(8) 2455066.95324 Flora 2455066.94989 1342182740 ChopNod(8) 2455066.95324 Flora 2455066.95371 1342182740 ChopNod(8) 2455066.95706 Flora 2455066.95371 1342182740 ChopNod(8) 2455066.95706 Flora 2455066.95753 1342182740 ChopNod(8) 2455066.96088 Flora 2455066.95753 1342182740 ChopNod(8) 2455066.96088 Flora 2455066.96135 1342182740 ChopNod(8) 2455066.96470 Flora 2455066.96135 1342182740 ChopNod 2455066.96470 2455066.96517 1342182740 ChopNod 2455066.96852 2455066.96517 1342182740 ChopNod 2455066.96852 2455066.96899 1342182740 ChopNod 2455066.97234 2455066.96899 1342182740 ChopNod 2455066.97234 2455066.97281 ChopNod 2455066.97616 2455066.97281 2455066.97616 2455066.97663 2455066.97663 Table B.1.

Article number, page 21 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h blueredblue 6.3695red 1.6898blue 6.4189 0.0671red 1.6457blue 0.0547 6.4396 0.0675red 1.6297green 0.0545 6.4403 0.0677 70red 19.4082 1.5864 160green 0.0545 6.338 0.0677 70red 19.3260 1.594 8.6829 160 0.1951green 0.0544 0.330 6.387 70red 0.096 19.0954 1.552 8.6496 160 0.1933blue 2.514 0.1012 0.333 6.408 2.514 70red 0.094 2.754 1.538 100 8.6476 34.9219 160 0.1910blue 2.514 0.0875 2.754 0.334 6.408 18.935 2.514red -21.7 0.094 2.754 1.497 100 8.6279 34.3522 160blue 2.514 -21.7 0.0874 2.754 0.334 0.3498 0.984 18.855 2.514red -21.7 0.092 2.754 8.191 100 8.6584 34.2017 160green 2.514 -21.7 1.866 0.1007 2.754 0.3435 0.980 18.630 2.514red -21.7 0.428 2.755 1.413 8.160 8.6435 8.2184 160green -21.7 1.866 0.0876 2.755 0.3420 0.968 70 1.866red -21.7 0.424 -31.8 1.413 8.158 34.748 3.7545 8.2927 160green -21.7 1.866 0.0874 1.413 0.0846 70 1.866red 0.424 -31.8 1.806 1.413 8.139 34.181 3.7759 8.2514 160blue -31.8 0.0641 1.413 0.0831 70 1.866red 1.866 0.426 -31.8 1.776 8.168 34.032 3.7667 14.8185 160blue 100 -31.8 0.0399 1.413 0.0827 1.413 1.866red 1.866 0.425 1.768 8.154 8.018 3.7481 14.5872 160blue 100 -31.8 -31.8 0.0398 1.413 0.1497 1.413 1.866red 1.866 0.424 0.417 3.542 8.090 3.7682 14.5726 160green 100 -31.8 -31.8 0.0641 1.413 0.1459 1.413 1.866red 2.365 0.191 0.420 3.562 8.050 3.7922 6.6105 160green -31.8 -31.8 0.0399 1.413 0.1458 1.981 70 2.365red 2.365 0.185 0.418 3.554 14.745 2.9327 6.5169 160green -31.8 0.0401 1.981 24.4 0.0691 1.981 70 2.365red 2.365 0.185 0.766 3.536 14.515 3.0178 6.4885 160blue 24.4 0.0597 1.981 24.4 0.0654 1.981 70 2.365red 2.365 0.190 0.754 3.555 14.500 2.9977 11.6244 160blue 100 24.4 0.0329 1.981 24.4 0.0651 1.981 2.365red 2.365 0.185 0.753 3.578 6.449 2.9883 11.4300 160blue 100 24.4 0.0327 1.981 24.4 0.1181 1.981 2.365red 2.365 0.186 0.336 2.767 6.358 2.9794 11.3862 160green 100 24.4 0.0600 1.981 24.4 0.1144 1.980 2.365red 2.525 0.152 0.330 2.847 6.330 2.9865 4.3902 160green 24.4 0.0325 1.980 24.4 0.1139 2.218 70 2.525red 2.525 0.148 0.329 2.828 11.567 1.9181 4.3461 160green -23.9 24.4 0.0326 2.218 0.0482 2.218 70 2.525 2.525 0.147 0.601 2.819 11.373 1.9979 4.2990 160 -23.9 -23.9 0.0554 2.218 0.0437 2.218 70 2.525 2.525 0.154 0.591 2.811 11.330 160 100 -23.9 -23.9 0.0238 2.218 0.0433 2.218 2.525 2.525 0.147 0.589 2.817 4.283 160 -23.9 100 -23.9 2.218 2.218 2.525 2.525 0.147 0.223 1.810 4.240 160 -23.9 100 -23.9 2.218 2.218 2.525 2.407 0.106 0.220 1.885 4.194 -23.9 -23.9 2.218 2.585 2.407 2.407 0.099 0.218 -23.9 2.585 22.8 2.585 2.407 2.407 22.8 2.585 22.8 2.585 22.8 22.8 (JD) Band e t (JD) s t continued. Target(8) Flora Obs. ID 1342182740 ChopNod Obs. 2455066.97998 mode 2455066.98045 (8) Flora(8) Flora(8) Flora(8) Flora(8) Flora 1342182740(8) Flora 1342182740 ChopNod(8) Flora 1342182740 ChopNod(8) 2455066.97998 Flora 1342182740 ChopNod(8) 2455066.98380 Flora 2455066.98045 1342182740 ChopNod(8) 2455066.98380 Flora 2455066.98427 1342182740 ChopNod(8) 2455066.98762 Flora 2455066.98427 1342182740 ChopNod(8) 2455066.98762 Flora 2455066.98809 1342210638 ChopNod(8) 2455066.99144 Flora 2455066.98809 1342210638 ChopNod(8) 2455066.99144 Flora 2455066.99191 1342210639 ChopNod(8) 2455531.73973 Flora 2455066.99191 1342210639 Scanmap(8) 2455531.73973 Flora 2455531.74021 1342210640 Scanmap(8) Flora 2455531.74239 2455531.74021 1342210640 Scanmap(8) Flora 2455531.74239 1342210641 Scanmap 2455531.74540 (8) Flora 2455531.74643 1342210641 ChopNod 2455531.74540 (8) Flora 2455531.74643 1342210642 ChopNod 2455531.74944 (8) 2455531.75042 Flora 1342210642 Scanmap 2455531.74944 (8) 2455531.75042 Flora 2455531.75089 1342210643 Scanmap(8) Flora 2455531.75307 2455531.75089 1342210643 Scanmap(8) Flora 2455531.75307 1342236950 Scanmap 2455531.75608 (8) Flora 2455531.75711 1342236950 ChopNod 2455531.75608 (8) Flora 2455531.75711 1342236951 ChopNod 2455531.76012 (8) 2455934.38240 Flora 1342236951 Scanmap 2455531.76012 (8) 2455934.38240 Flora 2455934.38287 1342236952 Scanmap(8) Flora 2455934.38505 2455934.38287 1342236952 Scanmap(8) Flora 2455934.38505 1342236953 Scanmap 2455934.38806 (8) Flora 2455934.38909 1342236953 ChopNod 2455934.38806 (8) Flora 2455934.38909 1342236954 ChopNod 2455934.39210 (8) 2455934.39308 Flora 1342236954 Scanmap 2455934.39210 (8) 2455934.39308 Flora 2455934.39355 1342236955 Scanmap(8) Flora 2455934.39574 2455934.39355 1342236955 Scanmap(8) Flora 2455934.39574 1342246945 Scanmap 2455934.39874 (8) Flora 2455934.39978 1342246945 ChopNod 2455934.39874 (8) Flora 2455934.39978 1342246946 ChopNod 2455934.40278 (8) 2456089.51768 Flora 1342246946 Scanmap 2455934.40278 (8) 2456089.51768 Flora 2456089.51816 1342246947 Scanmap(8) Flora 2456089.52034 2456089.51816 1342246947 Scanmap(8) Flora 2456089.52034 1342246948 Scanmap 2456089.52335 (8) Flora 2456089.52438 1342246948 ChopNod 2456089.52335 (8) Flora 2456089.52438 1342246949 ChopNod 2456089.52739 (8) 2456089.52837 Flora 1342246949 Scanmap 2456089.52739 (8) 2456089.52837 Flora 2456089.52884 1342246950 Scanmap(8) Flora 2456089.53103 2456089.52884 1342246950 Scanmap(8) Flora 2456089.53103 1342267585 Scanmap 2456089.53403 2456089.53506 1342267585 ChopNod 2456089.53403 2456089.53506 1342267586 2456089.53807 ChopNod 2456366.08142 1342267586 2456089.53807 Scanmap 2456366.08142 2456366.08190 1342267587 Scanmap 2456366.08408 2456366.08190 Scanmap 2456366.08408 2456366.08709 2456366.08812 2456366.08709 2456366.09113 Table B.1.

Article number, page 22 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h redbluered 1.9683blue 7.6828red 1.9436blue 0.0236 7.4917 0.0796red 1.9745 0.0555 7.4920 0.0750 1.9881 160 0.0236 0.0750 70 1.857 160 0.0238 7.645 70 0.097 1.834 160 0.398 7.454 2.407 70 0.107 1.863 160 2.407 2.585 0.387 7.455 2.407 0.098 2.585 1.876 2.407 22.8 2.585 0.387 2.407 0.098 22.8 2.585 2.407 22.8 2.585 2.407 22.8 2.585 22.8 2.585 22.8 22.8 823823 blue084 red084 46.5430 green429 red 12.0162 27.4459428 blue 0.4659610 red 12.1019612 0.1309 47.1886 0.2752 red blue 12.4594 0.1317 13.2821 0.4719 70 50.6065 160 100 46.311 0.1253 11.336 0.1335 26.776 2.406 0.5061 160 0.591 1.391 70 11.417 2.066 160 46.954 2.066 2.066 0.595 1.710 160 11.754 1.710 2.440 1.710 70 12.530 2.066 0.611 29.2 50.355 2.070 29.2 0.651 1.710 29.2 2.070 2.616 1.625 2.070 29.2 1.625 2.070 1.625 28.7 28.7 1.625 28.7 28.7 99639963 blue0223 red0223 12.0359 green0705 red 3.10640705 6.8973 blue 0.12221072 red 3.10751072 12.4995 blue 0.0606 0.07181439 red 3.21051439 12.5234 green 0.0606 0.1251 701806 red 11.976 3.17891806 7.0398 160 green 100 0.0346 0.1253 red 0.623 2.931 6.729 3.2046 6.9535 160 0.0343 0.0706 70 2.291 0.160 0.350 2.932 12.437 3.2273 160 0.0346 0.0697 2.057 70 2.291 2.291 0.160 0.646 3.029 12.461 160 100 -25.7 0.0348 2.057 2.057 2.291 2.291 0.158 0.647 2.999 6.868 160 -25.7 100 -25.7 2.057 2.057 2.291 2.291 0.156 0.357 3.023 6.784 160 -25.7 -25.7 2.057 2.057 2.291 2.291 0.158 0.352 3.045 -25.7 -25.7 2.057 2.058 2.291 2.291 0.159 -25.7 -25.7 2.058 2.058 2.291 -25.7 -25.7 2.058 -25.7 6506765067 blue65449 red65449 22.2603 blue65831 red 5.855165831 22.6012 blue 0.223666213 red 5.823066213 22.3633 blue 0.0783 0.227066595 red 5.917666595 22.4251 blue 0.0781 0.2246 7066977 red 22.150 5.877266977 22.1298 160 blue 0.0788 0.2252 7067359 red 1.151 5.524 22.489 5.873067359 22.6384 160 blue 0.0785 0.2223 7067741 red 1.905 0.291 1.169 5.493 22.252 5.960067741 22.6149 160 blue 0.0784 0.2274 1.622 7068123 1.905 red 1.905 0.290 1.156 5.583 22.314 5.924368123 22.5810 160 blue 0.0791 1.622 32.6 0.2271 1.622 7068504 1.905 red 1.905 0.294 1.160 5.545 22.020 5.868968504 22.3841 160 blue 32.6 0.0788 1.622 32.6 0.2268 1.622 7071359 1.905 red 1.905 0.292 1.144 5.541 22.526 5.899571359 22.5390 160 blue 32.6 0.0784 1.622 32.6 0.2248 1.622 70 1.905 red 1.905 0.292 1.171 5.623 22.502 5.9170 24.7791 160 32.6 0.0786 1.622 32.6 0.2264 1.622 70 1.905 1.905 0.296 1.169 5.589 22.469 6.2727 160 32.6 0.0788 1.622 32.6 0.2478 1.621 70 1.905 1.905 0.294 1.168 5.537 22.273 160 32.6 0.0641 1.621 32.6 1.621 70 1.905 1.905 0.292 1.157 5.566 22.427 160 32.6 1.621 32.6 1.621 70 1.905 1.905 0.293 1.165 5.582 24.656 160 32.6 1.621 32.6 1.621 1.905 1.905 0.294 1.281 5.918 32.6 1.621 32.6 1.621 1.905 1.905 0.308 32.6 1.621 32.6 1.621 1.905 32.6 1.621 32.6 32.6 (JD) Band e t (JD) s t continued. Target(8) Flora Obs. ID 1342267587 Scanmap Obs. mode 2456366.08812 2456366.09113 (8) Flora(8) Flora(8) Flora(8) Flora(8) Flora 1342267588(8) Flora 1342267588 ChopNod(18) Melpomene 1342267589 ChopNod(18) 2456366.09211 Melpomene 1342267589 1342179011 Scanmap(18) 2456366.09211 Melpomene 2456366.09258 1342267590 1342179011 Scanmap ChopNod(18) Melpomene 2456366.09476 2456366.09258 1342267590 1342179011 Scanmap ChopNod(18) 2455006.65020 Melpomene 2456366.09476 1342179011 Scanmap 2456366.09777 ChopNod(18) 2455006.65020 Melpomene 2456366.09880 2455006. 1342179011 2456366.09777 ChopNod(18) 2455006.65402 Melpomene 2456366.09880 2455006. 1342179011 2456366.10181 ChopNod(18) 2455006.65402 Melpomene 2455006. 1342179011 2456366.10181 ChopNod(18) 2455006.65784 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.65784 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.66166 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.66166 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.66548 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.66548 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.66929 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.66929 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.67311 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.67311 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.67693 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.67693 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.68075 Melpomene 2455006. 1342179011 ChopNod(18) 2455006.68075 Melpomene 2455006. 1342179012 ChopNod(19) 2455006.68457 Fortuna 2455006. 1342179012 Scanmap(19) 2455006.68457 Fortuna 2455006. Scanmap(19) Fortuna 2455006.68920 2455006. 1342183903(19) Fortuna 2455006.68920 2455006. 1342183903(19) ChopNod Fortuna 2455006. 1342183904(19) ChopNod Fortuna 2455089.82776 1342183904(19) ChopNod Fortuna 2455089.82776 2455089.82 1342184287(19) ChopNod Fortuna 2455089.83037 2455089.82 1342184287(20) Scanmap Massalia 2455089.83037 2455089.83 1342184288(20) Scanmap Massalia 2455097.85343 2455089.83 1342184288(20) Scanmap Massalia 1342188346 2455097.85343(20) Scanmap 2455097.87 Massalia 1342188346 ChopNod 2455097.87526(20) 2455097.87 Massalia 1342188347 ChopNod 2455097.87526(20) 2455097.89 Massalia 2455186.69915 1342188347 ChopNod(20) 2455097.89 Massalia 2455186.69915 2455186.6 1342188348 ChopNod(20) Massalia 2455186.70176 2455186.6 1342188348 Scanmap(20) Massalia 2455186.70176 2455186.7 1342188349 Scanmap(20) Massalia 2455186.70442 2455186.7 1342188349 Scanmap(20) Massalia 2455186.70442 1342188350 Scanmap 2455186.7 (20) Massalia 2455186.70808 1342188350 2455186.7 Scanmap 2455186.70808 1342188351 2455186.7 Scanmap 2455186.71175 1342188351 2455186.7 Scanmap 2455186.71175 Scanmap 2455186.7 2455186.71542 2455186.7 2455186.71542 2455186.7 2455186.7 Table B.1.

Article number, page 23 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv .4 .4 .4 (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h 98 green 31.3568 0.3142 100 30.592 1.590 2.773 2.324 -20.2 34603460 blue3980 red3980 blue 6.79934384 red 1.68124384 blue 6.85414529 0.0712 red 1.79564529 green 0.0547 6.74385048 0.0687 red 1.78205048 3.8860 green 0.02225452 0.0676 70 red 1.75825452 3.8115 160 green 0.0221 0.0437 6.7668863 70 red 1.586 1.74948863 3.7704 160 blue 0.0549 0.352 0.0384 6.8209382 70 red 0.096 1.694 1.72349382 160 blue 2.447 100 0.0218 0.354 5.6692 0.0380 6.7109786 2.447 red 0.089 2.556 1.681 3.791 1.34709786 160 blue 2.447 100 0.0216 2.556 0.349 5.66029931 0.0605 2.447 red -23.5 0.088 2.556 0.198 1.659 3.719 1.49309931 160 green 2.447 100 -23.5 0.0537 2.556 5.69910451 0.0567 2.447 red 2.447 -23.5 0.099 2.556 0.193 1.650 3.678 1.51960451 3.3662 160 green -23.5 0.0198 2.556 2.5560855 0.0571 2.447 70 red 2.447 -23.5 0.087 0.191 1.626 1.42260855 3.3433 160 green -23.5 -23.5 0.0200 2.556 0.0392 2.556 5.6414821 2.447 70 red 2.447 0.085 1.271 1.54774821 3.3796 160 green -23.5 -23.5 0.0539 2.556 0.294 0.0338 2.556 5.6325341 2.447 70 red 0.082 1.409 1.55105341 4.3600 160 green 2.721 100 -23.5 -23.5 0.0202 2.556 0.293 0.0342 5.6715745 2.721 red 0.074 2.866 1.434 3.284 1.97295745 4.3454 160 green 2.721 100 -23.5 0.0202 2.866 0.295 0.04805890 2.721 red 0.075 20.5 2.866 0.172 1.342 3.262 1.98545890 4.2912 160 blue 2.721 100 20.5 0.0556 2.866 0.04376409 2.721 red 2.721 0.085 20.5 2.866 0.170 1.460 3.297 1.98276409 160 blue 100 20.5 0.0237 2.866 7.1802 0.0432 2.8666813 2.721 red 2.721 0.077 20.5 0.171 1.463 4.254 1.90936813 160 blue 100 20.5 0.0237 2.866 7.4156 20.5 2.866 0.0748 2.721 red 2.721 0.077 0.222 1.861 4.239 1.9671 160 100 20.5 0.0554 2.866 7.3486 20.5 2.866 0.0743 2.721 2.726 0.108 0.220 1.873 4.186 1.9292 160 20.5 0.0236 2.866 20.5 2.510 0.0736 2.726 70 2.726 0.098 0.218 1.871 160 -21.7 20.5 0.0233 2.510 2.510 7.144 2.726 70 2.726 0.098 1.801 160 -21.7 -21.7 2.510 0.372 2.510 7.379 2.726 70 0.106 1.856 160 2.726 -21.7 -21.7 2.510 0.383 7.312 2.726 0.097 2.510 1.820 2.726 -21.7 2.510 0.380 2.726 -21.7 0.095 2.510 2.726 -21.7 2.510 2.726 -21.7 2.510 -21.7 2.510 -21.7 -21.7 .40121.40641 red.40641 green.41045 red 10.9059 4.8334.41045 green red 10.8409 4.9991 0.1092 0.0710 5.0059 0.1085 0.0517 100 160 0.0517 10.640 4.560 100 160 0.553 10.576 0.242 4.716 160 2.637 0.550 2.637 0.245 2.315 4.723 2.637 2.315 2.637 0.246 -22 2.315 -22.4 2.315 2.637 -22 -22.4 2.315 -22.4 .39053.39053 blue.39572 red.39572 19.1908 blue.39976 red 4.9996.39976 19.4078 blue 0.1931.40121 red 5.0909 19.2672 green 0.0721 0.1941 10.9087 5.0672 0.0525 0.1927 70 19.095 160 0.1109 0.0523 70 1.015 4.717 19.311 160 70 2.637 0.310 1.026 4.803 100 19.171 160 2.315 10.643 2.637 2.637 0.311 0.996 4.780 -22.4 2.315 2.315 0.553 2.637 2.637 0.249 -22.4 2.637 -22.4 2.315 2.315 2.637 2.315 -22.4 -22.4 2.315 -22 -22.4 (JD) Band e t (JD) s t continued. (29) Amphitrite(29) Amphitrite 1342205035(29) Amphitrite 1342205036 ChopNod(29) Amphitrite 1342205036 Scanmap(29) Amphitrite 2455462.40074 1342205037 Scanmap(52) Europa 2455462.40340 2455462 1342205037 Scanmap 2455462.40340 2455462 Scanmap 2455462.40744 2455462 1342191110 2455462.40744 2455462 ChopNod 2455462 2455251.47051 2455251.470 Target(20) Massalia 1342224165 ChopNod Obs. ID 2455757.13413 2455757.1 Obs. mode (20) Massalia(20) Massalia(20) Massalia 1342224165(20) Massalia 1342224166 ChopNod(20) Massalia 1342224166 Scanmap(20) Massalia 2455757.13413 1342224167 Scanmap(20) Massalia 2455757.13679 2455757.1 1342224167 Scanmap(20) Massalia 2455757.13679 1342224168 Scanmap 2455757.1 (20) Massalia 2455757.14083 1342224168 ChopNod 2455757.1 (20) Massalia 2455757.14083 1342224169 ChopNod 2455757.1 (20) Massalia 2455757.14481 1342224169 Scanmap 2455757.1 (20) Massalia 2455757.14481 2455757.1 1342224170 Scanmap(20) Massalia 2455757.14747 2455757.1 1342224170 Scanmap(20) Massalia 2455757.14747 1342241347 Scanmap 2455757.1 (20) Massalia 2455757.15151 1342241347 ChopNod 2455757.1 (20) Massalia 2455757.15151 1342241348 ChopNod 2455757.1 (20) Massalia 2456000.38816 1342241348 Scanmap 2455757.1 (20) Massalia 2456000.38816 2456000.3 1342241349 Scanmap(20) Massalia 2456000.39082 2456000.3 1342241349 Scanmap(20) Massalia 2456000.39082 1342241350 Scanmap 2456000.3 (20) Massalia 2456000.39486 1342241350 ChopNod 2456000.3 (20) Massalia 2456000.39486 1342241351 ChopNod 2456000.3 (20) Massalia 2456000.39884 1342241351 Scanmap 2456000.3 (20) Massalia 2456000.39884 2456000.3 1342241352 Scanmap(20) Massalia 2456000.40150 2456000.3 1342241352 Scanmap(20) Massalia 2456000.40150 1342252017 Scanmap 2456000.4 (20) Massalia 2456000.40554 1342252017 ChopNod 2456000.4 (20) Massalia 2456000.40554 1342252018 ChopNod 2456000.4 (20) Massalia 2456202.54774 1342252018 Scanmap 2456000.4 (20) Massalia 2456202.54774 2456202.5 1342252019 Scanmap(20) Massalia 2456202.55040 2456202.5 1342252019 Scanmap(20) Massalia 2456202.55040 1342252020 Scanmap 2456202.5 (20) Massalia 2456202.55444 1342252020 ChopNod 2456202.5 (20) Massalia 2456202.55444 1342252021 ChopNod 2456202.5 (20) Massalia 2456202.55843 1342252021 Scanmap 2456202.5 (29) Amphitrite 2456202.55843 2456202.5 1342252022 Scanmap(29) Amphitrite 2456202.56108 2456202.5 1342252022 Scanmap 1342205032(29) Amphitrite 2456202.56108 Scanmap 2456202.5 1342205032 ChopNod(29) Amphitrite 2456202.56512 2456202.5 1342205033 ChopNod(29) Amphitrite 2456202.56512 2455462.39006 2456202.5 1342205033 Scanmap(29) Amphitrite 2455462.39006 2456202.5 2455462 1342205034 Scanmap(29) Amphitrite 2455462.39272 2455462 1342205034 Scanmap 2455462.39272 1342205035 Scanmap 2455462 2455462.39675 ChopNod 2455462 2455462.39675 2455462 2455462.40074 2455462 2455462 Table B.1.

Article number, page 24 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h 9806 red06 green98 red 14.3521 31.842998 green43 red 14.6886 31.768043 0.1527 0.3185 blue51 red 14.698051 0.1475 54.9117 0.3177 blue43 red 14.4747 160 10043 0.1476 55.1936 blue 0.5495 13.54051 31.066 red 14.8255 160 10051 0.1538 55.2985 green 0.705 0.5520 1.614 13.85770 30.993 red 14.7799 21.2908 16070 0.1488 green 2.773 2.773 0.720 0.5530 1.611 70 13.86674 red 2.324 22.0940 160 2.324 54.639 9.603174 0.1484 0.2138 green 2.773 2.773 0.721 70 13.65519 red -20.2 10.2926 -20.2 2.324 2.839 21.9317 160 2.324 54.91919 0.2210 blue 2.773 0.1092 0.711 70 13.98638 red 2.773 -20.2 10.2345 -20.2 2.324 2.854 160 100 55.02338 0.1037 36.6076 0.2194 blue 2.773 0.727 2.324 13.94342 20.771 red 2.773 -20.2 10.0276 2.324 2.859 10042 0.1032 36.7495 160 blue 2.773 -20.2 0.725 0.3667 2.325 1.07950 21.555 red 2.773 -20.2 10.1105 2.325 160 9.059 10050 0.1130 36.8369 blue 2.773 2.907 -20.2 0.3675 2.325 1.12054 21.397 red 9.710 -20.2 0.473 10.0086 2.325 160 2.50554 0.1019 24.3770 blue 2.907 -20.2 0.3684 1.112 7058 0.505 2.907 red 9.655 -20.2 160 19.4 2.505 36.425 6.640758 0.1009 24.1829 green 2.907 2.505 0.2438 2.907 7062 0.502 red 9.460 1.893 14.2196 160 19.4 2.505 36.567 6.597562 2.505 green 19.4 0.0677 0.2419 2.907 7049 0.494 red 2.907 9.538 1.900 14.2814 160 19.4 36.654 6.591549 19.4 2.505 0.1423 green 0.0672 2.505 2.907 7069 0.496 red 2.907 9.442 1.905 12.3770 24.256 6.563469 19.4 2.505 160 0.1429 green 0.0672 19.4 2.505 2.907 7073 0.491 red 2.907 1.260 12.1872 6.265 100 24.063 5.669173 19.4 2.505 160 0.1254 green 0.0669 19.4 2.505 2.90718 13.873 red 3.066 0.326 1.250 12.1747 6.224 100 5.704118 19.4 2.505 160 0.1220 blue 0.0769 19.4 2.860 0.72137 13.933 3.066 red 3.066 0.324 6.218 100 5.736537 19.4 21.2326 160 0.1218 blue 3.066 -19.6 0.0585 2.860 2.860 0.72441 12.075 3.066 red 0.323 2.860 6.192 100 5.714941 20.8199 160 blue -19.6 3.066 -19.6 0.0588 2.860 0.2134 0.62859 11.890 3.066 red 0.322 -19.6 2.860 5.348 100 5.754259 20.9489 160 green -19.6 3.292 0.0773 2.860 0.2082 0.61878 11.878 3.066 red 0.282 -19.6 14.1364 3.574 5.381 5.768678 160 green -19.6 3.292 0.0590 2.860 0.2095 0.617 7082 3.292 red 0.280 13.8624 16.0 3.574 5.412 21.127 6.351982 160 0.1428 green -19.6 3.292 0.0591 3.574 70 3.292 red 0.281 1.098 13.7449 16.0 3.574 5.391 20.716 6.4743 160 0.1387 16.0 0.0821 3.574 70 3.292 3.292 0.284 1.077 16.0 5.428 100 20.845 6.4776 160 0.1375 16.0 0.0660 3.574 3.574 13.792 3.292 3.292 0.282 1.083 5.442 100 160 16.0 0.0661 3.574 16.0 3.574 0.717 13.524 3.292 3.292 0.283 5.992 100 160 3.410 16.0 3.574 16.0 3.574 0.703 13.410 3.292 0.315 3.265 6.108 160 3.410 16.0 3.574 16.0 0.697 3.410 0.318 -17.3 3.265 6.111 3.410 16.0 3.265 3.410 0.318 -17.3 3.265 -17.3 3.265 3.410 -17.3 -17.3 3.265 -17.3 (JD) Band e t (JD) s t continued. Target(52) Europa 1342191110 Obs. ID ChopNod 2455251.47051 Obs. 2455251.470 mode (52) Europa(52) Europa(52) Europa(52) 1342191111 Europa(52) 1342191111 Europa Scanmap(52) 1342191112 Europa Scanmap(52) 2455251.47317 1342191112 Europa Scanmap(52) 2455251.47317 1342191113 Europa Scanmap 2455251.476 (52) 2455251.47709 1342191113 Europa ChopNod 2455251.476 (52) 2455251.47709 1342191114 Europa ChopNod 2455251.479 2455251.48096(52) 1342191114 Europa Scanmap 2455251.479 2455251.48096(52) 2455251.481 1342191115 Europa Scanmap(52) 2455251.48362 2455251.481 1342191115 Europa Scanmap(52) 2455251.48362 1342212774 Europa Scanmap 2455251.486 (52) 2455251.48754 1342212774 Europa ChopNod 2455251.486 (52) 2455251.48754 1342212775 Europa ChopNod 2455251.490 2455578.31503(52) 1342212775 Europa Scanmap 2455251.490 2455578.31503(52) 2455578.315 1342212776 Europa Scanmap(52) 2455578.31769 2455578.315 1342212776 Europa Scanmap(52) 2455578.31769 1342212777 Europa Scanmap 2455578.320 (52) 2455578.32173 1342212777 Europa ChopNod 2455578.320 (52) 2455578.32173 1342212778 Europa ChopNod 2455578.324 2455578.32572(52) 1342212778 Europa Scanmap 2455578.324 2455578.32572(52) 2455578.326 1342212779 Europa Scanmap(52) 2455578.32837 2455578.326 1342212779 Europa Scanmap(52) 2455578.32837 1342223194 Europa Scanmap 2455578.331 (52) 2455578.33241 1342223194 Europa Scanmap 2455578.331 (52) 2455578.33241 1342223195 Europa Scanmap 2455578.335 (52) 2455736.71349 1342223195 Europa Scanmap 2455578.335 (52) 2455736.71349 1342223196 Europa Scanmap 2455736.716 (52) 2455736.71753 1342223196 Europa Scanmap 2455736.716 (52) 2455736.71753 1342223197 Europa Scanmap 2455736.720 (52) 2455736.72157 1342223197 Europa Scanmap 2455736.720 (52) 2455736.72157 1342239463 Europa Scanmap 2455736.724 (52) 2455736.72561 1342239463 Europa ChopNod 2455736.724 (52) 2455736.72561 1342239464 Europa ChopNod 2455736.728 2455972.44002(52) 1342239464 Europa Scanmap 2455736.728 2455972.44002(52) 2455972.440 1342239465 Europa Scanmap(52) 2455972.44268 2455972.440 1342239465 Europa Scanmap(52) 2455972.44268 1342239466 Europa Scanmap 2455972.445 (52) 2455972.44672 1342239466 Europa ChopNod 2455972.445 (52) 2455972.44672 1342239467 Europa ChopNod 2455972.449 2455972.45071(52) 1342239467 Europa Scanmap 2455972.449 2455972.45071(52) 2455972.451 1342239468 Europa Scanmap(52) 2455972.45336 2455972.451 1342239468 Europa Scanmap(52) 2455972.45336 1342250874 Europa Scanmap 2455972.456 (52) 2455972.45740 1342250874 Europa ChopNod 2455972.456 (52) 2455972.45740 1342250875 Europa ChopNod 2455972.460 2456181.72811 1342250875 2455972.460 Scanmap 2456181.72811 2456181.728 1342250876 Scanmap 2456181.728 2456181.73077 1342250876 Scanmap 2456181.73077 Scanmap 2456181.733 2456181.73481 2456181.733 2456181.73481 2456181.737 2456181.737 Table B.1.

Article number, page 25 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h 2727 blue46 red46 23.5759 blue50 red 6.312850 23.1652 blue 0.236729 red 6.466029 23.1100 green 0.0818 0.231748 red 6.442348 8.5334 green 0.0660 0.2311 7052 red 23.459 4.005252 8.4388 160 green 0.0657 0.0876 7097 red 1.219 5.955 23.050 4.002097 8.4216 160 blue 0.0656 0.0845 7016 red 3.410 0.313 1.198 6.100 22.995 4.024016 14.3813 160 blue 100 0.0421 0.0844 3.26520 3.410 red 3.410 0.317 1.195 6.078 8.325 3.687320 14.2226 160 blue 100 -17.3 0.0423 3.265 0.1453 3.265 3.410 red 3.410 0.316 0.433 3.779 8.233 3.9915 14.1690 160 100 -17.3 -17.3 0.0637 3.265 0.1423 3.265 3.410 3.413 0.202 0.428 3.776 8.216 4.0053 160 -17.3 -17.3 0.0420 3.265 0.1417 3.632 70 3.413 3.413 0.197 0.427 3.796 14.310 160 -17.3 0.0421 3.632 16.2 3.632 70 3.413 3.413 0.198 0.744 3.479 14.152 160 16.2 3.632 16.2 3.632 7018 3.413 3.413 0.187 0.735 3.766 14.09818 160 blue 16.2 3.632 16.2 3.63278 3.413 red 3.413 0.196 0.733 3.77978 12.8841 green 16.2 3.632 16.2 3.63160 3.413 red 3.413 0.197 3.413360 7.5464 blue 16.2 3.631 16.2 0.1305 3.63127 3.413 red 3.392527 12.7986 blue 16.2 0.0622 3.631 16.2 0.078194 red 3.528394 12.7487 green 16.2 0.0621 0.1280 7061 red 12.820 3.537861 7.5139 160 green 100 0.0376 0.127566 red 0.666 3.220 7.362 3.518366 7.5162 160 blue 0.0377 0.0753 7070 red 3.471 0.174 0.383 3.200 12.735 3.516670 13.1617 160 blue 0.0375 0.0753 3.575 7074 3.471 red 3.471 0.173 0.662 3.329 12.685 3.729174 13.1940 160 green 100 -16.1 0.0375 3.575 0.1317 3.57578 3.471 red 3.471 0.173 0.659 3.337 7.331 3.717478 7.8056 160 green 100 -16.1 -16.1 0.0395 3.575 0.1320 3.57554 3.471 red 3.471 0.174 0.381 3.319 7.333 3.694954 7.8038 160 blue -16.1 -16.1 0.0394 3.575 0.0782 3.575 7074 3.471 red 3.471 0.173 0.381 3.317 13.096 3.7048 160 blue -16.1 -16.1 0.0392 3.575 9.6119 0.0782 3.575 70 3.471 3.471 0.173 0.680 3.518 13.128 2.6562 160 100 -16.1 -16.1 0.0393 3.575 9.4513 3.575 0.0984 3.471 3.675 0.183 0.682 3.507 7.615 160 100 -16.1 -16.1 0.0584 3.575 3.548 0.0946 3.675 3.675 0.183 0.396 3.486 7.614 160 -16.1 3.548 16.1 3.548 3.675 70 3.675 0.181 0.396 3.495 160 16.1 3.548 16.1 3.548 9.564 3.675 70 3.675 0.182 2.506 16.1 3.548 0.497 16.1 3.548 9.404 3.675 0.139 3.781 16.1 3.548 0.489 16.1 3.781 4.146 3.781 16.1 4.146 -13.5 4.146 -13.5 -13.5 3160631606 blue32010 red32010 16.8546 blue32414 red 4.474032414 16.8668 green 0.168632818 red 4.494132818 9.7319 green 0.0466 0.1687 red 4.4932 9.7168 0.0468 0.0974 70 16.771 4.4787 160 0.0468 0.0973 70 0.871 4.221 16.783 160 100 0.0466 2.240 0.220 0.872 4.240 9.495 160 100 2.061 2.240 2.240 0.221 0.493 4.239 9.480 160 2.061 27.2 2.061 2.240 2.240 0.221 0.493 4.225 27.2 2.061 27.2 2.061 2.240 2.240 0.220 27.2 2.061 27.2 2.061 2.240 27.2 2.061 27.2 27.2 (JD) Band e t (JD) s t continued. Target(52) Europa 1342250877 Obs. ID ChopNod 2456181.73880 Obs. 2456181.739 mode (52) Europa(52) Europa(52) Europa(52) 1342250877 Europa(52) 1342250878 Europa ChopNod(52) 1342250878 Europa Scanmap 2456181.73880(52) 1342250879 Europa Scanmap(52) 2456181.74145 2456181.739 1342250879 Europa Scanmap(52) 2456181.74145 1342270731 Europa Scanmap 2456181.744 (52) 2456181.74549 1342270731 Europa ChopNod 2456181.744 (52) 2456181.74549 1342270732 Europa ChopNod 2456181.748 2456407.12182(52) 1342270732 Europa Scanmap 2456181.748 2456407.12182(52) 2456407.122 1342270733 Europa Scanmap(52) 2456407.12447 2456407.122 1342270733 Europa Scanmap(52) 2456407.12447 1342270734 Europa Scanmap 2456407.127 (52) 2456407.12851 1342270734 Europa ChopNod 2456407.127 (52) 2456407.12851 1342270735 Europa ChopNod 2456407.131 2456407.13250(54) 1342270735 Alexandra Scanmap 2456407.131 2456407.13250(54) 2456407.132 1342270736 Alexandra Scanmap 1342198509(54) 2456407.13516 2456407.132 1342270736 Alexandra Scanmap 1342198509(54) 2456407.13516 Scanmap Alexandra Scanmap 2456407.138 1342198510(54) 2456407.13920 Scanmap Alexandra 2456407.138 2455365.31305 1342198510(54) 2456407.13920 Scanmap Alexandra 2456407.142 2455365.31305 1342198511(54) Scanmap 2455365. Alexandra 2456407.142 2455365.31709 1342198511(54) Scanmap 2455365. Alexandra 2455365.31709 1342198512(65) Scanmap 2455365. Cybele 2455365.32113 1342198512(65) Scanmap 2455365. Cybele 2455365.32113(65) Scanmap 2455365. Cybele 2455365.32517(65) 2455365. 1342188352 Cybele 2455365.32517(65) 2455365. 1342188352 Cybele ChopNod(65) 2455365. 1342188353 Cybele ChopNod 2455186.72070(65) 1342188353 Cybele ChopNod 2455186.72070(65) 2455186.721 1342188354 Cybele ChopNod 2455186.72331(65) 2455186.721 1342188354 Cybele Scanmap 2455186.72331(65) 2455186.723 1342188355 Cybele Scanmap(65) 2455186.72597 2455186.723 1342188355 Cybele Scanmap(65) 2455186.72597 1342188356 Cybele Scanmap 2455186.728 (65) 2455186.72964 1342188356 Cybele Scanmap 2455186.728 (65) 2455186.72964 1342188357 Cybele Scanmap 2455186.732 (65) 2455186.73330 1342188357 Cybele Scanmap 2455186.732 (65) 2455186.73330 1342202949 Cybele Scanmap 2455186.735 (65) 2455186.73697 1342202949 Cybele Scanmap 2455186.735 (65) 2455186.73697 1342202950 Cybele Scanmap 2455186.739 (65) 2455421.39865 1342202950 Cybele Scanmap 2455186.739 (65) 2455421.39865 1342202951 Cybele Scanmap 2455421.401 (65) 2455421.40269 1342202951 Cybele Scanmap 2455421.401 (65) 2455421.40269 1342202952 Cybele Scanmap 2455421.405 (65) 2455421.40673 1342202952 Cybele Scanmap 2455421.405 2455421.40673 1342215367 2455421.409 Scanmap 2455421.41077 1342215367 2455421.409 ChopNod 2455421.41077 1342215368 2455421.413 ChopNod 2455627.36707 Scanmap 2455421.413 2455627.36707 2455627.367 2455627.36973 2455627.367 2455627.372 Table B.1.

Article number, page 26 of 28 V. Alí-Lagoa et al.: Thermal properties of large asteroids from Herschel PACS data (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h 7478 red78 blue23 red 2.683223 green 9.462942 red 2.677142 5.6620 green 0.029846 0.0947 red 2.642346 5.6760 green 0.0298 0.060009 red 2.703409 5.6426 160 green 0.0583 0.057013 70 red 2.531 2.685813 7.1442 160 green 100 0.0300 0.0566 9.41617 red 0.132 2.526 5.524 3.368017 7.1493 160 blue 100 0.0298 0.489 0.071621 3.781 red 0.132 0.288 2.493 5.538 3.384021 12.2847 160 blue 3.781 100 0.0361 4.146 0.071758 3.781 red 3.781 0.139 4.146 0.288 2.550 5.505 3.414958 12.4207 160 blue 100 -13.5 0.0363 4.146 0.1229 4.14678 3.781 red 3.781 -13.5 0.133 0.286 2.534 6.970 3.436178 12.6422 160 blue 100 -13.5 -13.5 0.0365 4.146 0.1243 4.14682 3.781 red 3.781 0.132 0.382 3.177 6.975 3.485482 12.5462 160 blue -13.5 -13.5 0.0367 4.146 0.1282 4.146 7027 3.781 red 2.852 0.206 0.382 3.192 12.224 3.490627 12.4542 160 green -13.5 -13.5 0.0626 4.146 0.1255 3.040 7046 2.852 red 2.852 0.207 0.635 3.222 12.359 3.426246 7.3112 160 green -13.5 0.0372 3.040 19.6 0.1246 3.040 7050 2.852 red 2.852 0.168 0.642 3.242 12.579 3.121950 7.1572 160 green 19.6 0.0366 3.040 19.6 0.0758 3.040 7058 2.852 red 2.852 0.169 0.654 3.288 12.484 3.355358 7.0523 160 green 19.6 0.0607 3.040 19.6 0.0717 3.040 7077 2.852 red 3.213 0.178 0.649 3.293 12.392 3.295577 5.7183 160 green 100 19.6 0.0360 3.040 19.6 0.0707 2.82781 3.213 red 3.213 0.172 0.644 3.232 7.133 2.540381 5.7043 160 green 100 19.6 0.0354 2.827 17.5 0.0606 2.82726 3.213 red 3.213 0.168 0.371 2.945 6.983 2.690526 5.7388 160 blue 100 17.5 0.0579 2.827 17.5 0.0573 2.82745 3.213 red 3.213 0.161 0.363 3.165 6.880 2.715145 160 blue 100 17.5 0.0299 2.827 9.7729 17.5 0.0576 2.82749 3.213 red 3.213 0.165 0.357 3.109 5.579 2.482849 160 blue 100 17.5 0.0301 2.827 9.6699 17.5 2.82772 0.1000 3.213 red 3.213 0.162 0.290 2.397 5.565 2.708372 160 green 100 17.5 0.0576 2.827 9.6333 17.5 2.82791 0.0968 3.213 red 3.103 0.134 0.289 2.538 5.599 2.685391 7.5224 160 green 17.5 0.0300 2.827 17.5 3.05795 0.0964 3.103 70 red 3.103 0.133 0.291 2.561 3.302595 7.3777 160 green -19.1 17.5 0.0298 3.057 0.0778 3.057 9.72440 3.103 70 red 3.103 0.134 2.342 3.435040 7.2630 160 blue -19.1 -19.1 0.0616 3.057 0.506 0.0739 3.057 9.622 3.103 70 red 0.131 2.555 3.3855 12.4087 160 3.103 100 -19.1 -19.1 0.0367 3.057 0.500 0.0728 9.585 3.103 0.133 3.057 2.533 7.339 3.0237 160 3.103 100 -19.1 0.0363 3.057 0.498 0.1259 3.103 -19.1 0.132 3.057 0.382 3.116 7.198 160 3.103 -19.1 100 0.0602 3.057 3.103 2.768 -19.1 0.169 3.057 0.374 3.241 7.086 160 -19.1 3.057 3.016 70 2.768 2.768 -19.1 0.169 0.368 3.194 12.347 160 -19.1 3.016 19.1 3.016 2.768 2.768 0.166 0.642 2.853 19.1 3.016 19.1 3.016 2.768 2.768 0.156 19.1 3.016 19.1 3.016 2.768 19.1 3.016 19.1 19.1 (JD) Band e t (JD) s t continued. Target(65) Cybele 1342215368 Obs. ID Scanmap 2455627.36973 Obs. mode 2455627.372 (65) Cybele(65) Cybele(65) Cybele(65) 1342215369 Cybele(65) 1342215369 Cybele Scanmap(65) 1342215370 Cybele Scanmap(65) 2455627.37377 1342215370 Cybele ChopNod(65) 2455627.37377 1342215371 Cybele ChopNod 2455627.376 2455627.37775(88) 1342215371 Thisbe Scanmap 2455627.376 2455627.37775(88) 2455627.378 1342215372 Thisbe Scanmap(88) 2455627.38041 2455627.378 1342215372 Thisbe Scanmap(88) 2455627.38041 Thisbe 1342203465 Scanmap 2455627.383 (88) 2455627.38445 Thisbe 1342203465 2455627.383 Scanmap(88) 2455627.38445 Thisbe 1342203466 2455627.387 Scanmap(88) Thisbe 2455434.22809 1342203466 2455627.387 Scanmap(88) Thisbe 2455434.22809 1342203467 Scanmap 2455434.231 (88) Thisbe 2455434.23212 1342203467 Scanmap 2455434.231 (88) Thisbe 2455434.23212 1342203468 Scanmap 2455434.235 (88) Thisbe 2455434.23616 1342203468 Scanmap 2455434.235 (88) Thisbe 2455434.23616 1342234460 Scanmap 2455434.239 (88) Thisbe 2455434.24020 1342234460 ChopNod 2455434.239 (88) Thisbe 2455434.24020 1342234461 ChopNod 2455434.243 (88) 2455912.48111 Thisbe 1342234461 Scanmap 2455434.243 (88) 2455912.48111 Thisbe 2455912.481 1342234462 Scanmap(88) Thisbe 2455912.48377 2455912.481 1342234462 Scanmap(88) Thisbe 2455912.48377 1342234463 Scanmap 2455912.486 (88) Thisbe 2455912.48781 1342234463 ChopNod 2455912.486 (88) Thisbe 2455912.48781 1342234464 ChopNod 2455912.490 (88) 2455912.49179 Thisbe 1342234464 Scanmap 2455912.490 (88) 2455912.49179 Thisbe 2455912.492 1342234465 Scanmap(88) Thisbe 2455912.49445 2455912.492 1342234465 Scanmap(88) Thisbe 2455912.49445 1342246229 Scanmap 2455912.497 (88) Thisbe 2455912.49849 1342246229 ChopNod 2455912.497 (88) Thisbe 2455912.49849 1342246230 ChopNod 2455912.501 (88) 2456075.76711 Thisbe 1342246230 Scanmap 2455912.501 (88) 2456075.76711 Thisbe 2456075.767 1342246231 Scanmap(88) Thisbe 2456075.76976 2456075.767 1342246231 Scanmap(88) Thisbe 2456075.76976 1342246232 Scanmap 2456075.772 (88) Thisbe 2456075.77380 1342246232 ChopNod 2456075.772 (88) Thisbe 2456075.77380 1342246233 ChopNod 2456075.776 (88) 2456075.77779 Thisbe 1342246233 Scanmap 2456075.776 (88) 2456075.77779 Thisbe 2456075.778 1342246234 Scanmap(88) Thisbe 2456075.78045 2456075.778 1342246234 Scanmap(88) Thisbe 2456075.78045 1342261457 Scanmap 2456075.783 (88) Thisbe 2456075.78449 1342261457 ChopNod 2456075.783 (88) Thisbe 2456075.78449 1342261458 ChopNod 2456075.787 (88) 2456311.51224 Thisbe 1342261458 Scanmap 2456075.787 (88) 2456311.51224 Thisbe 2456311.512 1342261459 Scanmap 2456311.51490 2456311.512 1342261459 Scanmap 2456311.51490 1342261460 2456311.517 Scanmap 2456311.51894 1342261460 2456311.517 ChopNod 2456311.51894 ChopNod 2456311.521 2456311.52293 2456311.521 2456311.52293 2456311.523 2456311.523 Table B.1.

Article number, page 27 of 28 A&A proofs: manuscript no. pacs_accepted_arxiv (deg.) α (au) ∆ (au) r (Jy) λ f σ (Jy) λ f m) µ ( λ (Jy) λ i f h σ (Jy) λ i f h 5959 blue63 red63 12.1697 blue red 3.3293 12.0804 0.1218 3.3148 0.0357 0.1209 0.0356 70 12.109 160 70 0.629 3.141 12.020 160 2.768 0.164 0.625 3.127 3.016 2.768 2.768 0.163 3.016 19.1 3.016 2.768 19.1 3.016 19.1 19.1 094094 green498 red498 2.6574 green902 red 1.2459902 2.6351 blue 0.0270306 red 1.2237306 blue 0.0180 4.4997 0.0268 red 1.2596 100 0.0179 4.5209 0.0452 2.593 1.2479 160 100 0.0181 0.0454 0.135 1.175 2.571 160 0.0180 70 3.121 0.062 0.134 1.154 160 3.366 4.477 3.121 70 3.121 0.061 1.188 160 3.366 0.233 17.5 3.365 4.498 3.121 0.063 1.177 3.121 17.5 3.365 0.234 17.5 202 3.121 0.062 3.365202 blue 3.121 17.5 3.365606 3.121 red 17.5 3.365606 15.5278 blue 17.5 3.365010 red 17.5 4.4116010 15.4842 green 17.5 0.1553414 red 4.3869414 9.2793 green 0.0460 0.1549 red 4.3750 9.2498 0.0458 0.0929 70 15.450 4.3709 160 0.0456 0.0926 70 0.803 4.162 15.407 160 100 0.0456 3.756 0.217 0.801 4.139 9.053 160 100 3.610 3.756 3.756 0.215 0.470 4.127 9.024 160 3.610 15.6 3.610 3.756 3.756 0.215 0.469 4.123 15.6 3.610 15.6 3.610 3.756 3.756 0.215 15.6 3.610 15.6 3.610 3.756 15.6 3.610 15.6 15.6 16301630 blue2138 red2138 blue 7.39592531 red 2.11542531 blue 7.55142676 0.0769 red 2.13962676 green 0.0561 7.54433183 0.0756 red 2.13853183 4.4976 green 0.02503576 0.0755 70 red 2.05933576 4.4689 160 green 0.0250 0.0492 7.359 70 red 1.996 2.1231 4.3672 160 0.0559 0.383 0.0450 7.514 70 0.115 2.018 2.0830 160 3.183 100 0.0249 0.391 0.0440 7.507 3.183 0.106 3.121 2.018 4.388 160 3.183 100 0.0246 3.121 0.390 3.183 -18.2 0.105 3.121 0.229 1.943 4.360 160 3.183 100 -18.2 3.121 3.183 3.183 -18.2 0.112 3.121 0.227 2.003 4.261 160 -18.2 3.121 3.121 3.183 3.183 -18.2 0.105 0.221 1.965 -18.2 -18.2 3.121 3.121 3.183 3.183 0.103 -18.2 -18.2 3.121 3.121 3.183 -18.2 -18.2 3.121 -18.2 (JD) Band e t (JD) s t continued. Target(88) Thisbe 1342261461 Obs. ID Scanmap 2456311.52559 Obs. mode 2456311.528 (88) Thisbe(88) Thisbe(88) Thisbe(93) Minerva 1342261461(93) Minerva 1342261462 Scanmap(93) Minerva 1342261462 Scanmap 1342204236(93) Minerva 2456311.52559 Scanmap 1342204236 Scanmap(93) Minerva 2456311.52962 2456311.528 1342204237 Scanmap(93) Minerva 2456311.52962 2456311.532 2455449.34794 1342204237 Scanmap(93) Minerva 2456311.532 2455449.34794 1342204238 Scanmap 2455449.35 (93) Minerva 2455449.35197 1342204238 Scanmap 2455449.35 (423) Diotima 2455449.35197 1342204239 Scanmap 2455449.35 (423) Diotima 2455449.35601 1342204239 Scanmap 2455449.35 (423) Diotima 1342191019 2455449.35601 Scanmap 2455449.35 (423) Diotima 1342191019 ChopNod 2455449.36005 2455449.35 (423) Diotima 1342191020 ChopNod 2455449.36005 2455449.36 (423) 2455250.91583 Diotima 1342191020 Scanmap 2455449.36 (423) 2455250.91583 Diotima 2455250.9 1342191021 Scanmap(423) Diotima 2455250.91849 2455250.9 1342191021 Scanmap(423) Diotima 2455250.91849 1342191022 Scanmap 2455250.9 (423) Diotima 2455250.92241 1342191022 ChopNod 2455250.9 (423) Diotima 2455250.92241 1342191023 ChopNod 2455250.9 (423) 2455250.92628 Diotima 1342191023 Scanmap 2455250.9 (511) 2455250.92628 Davida 2455250.9 1342191024 Scanmap(511) Davida 2455250.92894 2455250.9 1342191024 Scanmap(511) Davida 2455250.92894 Scanmap 2455250.9 1342217773(511) Davida 2455250.93287 2455250.9 1342217773 Scanmap(511) Davida 2455250.93287 2455250.9 1342217774 Scanmap(511) Davida 2455250.9 2455652.00901 1342217774 Scanmap(511) Davida 2455652.00901 1342217775 Scanmap 2455652.01 (511) Davida 2455652.01305 1342217775 Scanmap 2455652.01 2455652.01305 1342217776 Scanmap 2455652.01 2455652.01709 1342217776 Scanmap 2455652.01 2455652.01709 Scanmap 2455652.02 2455652.02113 2455652.02 2455652.02113 2455652.02 2455652.02 Table B.1.

Article number, page 28 of 28