Exp AstronDOI 10.1007/s10686-013-9357-y

ORIGINAL ARTICLE

Herschel celestial calibration sourcesFour large main-belt asteroids as prime flux calibratorsfor the far-IR/sub-mm range

Thomas Muller ·Zoltan Balog ·Markus Nielbock ·Tanya Lim ·David Teyssier ·Michael Olberg ·Ulrich Klaas ·Hendrik Linz ·Bruno Altieri ·Chris Pearson ·George Bendo ·Esa Vilenius

Received: 5 July 2013 / Accepted: 26 September 2013© Springer Science+Business Media Dordrecht 2013

Abstract Celestial standards play a major role in observational astrophysics. Theyare needed to characterise the performance of instruments and are paramountfor photometric calibration. During the Herschel Calibration Asteroid PreparatoryProgramme approximately 50 asteroids have been established as far-IR/sub-mm/mmcalibrators for Herschel. The selected asteroids fill the flux gap between thesub-mm/mm calibrators Mars, Uranus and Neptune, and the mid-IR bright calibra-tion stars. All three Herschel instruments observed asteroids for various calibrationpurposes, including pointing tests, absolute flux calibration, relative spectral response

T. Muller (�) · E. VileniusMax Planck Institute for Extraterrestrial Physics,PO Box 1312, Giessenbachstrasse, 85741, Garching, Germanye-mail: tmueller@mpe.mpg.de

Z. Balog · M. Nielbock · U. Klaas · H. LinzMax Planck Institute for Astronomy,Konigstuhl 17, 69117, Heidelberg, Germany

T. Lim · C. PearsonSpace Science and Technology Department, RAL, Didcot,OX11 0QX, Oxon, UK

D. Teyssier · B. AltieriEuropean Space Astronomy Centre (ESAC), ESA,Villanueva de la Canada, 28691 Madrid, Spain

M. OlbergOnsala Space Observatory, Chalmers University of Technology,43992 Onsala, Sweden

G. BendoUK ALMA Regional Centre Node, Jodrell Bank Centre for Astrophysics,Manchester, M13 9PL, UK

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function, observing mode validation, and cross-calibration aspects. Here we presentnewly established models for the four large and well characterized main-belt aster-oids (1) Ceres, (2) Pallas, (4) Vesta, and (21) Lutetia which can be consideredas new prime flux calibrators. The relevant object-specific properties (size, shape,spin-properties, albedo, thermal properties) are well established. The seasonal(distance to Sun, distance to observer, phase angle, aspect angle) and daily varia-tions (rotation) are included in a new thermophysical model setup for these targets.The thermophysical model predictions agree within 5 % with the available (andindependently calibrated) Herschel measurements. The four objects cover the fluxregime from just below 1,000 Jy (Ceres at mid-IR N-/Q-band) down to fluxes below0.1 Jy (Lutetia at the longest wavelengths). Based on the comparison with PACS,SPIRE and HIFI measurements and pre-Herschel experience, the validity of thesenew prime calibrators ranges from mid-infrared to about 700 μm, connecting nicelythe absolute stellar reference system in the mid-IR with the planet-based calibrationat sub-mm/mm wavelengths.

Keywords Herschel Space Observatory · PACS · SPIRE · HIFI · Far-infrared ·Instrumentation · Calibration · Celestial standards · Asteroids

1 Introduction

With the availability of the full thermal infrared (IR) wavelength range (from a fewmicrons to the millimetre range) through balloon, airborne and spaceborne instru-ments, it became necessary to establish new calibration standards and to develop newcalibration strategies. Instruments working at mm-/cm-wavelengths were mainly cal-ibrated against the planets Mars, Uranus and Neptune (e.g., [21, 22, 44, 62, 72]),while the mid-IR range was always tied to stellar models (e.g., [11, 12, 14, 19, 20,24, 66, 67, 82]). For the far-IR/sub-mm regime no optimal calibrators were availableright from the beginning: the stars are often too faint for calibration aspects whichrequire high signal-to-noise (S/N) ratios or are problematic in case of near-IR fil-ter leaks.1 The planets are very bright and not point-like anymore. They are causingsaturation or detector non-linearity effects. Between these two types of calibratorsthere remained a gap of more than two orders of magnitude in flux. This gap wasfilled by sets of well-known and well-characterized asteroids and their correspondingmodel predictions (e.g., [3, 26, 48, 50, 53, 75]). Figure 1 shows the flux-wavelengthregime covered by the three types of objects typically used for calibration purposesat far-IR/sub-mm/mm wavelength range.

The idea of using asteroids for calibration purposes goes back to IRAS [3]. TheIRAS 12, 25 and 60 μm bands were calibrated via stellar models and in that way con-nected to groundbased N- and Q-band measurements. But at 100 μm neither stellar

1Near-IR filter leaks are photometrically problematic when near-IR bright objects -like stars- are observedin far-IR bands.

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Fig. 1 Overview with the flux densities of the different far-IR/sub-mm/mm calibrators. The Uranus andNeptune SEDs represent the minimum and maximum fluxes during Herschel visibility phases. Three fidu-cial stars are also shown, their flux coverage is representative for the brightest stellar calibrators. For Ceresand Lutetia we show the minimum and maximum fluxes during Herschel observations

model extrapolations nor planet models were considered reliable. Asteroids solvedthe problem. Models for a selected sample of large main-belt asteroids were used to“transfer” the observed IRAS 60 μm fluxes out to 100 μm and calibrate in that waythe IRAS 100 μm band [3].

There was an independent attempt to establish a set of secondary calibrators atsub-millimetre (sub-mm) wavelengths to fill the gap between stars and planets [71].Ultra-Compact H-II regions, protostars, protoplanetary nebulae and AGB-stars wereselected, but often these sources are embedded in dust clouds which produce a strongand sometimes variable background. The modeling proves to be difficult and accuratefar-IR extrapolations are almost impossible.

The Infrared Space Observatory (ISO) [28] was also lacking reliable photometricstandards at far-IR wavelength (50–250 μm) in the flux regime between the stars [11,12, 24] and the planetary calibrators Uranus and Neptune [22, 29, 38, 62, 74]. Muller& Lagerros [46] provided a set of 10 asteroids, based on a previously developed ther-mophysical model code by Lagerros [32–34]. These sources have been extensivelyobserved by ISO for the far-IR photometric calibration, for testing relative spectralresponse functions and for many technical instrument and satellite purposes.

AKARI [59] followed the same route to calibrate the Far-Infrared Surveyor (FIS)[26] via stars, asteroids and planets in the wavelengths regime 50–200 μm.

The Spitzer mission [81] considered in the beginning only stars for calibrationpurposes. But due to a near-IR filter leak of the MIPS [68] 160 μm band, the calibra-tion scientists were forced to establish and verify calibration aspects by using coolerobjects. The asteroids served as reference for the flux calibration of the 160 μm bandas well as for testing the non-linear MIPS detector behaviour [75].

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In preparation for Herschel [64] and ALMA2 a dedicated asteroid programmewas established [53]. This led to a sample of about 50 asteroids for variouscalibration purposes. Along the mission only the 12 asteroids with the highest qualitycharacterization were continued to be observed for calibration.

Here we present the Herschel observations and the data reduction of all pho-tometrically relevant asteroid measurements (Section 2). First, the asteroid instru-mental fluxes in engineering units were converted to absolute fluxes using conver-sion factors derived from stellar calibrators (PACS), Neptune (SPIRE) and Mars(HIFI). Next, the absolute fluxes were corrected for differences in spectral energydistribution between the prime calibrator(s) and the asteroids to obtain mono-chromatic flux densities at predefined reference wavelengths. In Section 3 wedocument recently updated asteroid models for Ceres, Pallas, Vesta, and Lute-tia. The models are entirely based on physical and thermal properties taken fromliterature and derived from independent measurements, like occultation measure-ments, HST,3 adaptive optics, or flyby missions. We compare (Section 4) theabsolute model predictions with all available photometric Herschel (PACS [65],SPIRE [23], HIFI [13]) measurements and discuss the validity and limitations.The dispersion in the ratio of model to measured fluxes for the four aster-oids determines the error in the calibration factor. The conclusions are given inSection 5. It is important to note here that the derived Herschel flux densitiesof the asteroids were independently calibrated against 5 fiducial stars (PACS),the planet Neptune (SPIRE) and the planet Mars (HIFI). The asteroids aretherefore also serving as unique cross-calibration objects between the differentcalibration concepts, the different instruments, observing modes, wavelengths- andflux regimes.

2 Observations & data reduction

2.1 PACS photometer observations

The Photodetector Array Camera and Spectrograph (PACS [65]) on board theHerschel Space Observatory [64] provides imaging and spectroscopy capabilities.Here, we only considered photometric measurements of the four asteroids, takenwith the imaging bolometer arrays either at 70/160 μm (blue/red) or at 100/160 μm(green/red). Most of the observations were taken as part of calibration programmes,with the majority of the measurements taken in high gain and only a few in low gain.The observations have either been taken in scan-map mode or in chop-nod mode.The data were reduced in a standard way, following the steps defined in the offi-cially recommended chop-nod and scan-map reduction scripts, described in more

2http://en.wikipedia.org/wiki/Atacama Large Millimeter Array3Hubble Space Telescope

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detail in [2, 60], with flagging of bad and saturated pixels. The calibration was basedon the latest versions of the bolometer response file (responsivity: FM,7) and theflat-fielding (flatField: FM,3). The non-linearity correction was needed, with cor-rection of up to 6 % for the highest asteroid fluxes. The bolometer signals werealso corrected for the evaporator temperature effect (see [43]), with correction fac-tors of −0.3 % to 3.2 %. Since the asteroids have apparent Herschel-centric motionsof up to 80′′/h, the frames were projected in an asteroid-centered (co-moving) ref-erence frame for the final maps. We used map pixel sizes of 1.1′′, 1.4′′, and 2.1′′at 70, 100, and 160 μm, respectively, to sample the point spread function in anoptimal way.

PACS bolometer scan-map observations The scan-map observations of the fourprime asteroids are listed in Appendix Tables 2, 6, 9, 12 (observing mode ’PACS-SM’). They were obtained using the mini scan-map mode [1, 57] with the telescopescanning at a speed of 20′′/s along parallel legs of about 3′–4′ length. Typically 10scan-legs, separated by a few arcseconds, have been taken. The scans were performedin such a way that the source was moving along the array diagonals (70◦ and 110◦scan-angles in array coordinates) for optimized coverage and sensitivity. The datawere reduced in a standard way (see above), with details about the masking, high-pass filtering, speed selection and deglitching of the data given in [2]. We constructedfinal images in the asteroid co-moving reference frame for each individual OBSID4

and band. The combination of the scan and cross-scan observations was not necessaryfor our bright point-sources.

PACS bolometer chop-nod observations The chop-nod observations of the fourprime asteroids are listed in Appendix Tables 3, 7, 10, 13, 14, and 15 (observing mode’PACS-CN’). They were obtained using the point-source photometry AstronomicalObserving Template (AOT) that is carried out by chopping and nodding in perpen-dicular directions and with amplitudes of 52′′ (see [1, 57, 60] for further details). Thedata reduction included -in addition to what has been done for scan-maps- an adjust-ment for the apparent response drift and offset in this mode (see [60]) resulting incorrections of 4.3 % to 7.6 % for the four asteroids, depending on the time of theobservation (before/after OD 300) and the band [60]. We produced final point-sourcemaps in the asteroid co-moving reference frame.

Aperture photometry We applied aperture photometry with radii of 12′′ in blue/greenand 22′′ in red, centered on the source image in the final maps. Depending on theband, 78–82 % of the source flux is inside these apertures (see [40]). The sky noisein scan-maps was determined in a sky annulus with inner and outer radii of 35′′and 45′′, respectively (see [2]). The sky noise in the chop-nod images was takenfrom a sky annulus with inner/outer radii of 20′′/25′′ in the blue and green maps

4Herschel unique observation identifier

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and 24′′/28′′ in red maps (see [60]). We performed colour corrections [56] of 1.00,1.02,5 and 1.07 for the blue, green, and red band data to obtain monochromatic fluxdensities at the PACS key wavelength of 70.0, 100.0, and 160.0 μm, respectively.6

These corrections were calculated on basis of model SEDs for the four asteroids andcorrespond roughly to the corrections for a 200–300 K black body. The absolute fluxuncertainties were calculated by adding quadratically the measured sky noise (cor-rected for correlated noise, see [2]), 1 % for the uncertainties in colour correction, and5 % for errors related to the fiducial star models which are the baseline for the abso-lute flux calibration of the PACS photometer. The derived flux densities and errors(typically around 5–6 %) are given in Appendix Tables 16, 17, 18, 19 together withthe observing log and conditions (observation mid-time, object distance from Sunand Herschel, phase angle).

2.2 SPIRE photometer observations

The SPIRE [23, 76] photometer observations of the four prime asteroids are listedin Appendix Tables 4, 8, 11, 14. The data were taken in four different observingmodes “Sm Map” (small map), “Lg Map” (large map), “Scan” (scan map), “PS”(point-source), mainly as part of calibration programmes, but here we only use datataken in the standard small and large map modes. The measurements were reducedthrough HIPE7 version 11 -using the SPIRE Calibration Tree version 11- by SPIREinstrument experts and calibrated against a reference Neptune model (ESA4) [5,45, 63]. The processing of different observing modes is essentially identical, withthe exception of the so-called cooler burp correction which was only done for largemaps in a dedicated interactive analysis step. Point source photometry was extractedfrom Level 1 data using the timeline fitter task [5], fitting an elliptical Gaussian tothe asteroid in the co-moving reference frame. The object fluxes have been colour-corrected assuming a spectral index of 2 [79] to obtain mono-chromatic flux densitiesat 250, 350, and 500 μm (corrections are in the order of 5–6 % here). More detailsabout the reduction and calibration are given in Section 6.1 in [21]. The absoluteflux uncertainties were calculated by adding quadratically the individual errors fromthe Gaussian timeline fitting (typically well below 1 %), 2 % for the uncertaintiesin colour correction, and 5 % for errors related to the Neptune model which is thebaseline for the absolute flux calibration of the SPIRE photometer. The derived fluxdensities and errors (typically around 5–6 %) are given in Appendix Tables 16, 17,18, 19 together with the observing log and conditions (observation mid-time, objectdistance from Sun and Herschel, phase angle).

5The Vesta SED requires a colour correction value of 1.03 in the green band6The PACS photometric calibration is based on the assumption of a constant energy spectrum of theobserved source ν × Fν = λ × Fλ. Asteroid SEDs deviate from this assumption and colour-correctionsare required7HIPE is a joint development by the Herschel Science Ground Segment Consortium, consisting of ESA,the NASA Herschel Science Center, and the HIFI, PACS and SPIRE consortia.

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2.3 HIFI continuum observations

The HIFI [13] point-source observations of Ceres are listed in Appendix Table 5.The data were taken [41] in band 1a (OD 1392) and band 1b (ODs 923, 1247,1260) as part of two science programmes. Here we only consider the continuumfluxes of Ceres, which are a by-product of the data reduction and which were orig-inally not considered as relevant for the science case. The HIFI continuum fluxeswere derived from the observations taken during the four ODs. For each of the fourdata sets (i.e. for the 10 h of integration on OD 1392) all data from both polariza-tions -H and V- have been averaged. The conversion of double-sideband antennatemperatures to flux densities uses values for the aperture efficiencies derived fromobservations of Mars and are therefore tied to a model of this planet.8 The aper-ture efficiencies have recently been reviewed and we use the new values kindlyprovided to us by Willem Jellema (priv. comm.), which, at the frequencies consid-ered here, are smaller by 3.8 % and 5.9 % in the H and V polarization, respectively,than values quoted in [69]. The given flux densities are averages of both polar-izations (i.e. H and V) observed by HIFI and are derived from the median valuesof the observed continuum baselines. The error calculation takes into account thenoise r.m.s. after smoothing to a resolution of 100 MHz, quadratically added to theestimated 5 % error in the Mars model which we tie our calibration to. For con-tinuum measurements the side-band ratio errors are negligible, and standing waveeffects are also averaged out. The two polarizations of HIFI in band 1 are mis-aligned by 6.6′′, leading to a coupling loss of order 2 % (for a perfect Gaussianbeam and no satellite pointing error). Allowing for additional pointing errors, weestimate that the derived flux densities could be too low by ≈ 5 %. The derivedflux densities and errors are given in Appendix Table 16 together with the observinglog and conditions (observation mid-time, object distance from Sun and Herschel,phase angle).

3 Thermalphysical model and asteroid-specific model parameters

The applied thermophysical model (TPM) is based on the work by Lagerros[32–34]. This model is frequently and successfully applied to near-Earth asteroids(e.g., [52, 54, 55, 58]), to main-belt asteroids (e.g., [46, 51, 61]), and also to moredistant objects (e.g., [25, 39]). The TPM takes into account the true observing andillumination geometry for each observational data point, a crucial aspect for the inter-pretation of the main-belt asteroid observations which cover a wide range of phaseangles and helio-/observer-centric distances, as well as different spin-axis obliquities.

High quality size and geometric albedo values are fundamental for reliable TPMpredictions. For all four asteroids we used literature values, but only after a crit-ical inspection of the published sizes and albedos and their error estimates. TheTPM also allows one to specify simple or complex shape models and spin-vector

8http://www.lesia.obspm.fr/perso/emmanuel-lellouch/mars/

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Fig. 2 Left: Shape model of Ceres with the TPM temperature coding on the surface, calculated for theHerschel point-of-view on OD 1441, OBSID 1342270856, rotation axis is along the vertical direction.Right: the corresponding thermal light-curve at 100 μm with and without thermal effects included

properties. The one-dimensional vertical heat conduction into the surface iscontrolled by the thermal inertia �.9 The observed mid-/far-IR/sub-mm fluxes areconnected to the hottest regions on the asteroid surface and dominated by thediurnal heat wave. The seasonal heat wave is less important and therefore not con-sidered here. The infrared beaming effects (similar to opposition effects at opticalwavelengths) are calculated via a surface roughness model, described by segmentsof hemispherical craters. Here, mutual heating is included and the true craterillumination and the visibility of shadows is considered (Figs. 2, 3, 4, 5).

For the calculation of the Bond albedo (which is assumed to be close to thebolometric albedo) also the object specific slope parameters for the phase curveG and the absolute magnitudes H are needed (IAU two-parameter magnitude sys-tem for asteroids [6, 36]). The Bond albedo is given by pV ·q, with the geometricV-band albedo pV , and the phase integral q = 0.290 + 0.684·G. In cases wherepV was measured in-situ, only G is required, in cases where pV was not directlymeasured, we derived pV from HV and the object’s effective size Deff via: pV =10(2· log10(S0)−2· log10(Deff )−0.4·HV ), with the Solar constant, S0 = 1361 W/m2. Weused literature values for H-G based on large samples of measurements coveringmany aspect and phase angles from several apparitions. Typical uncertainties inG values have a negligible influence on the TPM flux predictions over the entireHerschel wavelength-range and for the accessible phase angles (approximatly15-30◦) for main-belt asteroids. Errors in H are directly influencing the geometricalbedo: 0.05 mag in H translate into a 5 % error in albedo, with a corresponding fluxchange well below 1 %.

9The thermal inertia � is defined as√

κρc, where κ is the thermal conductivity, ρ the density, and c theheat capacity.

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Fig. 3 Left: Shape model of Pallas with the TPM temperature coding on the surface, calculated for theHerschel point-of-view on OD 1295, OBSID 1342256236, rotation axis is along the vertical direction.Right: the corresponding thermal light-curve at 100 μm with and without thermal effects included

The level of roughness is driven by the r.m.s. of the surface slopes whichcorrespond to a given crater depth-to-radius value combined with the fraction f of thesurface covered by craters, see also Lagerros ([32]) for further details. For all fourtargets we used the “default” roughness settings (ρ = 0.7, f = 0.6) [47].

We used wavelength-dependent emissivity models with emissivities of 0.9 up to150 μm and slowly decreasing values beyond ∼150 μm. The “default” model -usedfor Ceres, Pallas, and Lutetia- has lowest emissivities of around 0.8 in the sub-mm-range, the Vesta-specific emissivity model is more extreme and has values goingdown to 0.6 at 600 μm. Both models are used as specified and applied in [46–48].

For the thermal inertia � we used a “default” value for large, regolith-coveredmain-belt asteroids, namely � = 15 Jm−2s−0.5K−1 [47]. This value is not very well

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Fig. 4 Left: Shape model of Vesta with the TPM temperature coding on the surface, calculated for theHerschel point-of-view on OD 1377, OBSID 1342263924, rotation axis is along the vertical direction.Right: the corresponding thermal light-curve at 100 μm with and without thermal effects included

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Fig. 5 Left: Shape model of Lutetia with the TPM temperature coding on the surface, calculated forthe Herschel point-of-view on OD 221, OBSID 1342188334, rotation axis is along the vertical direction.Right: the corresponding thermal light-curve at 100 μm with and without thermal effects included

constrained and in the literature one can find smaller values down to 5 Jm−2s−0.5K−1

(e.g., [61]) or larger values of 25 Jm−2s−0.5K−1 (e.g., [46]). The precise value hasvery little influence on far-IR and sub-mm-fluxes [49] -at least for large regolith-covered main-belt asteroids- and it agrees very well with the lunar value of � =39 Jm−2 s−0.5 K−1 [27] considering the lower temperature environment at 2-3 AUfrom the Sun which lowers the thermal conductivity within the top surface dust layerconsiderably.

3.1 (1) Ceres

Ceres is the largest and most massive asteroid in the main-belt. It is presumed to behomogeneous, gravitationally relaxed and it has a low density, low albedo and rel-atively featureless visible reflectance spectrum [78]. The shape that best reproducesthe available data (occultations, HST measurements, adaptive optics studies, light-curve, ...) is an oblate spheroid [7, 17, 42, 78] with an equatorial diameter of 974.6 kmand a polar diameter of 909.4 km, resulting in an equivalent diameter of an equal vol-ume sphere of 952.4 ± 3.4 km [78]. The semi-major axes ratios are therefore a/b =1.0 and b/c = 1.072. The spin-axis is within 3◦ of (λsv, βsv) = (346◦, + 82◦) [17]in ecliptic reference frame, with a siderial rotation period of 9.074170 ± 0.000001 h[10]. The spin-vector is therefore oriented close to perpendicular to the line-of-sightand the optical light-curve amplitude is generally small (up to 0.04 mag [46]). Thegeometric V-band albedo is pV = 0.090± 0.0055 [17, 37]. For the calculation of theBond albedo we used an absolute magnitude HV = 3.28 mag and a slope parameterG = 0.05 [30, 46].

3.2 (2) Pallas

Pallas has about half the size of Ceres and is considered as an intact proto-planet which has undergone impact excavation [73]. Its published size, shape, and

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spin-properties have substantially changed over the last years [8, 16, 18, 73, 80]. Weused the latest nonconvex shape model from DAMIT10 with a siderial rotation periodof 7.81322 h. This solution includes all available information from occultations, HST,light-curves over several decades, and adaptive optics measurements. The shape canroughly be described as a triaxial-ellipsoid body with a/b = 1.06, b/c = 1.09. Its spin-axis is oriented towards celestial directions (λecl, βecl) = (31◦ ± 5◦, −16◦ ± 5◦),which means it has a high obliquity of 84◦, leading to high seasonal contrasts. Shape-introduced light-curve amplitudes can reach up to 0.16 mag [31]. The effective size2×(abc)1/3, a critical parameter for our calculations, was given as 533 ± 6 km [18],545 ± 18 km [73], 513 ± 7 km [8]. We adopted the first value which has the small-est errorbar and which is based on multiple occultations, including one of the bestobserved occultation of a star ever. We use HV = 4.13 mag and G = 0.16 [30, 31,46]. Our geometric albedo pV = 0.139 was calculated from HV and the effective sizeof 533 km.

3.3 (4) Vesta

Vesta is one of the largest and the second most massive asteroid in the main-belt. Ithas recently been visited by the DAWN11 mission. Most of the key elements for ourthermophysical model purposes are very well known, but the final shape models arenot yet publically released. Our calculations are based on the HST shape model [77]with a spin-vector (λecl, βecl) = (319◦ ± 5◦, 59◦ ± 5◦), very close to values derivedrecently from DAWN [70]. The siderial rotation period is Psid = 5.3421289 h [15,77]. The obliquity of about 27 ◦ combined with a more extreme triaxial body leads toshape-introduced light-curve amplitudes of up to 0.18 mag [31]. We assigned a meansize of 525.4 ± 0.2 km [70], roughly corresponding to a triaxial-ellipsoid body witha/b = 1.03, b/c=1.25. We took HV = 3.20 mag and G = 0.34 [46], the correspondinggeometric albedo pV = 0.336 was calculated from the effective size of 525.4 km.

3.4 (21) Lutetia

Lutetia is significantly smaller and more irregularly shaped than the other threeobjects. Due to its unusual spectral type with indications of a high metal content,it was originally not considered in our list of potential flux calibrators. But Lutetiawas very well characterized by a ROSETTA12 flyby in 2011 and we took advan-tage of the derived, high-quality properties. Our shape model is the latest nonconvexshape model from DAMIT,13 which is based on a combination of flyby informa-tion, occultations, radiometry, light-curve datasets, radar echoes, interferometry, and

10Database of Asteroid Models from Inversion Techniques, http://astro.troja.mff.cuni.cz/projects/asteroids3D/11http://dawn.jpl.nasa.gov/12http://www.esa.int/Our Activities/Space Science/Rosetta13Database of Asteroid Models from Inversion Techniques, http://astro.troja.mff.cuni.cz/projects/asteroids3D/

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disk-resolved imaging [9]. It has a spin-vector of (λecl, βecl ) = (52◦ ±2◦, −6◦ ±2◦),and a siderial rotation period of Psid = 8.168271 h [9, 35]. The absolute effec-tive size of the final shape model is Deff = 99.3 km and the measured geometricalbedo is pV = 0.19 ± 0.01 [9]. Typical shape-introduced light-curve amplitudes canreach up to 0.25 mag [31]. The absolute magnitude and the slope paramemeter, bothnormalised to the mean light-curve value, are given as HV = 7.25 and G = 0.12 [4].

4 Results, validity and limitations

Based on the thermophysical model and object setup in Section 3, we calculatedTPM flux densities at the PACS, SPIRE, and HIFI reference wavelengths for themid-time of each observation (Start-time + 0.5×duration of each OBSID, Herschel-centric reference system). The calculations have been done for the true Herschel-centric observing geometry with the asteroid placed at the correct helio-centric andHerschel-centric distance, under the true phase angle and spin-vector orientation. Theobserved and calibrated mono-chromatic flux densities have then been divided by theTPM predictions. The ratios are shown in the following Figs. 6, 7, 8, 9, and are listedin Appendix Tables 16, 17, 18, 19, and discussed below.

Fig. 6 Observed and calibrated Herschel flux densities of Ceres divided by the corresponding TPM pre-dictions (one point per OBSID). The median ratios for each instrument and each band are given togetherwith the standard deviations of the ratios. For PACS and SPIRE we also give the ratios per observingmode. PACS data are shown as diamonds (chop-nod data) and squares (scan-map data), SPIRE data areshown as plus-symbols (large map mode) and crosses (small map mode), HIFI data are shown as triangles

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Fig. 7 Observed and calibrated Herschel flux densities of Pallas divided by the corresponding TPMpredictions, like in Fig. 6

Fig. 8 Observed and calibrated Herschel flux densities of Vesta divided by the corresponding TPMpredictions, like in Fig. 6

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Fig. 9 Observed and calibrated Herschel flux densities of Lutetia divided by the corresponding TPMpredictions, like in Fig. 6

Absolute flux level The median ratios for all four asteroids and in all PACS & SPIREbands are well within 1.00 ± 0.05. There are no systematic outliers visible. A fewindividual measurements are slightly outside the 5 % boundary, but here it is notclear if the problem is related to instrumental/technical issues or sky backgroundrelated effects. Our sources have apparent sky motions of up to about 80′′/h (as seenfrom Herschel) and they cross background sources and dense star fields. And indeed,Ceres, Vesta and Lutetia reached galactic latitudes below 5◦ during Herschel observ-ing periods and bright sources (not easily recognized in automatic processing) couldhave influenced the photometry in rare cases. The influence of lower S/N levelscan be seen in the increased ratio scatter in the PACS 160 μm and SPIRE 500 μmmeasurements of Lutetia.

The maximum-to-minimum observed flux ratios in a given band are 2.3, 2.7, 3.5,4.3 for Ceres, Pallas, Vesta, and Lutetia, respectively (see Appendix Tables 16, 17,18, 19). This flux change is mainly dominated by changing distances between theasteroid and Herschel, with smaller influences from changing heliocentric asteroiddistances and phase angles. The TPM setup handles these seasonal geometric effectswith high accuracy. We found no significant remaining trends in the obs/TPM-ratioswith helio-centric and Herschel-centric distance.

Short-term variations The four asteroids are not spherical and optical lightcurvesshow amplitudes of up to 0.25 mag. These variations are caused mainly by rota-tionally changing cross-sections and therefore expected to be seen in disk-integrated

Exp Astron

thermal emission as well. In our model setup this is handled by complex shapemodels combined with spin-vector information (derived from occultation results,light-curve inversion techniques, high resultion imaging techniques and/or flybyinformation), and object-specific zero-points in time and rotational phase. Our setupexplains the available optical light-curves and other cross-section related data verywell, but it is not entirely clear if such models would also explain the rotationalchanges in thermal emission. Figures 6, 7, 8, 9 show -at least in the most reliableshortest wavelength bands at 70 and 250 μm- very small standard deviations in theobs/TPM ratios. For Ceres and Pallas we find standard deviations of 2 %, while forthe more complex shaped objects Vesta and Lutetia we find 3 %. This very low scat-ter agrees with findings on non-variable reference stars (see [2]) and tells us thatthe shape and rotational properties of the four asteroids are modeled with sufficientaccuracy.

Spectral shape aspects The obs/TPM ratios for a given object are almost identical forall bands of the same instrument. This is an indication that our TPM reproduces theobserved slopes in spectral energy distribution (SED) correctly. The modeled objectSEDs are summing up all different surface temperatures over the entire disk. Here, atlong wavelength and close to the Rayleigh-Jeans SED approximation, the SEDs areclosely correlated with the disk-averaged temperatures, while at shorter wavelengths(e.g., in the mid-IR) the hottest sub-solar regions dominate the SED shapes. Theconstant ratios over all three bands of an instrument also confirm the validity of thestrongly band-dependent colour-correction (see Sections 2.1 and 2.2). These correc-tions are calculated from the lab-measured relative spectral response functions of theindividual bands [21, 56]. Our results show no problems with the tabulated colour-correction values, a nice confirmation that the bands are well characterized and thatthere are no indications for filter leaks.

PACS/SPIRE cross-calibration and emissivity aspects For the 3 bright sources Ceres,Pallas, and Vesta the SPIRE ratios are 2–5 % higher than the PACS ratios. The causeis not clear, but there are different possibilities: (i) A systematic difference in theabsolute flux calibrators (5 fiducial stars for PACS [2] and a specific Neptune modelfor SPIRE [5]). Both calibration systems are given with an absolute accuracy of ±5 %and the offset we see in the asteroids is within this range. Both calibration systemsunderwent recent adjustments and re-adjustments with typical changes of a few per-cent. Discussions are still ongoing and the related publications -possibly with slightadjustments- are in preparation. (ii) A flux-dependency in the reduction/calibrationsteps which is not correctly accounted for: the PACS asteroid data are corrected fordetector non-linearities (up to 6 % for the highest asteroid fluxes), but an absolutevalidation at these flux levels is difficult. The SPIRE asteroid data are well belowthe flux level of Neptune which is used as reference object and the asteroids alsomove much faster than Neptune on the sky. Both aspects might cause an offset of afew percent on the final fluxes. (iii) The asteroid models use a wavelength-dependentemissivity model [46–48] and the largest emissivity changes happen between 200 and500 μm. But if there are problems in the emissivity model solution we would expectto see obs/TPM ratios changing gradually with wavelengths and not in a step-function

Exp Astron

as we see it here. We also tested a constant emissivity model (ε = 0.9 = const.)which clearly confirms that lower and wavelength-dependent emissivities are neededto explain the SPIRE measurements. However, the effective emissivity changes arenot precisely known for the region beyond ≈150 μm where subsurface layers (proba-bly with different thermal properties [27]) start to become visible. A future scientificanalysis of all combined PACS and SPIRE observations might reveal a new andslightly different wavelength-dependent emissivity model for the large main-beltasteroids.

One additional element in this context is the outcome of a dedicated PACS/SPIREcross-calibration study for the fiducial calibration stars and -at a much higher fluxlevel- for the planets Uranus and Neptune. In this way, one could investigate furtherthe reason for the small jump between PACS and SPIRE fluxes.

There are a few additional points which deserve mentioning:

• For Lutetia we find significantly larger standard deviations in the obs/TPMratios at 350 and 500 μm, but Lutetia is already faint at these wavelength(below 600 mJy at 350 μm and some measurement are even below 100 mJyat 500 μm) and background contamination and instrument noise levels start tocontribute.

• The 70 μm obs/TPM ratio for Vesta is about 4 % higher than the ratios at 100and 160 μm. We don’t know the reason for this effect, but we speculate that thismight be the result of a broadband mineralogic surface feature covered by the70 μm-band (∼55–95 μm). We plan to follow this up via PACS spectrometermeasurements of Vesta.

• For the 3 brightest targets we also see a very small difference between PACSdata taken in chop-nod mode and scan-map mode. The chop-nod ratios are about1 % lower than the corresponding scan-map ratios. We expected to see slightlyunderestimated fluxes in the chop-nod mode for very bright targets (see [60]),but it was not clear how big the effect would be. Based on the asteroid results,we expect to see a 2–3 % flux differences for even brighter targets, like Neptuneand Uranus, between measurements taken in these two different PACS observingmodes.

• The HIFI ratios are very close to the PACS ratios and about 5 % lowerthan the SPIRE ratios. But the derived fluxes are very sensitive to point-ing errors. Additional pointing errors could increase the derived flux densitiesby up to ≈ 5 % which would then bring the HIFI ratios very close to theSPIRE ones.

• There was one SPIRE observation of Vesta (OD 411, OBSID 1342199329, LargeMap mode) which produced fluxes which are about 35 % higher than the cor-responding model predictions in all 3 bands, probably due to a contaminatingbackground source. We eliminated this measurement from our analysis.

• We see a 3–4 % offset between SPIRE large and small scan map observationsof Ceres and Pallas, but not for Vesta. This offset is not present in observa-tions taken in both modes close in time. The cause is therefore either relatedto satellite/instrument effects changing with time (like the changing telescope

Exp Astron

flux) or by a time-dependent thermal effect which is not covered by our currentmodel-setup. A first investigation seems to point towards a small effect relatedto subsurface emission which seems to play a role at the longest SPIRE wave-lengths and which is at present only approximated by our wavelength-dependentemissivity models.

• Ceres, Pallas, and Vesta also have SPIRE observations taken in non-standardscanning mode. A first comparison with our model predictions confirms thevalidity of the data. They will be included in future analysis projects.

Quality of model parameters The fact that our TPM predictions agree -on abso-lute scale- very well with the Herschel measurements does not automaticallymean that all our object properties (mainly effective size, albedo, thermal prop-erties) are correct. The object-related quantities have uncertainties and could beeven slightly off. But we aimed for finding the most accurate object sizes, andderived preferentially from direct measurements and published in literature. Thethermal properties influence the predictions in an absolute sense and also in awavelength-dependent manner. We took default values from literature to avoid anydependency of our object properties from Herschel-related information. Overall,our model settings allow us to reproduce the observed absolute fluxes and SEDshapes with high accuracy and we have therefore great confidence in our modelsolutions.

Accuracy We made a statistical analysis of the observation-to-model ratios for allfour asteroids (Table 1, Fig. 10) to see how many observational data points arematched by the corresponding TPM prediction.

For this comparison we considered the absolute flux errors for each individualmeasurement as it was produced by the general data reduction and calibration pro-cedure mentioned above. The absolute flux errors include the processing errors,

Table 1 Statistical comparison between observed and TPM fluxes

Object 70 μm 100 μm 160 μm 250 μm 350 μm 500 μm

1 Ceres 51/0 39/0 84/4 20/4 18/6 24/0

2 Pallas 20/0 19/1 40/0 11/2 8/5 12/1

4 Vesta 32/8 25/7 64/8 14/1 15/0 15/0

21 Lutetia 14/1 19/0 29/5 9/0 6/3 5/4

1-σ agreement 92 % 92 % 92 % 87 % 70 % 91 %

2-σ agreement 100 % 100 % 100 % 100 % 100 % 97 %

The numbers indicate how many observations are matched by the corresponding TPM prediction withinthe given 1-σ error bars and how many are not matched. The last two lines give the agreement per band inpercent, based on the 1-σ and 2-σ errors in the observed fluxes

Exp Astron

50 100 150 200 250 300 350 400 450 500 550

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Wavelength (µm)

Obs

erve

d / m

odel

CeresPallasVestaLutetia

Fig. 10 Dispersion in the ratios of measured-to-model fluxes for the four asteroids as a function of wave-length. The weighted mean ratios are shown with errorbars reflecting the absolute flux calibration ofindividual measurements as well as the variance of the sample

the photometry errors (corrected for correlated noise) and the absolute flux calibra-tion error as provided by the three instrument teams. In all three PACS bands morethan 90 % of all measurements agree within their 1-σ errorbars with the correspond-ing TPM prediction. In the SPIRE bands the agreement is still between about 70 %and 90 %. If we allow for 2-σ errorbars we find 100 % agreement for Ceres, Pallasand Vesta in all six bands. For Lutetia there are only two measurements in the 500 μmband which are outside the 2-σ threshold. Figure 10 shows the agreement betweenobservations and TPM predictions in a graphical way. For each object we calculatedthe weighted mean ratio and errorbars adding up quadratically the variance of theweighted mean and the weighted sample variance. These errorbars are dominatedby the 5 % absolute flux calibration errors of our measurements, the variance of theweighted mean (as can be seen in Figs. 6, 7, 8, 9) is typically 2–3 % only, with excep-tion of the long-wavelength channels for Lutetia. This excellent agreement betweenobserved and TPM fluxes confirms the validity of the four asteroids as prime calibra-tors on a similar quality level as given for the fiducial star models in the PACS range(5 %), the Neptune model in the SPIRE range (5 %), and the Mars model in the HIFIband 1a/1b (5 %).

Limitations Our comparison between TPM predictions and measurements is lim-ited to a wavelength range between about 50 μm (short wavelength end of thePACS 70 μm filter) and about 700 μm (long wavelength end of the SPIRE

Exp Astron

500 μm filter). The Herschel visibility constrained the tested phase angles tovalues between about 15◦ and 30◦ before and after opposition. Outside thesewavelengths and phase angle ranges the TPM might have slightly higher uncer-tainties. Some of the asteroids have complex shapes and the shape models usedmight not characterize the true shape very accurately. This could also cause smalldeviations between TPM predictions and the true measured fluxes for specificviewing geometries. The rotation periods are known with high accuracy for allfour asteroids and the applied spin vectors are of sufficient quality for the nextdecade.

Overall, the TPM deviations outside the specified wavelengths and phase-angleranges are expected to be small and absolute model accuracies of better than 10 %seem to be reasonable for all four asteroids. Further testing against additional ther-mal data is foreseen in the near future to cover the full ALMA and SPICA14

regime.

5 Conclusions

We find the following general results related to the 4 asteroids:

• The new asteroid models predict the observed fluxes on absolute scales withbetter than 5 % accuracy in the in the 50 to 700 μm range. This meansthat the effective size and albedo values in our model setup are of highquality.

• Shape and spin properties dominate the short-term brightness variations: ourshape, rotation-period and spin-axis approximations are sufficient for our pur-poses.

• In general, the rotational and seasonal flux changes are modeled with high qualityto account for short-term (rotational effects on time scales of hours) and long-term (effects with phase angle and changing distance to the Sun on time scalesof months or years) object variability.

• Our “default” description of the thermal properties is sufficient to explain theobserved far-IR/sub-mm fluxes. Please note that the Vesta emissivity is verydifferent from the emissivity model used for the other objects.

• The asteroid surfaces of all 4 asteroids are very well described by a low-conductivity, hence low thermal inertia surface regolith with very little heattransport to the nightside of the object (they are observed at phase angles up toabout 30◦).

• There are indications that Vesta has a broad shallow mineralogic emission featurewhich contributes up to 4 % to the total flux measured in the PACS 70 μmband.

14http://www.ir.isas.jaxa.jp/SPICA/SPICA HP/index English.html

Exp Astron

We find the following Herschel-related results:

• The PACS chop-nod and scan-map derived fluxes agree very well (within 1 %),although there seems to be a small tendency that the chop-nod fluxes are slightlyunderestimated for very bright targets.

• The SPIRE observation/model ratios for Ceres, Pallas, and Vesta are 2–5 %higher than the PACS related ones. This could be related to the very differentcalibration schemes of both instruments, but there is also the possibility of amodel-introduced effect (e.g., related to the object emissivity models).

• The reduced and calibrated HIFI continuum fluxes for Ceres agree very well withthe PACS measurements and confirm the high photometric quality of the HIFIcontinuum measurements.

Ceres, Pallas, Vesta, and Lutetia as prime calibrators:

• The new TPM setup for the four asteroids predicts the observed fluxes on abso-lute scales with better than 5 % accuracy in the wavelength range 50 to 700 μmand for phase angles between ∼15◦ and ∼30◦.

• Outside the Herschel PACS/SPIRE wavelength range and for extreme phaseangles we still expect that the absolute accuracy of the TPM predictions are betterthan 10 %.

Overall, our thermophysical model predictions for the four asteroids agree within5 % with the available (and independently calibrated) Herschel measurements. Theachieved absolute accuracy is similar to the ones quoted for the official Herschelprime calibrators, the stellar photosphere models, the Neptune and Mars planetmodels, which justifies to upgrade the four asteroid models to the rank of prime cal-ibrators. The four objects cover the flux regime from just below 1,000 Jy (Ceres atmid-IR) down to fluxes below 0.1 Jy (Lutetia at the longest wavelengths). Basedon the comparison with PACS, SPIRE and HIFI measurements and pre-Herschelexperience, the validity of prime calibrators ranges from mid-infrared to about600 μm, connecting nicely the absolute stellar reference system in the mid-IR withthe planet-based calibration at sub-mm/mm wavelengths.

Acknowledgments We would like to thank the PIs of the various scientific projects for permission touse their Herschel science data in the context of our calibration work.

Appendix

Overview of available Herschel photometric measurements

In the following tables we list the available photometric observations (calibration andscience observations) with one of the four asteroids in the field of view. Some ofthe early measurements were used with very different instrument settings and non-standard observing modes. The corresponding fluxes are not well calibrated and weexcluded them from our analysis.

Exp Astron

Tabl

e2

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rvie

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allr

elev

antH

ersc

hel-

PAC

Sph

otom

eter

scan

-map

obse

rvat

ions

of(1

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OB

SID

Prop

osal

Dur

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artt

ime

AO

RL

abel

1441

1342

2708

56D

DT

dboc

kele

328

620

13-0

4-24

T05

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49Z

PPho

to-C

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Vis

it12

1441

1342

2708

51D

DT

dboc

kele

328

620

13-0

4-24

T04

:04:

45Z

PPho

to-C

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Vis

it11

1441

1342

2708

46D

DT

dboc

kele

328

620

13-0

4-24

T02

:57:

05Z

PPho

to-C

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Vis

it10

1441

1342

2708

41D

DT

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328

620

13-0

4-24

T01

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57Z

PPho

to-C

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it09

1441

1342

2708

28D

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328

620

13-0

4-24

T01

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51Z

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Vis

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1441

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2708

23D

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328

620

13-0

4-23

T23

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43Z

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Vis

it07

1441

1342

2708

18D

DT

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328

620

13-0

4-23

T22

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42Z

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to-C

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Vis

it06

1441

1342

2708

13D

DT

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328

620

13-0

4-23

T21

:41:

50Z

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Vis

it05

1441

1342

2708

08D

DT

dboc

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328

620

13-0

4-23

T20

:37:

24Z

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Vis

it04

1441

1342

2708

03D

DT

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328

620

13-0

4-23

T19

:43:

14Z

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it03

1441

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98D

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328

620

13-0

4-23

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38Z

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328

620

13-0

4-23

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20Z

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1420

1342

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189

286

2013

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189

286

2013

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189

286

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110

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Exp Astron

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159

286

2012

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13:1

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070

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1237

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2520

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157

286

2012

-10-

02T

05:4

2:14

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2012

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2010

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1993

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1985

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1985

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1981

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1973

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1973

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1966

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1966

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1966

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2010

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1957

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485

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0.42

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3.50

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2.62

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485

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485

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485

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286

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1.66

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2.90

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PAC

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286

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1911

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1.66

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PAC

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Exp Astron

Tabl

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U]

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U]

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ode

286

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1911

3324

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1.67

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3.12

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2.90

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PAC

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286

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1.67

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3.13

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2.90

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PAC

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286

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1911

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1.66

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9.22

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2.75

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PAC

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286

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1.66

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3.17

32.

7502

2.90

2520

.159

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1.01

PAC

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N

286

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1911

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1.65

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6.58

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2.75

022.

9026

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242.

625

0.98

PAC

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286

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1911

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1.65

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0059

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3.18

22.

7502

2.90

2620

.159

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1.00

PAC

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N

485

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2624

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314

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4.92

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905

2.89

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8.01

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485

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0.43

314

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2.62

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0.4

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485

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485

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2.62

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0.4

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8.76

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3.10

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PAC

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743

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2.98

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743

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8.75

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2.63

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3.10

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1.01

PAC

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726

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1.62

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2.94

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2.98

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1.01

PAC

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1.62

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2.35

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9837

3.31

4317

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1.02

PAC

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N

726

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1.61

216

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296

2.98

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PAC

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726

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1.61

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2.35

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9837

3.31

4517

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1.02

PAC

S-C

N

759

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2225

6524

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4.80

170

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1.07

411

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2.98

392.

8904

20.0

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127

1.00

PAC

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N

759

1342

2225

6524

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4.80

170

160.

0058

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3.08

32.

9839

2.89

0420

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1.03

PAC

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N

759

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2225

6824

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4.81

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3.03

66.

788

2.98

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8903

20.0

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395

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PAC

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N

759

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2225

6824

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4.81

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0058

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3.09

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2.89

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PAC

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Exp Astron

Tabl

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U]

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769

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7.94

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PAC

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769

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3.39

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2.75

2020

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1.02

PAC

S-C

N

769

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2229

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801

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1.35

413

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2.98

342.

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868

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PAC

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N

769

1342

2229

3724

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5.08

801

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0064

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3.39

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9834

2.75

2220

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1.03

PAC

S-C

N

782

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2237

0324

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7.64

975

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0.31

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693

2.98

242.

5848

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160

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PAC

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N

782

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2237

0324

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7.64

975

160.

0073

.841

3.92

22.

9824

2.58

4819

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1.03

PAC

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N

782

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2236

9824

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7.61

318

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3.90

114

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2.98

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PAC

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N

782

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9824

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7.61

318

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3.89

42.

9825

2.58

5319

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1.03

PAC

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N

947

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2.53

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5.80

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2.93

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947

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3.06

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2.82

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947

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1237

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2.38

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PAC

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1237

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5.88

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1237

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2520

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5620

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4.74

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7240

2.38

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1.03

PAC

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N

1244

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2528

7224

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8.25

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2.71

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21.0

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608

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PAC

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N

1244

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2528

7224

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0.06

427

160.

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5.91

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7180

2.28

3721

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PAC

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N

1244

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2528

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359

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5.17

720

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PAC

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1244

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2528

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0.05

359

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5.41

52.

7180

2.28

3821

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0.99

PAC

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N

1420

1342

2692

7724

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5.50

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2.24

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2.59

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216

5.68

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1420

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2692

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5.50

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1420

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326

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326

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SPIR

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287

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ode

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1954

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1956

2524

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1.04

PAC

S-SM

160

1342

1861

3424

5512

5.57

249

160.

0021

.761

1.11

02.

4984

2.71

3021

.721

.297

1.02

PAC

S-SM

160

1342

1861

3724

5512

5.60

851

160.

0021

.943

1.11

92.

4984

2.71

2521

.721

.464

1.02

PAC

S-SM

348

1342

1956

2324

5531

3.63

068

70.0

018

8.28

69.

605

2.32

841.

8377

−24.

918

8.49

31.

00PA

CS-

CN

348

1342

1956

2324

5531

3.63

068

160.

0043

.230

2.28

92.

3284

1.83

77−2

4.9

45.3

950.

95PA

CS-

CN

348

1342

1956

2624

5531

3.64

113

100.

0010

2.34

85.

224

2.32

841.

8379

−24.

910

7.66

60.

95PA

CS-

CN

348

1342

1956

2624

5531

3.64

113

160.

0042

.787

2.27

72.

3284

1.83

79−2

4.9

45.2

050.

95PA

CS-

CN

Exp Astron

Tabl

e18

(con

tinu

ed)

OD

OB

SID

mid

-tim

e[J

D]

λ[μ

m]

FD[J

y]σ

[Jy]

r[A

U]

[A

U]

α[◦

]T

PM[J

y]FD

/TPM

Inst

r./M

ode

677

1342

2166

0724

5564

2.91

377

70.0

012

5.06

46.

380

2.15

972.

3601

25.2

127.

336

0.98

PAC

S-C

N

677

1342

2166

0724

5564

2.91

377

160.

0029

.649

1.56

72.

1597

2.36

0125

.230

.147

0.98

PAC

S-C

N

686

1342

2177

7724

5565

2.03

003

70.0

014

6.26

67.

466

2.16

242.

2633

26.2

138.

521

1.06

PAC

S-C

N

686

1342

2177

7724

5565

2.03

003

160.

0032

.604

1.70

12.

1624

2.26

3326

.232

.819

0.99

PAC

S-C

N

703

1342

2187

4624

5566

9.09

166

100.

0091

.008

4.64

42.

1688

2.07

6927

.592

.577

0.98

PAC

S-C

N

703

1342

2187

4624

5566

9.09

166

160.

0037

.926

1.99

52.

1688

2.07

6927

.538

.647

0.98

PAC

S-C

N

703

1342

2187

4324

5566

9.08

097

70.0

017

0.01

58.

674

2.16

882.

0770

27.5

164.

767

1.03

PAC

S-C

N

703

1342

2187

4324

5566

9.08

097

160.

0038

.333

2.01

82.

1688

2.07

7027

.539

.131

0.98

PAC

S-C

N

743

1342

2217

2624

5570

8.59

762

100.

0014

8.87

07.

596

2.18

901.

6459

26.5

147.

039

1.01

PAC

S-C

N

743

1342

2217

2624

5570

8.59

762

160.

0063

.044

3.29

42.

1890

1.64

5926

.561

.325

1.03

PAC

S-C

N

743

1342

2217

2324

5570

8.58

693

70.0

027

5.62

914

.062

2.18

901.

6461

26.5

259.

825

1.06

PAC

S-C

N

743

1342

2217

2324

5570

8.58

693

160.

0063

.173

3.31

12.

1890

1.64

6126

.561

.603

1.03

PAC

S-C

N

726

1342

2202

8924

5569

1.59

787

100.

0011

5.63

85.

900

2.17

941.

8279

27.8

117.

283

0.99

PAC

S-C

N

726

1342

2202

8924

5569

1.59

787

160.

0048

.637

2.56

42.

1794

1.82

7927

.848

.946

0.99

PAC

S-C

N

726

1342

2202

8624

5569

1.58

719

70.0

021

4.16

310

.926

2.17

941.

8280

27.8

206.

952

1.03

PAC

S-C

N

726

1342

2202

8624

5569

1.58

719

160.

0049

.079

2.57

72.

1794

1.82

8027

.849

.237

1.00

PAC

S-C

N

720

1342

2205

8524

5568

5.96

543

100.

0011

1.36

95.

683

2.17

651.

8899

27.9

112.

599

0.99

PAC

S-C

N

720

1342

2205

8524

5568

5.96

543

160.

0047

.085

2.47

12.

1765

1.88

9927

.946

.968

1.00

PAC

S-C

N

720

1342

2205

8224

5568

5.95

475

70.0

020

4.07

910

.410

2.17

651.

8900

27.9

196.

897

1.04

PAC

S-C

N

720

1342

2205

8224

5568

5.95

475

160.

0046

.909

2.47

12.

1765

1.89

0027

.946

.751

1.00

PAC

S-C

N

900

1342

2316

8824

5586

5.63

116

70.0

016

0.24

08.

175

2.32

232.

0156

−25.

515

8.57

51.

01PA

CS-

CN

900

1342

2316

8824

5586

5.63

116

160.

0035

.876

1.87

82.

3223

2.01

56−2

5.5

38.1

540.

94PA

CS-

CN

Exp Astron

Tabl

e18

(con

tinu

ed)

OD

OB

SID

mid

-tim

e[J

D]

λ[μ

m]

FD[J

y]σ

[Jy]

r[A

U]

[A

U]

α[◦

]T

PM[J

y]FD

/TPM

Inst

r./M

ode

900

1342

2316

9124

5586

5.64

184

100.

0085

.598

4.36

72.

3223

2.01

57−2

5.5

90.3

920.

95PA

CS-

CN

900

1342

2316

9124

5586

5.64

184

160.

0035

.410

1.86

52.

3223

2.01

57−2

5.5

37.9

190.

93PA

CS-

CN

1181

1342

2491

9224

5614

6.62

035

100.

0042

.930

2.19

12.

5479

2.81

3221

.243

.936

0.98

PAC

S-C

N

1181

1342

2491

9224

5614

6.62

035

160.

0017

.909

0.94

22.

5479

2.81

3221

.218

.509

0.97

PAC

S-C

N

1181

1342

2491

9324

5614

6.62

295

70.0

078

.925

4.02

62.

5479

2.81

3221

.276

.103

1.04

PAC

S-C

N

1181

1342

2491

9324

5614

6.62

295

160.

0017

.795

0.93

92.

5479

2.81

3221

.218

.476

0.96

PAC

S-C

N

1202

1342

2502

9724

5616

7.66

400

70.0

090

.450

4.61

52.

5560

2.55

8423

.091

.542

0.99

PAC

S-C

N

1202

1342

2502

9724

5616

7.66

400

160.

0021

.496

1.13

72.

5560

2.55

8423

.022

.279

0.96

PAC

S-C

N

1377

1342

2639

2024

5634

2.86

389

100.

0063

.413

3.23

62.

5563

2.17

98−2

2.5

67.9

920.

93PA

CS-

CN

1377

1342

2639

2024

5634

2.86

389

160.

0027

.137

1.45

02.

5563

2.17

98−2

2.5

28.6

980.

95PA

CS-

CN

1377

1342

2639

2324

5634

2.87

457

70.0

011

6.73

85.

956

2.55

632.

1799

−22.

511

6.72

11.

00PA

CS-

CN

1377

1342

2639

2324

5634

2.87

457

160.

0027

.244

1.46

72.

5563

2.17

99−2

2.5

28.4

740.

96PA

CS-

CN

1403

1342

2677

4724

5636

8.70

388

250.

008.

732

0.47

02.

5462

2.52

01−2

2.8

8.65

41.

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IRE

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1403

1342

2677

4724

5636

8.70

388

350.

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314

0.23

22.

5462

2.52

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2.8

4.27

91.

01SP

IRE

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1403

1342

2677

4724

5636

8.70

388

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0.11

12.

5462

2.52

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2.8

2.05

51.

00SP

IRE

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1388

1342

2653

8524

5635

3.78

877

250.

0010

.206

0.55

02.

5523

2.32

44−2

3.0

10.0

871.

01SP

IRE

-SM

1388

1342

2653

8524

5635

3.78

877

350.

005.

042

0.27

22.

5523

2.32

44−2

3.0

4.98

81.

01SP

IRE

-SM

1388

1342

2653

8524

5635

3.78

877

500.

002.

423

0.13

12.

5523

2.32

44−2

3.0

2.39

61.

01SP

IRE

-SM

1375

1342

2638

1124

5634

0.51

600

250.

0011

.703

0.63

02.

5571

2.14

90−2

2.3

11.9

980.

98SP

IRE

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1375

1342

2638

1124

5634

0.51

600

350.

005.

735

0.30

92.

5571

2.14

90−2

2.3

5.93

00.

97SP

IRE

-SM

1375

1342

2638

1124

5634

0.51

600

500.

002.

722

0.14

72.

5571

2.14

90−2

2.3

2.84

70.

96SP

IRE

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1201

1342

2503

2424

5616

6.19

958

250.

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073

0.48

92.

5555

2.57

6822

.98.

867

1.02

SPIR

E-S

M

Exp Astron

Tabl

e18

(con

tinu

ed)

OD

OB

SID

mid

-tim

e[J

D]

λ[μ

m]

FD[J

y]σ

[Jy]

r[A

U]

[A

U]

α[◦

]T

PM[J

y]FD

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Inst

r./M

ode

1201

1342

2503

2424

5616

6.19

958

350.

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447

0.24

02.

5555

2.57

6822

.94.

381

1.02

SPIR

E-S

M

1201

1342

2503

2424

5616

6.19

958

500.

002.

147

0.11

62.

5555

2.57

6822

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102

1.02

SPIR

E-S

M

1179

1342

2490

9024

5614

5.01

874

250.

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585

0.40

82.

5473

2.83

1421

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252

1.05

SPIR

E-S

M

1179

1342

2490

9024

5614

5.01

874

350.

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751

0.20

22.

5473

2.83

1421

.13.

581

1.05

SPIR

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M

1179

1342

2490

9024

5614

5.01

874

500.

001.

796

0.09

72.

5473

2.83

1421

.11.

718

1.05

SPIR

E-S

M

916

1342

2323

6924

5588

2.00

303

250.

0012

.440

0.67

02.

3385

2.23

40−2

5.1

12.2

031.

02SP

IRE

-SM

916

1342

2323

6924

5588

2.00

303

350.

006.

177

0.33

32.

3385

2.23

40−2

5.1

6.02

11.

03SP

IRE

-SM

916

1342

2323

6924

5588

2.00

303

500.

002.

972

0.16

02.

3385

2.23

40−2

5.1

2.88

71.

03SP

IRE

-SM

892

1342

2313

4724

5585

8.07

191

250.

0016

.451

0.88

62.

3148

1.91

59−2

5.3

16.8

110.

98SP

IRE

-SM

892

1342

2313

4724

5585

8.07

191

350.

008.

087

0.43

62.

3148

1.91

59−2

5.3

8.29

00.

98SP

IRE

-SM

892

1342

2313

4724

5585

8.07

191

500.

003.

897

0.21

02.

3148

1.91

59−2

5.3

3.97

40.

98SP

IRE

-SM

702

1342

2186

8824

5566

7.55

980

250.

0015

.521

0.83

62.

1682

2.09

3727

.414

.873

1.04

SPIR

E-S

M

702

1342

2186

8824

5566

7.55

980

350.

007.

676

0.41

32.

1682

2.09

3727

.47.

323

1.05

SPIR

E-S

M

702

1342

2186

8824

5566

7.55

980

500.

003.

695

0.19

92.

1682

2.09

3727

.43.

506

1.05

SPIR

E-S

M

669

1342

2159

9424

5563

4.38

330

250.

0011

.246

0.60

62.

1575

2.44

8024

.110

.902

1.03

SPIR

E-S

M

669

1342

2159

9424

5563

4.38

330

350.

005.

579

0.30

02.

1575

2.44

8024

.15.

366

1.04

SPIR

E-S

M

669

1342

2159

9424

5563

4.38

330

500.

002.

648

0.14

32.

1575

2.44

8024

.12.

568

1.03

SPIR

E-S

M

402

1342

1985

7524

5536

7.16

860

250.

0010

.810

0.58

22.

2764

2.41

31−2

5.1

10.5

381.

03SP

IRE

-LM

402

1342

1985

7524

5536

7.16

860

350.

005.

367

0.28

92.

2764

2.41

31−2

5.1

5.20

21.

03SP

IRE

-LM

402

1342

1985

7524

5536

7.16

860

500.

002.

545

0.13

72.

2764

2.41

31−2

5.1

2.49

51.

02SP

IRE

-LM

393

1342

1981

4224

5535

8.16

957

250.

0011

.444

0.61

62.

2849

2.32

05−2

5.7

11.3

671.

01SP

IRE

-LM

393

1342

1981

4224

5535

8.16

957

350.

005.

680

0.30

62.

2849

2.32

05−2

5.7

5.61

31.

01SP

IRE

-LM

Exp Astron

Tabl

e18

(con

tinu

ed)

OD

OB

SID

mid

-tim

e[J

D]

λ[μ

m]

FD[J

y]σ

[Jy]

r[A

U]

[A

U]

α[◦

]T

PM[J

y]FD

/TPM

Inst

r./M

ode

393

1342

1981

4224

5535

8.16

957

500.

002.

681

0.14

42.

2849

2.32

05−2

5.7

2.69

31.

00SP

IRE

-LM

381

1342

1973

1724

5534

7.15

618

250.

0011

.610

0.62

52.

2955

2.20

34−2

6.2

12.3

830.

94SP

IRE

-LM

381

1342

1973

1724

5534

7.15

618

350.

005.

996

0.32

32.

2955

2.20

34−2

6.2

6.11

40.

98SP

IRE

-LM

381

1342

1973

1724

5534

7.15

618

500.

002.

884

0.15

52.

2955

2.20

34−2

6.2

2.93

30.

98SP

IRE

-LM

381

1342

1973

1624

5534

7.14

027

250.

0012

.285

0.66

22.

2955

2.20

33−2

6.2

12.4

960.

98SP

IRE

-LM

381

1342

1973

1624

5534

7.14

027

350.

006.

265

0.33

72.

2955

2.20

33−2

6.2

6.17

01.

02SP

IRE

-LM

381

1342

1973

1624

5534

7.14

027

500.

002.

996

0.16

12.

2955

2.20

33−2

6.2

2.96

01.

01SP

IRE

-LM

369

1342

1966

6724

5533

5.10

704

250.

0014

.413

0.77

62.

3072

2.07

21−2

6.3

14.1

601.

02SP

IRE

-LM

369

1342

1966

6724

5533

5.10

704

350.

007.

121

0.38

32.

3072

2.07

21−2

6.3

6.99

31.

02SP

IRE

-LM

369

1342

1966

6724

5533

5.10

704

500.

003.

402

0.18

32.

3072

2.07

21−2

6.3

3.35

51.

01SP

IRE

-LM

354

1342

1957

5024

5531

9.94

391

250.

0016

.889

0.91

02.

3222

1.90

59−2

5.5

16.7

961.

01SP

IRE

-LM

354

1342

1957

5024

5531

9.94

391

350.

008.

487

0.45

72.

3222

1.90

59−2

5.5

8.29

41.

02SP

IRE

-LM

354

1342

1957

5024

5531

9.94

391

500.

004.

161

0.22

42.

3222

1.90

59−2

5.5

3.97

91.

05SP

IRE

-LM

Exp Astron

Tabl

e19

Phot

omet

ric

Her

sche

ldat

aof

(21)

Lut

etia

OD

OB

SID

mid

-tim

e[J

D]

λ[μ

m]

FD[J

y]σ

[Jy]

r[A

U]

[A

U]

α[◦

]T

PM[J

y]FD

/TPM

Inst

r./M

ode

1399

1342

2672

6424

5636

4.59

671

70.0

04.

399

0.22

42.

6964

2.42

94−2

1.8

4.48

20.

98PA

CS-

SM

1399

1342

2672

6524

5636

4.60

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70.0

04.

382

0.22

42.

6964

2.42

95−2

1.8

4.49

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1198

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859

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PAC

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400

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1984

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2.78

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400

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1984

9524

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5.22

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2.78

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1399

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2672

6124

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4.58

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2.42

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1399

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1198

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400

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400

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1984

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221

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221

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Exp Astron

Tabl

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OD

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Inst

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221

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400

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400

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400

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1984

9424

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400

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1984

9524

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Exp Astron

Tabl

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OD

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mid

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r[A

U]

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α[◦

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Inst

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ode

221

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1883

3424

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6.57

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221

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221

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221

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221

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221

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221

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221

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1399

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1.60

18−2

8.8

0.29

80.

97SP

IRE

-SM

423

1342

2002

0424

5538

8.83

050

250.

000.

272

0.01

62.

7189

3.05

43−1

9.4

0.28

10.

97SP

IRE

-SM

423

1342

2002

0424

5538

8.83

050

350.

000.

144

0.01

02.

7189

3.05

43−1

9.4

0.14

60.

99SP

IRE

-SM

423

1342

2002

0424

5538

8.83

050

500.

000.

065

0.00

92.

7189

3.05

43−1

9.4

0.07

30.

89SP

IRE

-SM

Exp Astron

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