The long-wavelength thermal emission of the Pluto-Charon system from Herschel observations. Evidence for emissivity effects

0.81 MB·

by  E. Lellouch

Astronomy&Astrophysicsmanuscriptno.27675˙final c ESO2016
(cid:13)
January22,2016
The long-wavelength thermal emission of the Pluto-Charon system
⋆
from Herschel observations. Evidence for emissivity effects.
E.Lellouch1,P.Santos-Sanz2,S.Fornasier1,T.Lim3,J.Stansberry4,E.Vilenius5,6,Cs.Kiss7,T.Mu¨ller6,G.Marton6,
S.Protopapa8,P.Panuzzo9,andR.Moreno1
1 LESIA,ObservatoiredeParis,PSLResearchUniversity,CNRS,SorbonneUniversite´s,UPMCUniv.Paris06,Univ.ParisDiderot,
SorbonneParisCite´,5placeJulesJanssen,92195Meudon,France
e-mail:[email protected]
6 2 InstitutodeAstrof´ısicadeAndaluc´ıa-CSIC,GlorietadelaAstronom´ıas/n,18008-Granada,Spain.
1 3 EuropeanSpaceAstronomyCentre(ESAC),P.O.Box78,E-28691VillanuevadelaCan˜ada,Madrid,Spain
0 4 SpaceTelescopeScienceInstitute,3700SanMartinDrive,Baltimore,MD21218USA
2 5 Max-Planck-Institutfu¨rSonnensystemforschung,Justus-von-Liebig-Weg3,37077Go¨ttingen,Germany
6 Max-Planck-Institutfu¨rExtraterrestrischePhysik,Giessenbachstraße,85748Garching,Germany
n
7 KonkolyObservatoryoftheHungarianAcademyofSciences,H-1121Budapest,KonkolyThegeMiklst15-17,Hungary
a
J 8 DepartmentofAstronomy,UniversityofMaryland,CollegePark,MD20742,USA
9 GEPI,Observatoire deParis,PSLResearchUniversity, CNRS,Univ. ParisDiderot, Sorbonne ParisCite´,5PlaceJulesJanssen,
1
92195Meudon,France
2
Received,November2,2015;Revised,December19,2015
]
P
ABSTRACT
E
. ThermalobservationsofthePluto-CharonsystemacquiredbytheHerschelSpaceObservatoryinFebruary2012arepresented.They
h
consist of photometric measurements with the PACS and SPIRE instruments (nine visits to the Pluto system each), covering six
p
- wavelengthsfrom70to500µmaltogether.ThethermallightcurveofPluto-Charonisobservedinallfilters,albeitmoremarginally
o at160andespecially500µm.PuttingthesedataintothecontextofolderISO,Spitzerandground-basedobservationsindicatesthat
r the brightness temperature (T ) of the system (rescaled to a common heliocentric distance) drastically decreases with increasing
t B
s wavelength,from 53Kat20µmto 35Kat500µm,andperhapseverlessatlongerwavelengths.Consideringavarietyofdiurnal
a and/or seasonal th∼ermophysical mode∼ls, weshow thatT values of 35Karelower thananyexpected temperature forthedayside
B
[ surfaceorsubsurfaceof PlutoandCharon, implyingalowsurfaceemissivity.Basedonmultiterrainmodeling, weinferaspectral

emissivitythatdecreasessteadilyfrom1at20-25µmto 0.7at500µm.Thiskindofbehaviorisusuallynotobservedinasteroids
1 ∼
(whenproper allowance ismade for subsurface sounding), but isfound inseveral icysurfaces of thesolar system. Wetentatively
v
identifythatacombinationofastrongdielectricconstantandaconsiderablesurfacematerialtransparency(typicalpenetrationdepth
6
1cm)isresponsiblefortheeffect.OurresultshaveimplicationsfortheinterpretationofthetemperaturemeasurementsbyREX/New
0 ∼
Horizonsat4.2cmwavelength.
6
5 Key words. Kuiper belt objects: individual: Pluto, Charon. Planets and satellites: surfaces. Methods: observational. Techniques:
0 photometric.
.
1
0
6 1. Introduction seasonalcycles must be at work, in which volatile N (and the
2
1 secondaryspeciesCH andCO)aresharedbetweenatmospheric
4
: The New Horizons flyby of the Pluto system on July 14, 2015 andsurfaceicereservoirsthroughsublimation/condensationex-
v
revealed Pluto and Charon as planetary worlds (Sternetal.,
i changes and volatile migration. These processes are related to
X 2015). Pluto appears to display an unexpected variety of ter- the temperature distribution across Pluto’s surface, which re-
rainmorphologies,suggestinga complexhistoryofsurfaceac-
r flects the balance between insolation, thermal radiation, ther-
a tivity. These include icy plains with evidence for glacier-like
malconduction,andlatentheatexchanges,anddependsonim-
flows of ice and polygonal ice patterns, mountain ridges sev-
portantparameterssuchasalbedo,emissivity,andthermaliner-
eralkilometershigh,anddark,cratered,ancientterrains,where
tia (see,e.g.,Hansen&Paige, 1996;Young, 2012).AtCharon,
irradiation of surface ices (N , CH , CO) and/or atmospheric
2 4 where no atmosphere has yet been detected, such resurfacing
production of organic tholins falling to the surface may be re-
processes are less obvious, although the distinctly red color of
sponsiblefor the dark redcolor. While the identificationof the
Charon’snorthpolarregionmayberelatedtoseasonalcoldtrap-
processesshapingthisrichgeologyisjustbeginning,italready
pingof volatiles in that region,followedby energeticradiation
seems clear that Pluto’s surface appearanceis to a large extent
(Sternetal.,2015).
sculptedbyinteractionsbetweenitsmobilevolatileices,evolv-
ing N -dominated atmosphere, and surface bedrock. Mars-like Temperature measurements on an icy surface are possible
2
from the temperature-dependentposition and shape of near-IR
⋆ Herschel is an ESA space observatory with science instruments absorption bands (e.g., Quirico&Schmitt, 1997; Trykaetal.,
providedbyEuropean-ledPrincipalInvestigatorconsortiaandwithim- 1994, 1995; Grundyetal., 1999; Grundy,Schmitt&Quirico,
portantparticipationfromNASA. 2002). This diagnostic is to be used by New Horizons/Ralph
1
Lellouchetal.:HerschelobservationsofPluto
(Reutersetal., 2008), for example, for the N (2-0) ice band at WeusedtheminiscanmapmodeforPACS,whichhasbeen
2
2.15µm.Theonlyothermethodfordeterminingsurfacetemper- demonstratedto bemoresensitive thanthe point-source(chop-
aturesisthermalradiometry.Thermalmeasurements(ingeneral nod)mode(Mu¨lleretal.,2010)1.Foreachfiltercombination(70
spatially unresolved) of the Pluto system at a variety of wave- /160µmor100/160µm),weacquireddataconsecutivelyintwo
lengths(from 20to1400µm)havebeenacquiredusingIRAS, scanningdirections(termed“A”and“B”),with70 and110 an-
◦ ◦
∼
ISO,andSpitzer,andanumberofground-basedmm/submmfa- gleswithrespecttothedetectorarrayandindividualintegration
cilities.Inparticular,theISOandSpitzermeasurementsclearly timesof286secperscan,i.e.,1144sec(4repetitions)perPACS
detected the Pluto+Charon thermal light curve that is associ- visit.ObservationaldetailsaregiveninTable1,wheretheA-B
atedwiththealbedocontrastsonPlutoandthediurnalvariabil- scanningsequencesareindicatedbyconsecutiveObs.IDnum-
ity of insolation. These measurements have provided the first bers.
determination of the thermal inertia of Pluto and Charon, and Far-infrared photometry can often be plagued by confu-
some constraints on their emissivity behavior over 20-160 µm sion noise, i.e., spatial variations in the sky emission at scales
(Lellouchetal.,2000a,2011). comparable to the PSF. The confusion noise is typically 5-7
∼
The operation of Herschel (Pilbrattetal., 2010) in 2009- mJy/beamin the SPIRE bands(Nguyenetal., 2010) andlower
2013 offered an opportunity to extend the study toward longer in the PACS bands, but Pluto’s 2012 position in star-crowded
wavelengths (70-500 µm), bridging the gap with the sub- regions of Sagittarius not far from Galactic center made sky
mm/mm measurements. Combined with previous Spitzer data, backgroundlevelsa priorimoresevere.Estimatesofconfusion
these measurements permit us to refine our estimates of levels at proposal stage indicated that even though the March
Pluto’s and Charon’s thermal inertia, and determine the long- 2012epochwasmostfavorableinthisrespect(andselectedfor
wavelengthbehaviorofthesystem’semission.Followinganini- that reason), it would be subject to confusion noise at the 5
∼
tial assessment of the data (Lellouchetal., 2013a), we present and 20 mJy in the PACS 100µm and 160µm beams, respec-
∼
a detailedreportof these observationsand their modeling.The tively,i.e.,anon-negligiblefractionoftheexpectedfluxesfrom
Herschel70-µmdatathataredescribedbelowhavealreadybeen Pluto ( 400 and 300 mJy, respectively). However, the proper
∼
usedtoderivelimitsontheamountofdustinthePluto–Charon motionofPlutoofferedthepossibilitytoobservethetargetsev-
system(Martonetal.,2015). eral times against different sky backgrounds, permitting us to
subtract the sky contribution. The efficiency of this “follow-
on”(a.k.a.second-visit)approachhasbeendemonstratedbythe
2. Herschelobservations
detection of numerous TNOs at the mJy level by Spitzer and
We obtained thermal photometry of the Pluto system with the Herschel(e.g.,Stansberryetal.,2008;Santos-Sanzetal.,2012).
two imaging photometers of Herschel, PACS (Photoconductor Forthe techniqueto work,the propermotionbetweentwo vis-
Array Camera and Spectrometer; Poglitschetal. (2010)) its should be significantly larger than the PSF size, but remain
and SPIRE (Spectral and Photometric Imaging Receiver; smallenoughthatatthesecondvisit,theobjectstillfallswithin
Griffinetal. (2010)), covering altogether six wavelengths. The the high-coveragearea of the map from the first visit. In prac-
SPIREinstrumentobservesa4’x8’fieldsimultaneouslyinthree tice,theseconditionsarebestmetforpropermotionsof30”–50”
bolometerarraysat250µm,350µm,and500µm,withrespec- forPACSobservationsand72”–150”forSPIRE.Inourobserv-
tive pixelsizes of 6”, 10”, and 13”. PACS can operate in three ing sequence, the propermotion of Pluto between two consec-
filters, centered at 70 µm (“blue”), 100 µm (“green”),and 160 utive visits ( 17 hour separation) was of 55–35arcsec, almost
∼
µm(“red”).However,asitincludestwodetectorarrays(64x32 entirelyinthe RA direction(anddecreasingwith time asPluto
pixels of 3.2”x 3.2” for blue/green and 32 x 16 pixels of 6.4” approachedstationarityonApril10,2012).Thus,forPACSob-
x 6.4” for red, each of them covering a FOV of 3.5’ x 1.75’), servations, each visit to Pluto could be used as second epoch
onlytwofilters outofthree(70/160µm or100/ 160µm) are measurementfortheprecedingand/orfollowingvisit(17hours
observedinparallel. before or after). For SPIRE, we often used more distant visits
For both instruments, the beam size (17”-35” FWHM for (i.e.,34or51hoursbeforeorafteragivenobservation)forthe
SPIRE and 5”-11” FWHM for PACS, depending on filter) en- second epoch,as differencemaps betweentwo contiguousvis-
compassed the entire 1”-wide Pluto system, thus including itswouldresultinthepositiveandnegativePlutoimagesinthe
thermalemissionfrom∼PlutoandCharon(withanegligiblecon- differentialmaptopartiallyoverlapat500µm.
tribution from the other four moons). All data were acquired
overthreeweeksinlateFebruarytomid-March2012,underthe
3. Datareduction
OT2_elellouc_2program(“Pluto’sseasonalevolutionandsur-
facethermalproperties”).We acquirednineobservationsofthe
PACS: Data reduction was initially performed within the
Plutosystemwith eachinstrument.Theyweretimedtosample
HerschelInteractiveProcessingEnvironment(HIPE;Ott,2010),
equally-spacedsubobserverlongitudes,soastoprovideamulti-
version12,usingitsdefaultFM7calibrationschemeandanop-
bandthermallightcurve.Inpractice,consecutivevisitstoPluto
timumscriptfor“bright”sources.EachPACSvisittoPlutopro-
werescheduledwithatimeseparationof 17hours,equivalent
vides two images (A and B scans) at 70 µm and 100 µm, and
∼
to 40 longitude.The SPIRE observationsoccurredoverFeb.
◦ four images at 160 µm. For the green (100 µm) and red (160
∼
29 – Mar. 6, 2012, while the PACS data were taken on Mar.
µm)data,eachimageofagivenvisitwasanalyzedincombina-
14–19,2012.Pluto’sheliocentricdistanceatthattimewasr =
h tionwiththecorrespondingimageoftheprevious(“before”)or
32.19 AU, the subsolar latitude was β = 47.0 , and the phase
◦ successive(“after”)visittoPluto.Theexceptiontothiswas,of
anglewas1.6 .
◦ course,forthefirst(resp.last) visittoPlutoforwhichonlythe
WeacquiredtheSPIREobservationsinthesmall-mapmode.
“after”(resp.“before”)imagecouldbeused.Thispermittedus
The telescope was scanned across the sky at 30”/sec, in two
nearlyorthogonal(84.8◦ angle)scan paths, uniformlycovering 1 See also AOT Release Note: PACS Photometer Point/Compact
anareaof5’x5’.EachSPIREvisittoPlutoamountedto1421 Source Mode 2010, PICC-ME-TN-036, Version 2.0, custodian Th.
sec,correspondingtotenrepetitionsofthescanningpattern. Mu¨ller(PACSPhotometerPoint/CompactSourceMode,2010).
2
Lellouchetal.:HerschelobservationsofPluto
Table1.Summaryofobservations
Obs.ID Instrument/Mode Filter StartTime T ∆a Longitudeb Fluxc
obs
(2012-) (sec.) (mJy)
1342239786 SPIREPhoto 250/350/500 02-2920:08:23 1421 32.649 28.0 179.9 2.7/107.9 2.9/ 58.4 3.5
1342239900 SPIREPhoto 250/350/500 03-0113:04:38 1421 32.638 347.5 176.8±2.0/105.8±3.0/ 56.0±3.5
1342239979 SPIREPhoto 250/350/500 03-0206:30:10 1421 32.627 306.8 174.8±3.0/106.2±2.9/ 57.7±3.5
1342240025 SPIREPhoto 250/350/500 03-0222:44:11 1421 32.617 268.8 175.5±2.9/104.9±3.1/ 58.6±3.5
1342241087 SPIREPhoto 250/350/500 03-0316:21:25 1421 32.606 227.4 171.9±2.8/106.0±3.1/ 59.4±3.6
1342241158 SPIREPhoto 250/350/500 03-0409:17:02 1421 32.596 187.6 170.7±2.9/106.2±3.0/ 56.5±3.5
1342240277 SPIREPhoto 250/350/500 03-0502:18:31 1421 32.585 147.6 174.9±2.9/106.3±3.0/ 56.5±3.5
1342240315 SPIREPhoto 250/350/500 03-0519:12:47 1421 32.574 107.9 184.9±2.9/111.9±3.0/ 59.8±3.5
1342240318 SPIREPhoto 250/350/500 03-0611:44:14 1421 32.563 69.1 186.9±3.0/116.6±2.9/ 63.9±3.5
1342241381-2 PACSPhoto 70/160 03-1403:02:01 2x286 32.442 358.7 321.9±8.6/ ± /331.0±10.1
1342241383-4 PACSPhoto 100/160 03-1403:13:39 2x286 32.442 358.2 ± /393.3 4.0/331.0±10.1
1342241418-9 PACSPhoto 70/160 03-1419:54:46 2x286 32.431 319.1 316.5 2.7/ ± /317.3±20.9
1342241420-1 PACSPhoto 100/160 03-1420:06:24 2x286 32.431 318.6 ± /406.1 7.9/317.3±20.9
1342241471-2 PACSPhoto 70/160 03-1512:58:39 2x286 32.419 279.0 312.2 7.3/ ± /313.3±20.0
1342241473-4 PACSPhoto 100/160 03-1513:10:17 2x286 32.419 278.6 ± /380.4 13.4/313.3±20.0
1342241509-0 PACSPhoto 70/160 03-1606:33:59 2x286 32.407 237.6 295.0 7.1/ ± /314.8±13.6
1342241511-2 PACSPhoto 100/160 03-1606:45:37 2x286 32.407 237.2 ± /377.2 3.6/314.8±13.6
1342241620-1 PACSPhoto 70/160 03-1700:10:12 2x286 32.395 196.3 299.8 3.5/ ± /309.9±10.5
1342241622-3 PACSPhoto 100/160 03-1700:21:50 2x286 32.395 195.8 ± /371.1 7.1/309.9±10.5
1342241655-6 PACSPhoto 70/160 03-1717:31:54 2x286 32.384 155.5 311.5 4.5/ ± /307.5±16.6
1342241657-8 PACSPhoto 100/160 03-1717:43:32 2x286 32.384 155.1 ± /379.3 9.3/307.5±16.6
1342241699-0 PACSPhoto 70/160 03-1811:04:14 2x286 32.372 114.3 342.1 2.8/ ± /329.7±12.6
1342241701-2 PACSPhoto 100/160 03-1811:15:52 2x286 32.372 113.9 ± /418.3 2.9/329.7±12.6
1342241865-6 PACSPhoto 70/160 03-1904:42:46 2x286 32.360 72.9 347.6 12.4/ ± /338.7±25.7
1342241867-8 PACSPhoto 100/160 03-1904:54:24 2x286 32.360 72.4 ± /426.9 6.2/338.7±25.7
1342241928-9 PACSPhoto 70/160 03-1920:44:31 2x286 32.349 35.2 349.1 4.4/ ± /353.0±18.5
1342241930-1 PACSPhoto 100/160 03-1920:56:09 2x286 32.349 34.8 ± /413.9 3.9/353.0±18.5
aObserver-centricdistance ± ±
bSubobservereastlongitudeatmid-point.Weadoptthesameorbitalconventionsas,e.g.,Buie,Tholen,&Wasserman(1997)and
Lellouchetal.(2011).ZerolongitudeonPlutoisthesub-Charonpoint.Thesubobserverpointlongitudedecreaseswithtime.
cColor-correctedfluxes.PACS160-µmfluxesaregivenfortheaverageoverfourconsecutiveObs.IDs(seetext)
to generate two backgroundmaps, which were then subtracted ate(towithin 0.01)forrespectivecolortemperaturesof47K,
±
from the individual image, providing a cleaner map suited for 45 K, and 43 K. The final flux values are gathered in Table 1.
photometry.Standardaperturephotometryon the resultingdif- Additionalsystematiccalibrationuncertainties(5%ofthemea-
ference image was performedwith our own IRAF/DAOPHOT- suredflux),whichdonotaffectthelightcurves,arenotincluded
based routines via a curve-of-growth approach to determine inTable1.
the optimum synthetic aperture and a Monte-Carlo method of
SPIRE:SPIREdatawerefirstprocessedusingHIPE,version
200 fictitious source implantations to estimate error bars (see
10,includingde-stripingroutinesthatminimizebackgrounddif-
Santos-Sanzetal.(2012)andKissetal.(2014)fordetails).The
ferencesbetweendataacquiredatdifferentepochsandthatprop-
method thus provided in general (i.e., except for the first and
erly correctthe signaltimeline. Then,mapswere producedus-
lastvisit,forwhichtwotimesfewervalueswereobtained)four
ingthestandardnaivemap-making,projectingthedataofeach
(in the green)or eight(in the red)individualvaluesof the flux
bandonthesame WorldCoordinateSystem(WCS) andapply-
(f, error bar σ) per visit. The sky subtraction did not bring
i i ingcross-correlationroutinesbetweentwoepochstocorrectfor
anynoticeableimprovementforblue(70-µm)data,whichhave
astrometry offsets. Finally, for each Pluto visit, several differ-
the least backgroundcontamination.Therefore,we simplyper-
ence maps were computed at each band by subtracting, from
formed aperture photometry on the original A and B images,
the map under consideration,maps taken at other epochs, sep-
providing two sets of values per visit. The optimum aperture
arated by 17, 34 and/or 51 hours (also depending on
radiiwere foundto be 5.5”,7.0”, and 10.5”in the blue, green, ∼ ± ± ±
theconsideredfilter).Photometryonthesedifferencemapswas
and red bands, respectively, i.e., close to the PSF FWHM at
thenperformedwithatwo-dimensionalcircularGaussianaper-
the corresponding wavelengths. For each filter and visit, the
ture with a fixed filter-dependentFWHM (PSF fitting), follow-
2 to 8 (1 to 4 for first and last visit) individually-determined
ingthemethoddescribedinFornasieretal.(2013).Thederived
fluxes were (error-bar weighted) averaged. To be conservative,
flux was then corrected by the instrumentpixellization factors,
we took the final error on the average flux to be max (std(f),
i i.e., dividingby 0.951,0.931,and 0.902for 250, 350, and 500
1/ 1 ), where std(f) is the standard deviation of the indi- µm, respectively. Finally, color corrections were estimated by
σ2 i
vidquPal fliuxes. Minor color corrections were finally applied, by convolvinga blackbodyemission at 35–40K, the approximate
system brightness temperatureat the SPIRE wavelengths, with
dividing the averaged fluxes and their error bars by factors of
the instrument spectral response profiles. These multiplicative
0.983(70-µm),0.982(100-µm),and1.000(160-µm),appropri-
colorcorrectionfactorswerefoundtobe0.974,0.976,and0.957
3
Lellouchetal.:HerschelobservationsofPluto
at 250, 350, and 500 µm, and applied to the individual Pluto- 4. Modeling
Charonfluxes.Thefinalsystemfluxforeachvisitwasthencom-
4.1.Qualitativeanalysis
putedastheweightedmeanoftheindividualfluxesbasedonthe
various differential maps (in a few cases after rejecting some Brightness temperatures of the Pluto-Charon system over 70-
outliers).Finalfluxeswithallcorrectionsincludedaregathered 500 µm as a function of rotational phase are shown in Fig.1.
in Table 1. Similar to PACS, the errors include the uncertain- Immediately apparentin the figure is that: (i) the mean bright-
ties provided by the Gaussian fitting algorithm, but do not ac- nesstemperature(T )ofthesystemdecreasessteadilywithin-
B
countforabsolutecalibrationuncertainties,whichareestimated creasingwavelengthfrom 46.5Kat70µmto 35Kat500µm;
tobe7%ofthemeasuredflux.ThefinalPACSandSPIREfluxes and (ii) the thermal light∼curve is detected at∼all wavelengths,
wereconvertedintosystembrightnesstemperatures(TB)byas- albeit somewhat marginallyat 160 µm and especially 500 µm,
suming a 1185 km radius for Pluto and 604 km for Charon. giventhehighererrorbarsofthesedata.At70and160µm,the
TheCharonradiusisbasedonstellaroccultation(Sicardyetal., dataare ofmuchhigherqualitythanwas possiblefromSpitzer
2006).TheadoptedPlutoradiusisclosetothebestguessvalue (see Fig. 2 from Lellouchetal. (2011); hereafter Paper I). All
from Lellouchetal. (2015), 1184 km. These values match ini- dataareconsistentwithmaximumfluxnearaneastlongitudeL
tial reports from New Horizons (606 3 km and 1187 4 km; =60-80andminimumfluxnearL=200-220.Morequantitati-
± ±
Sternetal., 2015).Results wouldbe insignificantlysensitiveto tively,sinusoidalfitstothedatayieldfluxmaximaatL=57 5,
further changes of the radii by a few kilometers. The adopted 50 8,42 22,57 10,76 17,and70 60for70,100,160,2±50,
valueforPluto’sradiusupdatesthevaluethatwasusedinprevi- 35±0,and5±00-µm±data.Th±us,withinm±easurementsuncertainties,
ousmodelingoftheISOandSpitzerdata(1170km).Theeffect alllightcurvesappearin phase(inparticular,thereisexcellent
isnegligibleat24µm(a 0.1KdecreaseintheTB)butnoten- phaseagreementbetweenthe70µm,100µmand250µmdata).
∼
tirelysoat500µm( 0.5Kdecrease). Out-of-phase light curves at the longest wavelengths had been
∼
envisagedinPaperI.
In Fig. 2, the Herschel measured brightness tempera-
tures are plotted as a function of wavelength and put into
the broader context of most previous thermal measurements
of the Pluto-Charon system. These measurements include (i)
PPPPPPAAAAAACCCCCCSSSSSS 777777000000 µµµµµµmmmmmm ISOPHOT60,100,150,and200µm photometry,takenmostly
444444888888 PPPPPAAAAACCCCCSSSSS 111110000000000 µµµµµmmmmm inFeb.-March1997(fivetoeightvisitstoPluto;Lellouchetal.
PPPPAAAACCCCSSSS 111166660000 µµµµmmmm
SSSPPPIIIRRREEE 222555000 µµµmmm (2000a));(ii)Spitzer/MIPS23.68,71.42,and156µmphotome-
SSSPPPIIIRRREEE 335550000 µµµmmm tryandSpitzer/IRSlow-resolutionspectroscopyover20-37µm
444444666666 recordedinAugust-September2004(eightvisitstoPlutoeach;
Paper I); (iii) additional Spitzer/MIPS data at 23.68 and 71.42
µm taken in April 2007(12 visits; see Fig. 13 of Paper I), and
unpublished156µmdatafromOctober2008(12visits);and(iv)
444444444444 anumberofground-basedmeasurementsatmm/sub-mmwave-
K)K)K)K)K)K) lengths from IRAM, JCMT, and SMA (Altenhoffetal., 1988;
e (e (e (e (e (e ( Stern,Weintraub&Festou, 1993; Jewitt, 1994; Lellouchetal.,
urururururur
atatatatatat 2000b; Gurwell,Butler&Moullet, 2011). We emphasize that
perperperperperper 444444222222 the SMA data separate Pluto from Charon, and we report the
mmmmmm
ss tess tess tess tess tess te aPnludtoIR-oSnldyatTaBfrformom20200405ataenigdh2t0lo1n0g.iItnudFeisgaurreep2l,oSttpeditzienrd/iMviIdPuS-
eeeeee
htnhtnhtnhtnhtnhtn ally.Wereinterpolate,tothesameeightlongitudes,theHerschel
gggggg 444444000000
bribribribribribri (70, 100, 160, 250, 350, and 500 µm), Spitzer 71.42 µm from
n n n n n n 2007, and ISO 60 and 100 µm data, all of which clearly show
oooooo
harharharharharhar light curves. For data in which we did not discern (or attempt
CCCCCC
++++++ to detect) a light curve, i.e., ISO 150 and 250 µm, Spitzer 156
oooooo 333333888888
utututututut µm from October 2008, and all of the ground-based data, we
PlPlPlPlPlPl
simply plotted the mean T averaged over the available mea-
B
surements. All of the ISO, Spitzer, and Herschel T in Fig. 2
B
333333666666 makeconsistentuseoftheabovePlutoandCharonradii.Incon-
trast, mm/sub-mm T simply use published values, because of
B
thedifficultyintrackingdowntheoriginallyusedradii.Allthese
thermalmeasurementsspan25years(1986-2012),aperiodover
333333444444 whichPluto’sheliocentricdistance(r )andsubsolarlatitude(β)
h
variedfrom29.7AU to32.2AU andfrom-4 to+47 , respec-
◦ ◦
tively.Whiletheeffectofachangeinthesubsolarlatitudecannot
beaccountedforwithoutadetailedmodel,theeffectofvarying
000000 555555000000 111111000000000000 111111555555000000 222222000000000000 222222555555000000 333333000000000000 333333555555000000
r ishandledbyrescalingthemeasuredT by1/√r totheepoch
EEEEEEaaaaaasssssstttttt lllllloooooonnnnnnggggggiiiiiittttttuuuuuuddddddeeeeee h B h
oftheSpitzer2004data(r =30.847AU).
h
Fig.1. Pluto-Charon thermal light curves in the six filters ob- Fig. 2 illustrates a number of important features. (i) The
servedwithPACSandSPIRE. difficult-to-explainPluto“fading”witnessedbySpitzer,i.e.,the
decrease by 2 K of the 71 µm T (and by 0.5 K at 24 µm)
B
∼ ∼
over2004-2007(PaperI)isnotconfirmedintheHerscheldata,
which indicates 70-µm T in good agreement with the Spitzer
B
4
Lellouchetal.:HerschelobservationsofPluto
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e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e IIIIIIIIIIIIIIIIIIIIRRRRRRRRRRRRRRRRRRRRAAAAAAAAAAAAAAAAAAAAMMMMMMMMMMMMMMMMMMMM ((((((((((((((((((((LLLLLLLLLLLLLLLLLLLLeeeeeeeeeeeeeeeeeeeelllllllllllllllllllllllllllllllllllllllloooooooooooooooooooouuuuuuuuuuuuuuuuuuuucccccccccccccccccccchhhhhhhhhhhhhhhhhhhh eeeeeeeeeeeeeeeeeeeetttttttttttttttttttt aaaaaaaaaaaaaaaaaaaallllllllllllllllllll.................... 22222222222222222222000000000000000000000000000000000000000000000000000000000000bbbbbbbbbbbbbbbbbbbb))))))))))))))))))))
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
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aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIISSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaannnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIISSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
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c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c OOOOOpppppeeeeennnnn ccccciiiiirrrrrcccccllllleeeeesssss ===== MMMMMIIIIIPPPPPSSSSS 22222000000000077777/////22222000000000088888
ririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririririri
ntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntntnt
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ocococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococococ MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaannnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn ελ = 1
elielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielielieli 4444444444444444444444444444444444444444444444444444444444444444444444444444444444455555555555555555555555555555555555555555555555555555555555555555555555555555555555 MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLoooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnngggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg..................................................................................==================================================================================77777777777777777777777777777777777777777777777777777777777777777777777777777777778888888888888888888888888888888888888888888888888888888888888888888888888888888888----------------------------------------------------------------------------------88888888888888888888888888888888888888888888888888888888888888888888888888888888880000000000000000000000000000000000000000000000000000000000000000000000000000000000 2222222222222222222222222222222222222222222222222222222222222222222222222222222222000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008888888888888888888888888888888888888888888888888888888888888888888888888888888888 MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaannnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIISSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
d td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td td t LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLoooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnngggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg..................................................................................==================================================================================33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333----------------------------------------------------------------------------------33333333333333333333333333333333333333333333333333333333333333333333333333333333337777777777777777777777777777777777777777777777777777777777777777777777777777777777
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLoooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnngggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg..................................................................................==================================================================================111111111111111111111111111111111111111111111111111111111111111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222----------------------------------------------------------------------------------111111111111111111111111111111111111111111111111111111111111111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222227777777777777777777777777777777777777777777777777777777777777777777777777777777777 IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIISSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
scalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscalscal 4444444444444444444444444444444444444444444444444444444444444444444444444444444444400000000000000000000000000000000000000000000000000000000000000000000000000000000000 LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLoooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnngggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg..................................................................................==================================================================================333333333333333333333333333333333333333333333333333333333333333333333333333333333344444444444444444444444444444444444444444444444444444444444444444444444444444444448888888888888888888888888888888888888888888888888888888888888888888888888888888888----------------------------------------------------------------------------------333333333333333333333333333333333333333333333333333333333333333333333333333333333355555555555555555555555555555555555555555555555555555555555555555555555555555555551111111111111111111111111111111111111111111111111111111111111111111111111111111111 2222222222222222222222222222222222222222222222222222222222222222222222222222222222MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII4444444444444444444444444444444444444444444444444444444444444444444444444444444444PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
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KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
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Fig.2.Brightnesstemperature(T )ofthePlutosystem.MostthermalobservationsfromISO,Spitzer,Herschel,andground-based
B
telescopesaregathered.Asdatawereacquiredatdifferentepochsspanning 25years,theT arerescaledby1/√r toacommon
B h
∼
epoch(September2004,r = 30.847AU). Solidlines:eightSpitzer/IRSspectraover21-37µm, takenin Aug.-Sept.2004ateast
h
longitudesof33(yellow),78(gray),122(lightblue),168(darkblue),213(red),257(green),302(pink),and348(black).Filled
circles:Spitzer/MIPSphotometricmeasurements,takenatsimilarlongitudes(37,80,127,172,218,264,307,and351,samecolor
codes)inSeptember2004.TheSpitzerdataaretakenfromLellouchetal.(2011)(PaperI).Opencircles:additionalSpitzer/MIPS
data at 71.42 µm from April 2007 (see Fig. 13 from Paper I). Triangles: Herschel data at 70, 100, 160, 250, 250, and 500 µm
fromthiswork.Filledsquares:datafromISOat60and100µmtakenin1997(Lellouchetal.,2000a).TheHerschel,Spitzer2007
andISOdataarereinterpolatedtotheeightlongitudesobservedbySpitzerin2004.TheISO100µm(resp.Spitzer2007)dataare
shiftedby3µm(resp.2µm)foreasierlegibility.Thecomparisonbetweentheopenandfilledcirclesat71µmillustratesthe“Pluto
fading” witnessed by Spitzer from 2004 to 2007. Additional data (averaged over longitudes, no error bar) from ISO at 150 and
200 µm, and from unpublishedSpitzer 156µm observationstaken in October 2008,are shown as filled squaresand open circles
respectively,underthelabels“MeanISO”and“MeanMIPS2008”.Forground-baseddatasetssamplingmorethanonelongitude,
onlytheaverageT isplotted.TheSMA-measuredT referstoPlutoonly.Thedottedlinesshowthermophysicalmodelfits(see
B B
text),calculatedfortheconditionsofSeptember2004.Graydottedline:parametersarefromCase 4inTable2.Bluedottedline:
same, but with spectral emissivities = 1. This latter case still producesbrightnesstemperaturesthat decrease with wavelength, a
consequenceofthespatialmixingofdifferentsurfacetemperatures.
2004data.(ii)The150-160µmT showlargedispersion.While temperature with wavelength over the entire thermal range (λ
B
theoriginalISO-150µm data(Lellouchetal.,2000a)indicated > 20 µm). Althoughdata in the sub-mm/mmrange show large
anomalouslyhighfluxes(T 50Kinaverage),theSpitzer/MIPS dispersion,the mostaccurateof them(i.e., the SMA data from
≥
156µmdatafromApril2004insteadpointedtoT <40K.The 2010 (Gurwell,Butler&Moullet, 2011) and the IRAM Feb.-
B
additionalSpitzer/MIPS156µmunpublisheddatafromOctober Mar. 2000 data from Lellouchetal. (2000b)) point to a 32 K
∼
2008(12visits)indicateamean(rescaled)valueof45.3Kwith brightnesstemperatureat1100-1300µm, i.e., a consistent“ex-
aformalerrorof1K,buta5.2Kdispersionoverthe12visits, trapolation”ofthetrendindicatedbytheHerscheldataintothe
whichisamorelikelyrepresentationofactualuncertainty.This mm range. Thusit appearsthat the Pluto-CharonT decreases
B
mean value is generally in line, albeit somewhat on the higher bymorethan30%ofitsvaluefrom20µm( 53K)to500µm
∼
side,withthe160µmT indicatedbyHerschel.(iii)Theensem- ( 35K)andbeyond.
B
∼
bleofdataclearlyoutlinesthedecreaseofthesystembrightness
5
Lellouchetal.:HerschelobservationsofPluto
4.2.Emissivity flectionatthesurface,whichcanbe characterizedbya Fresnel
coefficientwithmoderate( 2.3)dielectricconstant,characteris-
Qualitatively,adecreasingT withincreasingwavelengthcanbe ∼
B tic oflow-densitymaterial.Asdiscussedbelow,however,there
producedinseveralways:(i)aspatiallyconstantsurfacetemper-
areotherplanetarysurfaceswherethermalscatteringeffectsare
atureTandalow(butspectrallyconstant)surfaceemissivity;(ii)
demonstratedtooccur.
themixingofdifferentsurfacetemperatures.Suchamixingcan
In our previous works (Lellouchetal., 2000a, 2011), the
occur both on regionalscales (e.g., different Pluto and Charon
emissivityrequiredtomatchtheobservedISOorSpitzerfluxes
regionshavedifferenttemperaturesbecauseofdifferentalbedos
was defined in reference to a thermophysical model that only
or because they see different instantaneous insolations) and on
considered the surface temperatures. A complication was re-
smallscales(slopesatanyscales,i.e.,surfaceroughness,cause
latedtothemultiplicityofsurfaceterrains.Threeunits(N ice,
adjacent surface facets to see large variations of temperatures 2
CH ice,tholin/H Oice)wereconsideredforPlutoandonefor
due to shadows and/orre-radiation);and (iii) a decrease of the 4 2
Charon, and the approach was to (i) fix the spectral and bolo-
spectral emissivity with wavelength. Scenario (i) is technically
metric emissivity of all units except CH and (ii) adjust them
possible,butfittingtheHerschel-measuredbrightnesstempera- 4
for the CH unit, using for initial guidance expectations based
tures over70-500µm would requirea constantT 52.5K and 4
∼ onspectralpropertiesofices(Stansberry,Pisano&Yelle,1996).
animprobablylow( 0.57)spectrallyconstantsurfaceemissiv-
∼ Results(PaperI)suggestedalargedecreaseofthespectralemis-
ity. Rather,giventhe observedalbedovariegationonPluto and
sivityofCH ice,from 1at24µmto 0.4at200µm.However,
Charon,scenario (ii) must occur,at least on geographicscales. 4 ∼ ∼
possiblesubsurfacesoundingeffectswerenotconsidered,except
Based on multiterrain modeling of the Spitzer data, however,
inLellouchetal.(2000b),wherethenondetectionofthe1.2mm
Paper I found that a decrease of the spectral emissivity with
lightcurvewasinterpretedintermsofthemm-emissivityofthe
wavelength, i.e. scenario (iii), of some of the Pluto areas (the
tholin/H O ice unit. Furthermore, all of our previous thermo-
CH iceregions)wasalsorequired. 2
4 physical models were “diurnal-only”, i.e., they assumed equi-
Spectral “emissivity” is often loosely defined in the lit-
libriumof the diurnallyaveragedtemperatureswith the instan-
erature, and sometimes treated as a fudge factor in models.
taneousseasonalinsolation.Thermalinertiaeffectsonseasonal
In essence, it represents the ratio of the observed fluxes to
timescalesarethoughttobeimportantincontrollingthesurface-
model fluxes, but how much physics is put into the mod-
atmosphere exchanges (Young, 2012, 2013; Olkinetal., 2015;
els leads to different estimates of the “emissivity”. In early
Hansen,Paige&Young, 2015) and the atmospheric pressure.
works, surface temperatures were described in simplistic end-
Theymaybeimportanttoincludeforourpurposesbecausethey
member cases, such as the “nonrotating”or the “rapid rotator”
arelikelytoimpactthenear-surfacetemperatures.
cases. The adventof more elaborate models, such as the aster-
Alongwith the decreasingbrightnesstemperatureswith in-
oid STM (Lebofskyetal., 1986) and NEATM (Harris, 1998),
creasingwavelength,a strikingresultofthe Herschelmeasure-
and of physically-based, thermophysical models (TPM; e.g.,
mentisthelowT value( 35K)at500µm.Belowwedemon-
Spenceretal.,1989;Lagerros,1996;Mu¨ller&Lagerros,1998), B
∼
strate that such a T is lower than any expected value for the
provided a more realistic description of the surface tempera- B
dayside surface or subsurface of these bodies;thus, subsurface
ture distribution across airless bodies, and thereby a definition
sounding toward the longest wavelengthsis not the only cause
of spectral emissivity in reference to fluxes emitted from the
ofthedecreasingT ,sothat“true”emissivityeffects(asdefined
surface. However, a further complication is that, particularly B
perEquation(1))mustoccur.
atlongwavelengths,the surfacematerials’partialtransparency
may cause the emitted radiation not to originate at the surface
itself, but from some characteristic depth that depends on the
4.3.Thermalmodeling
materialabsorptioncoefficient.Therefore,theemittedfluxdoes
not just depend on the surface temperature,but on the thermal Onecomplicationassociatedwithmodelingoflong-wavelength
profilesT(z)withinthesubsurface.Considerationofthisaspect thermaldataisrelatedtotheunknownlevelprobedbytheemis-
leads to another definition of the emissivity, as the ratio of the sionwithinthesurface,comparedtothedepthoverwhichtem-
observedtothemodeledfluxes.Themodeledflux,Φ ,atsome perature changes occur (the thermal skin depth). Unlike in the
ν
frequencyν,isexpressedlocallyas,e.g.,(Keihmetal.,2013) thermalIR(e.g.,10-50µm),whereradiationisemittedfromthe
surfaceitself(withinafractionofamm),materialscanbetrans-
z dz
Φ = B (T(z))exp( ) (1) parentenoughinthesub-mmthatthermalradiationmightorig-
ν Z ν −L cosµ L cosµ inatefromlayers 10toseveralthousandtimesthewavelength
e e
∼
(i.e.,5 mmto 1mormoreat500µm).Thethermalskindepth
and spatially integrated over the object. Here B is the Planck
ν
function, Le is the electrical skin depth (inverse of the absorp- isrelatedtothethermalinertiaΓthroughds = ρΓcqPπ,whereρ
tioncoefficient),andµistheviewinggeometrydependentangle isdensity,cisheatcapacity,andPisthe(diurnalororbital)pe-
betweentheoutgoingradiationandthesurfacenormal. riod.Theparameterd isthereforenotcompletelydefinedbyΓ
s
Manyasteroidstudies(e.g.,Redman,Feldman&Matthews, sinceρandcmaynotbewellknown2.Still,usingtypicalnum-
1998; Mu¨ller&Lagerros, 1998), making use of surface tem- bersforρ(900kgm 3)andc(400Jkg 1K 1),athermalinertia
− − −
perature for reference, reported evidence for very low spectral Γ = 25 J m 2s 0.5K 1 (hereafter MKS) for Pluto leads to a di-
− − −
emissivities(0.6-0.7)inthemm/sub-mmranges,whichwereat- urnalskindepthof3cm,meaningthatsub-mmradiationcould
tributedtograinsizedependentsubsurfacescatteringprocesses. eitherprobewithinorbelowthediurnalskindepthandconceiv-
However,therecentcomprehensivestudybyKeihmetal.(2013) ablycouldevenencompassasubstantialfractionoftheseasonal
demonstrated that when allowance is made for subsurface
sounding(andfortheenhancementoftheinfraredfluxesbysur- 2 Itcanbeshown(see,e.g.,LeGalletal.(2014)andSchloerbetal.
faceroughness),theobservedmm/sub-mmfluxesaregenerally (2015)forrecentapplications)thattheoutgoingthermalradiationde-
consistentwithspectralemissivitiescloseto1(e.g.,0.95).This pendsontheratiooftheelectricskindepthL totherelevantthermal
e
suggeststhatno scatteringlosses occur,exceptforspecularre- skindepth,ratherthanontheirabsolutevalues.
6
Lellouchetal.:HerschelobservationsofPluto
skindepth(3.5mforΓ=25MKS).Amuchlargerthermaliner-
tia(Γ=1000-3000MKS)couldbemoreappropriateonseasonal
timescales(Olkinetal., 2015),however;thenthe seasonalskin
depthwouldextendseveralhundredsofmetersdeep.
Giventheseuncertainties,ourinitialapproachistoconsider
a number of situations of relative electrical, diurnal, and sea-
sonal skin depths. For that we first modelhorizontaland verti-
cal temperatures of a “mean” Pluto using a standard spherical
thermophysicalmodel(Spenceretal.,1989)3.By“meanPluto”,
we mean that we use a Bond albedo of 0.46 derived from a
meangeometricalbedo p =0.58andaplausiblephaseintegral
V
q = 0.8 (Lellouchetal., 2000a; Bruckeretal., 2009). A bolo-
metric emissivity of 1.0 is assumed and no surface roughness
effectsareincluded.Asdiscussedbelow,themodelisnotrele-
vant to the N -ice covered areas whose heat budget is affected
2
bysublimation/condensationterms.
4.3.1. Diurnal-onlymodels
Asafirststep,weconsidera“diurnal-only”model.Inthiscase,
the localinsolation is calculatedusing “fixed”heliocentricdis-
tanceandsubsolarlatituderelevanttoearlyMarch2012,which
leadsinparticulartozerotemperaturesinthepolarnightsouth-
wardof43 S4.Athermalinertiaof25MKSisassumed,follow-
◦
ing results from Paper I. Fig. 3 shows the resulting (i) surface
temperatures and (ii) “subdiurnal” temperatures, i.e., tempera-
turesatdepthsmuchbelowthediurnalskindepth,inbothcases
as seen from the observer (neglecting the small 1.6 phase an-
◦
gle).Surfacetemperatures(relevanttodayside)peaknear 56K
∼
at high northern latitudes and fall below 35 K at latitudes be-
low20 Sonly.Subdiurnaltemperatures,whichfollowlinesof
◦
equallatitude, areslightly colderthanthe surface temperatures
Fig.3. Apparent Pluto temperatures, as viewed by a near-Sun
by0-5K(exceptinthe6-10ammorninghourswheretheycan
observerin 2012,foradiurnal-onlymodelwiththermalinertia
be warmer than surface temperatures by up to 4 K). Planck-
Γ = 25 MKS, Bond albedo = 0.46 and bolometric emissivity
averaged disk surface (resp. subdiurnal) temperatures over 70-
ǫ = 1. Top: Surface temperatures.Bottom: Temperaturesat the
500µmare51.4–49.0K(resp.49.8–47.0K).Allthesetemper- b
bottomofthediurnallayer.
aturesarecomfortablyhigherthanthemeanT 35Kmeasured
B
∼
byHerschel-SPIREat500µm,indicatingthatsubsurfacesound-
ing within the diurnallayer is not the main culpritfor this low
perature;(ii)the“deep”temperature(i.e.,thetemperaturemuch
T .Considerationofapossiblepositivethermalinertiagradient
B belowthe seasonalskin depth);and(iii) the minimumvaluein
withdepthinthediurnallayerwouldnotchangethisconclusion
theseasonaltemperatureverticalprofileateachlatitude.Forthe
becausethesubdiurnaltemperatureisanincreasingfunctionof
lowthermalinertia(Γ= 25MKS)case,seasonaleffectsonthe
thermalinertia(e.g.,Fig.2ofSpenceretal.,1989).
diurnallyaveragedsurfacetemperaturearesmall.Thetempera-
tureprofileshowninthetoprightpanelofFig.4closelymatches
4.3.2. Seasonalmodels thesubdiurnaltemperaturemapofFig.3,exceptnearandwithin
thepolarnightwherethezerotemperaturesofthediurnal-only
Theaboveapproachdoesnotconsidertheimpactofthermalin-
modelarereplacedbymorephysical 20K-30Kvalues.Incon-
ertiaonseasonaltimescales.ContinuingwithaBondalbedoof ∼
trast,thismodelleadstorathercoldtemperaturesof30-36Kin
0.46andbolometricemissivityǫ =1,weshowinFig.4thesea-
b the “deep” (i.e., subseasonal) subsurface, with minimum tem-
sonaltemperaturefields for two differentvalues of the thermal
peraturesintheseasonallayeroccasionnallyfallingbelow30K
inertia,Γ=25MKSand3162MKS.Thefirstvalue,equaltothat
athighnorthernlatitudes.
consideredabovefordiurnal-onlymodels,representsthe situa- Thehigh(Γ=3162MKS)thermalinertiacase5 hasamuch
tionofnothermalinertiagradientwithdepth.Thesecondvalue moredramaticeffectonthediurnallyaveragedsurfacetempera-
representsoneofthehighthermalinertiacasesfavoredbysome
tures,whichnowshowstronglysubduedlatitudinalcontrastsof
of the recent climate models (Young, 2012, 2013; Olkinetal.,
3KforsouthpoletonorthpoleattheHerschelepoch.Inthis
2015).InFig.4,theleftpanelsshowthe2-D(time,season)di- ∼
situation,thedeeptemperaturesreflectthemeaninsolationover
urnallyaveraged(i.e.,subdiurnal)surfacetemperatures;theright
the entire orbitand are almosthemisphericallysymmetricwith
panels,whichpertaintotheepochoftheHerschelobservations,
maximaatthepoles,minimanear 30 latitude,andasecondary
◦
show the latitudinal profile of: (i) this diurnally averaged tem- ±
5 Thechoiceof3162MKSinYoung(2013)andOlkinetal.(2015)
3 https://www.boulder.swri.edu/˜spencer/thermprojrs/ isjustaneffectoftheirthermalinertiagrid,withtwovaluesperdecade,
4 This ignores internal heating. A typical radiogenic heating of 2.4 forparametersearches.Nophysicalinferenceshouldbedrawnfromthe
erg cm 2s 1 (Robuchon&Nimmo, 2011) would yield a 14 K polar factthat3162MKSishigherthanthethermalinertiaforsolidH Oat
− − ∼ 2
nighttemperatureforunitbolometricemissivity. 40K(2200MKS,Spencer&Moore,1992).
7
Lellouchetal.:HerschelobservationsofPluto
Fig.4.PlutotemperaturesfromaseasonalmodelwiththermalinertiasΓ=25MKS(top)and3162MKS(bottom).ABondalbedo
of0.46andbolometricemissivity ǫ = 1 are used.Left: “Surface”temperaturefieldsovera Plutoorbit.The dashedline indicates
b
theepochoftheHerschelobservations.Right:TemperaturesasafunctionoflatitudeforearlyMarch2012.“Surface”and“deep”
indicatetemperaturesatthetopandbottomoftheseasonallayer.“Minimum”referstotheminimumtemperaturewithintheseasonal
layerforeachlatitude.
maximumneartheequator.Thesedeeptemperaturesarein the the relative seasonal thermal inertias of Pluto and Charon are
range38K-39.5K,andtheminimumverticaltemperaturenever unknown.
fallsbelow37K.
Yet, the temperatures shown in Fig. 3 and 4 are only rel-
4.3.3. Commentsandimplicationsfortheoriginoflow evant to the Pluto units not covered by N2 ice. The heat bud-
brightnesstemperatures get of the latter is dominated by sublimation-condensationex-
changes, which, at a given point in time, maintain N to an
2
The temperaturesshown in Fig. 3 and 4 are likely to be lower isothermal state over the globe and the surface pressure to an
limitstothetemperaturesrelevanttotheHerschelobservations essentiallyconstantvalue(exceptfortopographiceffects)thatis
fora numberof reasons.First, theywere calculatedfora bolo- bufferedbytheN icetemperature(Young,2012).Themostre-
2
metricemissivityof1.0,which,ifanything,minimizesthecalcu- centvolatiletransportmodels(Young,2012,2013;Olkinetal.,
latedtemperatures.Second,the geometricalbedothathasbeen 2015; Hansen,Paige&Young, 2015) indicate N ice tempera-
2
used is the Pluto-average value. Because the brightest regions turesconstantlyabove34KthroughoutaPlutoyearaccordingto
aretypicallyassociatedwithN ice,thenon-N iceregionsare Hansen,Paige&Young(2015),andintherange37.5-39.5Kac-
2 2
darker and thus warmer than the calculation indicates. Third, cordingtoOlkinetal.(2015),withT(N ) 38.5Kin2012.The
2
∼
theabovecalculationsdonotincludeanyincreaseoftheeffec- surfacepressuredeterminationfromNewHorizonsis 10µbar
∼
tive emitting temperature due to roughness (those effects were in July 2015 (Sternetal., 2015), corresponding to equilibrium
incorporated in the form of a “thermophysical model beam- at 37.0 K (Fray&Schmitt, 2009). Because N is horizontally
2
ing factor” in Lellouchetal., 2000a, 2011). Finally, while the isothermal (i.e., does not show any diurnal temperature varia-
Herschel beam encompasses Pluto and Charon, the above cal- tion),itmustalsobeverticallyisothermal,atleastoverthediur-
culationspertaintoPlutoonly.Charon,whichisslightlydarker nalskindepth.AfirmlowerlimitoftheN temperatureispro-
2
than Pluto, and based on the Spitzer 24 µm data likely to have videdbythe shapeof the(2-0)bandat 2.15µm, whichclearly
a slightly smaller thermalinertia in the diurnallayer (Paper I), indicatesthatN isintheβphase(Trykaetal.,1994),i.e.,above
2
should therefore be warmer than Pluto on its dayside. This ar- the transition to cubicα phase at 35.6 K (Scott, 1976; Trafton,
gument cannot be applied to the seasonal models however, as 2015).AllofthissuggeststhatregionscoveredwithN iceare
2
8
Lellouchetal.:HerschelobservationsofPluto
alsowarmer,albeitnotnecessarilybymuch,thanthemean500- face6. Absorption coefficients for pure water ice (k ) at sub-
H2O
µmT thatwemeasure(35K,Fig.1). mm-to-cm wavelengths are discussed extensively by Ma¨tzler
B
(1998),whoalsoprovidesseveralanalyticformulationstoesti-
Theaboveconsiderationsshowthatinmostsituationsphysi-
matethemasafunctionoffrequencyandtemperaturealongwith
caltemperaturesatthesurfaceandinthesubsurfaceofPlutoand
illustrative plots. We use the Mishima,Klug&Whalley (1983)
Charonareconsiderablyhigherthantheobservedsystembright-
formulation(seeAppendixofMa¨tzler,1998).Itsapplicabilityis
ness temperaturesat 500 µm and beyond.The exceptionis the
normally restricted to temperatures above 100 K, but Fig. 2 of
caseofthesubseasonaltemperaturesforthecaseoflowseasonal
Ma¨tzler(1998)indicatesthetrendwithtemperature.Absorption
thermalinertia(25MKS,i.e.,comparabletothediurnalseasonal
coefficients extrapolated to 50 K (estimated as half the values
thermal inertia), which can be as low as 27-36 K (Fig. 4). We
at 100K) are shown in Fig. 5. At 500µm, our bestestimate is
conclude that the low observedT do not result from the tem-
B k =0.25cm 1,comparabletotheabovevaluesforCH and
peraturegradient(colderatdepthonthedayside)inthediurnal H2O − 4
N ices.Thecorrespondingpenetrationlengthisthereforecom-
layer,butcouldconceivablybeduetolong-wavelengthradiation 2
parable to the diurnal skin depth but remains negligible com-
probingasignificantportionoftheseasonallayer.Thissituation
paredtotheseasonalskindepth,evenforseasonalΓ=25MKS.
wouldrequirethat(i)the seasonalthermalinertia issmall, i.e.,
According to these calculations, the seasonal layer would be
thereisnosignificantverticalgradientofthethermalinertia,and
probedonlyatawavelengthof 4mmandbeyond.Wealsore-
(ii)thesurfacematerialistransparentenoughthatthermalradi- ∼
markthattheexpressionfromMishima,Klug&Whalley(1983)
ationprobesseveralmetersbelowthesurface.
would give a penetrationdepth of 56 m at 2.2 cm, which is an
Estimates of Pluto’s seasonal inertia have been obtained orderofmagnitudelargerthanindicatedbythelaboratorymea-
from climate models (Hansen&Paige, 1996; Young, 2013; surementsofPaillouetal.(2008).Inaddition,smallconcentra-
Hansen,Paige&Young, 2015; Olkinetal., 2015) designed to tionsofimpuritiescandramaticallyreducethemicrowavetrans-
matchtheatmosphericpressureevolutionwitnessedsince1988 parencyofwaterice(e.g.,Chyba,Ostro,&Edwards(1998)and
and constraints on Pluto’s albedo distribution based on HST referencestherein).Therefore,the abovecalculationslikely in-
measurements. In addition to thermal inertia, these models in- dicateupperlimitstotheactualpenetrationdepthofradiationin
cludefreeparameters,suchasthealbedosandbolometricemis- aH2Oicelayer,fromwhichweconcludethattheseasonallayer
sivitiesoftheN frostandtheinvolatilesubstrate,andtheamout isnotreachedattheHerschelwavelengths.
2
ofvolatileinventory.Oncetunedtothepressuremeasurements,
thesemodelscanalsopredicttheorbit-longevolutionofPluto’s
10000
atmosphere.The latest two models,publishedprior to the New
Horizons encounter,which give different priorities on the con-
1000
straintstofit,differratherradicallyintheirconclusionswithcon-
trastingbest-fitsolutionsfortheseasonalthermalinertia(10-42 1) 100
-m
MKSinHansen,Paige&Young(2015)vs1000-3162MKSfor c
Olkinetal. (2015)) and diverging conclusionsas to the fate of nt ( 10
e
the atmosphere in the upcoming decades. The analysis of New effici 1
Horizonsdata,particularlypolarnighttemperatureswith REX, co
n
should ultimately sort out this issue, but for now, we regard ptio 0.1
the seasonal thermal inertia of Pluto as significantly undercon- or
s
strained. Ab 0.01
However, even if the seasonal thermalinertia is small (i.e., 0.001
comparable to the thermal inertia in the diurnal layer), we be-
lievethatthesub-mmradiationdoesnotprobealargefractionof 0.0001 100 1000 10000
theseasonalskindepth(estimatedabovetobe3.5mforΓ=25 Wavelength (µm)
MKS). This stems from our estimate of the absorption coeffi- Fig.5. Absorptioncoefficientof H O ice, extrapolatedto 50 K
2
cientsof ices presenton Pluto surface,on which we nowelab- (seetextfordetails).
orate.ForN iceandCH ice,Lellouchetal.(2000a)presented
2 4
absorptioncoefficientsover30-300µmbasedbothonearlylab-
oratorydatacompiledbyStansberry,Pisano&Yelle(1996)and We concludethatthelowbrightnesstemperaturesobserved
on new optical constants measurements. These measurements atthelongestHerschelwavelengthscannotbeexplainedbysub-
(seeFig.8ofLellouchetal.(2000a))indicatetypicalabsorption surfacesounding,andimplyemissivityeffects.Inwhatfollows,
coefficientsof 0.5 cm 1 for N ice and 1 cm 1 for CH ice, we presentmodelsaimedatfitting the Herschellightcurvesto
− 2 − 4
i.e.,penetration∼depthsof2cmand1cm,∼respectively,whichis evaluate the mean spectral emissivity of the Pluto-Charon sys-
muchshallowerthantheabovevalueoftheseasonalskindepth. tem.
Thesignificanceofthesepenetrationdepthsisactuallyuncertain
becausethevolatileicesmightactuallyberestrictedtoaneven
4.4.FitofHerscheldata
thinnersurfaceveneer.
Using the above thermophysical models, we expand upon the
H O ice on Pluto has long escaped spectroscopic detec-
2 modelsdevelopedpreviouslyforfittingtheISOandSpitzerdata
tion, and based on initial New Horizons data appears to be ex-
(Lellouchetal., 2000a, 2011). Briefly, these models described
posedonlyinanumberofspecificlocations,usuallyassociated
thePluto-Charonsystemascomposedoffourunits(N ice,CH
withredcolor,suggestiveofwaterice/tholinmix(Grundyetal., 2 4
2015; Cooketal., 2015). Nonetheless, water ice is likely to be 6 Evidenceforwatericebedrocks isalsostronglysuggestedbythe
ubiquitous in Pluto’s near subsurface, given its cosmogonical NewHorizonsdiscoveryofseveralkilometerhightopographicfeatures
abundance, Pluto’s density, and its presence on Charon’s sur- onbothPluto’sandCharon’ssurfaces(Sternetal.,2015).
9
Lellouchetal.:HerschelobservationsofPluto
ice,H O/tholinmix,andCharon),withspecificdistributionsand
2
geometric and bolometric albedos constrained by Pluto’s opti-
cal light curve, permitting one to calculate the thermal radia-
tion (assumed Lambertian) of the entire system. The distribu-
tionofsurfaceunitswasbasedonvisibleimagingandphotom-
etry (HST, mutual events) and near-infrared Earth-based spec-
troscopy.Tocalculatethelocalsurfacetemperatures,adiurnal-
only thermophysical model was used for all four units except
N ice, which was maintained at a fixed N frost temperature.
2 2
Another special condition was that the CH temperature was
4
allowed to vary in accordance to thermophysical model pre-
dictions, but was capped at a maximum 54 K temperature to
account, in a simplified manner, for sublimation cooling ef-
fectsfor CH , which becomeimportantabovethis temperature
4
(Stansberryetal.,1996b).
This “end-member” description is obviously outdated by
the high-resolution New Horizons/LORRI imaging results
(Sternetal., 2015), but until high-resolution maps of compo-
sition and albedo from LORRI and Ralph are available, it re-
mains the only practical approach for our purpose. For now,
we only considered the distribution favored in Paper I (“g ”,
2
their Fig. 4), remarking its rather nice consistency with the
early LORRI/images (Fig. 6). Furthermore, this distribution is
also roughly consistent with early compositional results from
Fig.6.Top:AdoptedPlutounitsformodeling(white=N ,gray
NewHorizons/Ralph,whichshowbothN andCH inSputnik 2
2 4 = CH , black = H O/tholin). Bottom: Map of Pluto created
Planum, neither N nor CH in Cthulhu Regio, CH north of 4 2
2 4 4
from images taken from June 27 to July 3 by the Long Range
Cthulhu and in the north polar region, and N at mid-northern
2
Reconnaissance Imager (LORRI) on New Horizons, combined
latitudes (Grundyetal. (2015), L. Young, priv. comm). The
with lower resolution color data from the spacecraft’s Ralph
model free parameters are the thermal inertias of Pluto and
Charon(expressedintermsofthethermalparameterΘ7),plus instrument. See http://pluto.jhuapl.edu/Multimedia/Science-
Photos/pics/nh-pluto-map.jpg.CthulhuRegioisthedarkregion
the bolometric and/or spectral emissivity of some of the units,
covering 30 E-160 Elongitudes.SputnikPlanumisthesouth-
especially CH ice. Fitting the Spitzer 2004 light curve makes ◦ ◦
4 ∼
ern part of the bright region immediately to the east (informal
it possibleto estimate the thermalinertiasof Plutoand Charon
namesaretakenfromSternetal.,2015).
separatelybecausetheformerprimarilydictatesthe24µmlight-
curveamplitude,while thelatterdeterminesthelargecontribu-
tionofCharontotheobservedmean24-µmT (seePaperIfor
B
details). This implies that the other units besides CH ice are also sub-
4
We startbytestingthebest-fitmodelofPaperIdetermined jecttowavelength-dependentemissivities.Relaxingthehypoth-
fromtheSpitzer2004data.Inthisdiurnal-onlymodel,thespec- esisthatthespectralemissivityofCharonandoftheH O/tholin
2
tralandbolometricemissivityofCharonandoftheH O/tholin unitsareequaltounity,wesearchedforthespectralemissivity
2
unitofPlutowerefixedto1.Inferredparameterswerethether- (nowassumedforsimplicitytobethesameforCharonandthe
mal parameters of Pluto and Charon, Θ = 6 (i.e., Γ = 22 threePlutounits)thatpermitsafittoalllightcurves(case 3in
PL PL
MKS) and Θ = 4.5 (Γ = 22 MKS); bolometric emissiv- Table2).Thiscasepermitsagoodfit(notshowninFig.7)tothe
CH CH
ityofmethane,ǫ =0.7;andspectralemissivityofmethane, data,butwedonotregarditassatisfactorybecausetheassoci-
b,CH4
ǫ = 0.7, 0.6, and 0.45at 70, 100,and 160 µm, respectively. atedPlanck-averagedbolometricemissivityis0.82-0.85,which
CH4
AsindicatedbythethindottedlinesinFig.7, thismodel(case is inconsistent with the bolometric emissivities prescribed for
1inTable2),whichprovidesanexcellentfitoftheSpitzer2004 thetholin/H O,CH andCharonunits(1.0,0.7,and1.0,respec-
2 4
data,isinconsistentwiththeHerschelmeasurementsasityields tively).
brightnesstemperaturesthatare toolowat100and160µm,as The above results point to the need to revise the Spitzer-
wellastoomuchlight-curvecontrastatthesewavelengths.The derived models, and we here updated the fitting approach. For
firstdeficiencylargelyresultsfromthepoorqualityoftheSpitzer thesakeofsimplicity,weadoptedfiducialbolometricemissivi-
2004 156 µm measurements. These measurements, which are tiesof0.90forCharonandallPlutounits(forN ice,thebolo-
2
now shown to be inconsistent with other data (Fig.2), unduly metric emissivity is notexplicitlyused;insteada uniformtem-
skewed the model toward brightness temperatures that are too peratureisspecified).Wealsodonotincludea“beamingfactor”
low. This deficiencycan be correctedfor by adjustingthe CH4 in the thermophysicalmodel (as was done in Paper I), i.e., we
icespectralemissivities(to0.67,0.80,0.84,0.58,0.53,and0.43 ignoresurfaceroughnesseffects;thesearediscussedseparately
at 70, 100, 160, 250, 350, and 500 µm, respectively; case 2 later.With thesechangestothe model,theSpitzer-200424µm
in Table 2). However the synthetic light curves (long dashed- lightcurvewasrefitintermsofseparatethermalparametersfor
lines in Fig. 7) still have too much contrast, except at 70 µm. PlutoandCharonattheSpitzerepoch,adoptinga24µmemissiv-
ityof1.0forallunits.Best-fitΘ =7andΓ =3values(i.e.,
PL CH
7 Θ is related to the thermal inertia Γ by Θ = Γ√ω , where ω = Γ =26MKSandΓ =14MKS)wereobtained.Thethermo-
2π/(6.3872 days) is the body rotation rate, ǫ is theǫbσbToS3lSometric emis- phPLysicalmodelwastChHenre-runforthe2012conditions,search-
b
sivityofthesurface,σisStefan-Boltzmann’sconstant,andT isthe ing for the spectral emissivities (againassumed to be the same
SS
instantaneousequilibriumtemperatureatthesubsolarpoint, for all units) that are permitted to fit the ensemble of Herschel
10