Table Of ContentAstronomy&Astrophysicsmanuscriptno.boissier11 (cid:13)c ESO2011
January19,2011
Earth-based detection of the millimetric thermal emission of the
⋆
nucleus of comet 8P/Tuttle
J.Boissier1,2,3,O.Groussin4,L.Jorda4,P.Lamy4,D.Bockele´e-Morvan5,J.Crovisier5,N.Biver5,P.Colom5,E.
Lellouch5,andR.Moreno5
1 IstitutodiRadioastronomia-INAF,ViaGobetti101,Bologna,Italy(e-mail:[email protected])
2 ESO,KarlSchwarzschildStr.2,85748GarchingbeiMuenchen,Germany
3 Institutderadioastronomiemillime´trique,300ruedelapiscine,Domaineuniversitaire,38406SaintMartind’He`res,France.
4 Laboratoired’AstrophysiquedeMarseille,Universite´deProvence,CNRS,38rueFre´de´ricJoliot-Curie,13388MarseilleCedex13,
1 France
1 5 LESIA,ObservatoiredeParis,5placeJulesJanssen,92195Meudon,France.
0
2 Received–;accepted–
n
ABSTRACT
a
J
Context.Littleisknownaboutthephysicalpropertiesofcometarynuclei.Apartfromspacemissiontargets,measuringthethermal
8
emissionof anucleus isone ofthefew meanstoderiveitssize,independently of itsalbedo, andtoconstrainsomeof itsthermal
1 properties.ThisemissionisdifficulttodetectfromEarthbutspacetelescopes(InfraredSpaceObservatory,SpitzerSpaceTelescope,
HerschelSpaceObservatory)allowreliablemeasurementsintheinfraredandthesub-millimetredomains.
] Aims.Weaimatbettercharacterizingthethermal propertiesof thenucleusofcomet 8P/Tuttleusingmulti-wavelentghspace- and
P
ground-basedobservations,inthevisible,infrared,andmillimetrerange.
E
Methods.WeusedthePlateaudeBureInterferometertomeasurethemillimetrethermalemissionof comet8P/Tuttleat240GHz
h. (1.25mm)andanalysedtheobservationswiththeshapemodelderivedfromHubbleSpaceTelescopeobservationsandthenucleus
p sizederivedfromSpitzerSpaceTelescopeobservations.
- Results.WereportonthefirstdetectionofthemillimetrethermalemissionofacometarynucleussincecometC/1995O1Hale-Bopp
o in1997.UsingthetwocontactspheresshapemodelderivedfromHubbleSpaceTelescopeobservations,weconstrainedthethermal
r propertiesofthenucleus.Ourmillimetreobservationsarebestmatchwith:i)athermalinertialowerthan∼10JK−1m−2s−1/2,ii)an
t
s emissivitylowerthan0.8,indicatinganon-negligiblecontributionofthecoldersub-surfacelayerstotheoutcomingmillimetreflux.
a
[ Keywords.Comet:individual:8P/Tuttle–Radiocontinuum:planetarysystems–Techniques:interferometric
1
v
1. Introduction tationally influenced by the outer planets, supplied the popu-
5
1 lation of Jupiter-family short-period comets (now called eclip-
Much of the scientific interest in comets stems from their po-
4 tic comets EC, Duncanetal. 1988). Comets 19P/Borrelly and
tential role in elucidatingthe processesresponsiblefor the for-
3 9P/Tempel1,investigatedbytheDeepSpace1andDeepImpact
mationandevolutionoftheSolarSystem.Theyappearedinthe
. missionsrespectively,aretypicalcometsofthiscategory.
1 outer regions of the protoplanetary disk, when the giant plan-
0 Given their different origins and the different evolution
etswere formedbycore-accretion(Safronov&Zvjagina1969;
1 schemesfollowedsincetheirformation,onecouldexpecttoob-
Pollacketal. 1996) or disk instability (Cameron 1978; Boss
1 serve different physical properties for the NICs and ECs. For
2003). Together with the asteroids, Centaurs, and transneptu-
: thetimebeing,noobviouscorrelationbetweenthechemicaland
v nian objects, comets are the remnants of the planetesimals not
physicalpropertiesofacometanditsdynamicalclasshasbeen
i accumulatedintotheplanets.Cometsformedinthegiantplan-
X measured(Crovisieretal.2009).
ets regionwere ejected to the outerSolar System and formthe
r Oneofthepossiblewaystoinvestigatedifferencesbetween
Oort Cloud. Some of them return to the inner Solar System as
a
the two classes of comets is to measure their size distribution.
long-period comets (now called nearly isotropic comets NIC,
Duncanetal.1988),suchasC/1995O1Hale-Bopp,orbecome Reliable size determinations have been obtained for only 13
NICs (Lamyetal. 2004), using ground- and space-based tele-
periodic comets after several perihelion passages and shorten-
scopesinthe visibleandinfrareddomain.Therangeofradiiis
ing of their orbit due to gravitational perturbations. The later
surprisingly broad, from 0.4 to 37 km, much broader than that
ones constitute the Halley-familycomets (or returningNIC) to
which1P/Halleyand109P/Swift-Tuttlearesignificantrepresen- of the ECs but with only 13 objects, robust conclusions can-
tatives.Comet8P/Tuttlealsobelongstothisgroup:itsorbithasa notbedrawn.Furthermeasurementsarerequiredtoconfirmthis
higheclipticalinclination(55◦)withashortperiod(13.5years). trend. In this context, it is important to develop new methods
to obtainreliablesize estimatesfromthe Earth.Themillimetre
On the other hand, it is believed that the Kuiper Belt, gravi-
wavelengthrangeiswellsuitedforthispurposebecausetheat-
Sendoffprintrequeststo:J.Boissier mospheric transmission is better than in the infrared, and also
⋆ BasedonobservationscarriedoutwiththeIRAMPlateaudeBure becausetheALMAobservatorywillofferuniqueobservingca-
Interferometer. IRAM is supported by INSU/CNRS (France), MPG pabilitiesinthenearfuture.However,thefluxofacometnucleus
(Germany)andIGN(Spain). ismuchlowerinthemillimetredomainthanintheinfrared,and
2 J.Boissieretal.:Observationsof8P/TuttlewiththePlateaudeBureinterferometer
observations are still challenging and reserved to a few bright minetheabsolutefluxscale.Thepointingandfocuscorrections
comets.Whenavailable,datasetsatdifferentwavelengths(vis- weremeasuredevery40and80minutes,respectively.Somesin-
ible, infrared, millimetre) complete one another and allow de- gledishspectraoftheCH OHlineswererecordedallalongthe
3
tailedstudiesofthenucleusproperties. observing period. The sky contribution was cancelled in posi-
Comet 8P/Tuttle was observed in 1992 using the Nordic tionswitchingmode(ON-OFF),withaOFFpositiondistantof
OpticalTelescope(NOT)at6.3AUfromtheSunandappeared 5’fromthecomet.WedonotretrieveanyCH OHlinedetection
3
inactive at this time. From its apparent magnitude,the nucleus ininterferometricmodebutthelinesweredetectedin theON–
diameter was estimated to 15.6 km (Licandroetal. 2000), but OFF spectra. Their analysis is presented in Biveretal. (2008),
photographic observations performed in 1980 at 2.3 AU sug- togetherwithothersingledishobservationsof8P/Tuttle.
gestedanucleus3timessmallerorhighlyelongated.Theclose
Given the distance of the comet, the apparent diameter of
approach to the Earth in December 2007-January 2008 (0.25
a nucleus with a radius of 10 km is about 0.1′′ and we do
AU)anditssupposedlargesizemadeitaveryinterestingtarget
not expect to resolve the nucleus of 8P/Tuttle in the Plateau
forEarthbasedobservations.In2007-2008,thecometwas ob-
de Bure data. As a result, we analysedthe continuumobserva-
servedwith differenttechniquesin the visible (lightcurvemea-
tionsintheFourierplane,fittingtheFourierTransform(FT)of
surementswiththeHubbleSpaceTelescope(HST),Lamyetal.
a point source to the observed visibilities. We measure a flux
2010b), the infrared (Spitzer Space Telescope (SST) observa-
F = 2.4±0.7mJylocatedatanoffsetof(–0.5′′,–1.4′′)in(RA,
tions, Groussinetal. 2008, 2010) and the radio domains(radar
Dec) with respect to the pointed position (the astrometric pre-
experimentswithArecibo,Harmonetal.2010).Tocomplement
cision, estimated dividing the beam size by the signal to noise
this multi-wavelength set of observations, we observed comet
ratio,is∼0.3′′).Comparedtothelatestephemerissolution(JPL
8P/Tuttle with the Plateau de Bure Interferometer to measure
K074/27,includingobservationsperformeduptooctober2008)
themillimetrethermalemissionofitsnucleus.Theonlysimilar
the offset is (0.4′′,3.8′′). To illustrate the result of this fit, we
measurementof a comet nucleus was performed more than 10
presentinFig.1 therealpartofthevisibilitiesasa functionof
yearsago,in1997forcometHale-Bopp(Altenhoffetal.1999),
theuv-radius.Thevisibilitytablehasbeenshiftedtotheposition
which demonstratesthe difficutly of such observationsand the
wherethepointsourcewasfoundinthefit,sothattheimaginary
uniqueopportunityofferedbycomet8P/Tuttle.
partofthevisibilitiesisnullandtheirrealpartisthesourceflux.
In this paper we present the results of our observations of
Onthefigure,therealpartofthe visibilitieshasbeenaveraged
comet8P/TuttlecarriedoutwiththePlateaudeBureinterferom-
in30mbinsinuv-radius.Weoverplotthepointsourcefluxthat
eterat1.25mm(240GHz)inDecember2007-January2008.A
wasfoundbythefittingprocedure.Theabsolutefluxcalibration
descriptionoftheobservationsisgiveninSect.2.We analysed
addsanuncertaintyof20%onboththefluxanditsuncertainty.
thedatausingashapemodelofLamyetal.(2010b)andather-
Weestimatetheoverall±1σlimitsasF+1σ = 1.2×(F+1σ) =
mal model of the nucleus, which are described in Sect. 3. The
3.7mJyandF−1σ =0.8×(F−1σ)=1.4mJy.Fromthiswede-
resultsarepresentedinSect.4andsummarizedinSect.5.
ducethefinalfluxandcorrespondingerrorbarsF =2.4+1.3mJy.
−1.0
2. Observations
08 Jan. 2008: An updated solution of orbital elements (JPL
Comet 8P/Tuttle has been observed twice at a wavelength of K074/21) was used to compute the ephemeris of the comet at
1.25 mm (240 GHz) with the IRAM interferometer on 29 thisdate.OursingledishobservationsofthecometattheIRAM-
December2007and8January2008(Table1).TheIRAMinter- 30 m telescope (in early January, Biveretal. 2008) showed
ferometerisa6antennas(15meach)arraylocatedatthePlateau that its gas production was not sufficient to enable interfero-
deBure,intheFrenchAlps,andequippedwithheterodyne,dual metric study of the coma. As a result we dedicatedall the cor-
polarization, receivers operating around 1, 2 and 3 mm (230, relator units of the Plateau de Bure to continuum observations
150, and 100 GHz, respectively). On both observing dates the for this second run, without changing the observing frequency
array was set in a compact configurationwith baseline lengths 240GHz.Thisresultsinabandwidthof∼2GHz,whichrepre-
rangingfrom∼20to150m.Thisresultsinasynthesizedbeam sentsagainofafactor1.3inpointsourcesensitivitywithrespect
diameterofabout1.2′′ at240GHz.Thewholecalibrationpro- to the December observations. The comet was observed from
cess was performed using the GILDAS software packages de- 15 h UT to 21 h UT, under poor, degrading with time, phase
velopedbyIRAM(Pety2005). stabilityconditions(asystemtemperatureof200Kandaphase
rms of ∼30–100◦, depending on the baseline length). As a re-
sultweuseintheanalysisonlythe2firsthoursofobservations
29 Dec. 2007: For this first attempt, the comet was tracked
(1.3honsource),whentheconditionswerethebest.Although
using an ephemeris computed using the JPL solution K074/19
the integration time is longer for the December observing run,
for its orbital elements. The instrument was tuned in a way to
thelargerbandwidthinJanuaryresultsinalowerthermalnoise
search for CH OH lines around 241 GHz: 4 narrow correlator
3 forthisdataset.Thegaincalibrationsourceswere0235+164and
unitswerededicatedtotheCH OHlines,andatotalbandwidth
3 0048-097and3C454.3wasusedasareferencetodeterminethe
of1.2GHzwasusedtomeasurethecontinuumemissionofthe
absolutefluxscale.
comet.8P/Tuttlewasobservedfrom15hto23hUT,undercor-
rect conditions(system temperature of 200 K and a phase rms FittingtheFTofapointsourcetotheobservedvisibilitiesin
of∼30◦)duringthefirsthalf,until19hUT.Thesecondhalfof theFourierplane,weretrieveafluxof3.0±0.5mJylocatedatan
theobservationssufferedbadconditions(unstablephase,cloudy offset of (1.4′′,–0.1′′) in (RA, Dec) with respect to the pointed
weather) and is not usable. The final dataset represents ∼1.6 h position(theastrometricprecisionis ∼ 0.2′′).Comparedto the
on source aquired between 15 h UT and 19 h UT. The gain latest solution(JPL K074/27)the offsetis (1.8′′,1.2′′). Thisre-
calibration sources (observed every 22 minutes to monitor the sultisillustratedwiththerealpartofthevisibilitiespresentedas
instrumental and atmospheric phase and amplitude variations) afuctionoftheuv-radiusinFig.1.Takingintoaccounttheflux
were 0133+476 and 0059+581. MWC349 was used to deter- calibrationuncertainty,we obtain a flux of 3.0+1.2 mJy (1σ) or
−1.0
J.Boissieretal.:Observationsof8P/TuttlewiththePlateaudeBureinterferometer 3
Table1.LogofthePlateaudeBureobservationsofthecomet8P/Tuttle
Date UT Ephemeris ∆ r φa Fluxb
h
h AU AU mJy
29Dec.2007 15–19 JPLK074/19 0.26 1.11 54◦ 2.4±0.7
08Jan.2008 15–17 JPLK074/21 0.28 1.06 65◦ 3.0±0.5
aPhaseangleoftheobservations
bThefluxanditsuncertaintyaremeasuredbyafitofapointsourcetotheobservedvisibilities.Theabsolutefluxcalibrationaddsanuncertainty
of20%.
2008;Kobayashietal.2010).Hence,thecontributionofthedust
emission to the detected flux at 240 GHz in comet 8P/Tuttle
should not exceed 0.01 mJy, compared to the 3.0 mJy of the
nucleus.
3. NucleusthermalModel
3.1.Shapemodel
Harmonetal. (2008, 2010) interpreted their Arecibo radar ob-
servations of the nucleus of comet 8P/Tuttle as implying a
contact binary and proposed a shape model composed of two
spheroids in contact. Lamyetal. (2010b) found that the light
curveofthenucleusderivedfromtheirHubbleSpaceTelescope
observations indeed was best explained by a binary configura-
tion and derived a model composed of two spheres in contact.
However these two models profoundlydiffer first in the direc-
tion of the rotational axis and second, in the size ratio of the
twocomponentsofthenucleus.Groussinetal.(2010)usedboth
shapemodelstointerpretSpitzerSpaceTelescopethermallight
curves of the nucelus and concluded that the shape model of
Lamyetal.(2010b)bettermatchestheSSTobservations.
TheshapemodelofLamyetal.(2010b)consistsoftwocon-
tactsphereswithrespectiveradiiof2.6±0.1kmand1.1±0.1km;
a sphere with a radius of 2.8 km would have the same cross-
Fig.1.Realpartofthevisibilitiesasafunctionofuv-radiusfor section. The pole orientation is RA = 285◦ and Dec = +20◦,
theDecember(top)andJanuarydata(bottom).Thevisibilityta-
which gives an aspect angle (defined as the angle between the
bles have been shifted to the position found by the fitting pro- spinvectorandthecomet-Earthvector)of82◦ on29Dec.2007
ceduresothattheirrealpartrepresentsthepointsourceflux.To and 103◦ on 08 Jan. 2008, close to an equatorial view. The
increasethesignaltonoiseratioonindividualpoints,thevisibil-
rotational period is 11.4 h (Lamyetal. 2008) in this model.
itieshavebeenaveragedin30mbinsofuv-radius.Theresultof
Harmonetal. (2010) derived a more precise value of the pe-
thefittingprocedureintheuv-planeispresentedbythedashed,
riod based on the radar experiments carried out at Arecibo:
greyline.
11.385±0.004 h. By rotating the nucleus back from the radar
epoch to the HST epoch, we were able to connect the rotation
phases and thus determine the true or sidereal rotation period
3.0−+21..48mJy(3σ).Inthefollowinganalysis,weonlyusetheflux Psid =11.444±0.001h(seeLamyetal.2010b).
measuredonJanuary8,asitoffersabettersignaltonoiseratio. Inviewoftheabovediscussionweusedtwodifferentshape
Weassumethatthedetectedemissionissolelyduetothenu- modelsforouranalysis:i)asimplesphericalshapemodelwith
cleusthermalemission. Thecontributionof dustthermalemis- aradiusof2.8kmandii)themorecomplexandrealisticshape
sion is expectedto be weak,basedon previousobservationsof modelof Lamyetal. (2010b), made of two contactspheres. In
thedustcontinuuminthemillimetreandsubmillimetredomains thelatermodel,theshapeisdividedinto2560triangularfacets
(e.g. Jewitt&Luu 1992; Jewitt&Matthews 1997). For exem- of comparable size. We consider the size for these two shape
ple,usingtheJCMT(HPBW=19′′)Jewitt&Matthews(1997) modelsasrobust,sothatitisafixedparameter.
measured a flux of 6.4 mJy at 350 µm for comet C/1996 B2
(Hyakutake)atr =1.08AUand∆ = 0.12AU. Assumingthat
h 3.2.Thermalmodel
the dust opacity varies according to λ−0.89 (Jewitt&Matthews
1997) andthatthedustbrightnessdistributionvariesaccording Theinterpretationofthemillimetricobservationsrequiresather-
toρ−1,whereρisthedistancetonucleus,wederiveadustflux malmodelforthenucleus.Weusedthethermalmodelpresented
at240GHz of 0.05mJy fora beamsize of1′′anda geocentric in Groussin et al. (2010) for comet 8P/Tuttle and already ex-
distance of 0.26AU. Thegaseousactivityof 8P/Tuttle in early tensively described in several past articles (e.g., Groussinetal.
January 2008 was typically 5–10 times lower that the activity 2004;Lamyetal.2010a).Foreachfacetoftheshapemodel,we
ofHyakutakeatr =1.08AU(Mummaetal.1996;Bonevetal. solve for the surface energy balance between the flux received
h
4 J.Boissieretal.:Observationsof8P/TuttlewiththePlateaudeBureinterferometer
fromtheSun,there-radiatedflux,andtheheatconductioninto
thenucleus.Asthenucleusrotatesarounditsspinaxis,theillu-
minationchanges,andtheheatconductionequationiscomputed
for each facet considering a one-dimensional time-dependent
equation. The projected shadows are taken into account in our
model.Asaresult,weobtainedthetemperatureofeachfacetas
a function of time, over one rotation period. We then integrate
the flux over each facet to calculate the total millimetric flux
received by the observer as a function of time and wavelength
(1.25mm).
Theactiveareaof8P/Tuttleisrestrictedto<15%ofthesur-
face (Groussinetal. 2010). As for 9P/Tempel 1 with an active
areaof9%(Lisseetal.2005),thesublimationofwater icecan
beneglectedintheenergybalanceforthecalculationofthether-
malfluxemittedfromthenucleussurface(Groussinetal.2007).
4. Results
Fig.2.Thermallightcurveof8P/TuttleasseenfromthePlateau
Using the above simple spherical shape model with a radius
de Bure on 8 January 2008. We used our standard set of pa-
of 2.8 km and our thermal model with the parameters of rameters for the thermal inertia (I = 0), the beaming factor
Groussinetal. (2008) (thermal inertia I = 0 J K−1 m−2 s−1/2, (η = 0.7) and the emissivity (ǫ = 0.95). The shape model is
beaming factor η = 0.7, emissivity ǫ = 0.95), which thatof8P/TuttlederivedfromHubbleSpaceTelescopeobserva-
is in that case identical to the Standard Thermal Model
tions(Lamyetal.2008,2010b).Thelightcurvehasbeenphased
(Lebofsky&Spencer 1989), we obtain a millimetric flux of
relativelytotheradarobservationsofHarmonetal.(2010),per-
5.6mJyat1.25mmon8Jan.2008.Thisislargerthan,though formed∼10rotation periodsearlier. The maximum(resp. min-
barelyinagreementwith,ourobservedfluxof3.0+1.2mJy(1σ)
−1.0 imum) flux correspondsto the emission of a spherical nucleus
or3.0+2.4mJy(3σ),whichinfactcorrespondstoasmallerradius of 2.8km (resp. 2.5km). Thehorizontalthick solid line corre-
−1.8
ofr = 2.0±0.4km(1σ)usingthesamethermalmodelandpa- spondstotheobservationtimeatPlateaudeBure(2hlong).
rameters.Inordertoinvestigatetheoriginofthisdiscrepancywe
studiedtheinfluenceofseveralparametersinthecalculationof
thefluxat1.25mm:i) shape,ii) thermalinertia I, iii)beaming
factor η, and iv) emissivity ǫ from the surface and sub-surface
epoch,therotationphaseis-5±1.5◦with0◦beingthetimewhen
layers.Ourgoalistoinvestigatewhichoftheseparameterscan
the nucleusisseen broadside,with thelargerlobeapproaching
helptodecreasethenucleusfluxtomakeitcompatiblewithour
(Harmonetal.2010)andcorrespondstothemaximumthatfol-
observations.
lows the lightcurve minimum in Fig. 2, on Jan. 8.75. The 1.5◦
errorbaronthereferenceaddsanother3minofuncertaintyon
4.1.Shapeeffect therephasing.Thetotaluncertaintydoesnotexceed5min and
is small in comparison with the length of the Plateau de Bure
The simple calculation described above has been made using
observations(2h).
our spherical shape model with a radius of 2.8 km. As de-
ThelightcurvepresentedinFig.2hasbeenrephasedandone
scribed in Sect. 3, a more realistic shape model exists, com-
canseethatthePlateaudeBureobservations(aroundJan.8.67)
posed of two contact spheres (Lamyetal. 2008, 2010b). With
wereperformedarounditsminimum.Underthestandardparam-
this shapemodel,the fluxis nomore constantwith time as for
eters, we expect a flux of ∼4.45 mJy at that time. This is still
the spherical case, but changes during the nucleus rotation to
higherthanthe3.0+1.2 mJymeasuredwiththePlateaudeBure,
produce a thermal lightcurve. Under our standard assumptions −1.0
thus we assessed the impact of differentthermal parametersof
(I = 0,η = 0.7,ǫ = 0.95) we calculated the synthetic thermal
thenucleustoinvestigatethisdiscrepancy.
lightcurveofthisshapemodel,asillustratedinFig.2.Theflux
varies with time, with a minimum of ∼4.45 mJy and a maxi-
mumof∼5.65mJy.Themaximumfluxisreachedwhenthepri-
4.2.Thermalinertiaeffect
maryandsecondaryarebothilluminated,andthisisequivalent
toasphericalnucleusofradius2.8kmasexplainedinSect.3.1. We present in Fig. 3 the thermal lightcurve expected from the
The minimum flux is reached when the secondary eclipses the comet 8P/Tuttle for different values of the nucleus thermal in-
primary, and this is equivalent to a spherical nucleus of radius ertia. When the thermal inertia increases, the diurnal temper-
2.5 km. As the amplitude of the ligth curve is large (1.2 mJy), ature variations decrease: the temperatures become cooler on
dependingonthe timeofobservation,theobservedfluxcanbe the day side and warmer on the night side. In our case, since
quitedifferent. the phase angle is large (65◦), the heating on the night side is
Using the sidereal rotation period of 11.444±0.001 h, we morepronouncedthanthecoolingonthedayside,andoverall,
phased the observations performed at Plateau de Bure on 8 the observed flux becomes larger as thermal inertia increases.
Jan. 2008with the Arecibo radar experimentsof Harmonetal. It is clear from Fig. 3 that a larger thermal inertia does not
(2010) performed in early January 2008. The reference epoch helptosolveourissue asthe fluxonlygetslarger.Intherange
oftheAreciboradarstudyisJan.4.0046,i.e.∼10rotationperi- 0-200 J K−1 m−2 s−1/2 for the thermal inertia estimated by
odsearlier than our observations,which translates to an uncer- Groussinetal.(2008),wethenfavourthelowervalues(typically
tainty of 0.0004 day, i.e. less than 1 minute. At the reference ≤10JK−1m−2s−1/2).
J.Boissieretal.:Observationsof8P/TuttlewiththePlateaudeBureinterferometer 5
Fig.3. Expected thermal lightcurvesof the comet 8P/Tuttle at Fig.5. Expected thermal lightcurves of the comet 8P/Tuttle at
1.25 mm for differentvaluesof the nucleusthermal inertia be- 1.25 mm for different values of the surface emissivity ǫ rang-
tween 0 (in red) and 300 MKS (in blue). The beaming factor ing from 1 (highest, solid red line) to 0.4 (lowest, dashed yel-
is η = 0.7 and the emissivity ǫ = 0.95. The geometrical con- low line). The thermal inertia is I = 0 and the beaming factor
ditions are that of the observations of 8P/Tuttle on 08 January η = 0.7.Thegeometricalconditionsareidenticalto thatof the
2008(r =1.07AU,∆=0.28AU,phaseangleφ=65◦). observationsof8P/TuttleinJanuary2008.
h
which is a small improvementbut not sufficient to explain the
observedfluxof3.0mJy.
The SST observations of comet 8P/Tuttle (Groussinetal.
2008, 2010) suggested a beaming factor η on the order of 0.7.
Thisvalueisconstrainedbytheinfraredspectrograph(IRS)ob-
servations,whichlastedonly10minutes,ashorttimecompared
to the rotation period of ∼11.4 h. The SST observations per-
formed on 2.76 Nov. 2007 and, 141 periods later, the nucleus
wasinthesamerotationphaseon8.65±0.02Jan,2008,exactly
at the time of the Plateau de Bure observations (Fig. 2). As a
result,althoughhigherηvaluescorrespondto lowermillimetre
fluxes,we favourthe η = 0.7, whichis well constrainedby the
Spitzerobservations.
Delbo´ etal. (2003) suggested an increase of the beaming
factor with phase angle for Near-Earth Asteroids (NEAs). If
confirmed,this trendscould explain why our observationsper-
formedat65◦phaseanglefavoralargervalueofη,closetoone,
while SST observations performed at 39◦ phase angle favor a
Fig.4. Expected thermal lightcurves of the comet 8P/Tuttle at
smaller value, close to 0.7. However, according to Delbo´ etal.
1.25mm fordifferentvaluesof the surfacebeamingfactor(η).
(2003),theirstatisticislowandmoreobservationsarerequired
The thermal inertia is I = 0 and the emissivity ǫ = 0.95. The
toconfirmthistrend.
geometricalconditions are identical to that of the observations
Finally, it cannot be excluded that the effect of the rough-
of8P/TuttleinJanuary2008.
ness (η) may be wavelength dependent. Roughness at micron
scale could indeed be more importantthan at millimetre scale,
resulting in a smaller beaming factor in the infrared. But this
4.3.Beamingfactoreffect
pointcannotbeconfirmedsincewecannotruleoutafractalsur-
WepresentinFig.4thethermallightcurveemittedbyoursyn- face,inwhichcase theroughnesswouldbemoreorless scale-
thesized, bilobate nucleus as a function of the beaming factor independent.
η. In our thermal model, the beaming factor follows the strict
definitiongivenbyLagerros(1998)whereitonlyreflectsthein-
4.4.Emissivityanddeptheffect
fluenceofsurfaceroughnessandηmustbelowerorequalto1.0.
Inaddition,accordingtoLagerros(1998),ηmustbelargerthan The thermal flux emitted from the nucleus is proportional to
0.7to avoidunrealisticroughness,with r.m.s.slopesexceeding the surface emissivity, as illustrated in Fig. 5. The flux at the
45◦.Theacceptablerangeforηisthen0.7-1.0,asillustratedin lightcurve minimum is in 1σ agreement with our observations
Fig.4.Whenroughnessincreases(i.e.,ηdecreases),thesurface for an emissivity lower than 0.8. While the surface emissivity
temperatureincreasesduetoself-heatingonthesurface,andthe of small bodies in the mid-infrared is close to unity, it is still
totalfluxincreases.Changingηfrom0.7(Groussinetal.2008) unknown at millimetre wavelengths and might be lower than
to 1.0 decreases the minimum flux from 4.45 mJy to 4.1 mJy, in the mid-infrared. This point has already been addressed by
6 J.Boissieretal.:Observationsof8P/TuttlewiththePlateaudeBureinterferometer
Ferna´ndez (2002) for comet C/1995 O1 Hale-Bopp, where an Table 2.Nucleusthermalfluxintegratedoverdepth,compared
emissivityof0.5isrequiredinthemillimeticrangetoreconcile topuresurfaceemission(1.0).
the nucleus sizes derived from infrared and millimetric obser-
vations. Based on asteroid observations in the sub-millimetre, Thermalinertia Relativedepth-integratedflux
Redmanetal.(1998)foundthattheemissivityof7asteroidsde- JK−1m−2s−1/2
creaseswithincreasingwavelength.Theobservationsofasteroid
3 0.83
(2867)Steinsat1.6and0.53mmperformedwith theradiome-
5 0.84
ter MIRO onboard the Rosetta spacecraft confirm this trend:
10 0.86
Gulkisetal.(2010)foundanemissivitydecreasingfrom0.85–9
50 0.88
at 1.6 to 0.6–0.7 at 0.53 mm. A low millimetric emissivity of
100 0.91
0.6 was also foundfor asteroid 4 Vesta by Mueller&Lagerros
(1998).Overall,thismeansthatourvalues(ǫ < 0.8)areplausi-
ble.
A possible physical explanation for the lower emissivity is
thatapartofthemillimetrethermalfluxarrisesfromsub-surface
layerswhicharecolderthanthesurfaceitself.Suchatempera-
ture gradient is expected given the low thermal intertia of the
nucleus. The depth of the main contributing layer depends on
thematerialopacity,whichisunknown.Measurementsonrocks
showedthatinmostmaterialsthisdepthliesbetween3and100λ
(Campbell&Ulrichs1969). A depthof 10λis commonlyused
when dealing with planetary surfaces (e.g. 11λ is used for the
martiansurfaceregolith,Muhleman&Berge1991;Goldinetal.
1997).Dependingontheupperlayerstemperaturegradient(con-
troled by the thermal inertia) and the relative contribution of
the different layers to the overall emission, the resulting spec-
tralemissivityofthesurfacecanbesignificantlylowerthanthe
usualinfraredvalueclosetounity.
Inorderto investigatethiseffect,wecalculatedthenucleus
integratedfluxasa functionofdepth(downto20cm),relative
tothesurfaceflux,fordifferentthermalinertiavalues.Figure6
illustrates our results: as we observedthe afternoonside of the
Fig.6. Thermal emission from a sub-surface layer (relative to
nucleus, the shadowed part that we see is still warm because surface emission) as a function of its depth different values of
of thermal inertia and the contribution of the first sub-surface
thethermalinertia.
layersis comparableor largerto the surface, downto a certain
depth(thatdependsonthethermalinertia)whereitdropssince
diurnaltemperaturevariationsbecomenegligible.
AssumingaPoissonianweightedfunction(thatpeaksat10λ)
to describe the relative contributions of the sub-surface layers,
whichseemstobeagoodapproximationcomparedtothework
ofMoullet(2008),weintegratetheweigthedfluxfromFig.6as
afunctionofdepth,toderivetheeffectiveoutcomingfluxcom-
pared to a pure surface emission. The results are presented in
Table 2. Depending on the thermal inertia, the flux is reduced
by 9% to 17% compared to a pure surface emission. For low
thermalinertia(≤10JK−1m−2s−1/2),whichareinbetteragree-
mentwithourobservationsasexplainedinSect.4.2,thefluxis
reducedby 14-17%,which correspondsto an “effective”emis-
sivityof 0.79-0.82assumingourstandardsurfaceemissivityof
0.95.AccordingtoFig.5andasexplainedabove,thisallowsto
matchourobservationswithin1σ.
Our results confirmthat a low emissivity in the millimetric
wavelength range can result from the emission of sub-surface
layerswith a low thermalinertia.In the mid-infrared,typically
around10µm,10λcorrespondsto0.1mm,adepthoverwhich Fig.7. Same Figure as Fig. 2 but for I = 0, ǫ = 0.8, η = 0.7
the flux is close the surface flux (Fig. 6), explaining why the (red curve) or η = 1.0 (blue curve). For η = 1.0, which is our
above effect only matters in the millimetric wavelength range preferedvalue,abouthalfofthethermallightcurveagreeswith
and beyond, in the centimetric and radar wavelength range. ourobservationsatthe1σlevel.
However, for the centimetric and radar, there exists a few no-
tableexceptions,andinparticularGanymede,whichcentrimet-
ric emission corresponds to a brightness temperature of about
55-88K,belowanyacceptablesub-surfacetemperatureforthis
body(Muhleman&Berge 1991), and whose radar reflectionis higher reflectivity must also be invoked, likely resulting from
highly anomalous (Ostro&Shoemaker 1990). In this case, a backscatteringofthesurface.
J.Boissieretal.:Observationsof8P/TuttlewiththePlateaudeBureinterferometer 7
5. Summary Gulkis,S.,Allen,M.,Backus,C.,etal.2007,P&SS,55,1050
Gulkis,S.,Keihm,S.,Kamp,L.,etal.2010,P&SS,58,1077
We report here the first detection of the thermal emis- Harmon,J.K.,Nolan,M.C.,Giorgini,J.D.,&Howell,E.S.2010,Icarus,207,
sion of a cometary nucleus at millimetre wavelength since 499
C/1995O1Hale-Bopp,performedatPlateaudeBureon8Jan. Harmon, J. K., Nolan, M. C., Howell, E. S., & Giorgini, J. D. 2008, LPI
Contributions,1405,8025
2008.UsingtherotationperiodderivedbyHarmonetal.(2010),
Jewitt,D.&Luu,J.1992,Icarus,100,187
we phased our observations with respect to their radar exper-
Jewitt,D.C.&Matthews,H.E.1997,ApJ,113,1145
iments and found that Plateau de Bure observations were per- Kobayashi,H.,Bockele´e-Morvan,D.,Kawakita,H.,etal.2010,A&A,509,A80
formedataminimumofthelightcurve.Weusedtheshapemodel Lagerros,J.S.V.1998,A&A,332,1123
developpedbyLamyetal.(2010b)for8P/Tuttlenucleustocom- Lamy,P.,Groussin,O.,Fornasier,S.,etal.2010a,A&A,516,A74
Lamy,P.,Jorda,L.,Toth,I.,etal.2010b,inpreparation
putethermalemissionlightcurvesusingdifferentthermalparam-
Lamy,P.L.,Toth,I.,Fernandez,Y.R.,&Weaver,H.A.2004,CometsII,ed.M.
etersets.Fromouranalysis,wecanconcludethattomatchour C.Festou,H.U.Keller,H.A.Weaver,223
observed flux of 3.0+1.2 mJy at 1.25 mm, the thermal inertia Lamy,P.L.,Toth,I.,Jorda,L.,etal.2008,BAAS,40,393
−1.0
of the nucleus should be low, typically ≤10 J K−1 m−2 s−1/2, Lebofsky, L. A. & Spencer, J. R. 1989, in Asteroids II, ed. R. P. Binzel,
T.Gehrels,&M.S.Matthews,128–147
in agreement with the range 0-200 J K−1 m−2 s−1/2 derived
Licandro,J.,Tancredi,G.,Lindgren,M.,Rickman,H.,&Hutton,R.G.2000,
from Spitzer observations (Groussinetal. 2008). In addition, Icarus,147,161
the millimetric emissivity of the nucleus should be lower than Lisse,C.M.,A’Hearn,M.F.,Groussin,O.,etal.2005,ApJ,L625,L139
0.8. According to our thermal model, such a low value can be Moullet,A.2008,PhDthesis,The`sededoctoratdel’Universite´Paris7Diderot
Mueller,T.G.&Lagerros,J.S.V.1998,A&A,338,340
due to the non-negligibleemission of the sub-surfacelayers of
Muhleman,D.O.&Berge,G.L.1991,Icarus,92,263
the nucleus, which are colder than the surface at depth of a Mumma,M.J.,Disanti,M.A.,DelloRusso,N.,etal.1996,Sci,272,1310
few millimetre or more for low thermal inertia values. Similar Ostro,S.J.&Shoemaker,E.M.1990,Icarus,85,335
and even lower values of the millimetric emissivity have been Pety, J. 2005, in SF2A-2005: Semaine de l’Astrophysique Francaise, ed.
F.Casoli,T.Contini,J.M.Hameury,&L.Pagani,721
already mentionned to explain the low flux emitted by aster-
Pollack,J.B.,Hubickyj,O.,Bodenheimer,P.,etal.1996,Icarus,124,62
oids(Redmanetal.1998;Mueller&Lagerros1998;Ferna´ndez
Redman,R.O.,Feldman,P.A.,&Matthews,H.E.1998,ApJ,116,1478
2002). As to the beaming factor, the lowest flux of the lightu- Safronov,V.S.&Zvjagina,E.V.1969,Icarus,10,109
curve is in 1σ agreementwith our observed flux for any value
inthe plausiblerange0.7–1.0,with a betteragreementtowards
higheredge.Howeverwefavourη=0.7,theonlyvalueinagree-
ment with Spitzer (IRS) observations (Groussinetal. 2010).
Fromtheaboveconclusions,wegeneratedasyntheticlightcurve
forthenucleusofcomet8P/Tuttle,asobservedfromthePlateau
de Bureon8 Jan. 2008,usingthefollowingparameters: I = 0,
ǫ = 0.8and η in the range0.7-1.0to coverthe possible values.
TheresultisillustratedinFigure7.
In the future, the Rosetta spacecraft, equipped with a mi-
crowaveinstrumentoperatingat190and562GHz(Gulkisetal.
2007), will provide an unequaled dataset to study the surface
ofacometarynucleusanditsthermalproperties.Itwillbealso
importanttorepeatground-basedstudiesonothercomets,tode-
terminewhetherallcometspresentsimilarpropertiesorif they
change from one comet to another, revealing different surface
natures. The (sub-)millimetre interferometer ALMA will offer
a significant gain in sensitivity and allow similar studies on a
larger sample of comets, from both the ecliptic and the Oort
clouddynamicalclasses.
Acknowledgements. Theresearchleadingtotheseresultshasreceivedfunding
fromtheEuropeanCommunity’sSeventhFrameworkProgramme(FP7/2007–
2013)undergrantagreementNo.229517
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