ApJ manuscript on the origin of the zodiacal cloud

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COMETARY ORIGIN OF THE ZODIACAL CLOUD AND CARBONACEOUS
MICROMETEORITES. IMPLICATIONS FOR HOT DEBRIS DISKS
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2010 ApJ 713 816
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TheAstrophysicalJournal,713:816–836,2010April20 doi:10.1088/0004-637X/713/2/816
(cid:2)C2010.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedintheU.S.A.
COMETARYORIGINOFTHEZODIACALCLOUDANDCARBONACEOUSMICROMETEORITES.
IMPLICATIONSFORHOTDEBRISDISKS
DavidNesvorny´1,2,PeterJenniskens3,HaroldF.Levison1,2,WilliamF.Bottke1,2,DavidVokrouhlicky´4,
andMatthieuGounelle5
1DepartmentofSpaceStudies,SouthwestResearchInstitute,1050WalnutSt.,Suite400,Boulder,CO80302,USA
2CenterforLunarOrigin&Evolution,NASALunarScienceInstitute,Boulder,CO80302,USA
3CarlSaganCenter,SETIInstitute,515N.WhismanRoad,MountainView,CA94043,USA
4InstituteofAstronomy,CharlesUniversity,VHolesˇovicˇka´ch2,18000Prague8,CzechRepublic
5MuseumNationald’HistoireNaturelle,LaboratoiredeMine´ralogieetCosmochimieduMuse´um,61rueBuffon,75005Paris,France
Received2009October26;accepted2010February28;published2010March26
ABSTRACT
The zodiacal cloud is a thick circumsolar disk of small debris particles produced by asteroid collisions
and comets. Their relative contribution and how particles of different sizes dynamically evolve to produce the
observed phenomena of light scattering, thermal emission, and meteoroid impacts are unknown. Until now,
zodiacal cloud models have been phenomenological in nature, composed of ad hoc components with properties
not understood from basic physical processes. Here, we present a zodiacal cloud model based on the orbital
propertiesandlifetimesofcometsandasteroids,andonthedynamicalevolutionofdustafterejection.Themodel
isquantitativelyconstrainedbyInfraredAstronomicalSatellite(IRAS)observationsofthermalemission,butalso
qualitativelyconsistentwithotherzodiacalcloudobservations,withmeteorobservations,withspacecraftimpact
experiments,andwithpropertiesofrecoveredmicrometeorites(MMs).WefindthatparticlesproducedbyJupiter-
familycomets(JFCs)arescatteredbyJupiterbeforetheyareabletoorbitallydecouplefromtheplanetanddrift
downto1AU.Therefore,theinclinationdistributionofJFCparticlesisbroaderthanthatoftheirsourcecomets
and leads to good fits to the broad latitudinal distribution of fluxes observed by IRAS. We find that 85%–95%
of the observed mid-infrared emission is produced by particles from JFCs and <10% by dust from long-period
comets.TheJFCparticlesthatcontributetotheobservedcrosssectionareaofthezodiacalcloudaretypicallyD ≈
100μmindiameter.Asteroidaldustisfoundtobepresentat<10%.Wesuggestthatspontaneousdisruptionsof
JFCs,ratherthantheusualcometaryactivitydrivenbysublimatingvolatiles,isthemainmechanismthatliberates
cometaryparticlesintothezodiacalcloud.Theejectedmmtocm-sizedparticles,whichmayconstitutethebasic
grain size in comets, are disrupted on (cid:2)10,000 yr to produce the 10–1000 μm grains that dominate the thermal
emissionandmassinflux.BreakupproductswithD >100μmundergoafurthercollisionalcascadewithsmaller
fragmentsbeingprogressivelymoreaffectedbyPoynting–Robertson(PR)drag.UponreachingD <100μm,the
particles typically drift down to <1 AU without suffering further disruptions. The resulting Earth-impact speed
and direction of JFC particles is a strong function of particle size. While 300 μm to 1 mm sporadic meteoroids
are still on eccentric JFC-like orbits and impact from antihelion/helion directions, which is consistent with the
aperture radar observations, the 10–300 μm particles have their orbits circularized by PR drag, impact at low
speeds,andarenotdetectedbyradar.OurresultsimplythatJFCparticlesrepresent∼85%ofthetotalmassinflux
atEarth.Sincetheiratmosphericentryspeedsaretypicallylow(≈14.5kms−1 meanforD = 100–200μmwith
≈12kms−1 beingthemostcommoncase),manyJFCgrainsshouldsurvivefrictionalheatingandlandonEarth’s
surface. This explains why most MMs collected in antarctic ice have primitive carbonaceous composition. The
presentmassoftheinnerzodiacalcloudat<5AUisestimatedtobe1–2×1019 g,mainlyinD = 100–200μm
particles. The inner zodiacal cloud should have been >104 times brighter during the Late Heavy Bombardment
(LHB) epoch ≈3.8 Gyr ago, when the outer planets scattered numerous comets into the inner solar system. The
bright debris disks with a large 24 μm excess observed around mature stars may be an indication of massive
cometarypopulationsexistinginthosesystems.Weestimatethatatleast∼1022,∼2×1021,and∼2×1020 gof
primitive dark dust material could have been accreted during LHB by the Earth, Mars, and Moon, respectively.
Keywords: comets:general–minorplanets,asteroids:general–zodiacaldust
amountofscatteredlight(Hong1985;Kniessel&Mann1991;
1.INTRODUCTION
Ishiguroetal.1999;Hahnetal.2002),theDopplershiftsofthe
The zodiacal cloud is a dynamic assembly of meteoroids in solar Mg i Fraunhofer line (Hirschi & Beard 1987; Mukai &
bound orbits around the Sun. The orbits depend on particle Mann1993;Clarkeetal.1996;Reynoldsetal.2004),andthe
size, location in the cloud, and the type of parent body. more easily to interpret thermal emission observed in various
Interstellardustparticlesthatpassthroughthesolarsystemare linesofsight(Kelsalletal.1998;Marisetal.2006).Particularly
notconsideredinthispaper,noraresmallmeteoroidfragments good scattered light observations came from the Clementine
that move out of the solar system on hyperbolic orbits (“beta- mission(Hahnetal.2002),whilethermalinfraredobservations
meteoroids”). aremostlyfromtheInfraredAstronomicalSatellite(IRAS;Low
Traditionally, the zodiacal cloud has been described with etal.1984;Hauseretal.1984;Goodetal.1986;Sykes1990),
phenomenological models of dust distributions to explain the the Cosmic Background Explorer (COBE; Reach et al. 1995;
816
No.2,2010 COMETARYORIGINOFTHEZODIACALCLOUD 817
Kelsall et al. 1998), the Midcourse Space Experiment (MSX; all current satellite impact models use meteoroid velocity
Priceetal.2003),theInfraredSpaceObservatory(ISO;Fixsen distributions (both magnitude and spatial direction) derived
&Dwek2002;Leinertetal.2002;Reachetal.2003;Mueller from meteor observations (Taylor & Elford 1998; Jones &
et al. 2005), and the Spitzer Space Telescope (Bhattacharya & Brown1993;Brown&Jones1999;Brown&Campbell-Brown
Reach2004;Reachetal.2007). 2003), which pertain to much bigger particles than typically
Thephenomenologicalmodelssuccessfullydescribethesize, encounteredbysatellites.
spatial and velocity distributions of dust particles in the solar In this paper, we investigate what fraction of the zodiacal
system(e.g.,Gru¨netal.1985;Divine1993;Dikarevetal.2004). cloudisduetocometaryversusasteroidaldustbycalculatingthe
They are particularly useful for accessing the satellite impact evolutionofdustparticlesundersolarradiationforcesandplan-
hazard,designingspacecraftimpactexperimentsandstudiesof etaryperturbations(includingresonancesandcloseencounters),
extrasolaremissionsourcessuchasthecosmicmicrowaveback- ejectedfrommodelpopulationsofallpotentialsources(notjust
ground(e.g.,Kelsalletal.1998).Thephemenologicalmodels, representativeexamples).Thesourcepopulationsincludeaster-
however, fall short in answering basic questions related to the oids,activeandmostlydormantJupiter-familycomets(JFCs),
originofthezodiacalcloud,itstemporalbrightnessvariability, Halley-typecomets(HTCs),andlong-periodOort-cloudcomets
and the provenance of interplanetary particles collected at the (OCCs).Inrecentyears,muchinsightwasgainedintothedy-
Earth.Consequently,theoriginofthezodiacalcloud,interplane- namicalcharacteristicsofthesepopulationsandthenumberof
tarydustparticles(IDPs)collectedinEarth’sstratosphere(e.g., asteroids and comets that can contribute dust to the zodiacal
Love & Brownlee 1993), and micrometeorites (MMs) on the cloud(e.g.,Levison&Duncan1994,1997;Jedicke&Metcalfe
ground (Taylor et al. 1996; Engrand & Maurette 1998; Farley 1998; Wiegert & Tremaine 1999; Dones et al. 2004; Francis
etal.1998,2006;Genge2006)isstillamatterofconsiderable 2005; Gladman et al. 2009). At the same time, it was realized
debate. This limits our ability to link the detailed laboratory that mostly dormant JFCs are the main source of meteoroid
studiesofIDPsandMMstothepropertiesoftheirparentbod- streamsintheinnersolarsystem(Jenniskens2006,2008)and
ies, and to use the zodiacal cloud as a valuable reference for responsible for the antihelion/helion sources in the sporadic
studiesoftheexozodiacaldebrisdisks. meteoroidbackground(Jenniskens2006;Wiegertetal.2009).
Detailed dynamical models can be more useful in this Here,wecouplethesenewinsightstodynamicalbehaviorof
context. At the root of dynamical models are the physical cometaryandasteroidaldustinordertoevaluatethecontribution
properties of interplanetary dust, such as density, geometric ofvarioussourcestothethermalemissionofzodiacaldustand
albedo, elemental composition, mineralogy, tensile strength, the influx of MMs.We show thatJFCs are the main source of
heat capacity, etc. (e.g., Dumont & Levasseur-Regourd 1988; zodiacaldustinside5AUandthemostlikelysourceoftheMMs
McDonnell&Gardner1998;Gustafson1994;Gustafsonetal. foundonEarth.Ourresultsalsoprovidequantitativeconstraints
2001;Levasseur-Regourdetal.2001),whichdeterminethebe- ondustlifetimes,influxrates,andvelocitydistributionsdirectly
haviorofparticlesininterplanetaryspace(e.g.,planetarypertur- from the known abundances of meteoroid parent bodies. The
bations,collisions,sublimation,sputtering)andtheirinteraction resultsareusedtoquantifythepropertiesofzodiacaldustcloud
with a detector (e.g., ablation of MMs in Earth’s atmosphere, in the past and discuss implications for studies of exozodiacal
3Heretention,thermalradiation,lightscattering).Indynamical debrisdisks.
models,theindividualparticlesaretrackedbynumericalcodes TosetupthestageforourmodelingdescribedinSection3,we
astheyevolvebyvariousprocessesfromtheirsources(assumed discuss IRAS observations of the zodiacal cloud in Section 2.
to be, e.g., asteroids, comets, satellites or Kuiper Belt objects) Results are presented in Section 4. In Section 5, we estimate
tosinks(e.g.,whentheysublimate,disrupt,impactorleavethe thecurrentandhistoricalterrestrialaccretionratesofdustand
solarsystem).Insightsintotheoriginofthezodiacalcloudcan discuss the implications of our work for studies of MMs and
be obtained by calibrating the results of dynamical models on debris disks. Comet disruptions/splitting events are reviewed
observations. in Section 6. We suggest that they are the main mechanism
Untilnow,detaileddynamicalmodelshavebeenonlydevel- bywhichthecometaryparticlesareliberatedfromtheirparent
oped for asteroidal dust to explain the origin of the zodiacal bodies into the zodiacal cloud. The mass-loss rate from JFCs
dustbands(e.g.,Dermottetal.1984;Groganetal.1997,2001; mustbelargeenoughtosupplytheIDPcomplexagainstlosses
Reach et al. 1997; Nesvorny´ et al. 2006; Vokrouhlicky´ et al. (Lisse2002).Previousworkandoriginofdustparticlesbeyond
2008) and trapped dust in Earth’s Langrange points first seen JupiterarediscussedinSections7and8,respectively.
inIRASobservations(Dermottetal.1994b).Ithasbeenestab-
2.CONSTRAINTS
lishedthatthedustbandsoriginatefromtheyoungestasteroid
families (Nesvorny´ et al. 2003, 2008). However, claims that Ourprimaryconstraintsaretheobservationsofthezodiacal
asteroids are a major if not dominant source of zodiacal dust, cloudbyIRASwhichhavebeenconfirmedbyCOBEandSpitzer
by assuming that all main belt asteroids contribute dust (e.g., (Hauseretal.1984;Lowetal.1984;Kelsalletal.1998;Sykes
Dermott et al. 1995; Durda & Dermott 1997; Kortenkamp & etal.2004).IRASmeasuredmid-infrared(MIR)fluxesinfour
Dermott1998),haveremainedindoubt. filters with effective wavelengths of 12, 25, 60, and 100 μm.
Models of the zodiacal cloud need not only explain line- Thesefilterscanbeusedaswindowsintothedustdistribution
of-sight properties, but also the observed influx of meteors atdifferentdistancesfromtheSun.Measurementsinthe12μm
(see Ceplecha et al. 1998; Jenniskens 2006, for a review) and IRAS band are mainly sensitive to distributions of particles
the impact rate of meteoroids on satellites (Love & Brownlee at ∼1–2 AU, while the 25 and 60 μm band measurements
1993).Untilnow,modelsthatweredevelopedtoexplainthese preferentially detect thermal emission from larger distances.
dynamical phenomena (e.g., Gru¨n et al. 1985; Divine 1993; IRASobservationsinthe100μmbandarelessusefulforprobing
Staubachetal.1997;Dikarevetal.2004)werebasedonadhoc thethermalradiationofdustparticlesintheinnersolarsystem.
populations of meteoroids in various types of orbits without IRAS showed that the MIR brightness of the zodiacal cloud
a dynamical underpinning to sources and sinks. Moreover, peaksattheeclipticandhasbroadwingsthatextendalltheway
818 NESVORNY´ ETAL. Vol.713
Figure1.UppersolidlinesineachpanelshowIRASscan180_24(seeTable3inNVBS06)thathasbeensmoothedbyalow-passfiltertoremovepointsourcesand
instrumentalnoise.Differentpanelsshowfluxesat12,25,60,and100μmIRASwavelengths.Thebottomsolidlinesshowthecontributionofthreemainasteroiddust
bandstotheobservedfluxes.AccordingtoNVBS06,thesedustbandscontributetotheobservedfluxesby≈9%–15%within10◦totheecliptic,and<5%overall.
Thestrongsignalat100μmbetweenlatitudesb≈−80◦andb≈−30◦isthegalacticplaneemission(alsoapparentat60μm).FigurefromNVBS06.
to the ecliptic poles (Figure 1). The variation with the ecliptic bygravitationalperturbationsfromJupiter(Dermottetal.1995,
longitude is minimal indicating that the zodiacal cloud is a 2001).Sincewearenotinterestedinthesedetailedfeaturesof
nearlysymmetricaldiskofcircumsolarparticlesthatisroughly the zodiacal cloud here, we removed them by combining the
centeredattheSun(e.g.,Staubachetal.2001).Thesignificant selectedIRASscansintoarepresentativeprofile.Thiswasdone
flux received from the ecliptic poles (∼1/3–1/4 of the ecliptic byfirstshiftingthescansbyasmallvalueinlatitude(<2◦),so
flux) also suggests that the cloud must be rather thick in the that the peak of emission was centered exactly at b = 0, and
normaldirectiontotheeclipticplane. calculatingtheaveragefluxfromallselectedscansasafunction
Following Nesvorny´ et al. (2006, hereafter NVBS06), we ofb.Weendedupwithprofilesshowingthemeanfluxesat12,
selectedseveralrepresentativeIRASscansthatmetthefollowing 25, and 60 μm wavelengths as a function of ecliptic latitude
conditions.(1)Weusedscansthatcoveredacontinuousrange (Figure2).Theseprofilesrepresentthemainconstraintsonthe
of ecliptic latitudes from b < −80◦ to b > 80◦. (2) We work described here. Additional constraints are discussed in
did not use scans that had gaps created when the telescope Section4.3.
skipped over bright sources. (3) We did not use scans that
showed strong emission from extrasolar sources such as the
3.MODEL
galacticplane,galacticcirrus,pointsources,etc.(4)Werequired
that the selected scans covered all values of ecliptic longitude Our model of the zodiacal cloud has four parts: we (1)
and the available range of solar elongations, l(cid:6). Tables 2 and define the initial orbital distributions of particles for different
3 in NVBS06 list the basic information about the selected sources (asteroid and comet populations), (2) track the orbital
scans. evolutionofparticleswithvarioussizesfromsourcestosinks,
Inthiswork,weonlyconsiderscanswithl(cid:6) ≈ 90◦.Thisis (3)determinethethermalinfraredemissionfromthesesynthetic
mainly done because the detail variation of brightness with l(cid:6) particle distributions, and (4) model the detection of their
is difficult to characterize as it requires an appropriate model emission by IRAS. These model components are described
forthecollisionaldisruptionofparticles(NVBS06).Wedonot below.
includetheeffectsofcollisionsbetweenparticlesinourmodel To simplify things, we do not initially account for the
(except in Section 4.2, where a simple model for collisions is collisional disruptions of dust particles in the model. This is a
used).Theconsideredvalueofl(cid:6)isinthemiddleoftheavailable majorassumptionwhichweverifyinSection4.2.Forexample,
rangeandthusbestrepresentsIRASobservations. NVBS06 showed how the collisional disruption of particles,
Thezodiacalcloudisknowntobewarpedandhaveacenter andproductionofsmallerdaughterproducts,affectthespatial
thatisslightlyoffsetfromtheSun.Thesefeaturesareproduced distributionofparticlepopulationsintheasteroidaldustbands.
No.2,2010 COMETARYORIGINOFTHEZODIACALCLOUD 819
dustbandshavebeenidentified(Sykes1990).Sincethesedust
bandsaremuchfainterthanthethreemaindustbands,Nesvorny´
etal.resultssettheupperlimitonthecontributionofidentified
asteroidbreakupstothezodiacalcloud.
Theorbitaldistributionoftheasteroidbeltsource(2)ismod-
eledbyusingtheobservedorbitaldistributionofasteroidswith
D > 15 km. We obtained this distribution from the ASTORB
catalog (Bowell et al. 1994). This sample should be complete
andunbiased(Jedicke&Metcalfe1998;Gladmanetal.2009).
TheorbitaldistributionofasteroidswithD <15km,whichmay
beabetterproxyfortheinitialdistributionofdustproducedin
mainbeltcollisions(Sykes&Greenberg1986),isroughlysim-
ilartothatoflargeasteroids.Thus,theorbitaldistributionthat
weuseshouldbeareasonableassumptionfor(2).
The orbital distributions obtained by numerical integrations
oftestparticletrajectoriesfromindividualcometswouldsuffer
Figure2.MeanIRASprofilesat12,25,and60μmwavelengths.Tomakethese from the heavily biased comet catalogs. Moreover, there are
profiles,theselectedIRASscanswerecenteredattheecliptic,smoothedbya hundreds of known comets, each producing dust at a variable
low-passfilter,andcombinedtogether.Thegrayrectanglesatl < −78◦ and
40◦<l<70◦blockthelatituderangewherethemeanfluxesweresignificantly andtypicallyunknownrate.Inaddition,itisalsopossiblethat
the present zodiacal dust complex contains particles from lost
affectedbythegalacticplaneemission.Wedonotusetheexcludedrangein
thiswork.Theuncertaintiesofthemeanfluxvaluesarenotshownherefor parentsassuggestedbytheorphanedType-IItrails(Sykes1990)
clarity; they are too small to clearly appear in the plot. The characteristic andidentificationofmeteoroidstreamswithdisruptedJFCs(see
errors at different wavelengths averaged over latitudes are σ12μm = 0.59 Jenniskens(2008)forareview).Inviewofthesedifficulties,we
MJysr−1,σ25μm =1.1MJysr−1,andσ60μm =2.7MJysr−1.Theyincrease resortedtothefollowingstrategy.
withwavelengthduetothelargerroleofgalacticemissionatlongerwavelengths.
The orbital distribution of JFCs was taken from LD97 who
followedtheevolutionofbodiesoriginatingintheKuiperBelt
Theworkdescribedhere,however,islesssensitivetocollisional
as they are scattered by planets and evolve in small fractions
processesbecausetheoverallgrossshapeofthezodiacalcloud
into the inner solar system. Starting at the time when the
should be mainly controlled by the orbital distribution of its
comets’periheliondistance,q,firstdropsbelow2.5AUinthe
source population(s), violent dynamics of particles moving on
LD97 simulations, we include it as an active JFC in our list
planet-crossing orbits, and the effects of Poynting–Robertson
of source objects. LD97 showed that the orbital distribution
(PR)drag.Thesefeatures/processesareincludedinourmodel
of visible JFCs obtained in this way nicely approximates
aswedescribebelow.
the observed distribution. Moreover, LD97 argued that the
inclinationdistributionofnewJFCs(reachingq < 2.5AUfor
3.1.Sources the first time) is relatively narrow. The inclination distribution
widensatlatertimesastheJFCorbitsbecomemorespreadby
Ourmodelstartswiththesourcepopulationofobjects.This Jupiterencounters.
may be either of the following: (1) individual asteroid groups Bycomparingthewidthofthemodelinclinationdistribution
suchastheKarin,Veritas,orBeagleasteroidfamilies(NVBS06; with that of the observed JFCs, LD97 were able to estimate
Nesvorny´ et al. 2008), (2) asteroid belt as a whole, (3) active the fading lifetime of JFCs, t , defined as the characteristic
JFC
JFCsdefinedbytheirdebiasedorbitaldistributionobtainedfrom time between their first and last apparitions. They found that
Levison & Duncan (1997, hereafter LD97) and their physical t = 12,000 yr with a 90% confidence interval 3000 <
JFC
lifetime, (4) JFCs with orbital distribution similar to (3) but t <30,000yr.SeeFigure3foranillustrationofthesteady-
JFC
dynamically evolved beyond their nominal active lifespan, (5) state JFC orbit distribution for t = 12,000 yr. This is our
JFC
HTCs, and (6) OCCs. These source populations are described initialdistributionofparticlesproducedbyactiveJFCs.Weuse
inamoredetailbelow. t asafreeparameterinourmodelwithvalues extending to
JFC
We ignore the contribution of interstellar dust particles t =100,000yrtoaccountforthepossibilitythatanimportant
JFC
becausethermalemissionfromthesesmallparticles(diameter dustcomponentmaybeproducedbyolddormantJFCsasthey
D <1μm)wouldcreatediagnosticspectralfeaturesintheMIR spontaneouslydisrupt.
wavelengthsthatarenotobserved(e.g.,Reachetal.2003).More OurmodelsfortheorbitaldistributionsofHTCsandOCCs
specifically, observations of the MIR spectrum of the zodiacal are simpler than the one described for JFCs above, because
cloudbyReachetal.(2003)suggestthatthebulkofthezodiacal we do not have in hand an appropriate numerical model that
cloudisproducedby∼10–100μmparticles.Wealsoignoredust we could use with confidence. Fortunately, this is not a major
producedbydisruptivecollisionsintheKuiperBelt(hereafter limitationfactorinthisworkbecauseourmainresultsdescribed
KB dust) because Landgraf et al. (2002) and Moro-Mart´ın & in Section 4 are not sensitive to the detailed properties of the
Malhotra(2003)showedthatKBdustparticlesshouldrepresent HTCsandOCCspopulations.
onlyaminorcontributiontotheinnerzodiacalcloud. ForHTCs,weassumethatthedifferentialdistributionofthe
Resultsfor(1)weretakenfromNVBS06andNesvorny´ etal. periheliondistance,dN(q),isdN(q)∝qdq,andsetanupper
(2008)whofoundthatthethreemaindustbandsdiscoveredby limitofqat3AU.HTCstypicallybecomevisible/activeonlyif
Lowetal.(1984)originatefromtheKarin,Veritas,andBeagle theyreachq <3AU.Similarly,thecumulativesemimajoraxis
asteroidfamilies.Accordingtotheseresults(Figure1),thethree distribution of HTCs, N(< a), is assumed to be N(< a) ∝ a
maindustbandsrepresentonly≈9%–15%ofthezodiacalcloud with an upper cut on a at 50 AU. The differential inclination
emissionattheeclipticand<5%overall.Aboutadozenother distribution dN(i) is taken from Levison et al. (2006). This
820 NESVORNY´ ETAL. Vol.713
Theindividualcometsinourmodelareassumedtocontribute
inroughlythesameproportiontothecircumsolardustcomplex.
The reasoning behind this assumption is that if an individual
super-cometwerethedominantsourceofcircumsolardust,the
zodiacalcloudwouldnothavesuchasmoothandsymmetrical
structure. In fact, the observed smooth structure of the zodi-
acal cloud probably implies a source population that contains
numerousobjectsthatarewellmixedintheorbitalspace.
3.2.OrbitEvolution
The orbits of particles were tracked using the Wisdom–
Holman map (Wisdom & Holman 1991) modified to include
effects of radiation forces (Burns et al. 1979; Bertotti et al.
(cid:9)
2003).TheaccelerationF onaparticleduetotheseforcesis
(cid:2)(cid:3) (cid:4) (cid:5)
˙ (cid:9) (cid:9)
F(cid:9) =βGm(cid:6) 1− R R − V , (2)
R2 c R c
(cid:9) (cid:9)
where R is the orbital radius vector of the particle, V is its
velocity,Gisthegravitationalconstant,m(cid:6) isthemassofthe
Sun,cisthespeedoflight,andR˙ = dR/dt.Theacceleration
(2) consists of the radiation pressure and velocity-dependent
Figure3.OrbitaldistributionofJFCsfromtheLD97model.Panelsshowthe PR terms. Parameter β is related to the radiation pressure
periheliondistance(a),andinclination(b),asfunctionsofthesemimajoraxisfor coefficient,Q ,by
JFCswithq<2.5AUandtJFC=12,000yr.SeeSection3.1forthedefinition pr
oftJFC.The2:1and3:2mean-motionresonanceswithJupitercorrespondtothe Q
gapsinthedistributionata ≈3.3and3.96AU,respectively.Theinclination β =5.7×10−5 pr, (3)
distributionofJFCsshownhereisremarkablysimilartothatobtainedbyDi ρs
Sistoetal.(2009;theirFigure10).
where radius s and density ρ of the particle are in cgs units.
distributioncanbeapproximatelydescribedby PressurecoefficientQprcanbedeterminedusingtheMietheory
(Burnsetal.1979).WeusedQ =1whichcorrespondstothe
pr
dN(i)∝sin(i)e−12(σi)2di (1) geometricalopticslimitwheresismuchlargerthantheincident-
lightwavelength.Weassumedthatthesolar-winddragforcehas
withσ =30◦. thesamefunctionalformasthePRtermandcontributesby30%
According to√Francis (2005), the long-period comets have tothetotaldragintensity(Gustafson1994).
dN(q) ∝ (1+ q)dq forq < 2AU.Forq > 2AU,Francis’ WeusedparticleswithdiameterD =2s =10,30,100,200,
study predicts dN(q) being flat or declining while we would 300, 1000 μm and set their bulk density to ρ = 2 g cm−3.
expecttheperiheliondistributiontoincreasewithq.Itprobably For comparison, Love et al. (1994) reported ρ ≈ 2 g cm−3
just shows that the distribution is not well constrained for for stratospheric-collected IDPs, while McDonnell & Gardner
q > 2 AU. We use dN(q) ∝ 2.41(q/2)γ dq for q > 2 AU (1998)foundmeanρ =2–2.4gcm−3fromtheanalysisofdata
with 0 < γ (cid:3) 1. The semimajor axis values of OCCs are set collectedbytheLDEFandEurecasatellites.Ontheotherhand,
between 10,000 and 50,000 AU, which is known as the Oort densityof1gcm−3hasbeenoftenassumedforcometarymatter
spike (Wiegert & Tremaine 1999). We also use a = 1000 AU (e.g.,Joswiaketal.2007;Wiegertetal.2009).Gru¨netal.(1985)
to check on the dynamical behavior of dust particles launched suggested that 20%–40% of particles may have low densities
fromthereturningOCCs.TheinclinationdistributionofOCCs whereas most meteoroids have ρ = 2–3 g cm−3. Our results
issettobeuniformlyrandombetween0◦and180◦. maybeeasilyrescaledtoanyρ valueandweexplicitlydiscuss
Wetestedtwodifferentmethodstolaunchparticlesfromtheir theeffectofρ whereveritisappropriate.
source objects. In the first method, chosen to approximate the The particle orbits were numerically integrated with the
ejectionofparticlesfromactivecomets,welaunchedparticles swift_rmvs3 code (Levison & Duncan 1994) which is an
attheperihelionwhenthemeananomalyM =0.Inthesecond efficient implementation of the Wisdom–Holman map and
method, we launched particles along the orbit with uniform which, in addition, can deal with close encounters between
distribution in M. This second method is more appropriate for particles and planets. The radiation pressure and drag forces
the asteroidal particles and for particles produced by comet wereinsertedintotheKeplerianandkickpartsoftheintegrator,
disruptions. Indeed, the identified comet disruptions do not respectively. The change to the Keplerian part was trivially
seem to be correlated in any way with the perihelion passage done by substituting m(cid:6) by m(cid:6)(1−β), where β is given by
(e.g., Weissman 1980). The two ejection methods produced Equation(3).
comparableresults.Giventhatdisruptionsshouldrepresentthe Thecodetrackstheorbitalevolutionofaparticlethatrevolves
main mass loss in comets (see Section 6), we use the second aroundtheSunandissubjecttothegravitationalperturbations
methodforallresultspresentedinSection4.Tosimplifythings, of seven planets (Venus to Neptune) until the particle impacts
we neglect the ejection velocities of dust particles from their a planet, is ejected from the solar system, or drifts to within
parent object and assume that they initially follow the parent 0.03 AU from the Sun. We removed particles that evolved to
object’sorbitmodifiedbytheradiationpressure. R <0.03AUbecausetheorbitalperiodforR (cid:2)0.03AUisnot
No.2,2010 COMETARYORIGINOFTHEZODIACALCLOUD 821
properly resolved by our integration time step. In Section 4.2, thermallyradiatingparticlewithdiameterD.S(R,L,B)defines
wealsoconsidertheeffectofcollisionaldisruptionbyremoving thespatialdensityofparticlesasafunctionoftheheliocentric
particles from the simulations when they reach their assumed distance, R, longitude, L, and latitude, B (all functions of r
physicallifespan.Wefollowed1000–5000particlesforeachD, as determined by geometry from the location and pointing
source,andparametervalue(s)thatdefinethatsource. direction of the telescope). N(D;a,e,i) is the number of
particleshavingeffectivediameterDandorbitswithsemimajor
3.3.ThermalEmissionofParticles axis,a,eccentricity,e,andinclination,i.
WeevaluatetheintegralinEquation(6)bynumericalrenor-
Particles were assumed to be isothermal, rapidly rotating
malization(seeNVBS06).F(D,r)iscalculatedasdescribedin
spheres.Theabsorptionwasassumedtooccurintoaneffective
Section 3.3. N(D;a,e,i) is obtained from numerical simula-
crosssectionπs2,andemissionoutof4πs2.Theinfraredflux
tionsinSection3.2.S(R,L,B)usestheoreticalexpressionsfor
density (per wavelength interval dλ) per unit surface area at
the spatial distribution of particles with fixed a, e, and i, and
distancerfromathermallyradiatingparticlewithradiussis
randomizedorbitallongitudes(Kessler1981;NVBS06).
s2 Weassumethatthetelescopeislocatedat(xt =rtcosφt,yt =
F(λ)=(cid:8)(λ,s)B(λ,T) , (4) r sinφ,z = 0) in the Sun-centered reference frame with
r2 rt =1At Ut.Itsviewingdirectionisdefinedbyaunitvectorwith
t
where (cid:8) is the emissivity and B(λ,T) is the energy flux at components(xv,yv,zv).InEquation(6),thepointingvectorcan
(λ,λ+dλ)persurfaceareafromablackbodyattemperatureT: bealsoconvenientlydefinedbylongitudelandlatitudebofthe
pointingdirection,wherex =cosbcosl,y =cosbsinl,and
v v
B(λ,T)= 2πλh5c2 (cid:6)ehc/λkT −1(cid:7)−1. (5) lz(cid:6)v ==si9n0b◦.AansddecsaclrciubleadteinthSeectthioenrm2,awl eflufixxtohfevsoalraiorueslopnagrattiicolne
populations as a function of b and wavelength. The model
Inthisequation,h=6.6262×10−34JsisthePlanckconstant, brightness profiles at 12, 25, and 60 μm are then compared
c = 2.99792458 × 108 m s−1 is the speed of light, and withthemeanIRASprofilesshowninFigure2.
k =1.3807×10−23 JK−1istheBoltzmannconstant.Weused To check our code, known as Synthetic InfraRed Telescope
(cid:8) =1whichshouldberoughlyappropriateforthelargeparticles (SIRT), we programmed a particle version of the algorithm,
usedinthiswork.SeeNVBS06foramoreprecisetreatmentof whichshouldbeinmanywayssimilartothecorealgorithmin
(cid:8)(λ,s)fordustgrainscomposedofdifferentmaterials. SIMUL (Dermott et al. 1988; see also Dermott et al. 2001).
TodeterminethetemperatureofaparticleatdistanceRfrom The particle version inputs the orbital elements of particles
the Sun, we used the temperature variations with R that were obtained in the orbital simulations (Section 3.2) and produces
proposed by different authors from spectral observations of their orbit clones that are uniformly spread over 2π in mean
the zodiacal cloud (e.g., Dumont & Levasseur-Regourd 1988; anomalyM.Thus,everytestparticleisassumedtotraceacloud
Renardetal.1995;Leinertetal.2002;Reachetal.2003).For of real particles having the same orbit as the test particle but
example,Leinertetal.(2002)proposedthatT(R)=280/R0.36 different angular locations along the orbit. See Vokrouhlicky´
K near R = 1 AU from ISOPHOT spectra. We used T(R) = et al. (2008; their Section 2.5) for a technical description of
T /Rδ K, where T is the temperature at 1 AU and δ is the algorithm. This procedure is based on the assumption that
1AU 1AU
a power index. We varied T and δ to see how our results any concentration of particles with a specific M value would
1AU
depend on these parameters. Values of T ≈ 280 K and be quickly dispersed by the Keplerian shear. We employ this
1AU
δ = 0.5 correspond to the equilibrium temperature of large proceduretoimprovetheresolution.Withoutit,thenumberof
darkparticles.Valuesδ <0.5wouldbeexpected,forexample, integrated test particles would be too small to obtain a useful
for fluffy particles with small packing factors (e.g., Gustafson result.
et al. 2001). Note that the power law is used here as a simple Tobeabletocomparetheresultsoftheparticlealgorithmwith
empiricalparameterizationofthetemperaturegradient.Thereal SIRT,theparticlealgorithmmustalsousesmoothdistributions
temperaturegradientislikelytobeamorecomplicatedfunction in perihelion longitude (cid:11) and nodal longitude Ω. This is
oftheheliocentricdistance(andparticleproperties). achieved by generating additional orbital clones with (cid:11) and
Ω uniformly spread over 2π. Figure 4 shows examples of the
3.4.SyntheticObservations results obtained from the particle algorithm and SIRT. The
agreement between the two codes is excellent which gives us
TocompareourresultswithIRASobservationsdescribedin
confidencethatbothcodesworkproperly.WefindthattheSIRT
Section 2, we developed a code that models thermal emission
algorithmbasedontheKesslerdistributionismuchfasterthan
from distributions of orbitally evolving particles and produces
theparticleone.Forthisreason,weusetheoriginalSIRTcode
infrared fluxes that a space-borne telescope would detect de-
inthisstudy.
pendingonitslocation,pointingdirection,andwavelength.See
NVBS06foradetaileddescriptionofthecode.
4.RESULTS
In brief, we define the brightness integral along the line of
sightofaninfraredtelescope(definedbyfixedlongitudeland Our primary model parameters are the relative contribution
latitudebofthepointingdirection)as ofdifferentsourcestothezodiacalcloud.Thetotalmodelflux
(cid:8) (cid:8) (cid:8) asafunctionoftheeclipticlatitudeisobtainedas
∞
dadedi drr2 dDF(D,r)N(D;a,e,i)S(R,L,B),
F (b)=α F +α F +α F +α F ,
a,e,i 0 D model AST AST JFC JFC HTC HTC OCC OCC
(6) (7)
where r is the distance from the telescope and F(D,r) is the whereαarecoefficientsthatsatisfyα +α +α +α =
AST JFC HTC OCC
infrared flux (integrated over the wavelength range of the 1,andF ,F ,F ,andF aremodelfluxesobtainedfor
AST JFC HTC OCC
telescope’s system) per unit surface area at distance r from a differentsources.Wenormalizethemsothattheeclipticmodel
822 NESVORNY´ ETAL. Vol.713
Figure 4. Comparison between results obtained from the particle algorithm Figure5.Comparisonofthe25μmprofilesproducedbydifferentsourceswith
(dots)andSIRT(solidlines).Case1correspondstoasteroidalparticleswith IRASobservations.TheblacklineshowsourmeanIRASscanforl(cid:6) = 90◦.
a =2.5AU,e=0.1,andi =10◦.Case2correspondstocometaryparticles The colored lines show profiles expected from different source populations:
crossingEarth’sorbitwitha = 1AU,e = 0.5,andi = 50◦.Inbothcases, asteroids(green),JFCs(red),andHTCs(blue).TheOCCflux,notshownhere
we assumed that particles have D = 100 μm and are distributed randomly forclarity,isanearlyconstantfunctionoflatitude.Themaximumfluxineach
inΩ,(cid:11),andM.Thefluxat25μmwasnormalizedtoapopulationof1015 profilehasbeennormalizedto1.WeusedD=100μmandtJFC=12,000yr.
particlesinCase1and2×1015particlesinCase2.Observationswithrt=1AU ThemaindifferencesbetweenprofilesarenotsensitivetotheexactchoiceofD
andl(cid:6) =90◦wereassumed.InCase2,theparticlealgorithmshowsascatter andothermodelparameters.
aroundtheexactsolutionduetotheroughresolutionofthedistributionnearthe
telescope’slocation.Weused5×1010orbitclonesintheparticlealgorithm.
fluxfromeachsourceisequaltothatofthemeanobservedflux
atb =0.Coefficientsαthereforegivetherelativecontribution
ofdifferentsourcesattheecliptic.
The model flux profiles depend on the particle size, wave-
length, and for JFCs also on the assumed value of t . As
JFC
described in Section 3.2, we tracked particles with 10 <
D <1000μm.Thesedifferentsizesaretreatedindividuallyin
Equation(7).Inparticular,wedonotattempttoconstructplau-
sible size–frequency distributions for different sources. It is
therefore assumed that a single characteristic particle size, or
a narrow range of sizes, can be effectively used to model the
observedMIRflux.Thisassumptionneedstobeverifiedlater.
InSection4.1,wefirstconsideramodelwherethelifespan
of particles is limited by their dynamical lifetime. Effects of
Figure6.Dependenceoftheshapeof25μmprofilesproducedbyasteroidal
particledisruptionsarediscussedinSection4.2. particlesonD.Thedashedlineshowsthemean25μmIRASprofileforl(cid:6)=90◦.
Theuppersolidcurvesshowthemodelresultsforthesamewavelengthand
elongation.Thebottomlinesshowtheresidualfluxobtainedbysubtractingthe
4.1.Collision-freeModel modelfluxfromthemeanIRASprofile.ResultsforD=30,100,and300μm
asteroidalparticlesareshownwithslightlybroaderprofilescorrespondingto
Figure 5 shows the 25 μm flux of D = 100 μm particles largerD.TheprofilesforD=10and1000μm,notshownhere,arenarrower
produced by different source populations. Note that these than the ones for D = 30 μm. For D = 1000 μm, this is mainly due to
profiles do not sensitively depend on the particle size (see theeffectsofdisruptivecollisionsthatdestroylargegrainsbeforetheycould
evolvedownto1AU(seediscussioninSection4.2).Noneofthemodelprofiles
Figures6and7fortheresultsfordifferentD).Instead,themain
obtainedwithasteroidalparticlescanmatchIRASobservations.
differences between results for different source populations in
Figure5reflecttheinitialorbitdistributionofparticlesineach
source and their orbit evolution. Therefore, these profiles can The profile produced by HTC particles is much broader
helpustoidentifythesourcepopulation(s)thatcanbestexplain than the observed one (Figure 5). In this case, the magnitude
IRASobservations. of the polar fluxes is ≈1/2 of that near the ecliptic. This
The asteroidal particles produce a profile with a very sharp result reflects the very broad inclination distribution of HTCs
peak centered at the ecliptic. The emission from asteroidal (Section3.1).ApotentiallysignificantcontributionofHTCsto
particles near the ecliptic poles is relatively faint. The polar the zodiacal cloud is also problematic because the two large
emission comes from the particles that evolved by PR drag HTCs, 109P/Swift-Tuttle and 1P/Halley, tend to librate about
froma > 2AUtoR = 1AU.Whilemostasteroidalparticles mean-motion resonances, causing relatively stable orbits for
indeed reach 1 AU, they pass too briefly near b = ±90◦ to longperiodsoftime.Thus,dustreleasedbyHTCsisexpected
produce important polar fluxes. This is why most radiation is to be concentrated along certain locations on the sky making
received from b ∼ 0, where the telescope collects the thermal it difficult to explain the smooth profile of the zodiacal dust.
emission of particles over a wide distance range. A broader Note also that Altobelli et al. (2007) have not detected HTC
distributionoforbitalinclinationsisapparentlyneededtomatch particleimpactsintheCassinidustexperiment,indicatingthat
IRASmeasurements. HTCparticlesarerelativelysparse.
No.2,2010 COMETARYORIGINOFTHEZODIACALCLOUD 823
orbitallydecouplefromtheplanetanddriftdownto1AU.This
results in a situation where the inclination distribution of JFC
particlesissignificantlybroader(≈20◦ meaniforR < 3AU)
thanthatoftheirsourceJFCs.ThisexplainsFigure5andshows
limitations of the arguments about the zodiacal cloud origin
basedonthecomparativeanalysisofsources(e.g.,Hahnetal.
2002).
WewillnowaddressthequestionofhowtheMIRfluxesfrom
theJFCparticlesdependonDandt .Wedefine
JFC
(cid:8)
1 π/2 [F (b)−F (b)]2
η2 = IRAS model db, (8)
π −π/2 σ2(b)
whereF isthemeanIRASflux,σ isthestandarddeviation
IRAS
of F determined from the spread of representative IRAS
IRAS
scansforeachb(Section2),andF = F (i.e.,α = 1
model JFC JFC
andα = α = α = 0inEquation(7)).Notethatthe
AST HTC OCC
integrationinEquation(8)issettoavoidtheintervalsinbwith
stronggalacticemission.
While the definition of η2 in Equation (8) is similar to the
usualχ2 statistic(e.g.,Pressetal.1992),wewillnotassigna
rigorous probabilistic meaning to the η2 values obtained from
Equation (8). This is mainly because it is not clear whether
the σ values computed in Section 2 from the IRAS data can
adequately represent the measurement errors. Instead, we will
Figure7.Dependenceoftheshapeof25μmprofilesproducedbyJFCparticles use Equation (8) only as an indication of whether a particular
onDandtJFC.ThepanelsshowresultsfordifferenttJFC:(a)tJFC=12,000yr, modelismorereasonablethananotherone.Modelswithη2 (cid:2)1
d(ba)shtJeFdCli=ne3in0e,0a0ch0pyarn,e(lc)shtoJFwCs=the5m0,e0a0n025yrμ,manIdR(AdS)ptJrFoCfil=efo1r0l0(cid:6),0=0090y◦r..TThhee wgiivlelsbeη2gi=ven5.p1r.iority.Forareference,theJFCmodelinFigure5
uppersolidcurvesshowthemodelresultsforthesameelongation.Thebottom
linesshowtheresidualfluxobtainedbysubtractingthemodelfluxesfromthe We calculated η2 as a function of D and tJFC to determine
meanIRASprofile.ResultsforD=10,30,100,300,and1000μmareshownin which values of these parameters fit IRAS observations best.
eachpanelwithbroaderprofilescorrespondingtolargerD.Someofthesemodel Wefoundthatthebestfitswithη2 < 10occurfor30 (cid:3) D (cid:3)
pDro>file3s00doμmno,tamndatDch=IR1A0Sμombscearvnabtieonclsewarelyll.ruSlpeedcoifiuct.ally,tJFC >50,000yr, 100μmandtJFC (cid:3)30,000yr.
Figure 7 illustrates how the shape of the 25 μm profile
producedbyJFCparticlesdependsonDandt .Theprofiles
JFC
TheOCCparticles,whichhaveanearlyisotropicinclination become wider with increasing D and t values. For t =
JFC JFC
distribution, produce the MIR flux that is constant in latitude 12,000yr,thebestresultswereobtainedwithD = 30μmand
(not shown in Figure 5). Therefore, the ecliptic and polar D = 100 μm (η2 = 3.2 and 5.1, respectively). The profiles
fluxes from OCC particles are roughly the same and do not forD = 10μmaretoonarrowandclearlydonotfitdatawell
match observations. We conclude that a single-source model (η2 =70),whilethoseforD =1000μmareslightlytoowide
witheitherasteroidal,HTC,orOCCparticlescannotmatchthe (η2 =58).Wealsofoundthattherearenoreallygoodfitswith
observedprofileofthezodiacalcloud. t > 30,000 yr, because the profiles are too broad near the
JFC
WeareleftwithJFCs.Itisnotablethatthewidthandshapeof eclipticindependentlyoftheparticlesize.
theJFCprofileinFigure5closelymatchobservations.Theonly Thebestsingle-sourcefitsdiscussedabovehaveη2 >1which
slightdifferenceisapparentforlargeeclipticlatitudeswherethe is not ideal. According to our additional tests this is probably
modelflux,shownhereforD =100μmandtJFC =12,000yr,is notduetothecoarseresolutionandstudiedrangeofDandtJFC.
slightlyweakerthantheonemeasuredbyIRAS.Wewilldiscuss Instead, this may point to (1) a subtle problem with our JFC
thissmalldifferencebelowandshowthatitcouldbeexplained model,and/or(2)thepossibilitythatadditionalminorsources
if: (1) slightly smaller JFC particles were used, and/or (2) the (such as asteroids, OCCs, or HTCs) should be included in the
zodiacalcloudhasafaintisotropiccomponent.Wethusbelieve model.Option(1)isdifficulttotestunlessabettermodelofthe
thatthecloseresemblanceofourmodelJFCprofilewithIRAS JFCpopulationbecomesavailable.Here,weconcentrateon(2)
dataisastrongindicationthatJFCsarethedominantsourceof becauseanampleevidenceexists(e.g.,for∼10%near-ecliptic
particlesinthezodiacalcloud. asteroid contribution from asteroid dust band modeling) that
SinceasteroidsandactiveJFCshavesimilarinclinationdis- theseadditionalsourcesmayberelativelyimportant.
tributions (Hahn et al. 2002), it may seem surprising that JFC We start by discussing the results obtained by assuming
particlesproducesubstantiallywiderMIRfluxprofilesthanas- that the zodiacal cloud has two sources. The motivation for
teroidal particles. By analyzing the results of our numerical considering the two-source model was the following. First,
integrations,wefindthattheencounterswithterrestrialplanets we wanted see whether a combination of two sources could
and secular resonances are apparently not powerful enough to successfully fit the observed profile. Second, we attempted to
significantlyaffecttheinclinationdistributionofdriftingaster- place upper limits on the contributions of asteroid, OCC, and
oidal particles. The inclination distributions of the asteroidal HTC sources. While it is obvious that models with more than
particles and their source main belt asteroids are therefore es- two sources can be tuned to fit the data better, it is not clear
sentially the same (≈10◦ mean i). On the other hand, we find whethermorethantwosourcesareactuallyrequired.Ourtwo-
thatJFCparticlesarescatteredbyJupiterbeforetheyareableto sourcemodelswereusedtotesttheseissues.
824 NESVORNY´ ETAL. Vol.713
Figure 8. Examples of fits where we modeled the zodiacal cloud as having
twosources.Fluxesat25μmareshown.(a)Thebest-fitmodelwithasteroid
andOCCsources.ThismodeldoesnotfitIRASobservationswell.Themodel
profileistoonarrowneartheeclipticandtoowideoverall.(b)Ourbesttwo-
sourcemodel.Here,weusedαJFC =0.97,αOCC =0.03,D =100μm,and
tJFC=12,000yr.Thefaintisotropiccomponentimprovesthefitqualitysothat Figure9.ModelconstraintsonthecontributionofasteroidandOCCparticles
η2=0.36in(b).Thismaysuggestthatthezodiacalcloudcontainsasmallbut tothezodiacalcloud.Here,weusedathree-sourcemodelwithD =100μm
significantfractionofOCCparticles. and αHTC = 0. For a range of the αOCC and αAST values, we set αJFC =
1−αOCC−αAST,andcalculatedη2(Equation(8))foreachmodel.Thecontours
showη2=3,10,and30.Theshadedareadenotestheparametersofourbest-fit
In the first test, we used the two-source model with aster- modelswithη2 <1.ThesemodelshaveαOCC <0.13andαAST <0.22thus
oids and OCCs (i.e., α = α = 0 in Equation (7)). We placinganupperlimitonthenear-eclipticcontributionofasteroidandOCC
JFC HTC particles.
found that this particular model produces unsatisfactory fits
(η2 > 10) to IRAS observations for all particle sizes consid-
ered here (10–1000 μm) (Figure 8(a)). The model profile is smallasteroid/OCCcomponents(αAST (cid:2)0.2andαOCC (cid:2)0.1).
significantlynarrowerneartheecliptic,wheretheasteroidcom- To verify this conclusion, we considered three-component
ponentprevails,andistoowidefor|b| (cid:4) 40◦,wheretheOCC models with αHTC = 0 and used αJFC, αAST, and αOCC as
component prevails. This happens mainly due to the fact that free parameters. We found that the best two-source fit with
theasteroiddustisconfinedtotheeclipticplaneandproduces αJFC =0.97andαOCC =0.03cannotbesignificantlyimproved
averynarrowprofileneartheecliptic(Figure5).Wealsofind byincludingasmallasteroidcontribution.Similarly,thefitwith
it unlikely that two so distinct populations of objects, such as αJFC = 0.9 and αAST = 0.1 cannot be improved by adding a
themainbeltasteroidsandOCCs,wouldhavecomparabledust smallOCCcontribution.Thus,theasteroid/OCCcontributions
production rates. Thus, we believe that the two-source model cannot be constrained independently because their effects on
withasteroidandOCCdustcanbedismissed. the combined profiles can be compensated by adjusting the D
Inthesecondtest,wesetαOCC = αHTC = 0andconsidered andtJFCvaluesofthedominantJFCparticles.
models of the zodiacal cloud with the JFC and asteroid com- If we set the parameters of the dominant JFC particles to
ponents. We found that a small contribution of asteroid dust be D = 100 μm and tJFC = 12,000 yr, however, the αAST
can improve the fits. For example, η2 = 0.92 for the D = and αOCC values can be constrained much better (Figure 9).
30 μm JFC particles with αJFC = 0.9 and tJFC = 12,000 yr, For example, models with η2 < 1 require that αAST < 0.22
and D = 100μm asteroidal particles with αAST = 0.1. This and αOCC < 0.13. Thus, under reasonable assumptions, the
represents a significant improvement from η2 = 3.2 that we contributionofasteroidparticlestothenear-eclipticIRASfluxes
obtainedforasingle-sourcemodelwithJFCparticlesonly.Val- isprobably<10%–20%,inagreementwiththeresultsobtained
ues α (cid:4) 0.3 are clearly unsatisfactory because η2 > 10 in NVBS06 from modeling of the asteroid dust bands. This
AST
for α > 0.3. Also, η2 > 3.1 for α > 0.2 which shows means that asteroid dust contributes only by <10% to the
AST AST
that the fit does not improve when we add a (cid:4)20% asteroid overallzodiacaldustemissionatMIRwavelengths.Thethermal
contribution. These results suggest that a very large asteroid emission of OCC particles can constitute as much as ∼10%
contributiontothezodiacalcloudcanberuledout.Thisagrees of the near-ecliptic emission with ≈5% providing the best fits
withtheconclusionsofNVBS06whofoundthatα (cid:2) 0.15 (Figure 9). When integrated over latitude, the overall OCC
frommodelingofthemainasteroiddustbands. AST componentinthezodiacalcloudislikelytobe(cid:2)10%.6
Finally,thetwo-componentmodelwiththeJFCandisotropic For the sake of consistency with the results suggested from
OCC sources can fit the data very well (Figure 8(b)). With modelingoftheasteroiddustbands(seeSection3.1;NVBS06),
D =100μmandt =12,000yr,correspondingtooneofour weimposeasmallasteroidcontributionintheJFC/OCCmodel.
JFC
bestsingle-sourcefitswithJFCs,α =0.97andα =0.03, Figure10showsourpreferredfitatdifferentIRASwavelengths.
JFC OCC
wefindthatη2 =0.36,byfarthebestfitobtainedwithanytwo- The η2 values of this fit in different wavelengths are the
sourcemodel.AsFigure8(b)shows,thefitisexcellent.Wemay following:0.29at12μm,0.35at25μm,and0.06at60μm.This
thusfindanevidenceforasmallcontributionofOCCparticles is very satisfactory. Since our model does notinclude detailed
to the zodiacal cloud. A much larger OCC contribution is not emissivity properties of dust grains at different wavelengths
supported by the data because the fit gets significantly worse
forαOCC > 0.1.Forexample,η2 > 10forαOCC > 0.15which 6 Notethatweareunabletodistinguishinthemodelbetweentheuncertainty
isclearlyunsatisfactory.AlargecontributionofOCCparticles ininstrumentalisotropicbrightnessofIRASmeasurementsandtheOCC
canthereforeberejected. contribution.Wealsodonotknowhowmuchofthebrightnessofthefaintest
partoftheskyiscosmological(orgalactic).Forthesereasons,theOCC
We propose based on the results described above that the
contributiontothezodiacalcloudisdifficulttocalibratefromIRAS
zodiacal cloud has a large JFC component (αJFC (cid:4) 0.9), and observationsalone.