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文档介绍:该【Linking Uranus’ temperature profile to wind-induced magnetic fields 2021 Deniz Soyuer 】是由【元春文档】上传分享,文档一共【6】页,该文档可以免费在线阅读,需要了解更多关于【Linking Uranus’ temperature profile to wind-induced magnetic fields 2021 Deniz Soyuer 】的内容,可以使用淘豆网的站内搜索功能,选择自己适合的文档,以下文字是截取该文章内的部分文字,如需要获得完整电子版,请下载此文档到您的设备,方便您编辑和打印。MNRAS507,1485–1490(2021)/mnras/stab2274
AdvanceAccesspublication2021August6
LinkingUranus’temperatureprofiletowind-inducedmagneticfields
DenizSoyuer‹andRavitHelled
CenterforTheoreticalAstrophysicsandCosmology,InstituteforComputationalScience,UniversityofZurich,Winterthurerstrasse190,CH-8057Zurich,
Switzerland
;inoriginalform2021June10
ABSTRACTDownloadedfrom
ThelowluminosityofUranusisstillapuzzlingphenomenonandhaskeyimplicationsforthethermalandcompositional


ω=ω+ω
backgroundmagneticfieldintheplanets,inducingpoloidalandtoroidalfieldperturbationsBBPBTviatheω-effect.
ωα
ToroidalperturbationsBTareexpectedtodiffusedownwardsandproducepoloidalfieldsBPthroughturbulentconvectionvia
ω
theα-effect,comparableinstrengthtothoseoftheω-effect,
variousUranusmodelsintheliterature,wegeneratewinddecayprofilesbasedonOhmicdissipationconstraintsassumingan
ionicallyconductingH2–He–,zonalwinds
needtodecayto∼

toO()
spatiallycorrelatedwithUranus’zonalflowscouldbeusedtoconstrainUranus’interiorstructure,andpresentsafurthercase
fortheinsituexplorationofUranus.
Keywords:methods:dataanalysis–planetsandsatellites:composition–planetsandsatellites:individual:Uranus–planets
andsatellites:interiors–planetsandsatellites:magneticfields.
Thelasttwodecadeshaveseendramaticimprovementsinmod-
1INTRODUCTION
ellingdynamosofSolarsystemgiants(Stanley&Bloxham2004,
TheSolarsystem’sgiantplanetsprovideuswithanexceptionalop-2006;;Dietrich&Jones2018;Wichtetal.
portunityforstudyingthephysicsofhigh-pressure,rotatingsystems2019),butourunderstandingofplanetarymagneticfieldsisstill
,
SaturnhavebeenrelativelywellstudiedcomparedtoUranusandislinkedtothefactthatthemagneticfieldsaremeasuredexternal
Neptune,whichremaintheleastexploredSolarsystemplanetstototheplanets,whereasthefielditselfisgenerateddeeperinside

Neptuneiscurrentlybeingthoroughlyassessedbytheplanetaryauniquesolutiontothedynamoregionthatgeneratesmostof
sciencecommunity(;
;;,b;Helled&thepeculiarmagneticfieldsoficegiants(Soderlund&Stanley
Fortney2020;;),andvarious2020),duetotherelativelackofdataformodellingthemagnetic
missionconceptshavealreadybeingdiscussed((Holme&Bloxham1996),thecompositions(Helledetal.
2020;;;).The2011;),andtheheattransfermechanisms
underexplorationofUranusandNeptuneisunfortunate,astheseinsidetheplanets(Podolak,Helled&Schubert2019;Vazan&
planetsexhibithighlymultipolarandnon-axisymmetricmagneticHelled2020).Understandingtheobservedsurfacemagneticfield
fields(Connerney,Acuna&Ness1987,1991;Holme&BloxhamofUranusandNeptunedoesnotonlyinvolvemodellingthedynamo
1996),arecompositionallymorediversethanthegasgiants(Helledgenerationregion,butalsotheshallowregionquasi-dynamoaction,
;),andhaveasignificantcontrastinwhichcouplesthezonalwindstothebackgroundmagneticfield.
,Neptune’senergybalance(
theratioofemittedthermalenergytoabsorbedsolarenergy)–giants(Cao&Stevenson2017;Galanti&Kaspi2021),whereitwas
,whereasUranusisalmostinequilibriumfoundthatpoloidalmagneticfieldperturbationsthatarespatially
withthesolarflux(;Pearl&Conrath1991).correlatedwiththezonalflowswerepossible(withthestrengthof
–1percentofthebackgroundfield),andthatthezonalwind–
magneticfieldinteractioninthesemiconductingregionofgasgiants
E-mail:deniz.******@.
CTheAuthor(s)2021.

CommonsAttributionLicense(/),whichpermitsunrestrictedreuse,distribution,andreproductioninanymedium,
providedtheoriginalworkisproperlycited.

.
Lettersfollowingthemodelnumber(,U1b,andU1c)representdifferenttemperatureprofilesforthesamedensity/
originalnamesofthestructuremodelsintheirrespectivepapersareshownontheright-handcolumn.
Density/pressureprofileTemperatureprofileRotationperiodConvectivelayersOriginalname
U1aNettelmannetal.(2013)Nettelmannetal.(2013)
U1bNettelmannetal.(2013)Podolaketal.(2019)
U1cNettelmannetal.(2013)Podolaketal.(2019)
U2Nettelmannetal.(2013)Nettelmannetal.(2013)
U3Vazan&Helled(2020)Vazan&Helled(2020)–V3
U4Vazan&Helled(2020)Vazan&Helled(2020)–V4
U5aHelledetal.(2011)Podolaketal.(2019)
U5bHelledetal.(2011)Podolaketal.(2019)
U5cHelledetal.(2011)Podolaketal.(2019)–
Downloadedfrom
WeestimatethestrengthoftheshallowlayercouplingoftheThedifferentEOSsarecombinedusingtheaboveisothermal–
magneticfieldtothezonalwindsbyusingtheelectricalconduc-isobaricidealvolumelaw,whichisagoodapproximationunder
tivityprescriptionforH2–He–H2OmixturesprovidedinSoyuer,therangeofconditionsexploredinthisworkforhydrogen–helium
Soubiran&Helled(2020).InspiredbyCao&Stevenson(2017),(),forwater–hydrogen(Soubiran&Militzer
welookforpoloidalfieldperturbationstothebackgroundmagnetic2015),andforternarymixtures(Soubiran&Militzer2016).(d)
fieldinducedbythisinteraction,viaasimplifiedα–.
BycompilingsetsofzonalwinddecayprofilesobeyingOhmic
dissipationconstraints,weestimatethemagnitudeofpoloidalfield
,
oursimpleestimateisnotexpectedtocapturethecompletephysical
EstimatingtheionicconductivityofanyH–He–[liquidice]mixture
,thegoalofthisshortpaperistodraw2
isdifficult,letalonegeneralizingthecalculationtovariousmixture
attentiontothismechanism,andshowthatamissiontoUranuscan
,themostnotablemeasurementofelectrical
significantlyimproveourunderstandingofitsdynamics,magnetic
conductivityofamixtureresemblingtheinteriorsofUranusand
field,andcomposition.
NeptunehasbeencarriedoutbyNellisetal.(1988).InNellisetal.
(1988),theelectricalconductivityofa‘syntheticUranus’mixture
2URANUSMODELScomposedofwater,ammonia,andisopropanol(C3H8O)hasbeen
(correspondingto5000Kintheirmodel).

issimilartothatofpurewater,measuredbyHamann&Linton
WeconsiderfivedifferentUranusdensity/pressureprofileswithnine
(1966)andMitchell&Nellis(1982)forroughlythesameregime.
associatedtemperatureprofilestakenfromHelledetal.(2011),
Lately,laser-drivenshock-compressionexperimentshaveverifiedthe
Nettelmannetal.(2013),Podolaketal.(2019),Vazan&Helled
superionicconductionofwaterice(),andammonia
(2020)summarizedinTable1,andexplainedindetailinSoyuer
()underplanetaryconditions.
etal.(2020).Thesemodelscoverawiderangeofthermodynamic
InSoyueretal.(2020)wehavedevelopedamodelforestimating
parametersandalsoemploydifferentheattransfermechanisms
theionicconductivityofH–He–HOmixturesunderplanetary
(convection,doublediffusiveconvection,andconduction)andwere22
–dissipation
,U1ais
theorem,wheretheautocorrelationofmicroscopiccurrentsislinked
athree-layeradiabaticprofilebyNettelmannetal.(2013),U1band
totheelectricconductivityofionsinamixture,takingintoaccount
U1carethemodifieddoublediffusivetemperatureprofilestoU1aby
thediffusion,electricalcharge,andnumberdensityofvarious
Podolaketal.(2019).U2isagainathree-layeradiabaticprofileby
–He–
Nettelmannetal.(2013),withamodifiedrotationperiodobtainedby2
HOmixturesthatfittoUranusstructuremodelsusingtheEOSs
Helled,Anderson&Schubert(2010).U3andU4arenon-adiabatic2

modelsbyVazan&Helled(2020),evolvedusingvariousprimordial
prescriptionwereferthereadertoSoyueretal.(2020).
compositiondistributionsandinitialenergybudgets,tofitpresent
(e)showstheradialelectricalconductivityprofilescalculated
,U5b,andU5careempiricaldensityprofiles
-
byHelledetal.(2011)withvariousgluedtemperatureprofilesby
encebetweeninteriorstructuremodelsthereisasignificantvariation
Podolaketal.(2019),
inelectricalconductivityvalues(reachinguptothreeordersof
showthedensity,pressure,andtemperatureprofilesofthemodels
).Hottermodelsreachhigherconductivitylevels

mainlyduetohighermetallicities()
Forthepurposeofthisworkweassumetheregionweareinterested
andduetotheincreaseinthefractionofionizedHandOspecies
inUranusiscomposedofaH–He–HOmixturegivenby
22withtemperature.
1XYZ
=++,(1)
ρρH2ρHeρH2O

withaprotosolarratioofX/Y=.Forhydrogenand
heliumweadopttheequationofstate(EOS)developedbyChabrier,Uranusexhibitsfastzonalwindsonthesurfacewithspeedsreaching
Mazevet&Soubiran(2019)andforwaterthatofShahetal.(2021).uptoroughly200ms−
MNRAS507,1485–1490(2021)
MagneticfieldperturbationsinUranus1487
Downloadedfrom
Figure1.(a)RadialdensityprofilesofvariouspublishedUranusstructuremodels(;;;Vazan&
Helled2020).(b)Radialpressureprofilesofthesamemodels.(c)Variousradialtemperatureprofilescorrespondingtotheinteriorstructureprofilesbycolour.
Differentlinestylesrepresentalternativetemperatureprofilesforthesamecoloureddensity/pressuremodel.(d)Inferredradialmetallicityprofilesassumingan
ideallymixedH2–He–H2Omixtureandtheaforementionedequationsofstate(EOSs).(e)Radialelectricalconductivityprofilescalculatedusingtheinterior
structureprofiles,usingtheprescriptioninSoyueretal.(2020)forionicallyconductingH2–He–H2Omixtures.(f)Thehighestallowedrmszonalflowspeeds
foreachinteriorstructuremodel,,U4,andU5c,windsneedtodecayto∼
,weexcludethemfromourperturbationanalysisandomittheminthelastpanel.
windprofilehasaretrogrademotionaroundtheequatorandprogradeanexponentialdecayforsimplicitywithane-foldingdepthH:
motionathigherlatitudes,fitby
B(r,H)=exp((r/RU−1)/H).(4)
==×+−1
vϕ,U(rRU,θ)170()ms,(2)
whereθisthecolatitude().
ItiscommonlyassumedthatthesurfacewindscontinuedownwardThe