Standard Solar models in the Light of New Heliosei

arXiv:astro-ph/9906382v124Jun1999Received1999March2;accepted1999April26PreprinttypesetusingLATEXstyleemulateapjSTANDARDSOLARMODELSINTHELIGHTOFNEWHELIOSEISMICCONSTRAINTSII.MIXINGBELOWTHECONVECTIVEZONEA.S.BRUN1,2,S.TURCK-CHIEZE1DSM/DAPNIA/Serviced’Astrophysique,CEASaclay,91191Gif-sur-Yvette,FranceandJ.P.ZAHN2D´epartementd’AstrophysiqueStellaireetGalactique,ObservatoiredeParis,SectionMeudon,92195Meudon,FranceReceived1999March2;accepted1999April26ABSTRACTInpreviouswork,wehaveshownthatrecentupdatedstandardsolarmodelscannotreproducetheradialprofileofthesoundspeedatthebaseoftheconvectivezoneandfailtopredictthephotosphericlithiumabundance.Inparallel,helioseismologyhasshownthatthetransitionfromdifferentialrotationintheconvectivezonetoalmostuniformrotationintheradiativesolarinterioroccursinashallowlayercalledthetachocline.Thislayerispresumablytheseatofalargescalecirculationandofturbulentmotions.Here,weintroduceamacroscopictransportterminthestructureequations,whichisbasedonahydrodynamicaldescriptionofthetachoclineproposedbySpiegel&Zahn,andwecalculatethemixinginducedwithinthislayer.Wediscusstheinfluenceofdifferentparametersthatrepresentthetachoclinethickness,theBrunt-V¨aiss¨al¨afrequencyatthebaseoftheconvectivezone,andthetimedependenceofthismixingprocessalongtheSun’sevolution.Weshowthattheintroductionofsuchaprocessinhibitsthemicroscopicdiffusionbyabout25%.Startingfrommodelsincludingapre-mainsequenceevolution,weobtain:a)agoodagreementwithobservedphotosphericchemicalabundanceoflightelementssuchas3He,4He,7Liand9Be,b)asmoothcompositiongradientatthebaseoftheconvectivezone,andc)asignificantimprovementofthesoundspeedsquaredifferencebetweentheseismicSunandthemodelsinthistransitionregion,whenweallowthephotosphericheavyelementabundancetoadjust,withintheobservationalincertitude,duetotheactionofthismixingprocess.Theimpactonneutrinopredictionsisalsodiscussed.Subjectheadings:Sun:interior,Sun:tachocline,Sun:oscillations,abundances,lithium,neutrinos1.INTRODUCTIONThevalidationofsolarstructureiscrucialtocheckthehypothesesusedinstellarevolutionmodelling.ItallowsalsotheheliumcontentatthebirthoftheSuntobedetermined,whichiskeytogalacticenrich-mentandforpredictingthepresentneutrinoemissionfluxes.Withthesupportofhelioseismology,wearenowabletoconstrainthesophisticatedcalculationsperformedtodescribethepresentstructureoftheSun.Veryrecently,atremendouseffortusinggroundbasednetworksandspaceexperimentshasbeenmadetoimprovetheaccuracyoftheseismictoolatalevelwheredifferenceswiththetheoreticalestimatesaresignificant.Consequently,ithasbeendemonstratedthatthisdisciplinehasthepotentialtocheckclassi-calstellarstructureforsolar-typestarsinthehydro-genburningphase(Tomczyketal.1995,Kosovishevetal.1997,Turck-Chi`ezeetal.1997,Christensen-Dalsgaard1998...).Inparallel,thedevelopmentofneutrinodetectorsinparticlephysicshastheobjectiveofdeterminingthepropertiesoftheseparticles.Inthisresearch,theSunplays,onceagain,aspecificroleasasourceofelectronicneutrinosνewhichcouldbetransformedintootherflavorsbeforereachingthedetectorsonEarth(Hata&Langacker1997,Bahcall,Krastev&Smirnov1998).Thesolarconditionsarereallyinac-cessibleinexperimentsonEarth,soonemustpre-dictpreciselytheemittedneutrinofluxesinordertoprogressinourknowledgeoftheseparticlesandthesolarcore.Atfirstglance,helioseismologyshowsthatthestan-12dardsolarframeworkiscorrect(Brun,Turck-Chi`eze&Morel1998;hereafterpaperI).Itisneverthelessextremelyclearthatstandardmodelshavealwaysfailedtoanswersomewellknownquestionsoranoma-liesduetoitssimplifiedassumptions(Turck-Chi`ezeetal.1993).Theseopenquestionsconcerntheef-fectoftherotationandmagneticfield,thehistoryoftheangularmomentum,therealwaytheconvectionacts,theunexplainedphotosphericabundancesasthephotosphericlithiumdepletionandthepresenceofmixingatdifferentlocationsinsidethestars.RecentresultsobtainedwiththeSOHOsatellite(Fr¨ohlichetal.,1997,Kosovishevetal.1997,Gabrieletal.1997)andgroundnetworkshavedemonstratedthatthereexistssignificantdifferencesinthesquareofthesoundspeedbetweentheSunandthemodels(Koso-vishevetal.1997,Turck-Chi`ezeetal.1997).Someofthemcanbeattributedtouncertaintiesinthemi-croscopicdescriptionoftheSun,whilesomeothersmustbethesignofmissingprocessesinthestandardsolarframework.Theideaofthispaperistointroduceanewterminthestellarstructureequationsinordertoprogressbeyondthestandardframework.Thisnewtermde-scribessomephysicalprocesseswhicharepresumablypresentinourstarassuggestedbythedifferentialro-tationprofile.Inthisstudy,wehopetotreatmorecorrectlythetransitionlayerbetweentheconvectiveandradiativezones,withthehelpofcrucialmeasuredhelioseismicvariables.Themainreasonsforourin-terestinthislayerare:•Thechangeofrotationrate(solid⇒differen-tial)measuredbyhelioseismology(Thompsonetal.1996,Kosovichevetal.1997)devel-opsprobablysometurbulentmixinginashal-lowlayer(tachocline)whichcouldbewherethemagneticfieldisanchoredandamplifiedbydynamoprocess(Sch¨ussler1987,Choudhuri,Sch¨ussler&Dikpati1997),•Thefactthatthestandardsolarmodelframe-workincludingmicroscopicdiffusionandele-mentsettlinghasfailedtotreatthistran