198 8ApJ. . .331L. .213 3 1 37 solar neutrinoproblemascosmions. massive particlesasWIMPs,andto thesubsetofparticlesthatresolve must alsoremainintheSun,if theyaretobeeffectiveinenergy the p-modesplittingdiscrepancy. “ solutions”tothesolarneutrinoproblem,whichexacerbate energy transport.Thiscontrastswithallotherextantintrinsic crepancy betweenobservedlow-degreep-modefrequency splittings andtheoryinsolarmodelsthatincludeWIMP Christensen-Dalsgaard (1986)haveshownthatthereisno dis- Gough, andVahia(1986)Däppen,Gilliland, and energy lossmechanism.Therefore,whilecoolingthecentral outer, moremassiveportionsofthecoremodestly.Faulkner, temperature significantly,theyalsoraisetheof the mions serveasanenergytransportmechanism,not an high-energy neutrinos.Itisimportanttonotethatthecos- the reducedcoretemperaturelowersrateofproduction detected byDavis,isstronglytemperature-dependent.Thus, which isexpectedtobethesourceofmostneutrinos central temperature.ThereactionrateofthePPIIIchain, and Spergel1985;Gillilandetal.1986). transport energyeffectivelyinthecoreandreduceSun’s matter. Throughoutitslifetime,theSunaccretescosmions, could besolvedbythesameparticle(Steigmanetal.1978; accumulating ~5x10~Minitscore.Theseparticles Spergel andPress1985;FaulknerGilliland and ourcollaboratorshavesuggestedthatbothproblems neutrinos intheC1detector(BahcallandUlrich1988).We standard modelsofthesolarinteriorandobservedflux do weunderstandthesourceofdiscrepancybetween not knowwhatcomprises90%ofthemassourGalaxy,nor missing massproblemsandthesolarneutrinoproblem.Wedo 2 3 e 1 The AstrophysicalJournal,331:L21-L24,1988August1 © 1988.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. OnleavefromPrincetonUniversity Observatory. InthisLetter,wewillrefertothe entireclassofweaklyinteracting, LickObservatoryBulletin,No.1108. The cosmionsmustnotonlybecapturedbytheSun,but In thisscenario,thecosmionscompriseGalacticdark Two oftheoutstandingproblemsinastrophysicsare 18Thls Letter © American Astronomical Society •Provided bythe NASAAstrophysics Data System Subject headings:darkmatter—nuclearreactionsstars:horizontal-branchinteriors no effectonthelaterstagesofstellarevolution. WIMPs eitherrapidlyevaporatefromhorizontal-branchstarsorareinefficientatenergytransport.Theyhave Ii/tI'™' ,reconsiderstheroleofcosmionsinhorizontal-branchstars.Wedemonstratethat isothermal^e thecoresofhorizontal-branchstars;thiswouldsuppressconvectionandalter core oftheSunandsolvesolarneutrinoproblem.Renzinihassuggestedthattheseparticleswouldalso msm mstars.Inpreviouspapers,weandourcollaboratorshaveshownthatWIMPscanisothermalizethe Weakly interacting,massiveparticles(WIMPsorcosmions)canbeanimportantenergytransportmecha- 1 WEAKLY INTERACTING,MASSIVEPARTICLESINHORIZONTAL-BRANCHSTARS I. INTRODUCTION Lick Observatory,BoardofStudiesinAstronomyandAstrophysics,UniversityCalifornia,SantaCruz Received 1988March1;acceptedApril28 Institute forAdvancedStudy 2 David N.Spergel John Faulkner ABSTRACT L21 AND 2 rated inavery short timeonreachingtheHB stage(in<10yr HB convectivecores—isprecisely whytheparticlesareevapo- scale heightisoftheorder or exceedsthephysicalsizeof the strongestpointinhisargument—the factthatthecosmion comparable totheirorbitallengths. Includingthesecorrections vitiates Renzini’sconclusions. WIMP energytransportwhentheirmeanfreepathsare not ration ofWIMPsfromHBstars,and(2)thesuppression of has, however,ignoredtwoimportanteffects:(1)theevapo- of thecosmionexplanationforsolarneutrinoproblem. He ages inferredfromstarcounts. branch lifetimewouldproduceadiscrepancywiththerelative the horizontal-branchlifetimerelativetoasymptoticgiant horizontal branchtotheasymptoticgiantbranch.Shortening would rapidlyexhaustitssupplyofheliumandevolvefrom the core convectionandconsequentsemiconvection,the core cores ofHBstars,thussuppressingcoreconvection.Without cores. Renziniclaimsthatcosmionswillisothermalizethe branch starstransformheliumintocarbonintheirconvective port inthecoresofhorizontal-branch(HB)stars.Horizontal- more advancedevolutionarystagesoflow-massstars.Hehas suggested thatcosmionswouldsignificantlyalterenergytrans- posed thatsatisfytheannihilationconstraint. et al.1985).Severalextensionsofthestandardmodel(Gelmini, Hall, andLin1987;RabyWest1987a,b)havebeenpro- below thatneededtosolvethesolarneutrinoproblem(Krauss and theirresultingequilibriumabundancewouldbereduced massive neutrinos)wouldannihilatesignificantlyintheSun cle physicsdarkmattercandidates(photinos,higgsinos,and metry betweencosmionandanticosmion.Manypopularparti- to theirscatteringcrosssectionortheremustbeanetasym- lation crosssectionatlowenergiesmustbesuppressedrelative cosmions aretoavoidself-annihilationintheSun,theirannihi- Gilliland 1985;GriestandSeckel1987;Gould1987a).Ifthe will beunimportant(SpergelandPress1985;Faulkner transport. Ifthecosmionmassexceeds~4GeV,evaporation Indeed, in§II,weshallshow thatwhatRenziniconsiders Renzini’s arguments,ifcorrect,wouldthreatentheviability Renzini (1987)hasstudiedtheeffectsofcosmionson 198 8ApJ. . .331L. .213 41216 2 L22 for themostdesirablecasesfromsolarneutrinopointof view). are optimalfortransportingenergyeffectivelyintheSun,need coupled onlythroughaspin-dependentaxialcoupling,thenits cant inthecoreofanHBstar,whichiscomposedprimarily effective (abundance-weighted)crosssectionwouldbeinsignifi- not beefficientatenergytransportinHBstars.Ifthecosmion cosmion coupledthroughvectorcouplings,itseffectivecross spin-zero nuclei,He,C,and0.Ontheotherhand,if horizontal-branch stars,notonlyarecosmionsineffectual,but reasons, energytransportissuppressed. than inthesolarcore.Inbothcases,thoughforopposite section wouldbemuchlargerintheheavynuclei-richHBcore the entireclassofWIMPsdonotalterHBevolution. estimated therateofcaptureWIMPsmass,m,withan WIMPs withbaryonsinthestars.PressandSpergel(1985) particles willbecapturedintostarsthroughcollisionsofthe mass, M*,andradius,R*: elastic scatteringcrosssectionoffnucleons,
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