Probing the Universe After Cosmological Recombination Throug(2)

Thelithiumchemistrycouldalsobea ectedbyalargedriftvelocitybetweentheLiI uidandthehydrogenplasma.Toexaminethise ect,weconsidertheequationofmotionfortheLiI uid(Burgers1969),

mLiI dvLiI

XLiItLiI+mpWLiI(v vLiI).(12)

HereWLiI=Σkµk:LiWk:LiisthecollisionrateofaLiatomwiththegas,whereWk:LiI=nk σk:LiIv ,andµk:Li=[mkmLi/mp(mk+mLi)].Theindexkrunsoverallotherparticlespeciesinthegaswhichareassumedtomoveatacommonbulkvelocityvbecausetheyarenotsubjecttotheresonantdragforce.Thegeometriccross-sectionofLiIatoms,σLiI～10 15cm2,couplesthemtotherestofthegasonatimescale～107s,muchshorterthantheHubbletime,H 1～3×1013s

I show that neutral lithium couples strongly to the cosmic microwave background (CMB) through its 6708A resonant transition after it recombines at z~500. At observed wavelengths of <335 micron, the CMB anisotropies are significantly altered since the optic

atz～103.Hence,wemayignorethetermsontheleft-hand-sideinequation(12),aswellastheperturbedgravitationalforcewhichisofthesameorder.Theremainingtermsgivethesolution,

(v vLiI)

1+Y(13)

whereY=WLiItLiIXLiI/ALi.SubstitutingALi=7,we ndthatWLiI≈10 7[(1+z)/103]3.5s 1,andthatY 1atz<～400,afterlithiumrecombination.Athigherredshifts,theassumptionthatvLiI=vseemsnottoapplyandonemaywonderwhetherthedragtimeinequation(6)shouldbemultipliedbyafactorof(v/vLiI)=(1+Y)/Y>1,sincethedragforceactsonvLiIandnotonv.InthiscontextitiscrucialtorealizethattheLiInucleidonotmaintaintheiridentityasneutralatoms;infact,theycontinuouslyformandgetionizedonatimescalemuchshorterthanaHubbletime.Thecross-sectionforCoulombcollisionsofLi+isfargreaterthanthatofLi√I,σLi+=2

I show that neutral lithium couples strongly to the cosmic microwave background (CMB) through its 6708A resonant transition after it recombines at z~500. At observed wavelengths of <335 micron, the CMB anisotropies are significantly altered since the optic

largewavenumbers,becausethelastscatteringsurface(or“visibilityfunction”)fortheresonanceisextremelythin.Theincreaseinamplitudeofsub-horizon uctuationsbetweenz=103andz=500wouldenhancethenewanisotropiesrelativetotheoriginalonesandintroduceadistortionoforderunityintheoriginalanisotropyspectrumonthesescales.Theanisotropyspectrumwouldbemodi edatmultipolemoments >～100,aroundandbelowtheangularscaleofthe rst√acousticpeak(whichisafactorof～

Bν= dlnBνT= hν

T=15.78× 500

T,(14)

wherezistheredshiftbeingprobedandwehavesubstitutedBν(T)∝exp( hν/kT).Hencethe rstacousticpeakwouldcorrespondtobrightness uctuationsofupto～5×10 4.

Atagivenobservedwavelength,theredshiftthicknessofthescatteringshellisonlydeterminedbytwocontributions:(i)thepossibilitythataphotonatthiswavelengthwaseitherabsorbedby

0transitionwithλ=6707.76 0the22S–22P3Aorataslightlylowerredshiftbythe22S–22P10/2/2

transitionwithλ0=6707.91 A(Radzig&Smirnov1985),yielding[ z/(1+z)]=2.2×10 5;and(ii)thethermalwidthoftheline3,[ z/(1+z)]=( λ/λ)th≈10 5.Inpractice,theminimumthicknesswouldbelimitedbytheband–widthofthedetector.Themaximumband–widthandminimumangularresolutionshouldbetunedtomatchtheexpectedcoherencelengthofthepeculiarvelocity eldatz～500,whichcorrespondsto( λ/λ)～0.2and θ～6′orequivalently ～103.

Observationsatdi erentfar–infrared(FIR)wavelengthswouldprobedi erentthinslicesofstructureintheearlyuniverse.Theanisotropypatternwouldvarygraduallyasafunctionofwavelengthand“3Dtomography”isinprinciplepossible,bywhichonemayprobecorrelationsinthestructurealongtheline-of-sight.ThefeasibilityofthismeasurementmightbeseverelycompromisedbytheanisotropiesoftheFIRforeground.Unfortunately,350µmisjustthewavelengthwheretheCMBintensityblendsintotheextragalacticFIRforeground(seeFig.1inScottetal.2001).However,thecontributionofdiscretesources(seeFig.6inKnoxetal.2001)couldbeseparatedoutthroughobservationsatshorterwavelengthswithahigherangularresolution.Furthermore,continuumforegroundemissionwouldresultinsimilaranisotropiesforall

I show that neutral lithium couples strongly to the cosmic microwave background (CMB) through its 6708A resonant transition after it recombines at z~500. At observed wavelengths of <335 micron, the CMB anisotropies are significantly altered since the optic

wavelengthswithinabandwidth( λ/λ)～1,whiletheCMBanistropieswouldvaryconsiderablyacrosssuchabandsinceitswidthcorrespondsto z/(1+z)～1.Subtractionofanisotropymapsatslightlydi erentwavelengthswithinsuchabandcanthereforebeusedtoisolateouttheCMBcomponent(aslongasthesewavelengthsdonotoverlapwithstrongemissionlinesfromtheforegroundsources).For <～100,theanisotropiesshouldhavethesamepower-spectrumasmeasuredbyMAPorPlanckatmuchlongerwavelengths.ThepredictablecorrelationsbetweenthetemperatureandpolarizationpatternsoftheCMBandtheirgeneralstatisticalpropertiescouldbeusedtofurtherenhancethesignal-to-noiseratio(Zaldarriaga&Loeb2001).Obviously,thesedi cultobservationsneedtobemadethroughholesintheGalacticdustemissionathighGalacticlatitudes.

4.Conclusions

The6708 AresonanttransitionofneutrallithiumprovidesapreviouslyunexploredcouplingbetweenthebaryonsandtheCMBaftercosmologicalrecombination.Thelithiumopacityissubstantialatobservedwavelengths<～335[(1+zLiI)/500]µm,wherezLiIistheredshiftatwhich～50%ofthelithiumrecombines.Atthesewavelengths,theCMBanisotropiesonsub-degreeangularscaleswouldbesigni cantlyaltered,duetothe niteopticaldepthforresonantscattering,τLiI≈0.5[(1+zLiI)/500]3/2.Thisscatteringwouldgeneratenewtemperatureandpolarizationanisotropiesatmutipolemoments >～100.ThedetectionoftheseanisotropiesdependsontheprospectsforcleaningtheexpectedanisotropiesoftheFIRforeground(Knoxetal.2001),andmaybefeasiblethroughthesubtractionofanisotropymapsforpairsofslightlydi erentwavelengths.

TherelevantwavelengthrangeoverlapswiththehighestfrequencychannelofthePlanckmission(352µm)andwiththeproposedbaloon–borneExplorerofDi useGalacticEmissions …… 此处隐藏：5407字，全部文档内容请下载后查看。喜欢就下载吧 ……