Probing the Universe After Cosmological Recombination Throug

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

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aProbingtheUniverseAfterCosmologicalRecombinationThroughtheE ectofNeutralLithiumontheMicrowaveBackgroundAnisotropiesAbrahamLoebAstronomyDepartment,HarvardUniversity,60GardenStreet,Cambridge,MA02138;aloeb@cfa.harvard.eduABSTRACTIshowthatneutrallithiumcouplesstronglytothecosmicmicrowavebackground(CMB)throughits6708 Aresonanttransitionafteritrecombinesatz～500.Atobservedwavelengthsof<depthforresonant～335µm,theCMBanisotropiesaresigni cantlyalteredsincetheopticalscatteringbyneutrallithiumissubstantial,τLiIThescatteringwouldsuppresstheoriginalanisotropies,butwillgeneratestrong～new0.5.anisotropiesintheCMBtemperatureandpolarizationonsub-degreescales( >Observationsatdi erentwavelengthsinthisspectralregimecanprobedi erent～100).thinslicesoftheearlyuniverse.Theanisotropynoisecontributedbycontinuumradiationfromforegroundfar–infraredsourcescouldbetakenoutbysubtractingmapsatslightlydi erentwavelengths.Detectionoftheabovee ectscanbeusedtostudystructureatz<～500andtoconstraintheprimordialabundanceandrecombinationhistoryoflithium.Subjectheadings:Cosmology:theory—cosmicmicrowavebackground1.Introduction

ThedynamicalcouplingbetweenthebaryonsandtheCosmicMicrowaveBackground(CMB)duringtheepochofcosmologicalrecombination(z～103)iscommonlyassumedtobemediatedonlythroughThomsonscattering(Peebles&Yu1970).Thiscouplingbecomesine ectivewhenhydrogenrecombines,ataroundthesametimewhentheuniversebecomestransparent,andhenceitleavesaclearsignatureonthetemperatureanisotropiesoftheCMB(White,Scott,&Silk1994,andreferencestherein).Forthcomingsatellitemissions,suchasMAP1in2001orPlanck2in2007,o erthesensitivitytoprobedeviationsfromthissimplemodelatthepercentlevel(Scott1999;Yu,Spergel,&Ostriker2001).

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

InthisLetter,Iexaminethepotentialsigni canceofthecouplingbetweenthecosmicgasandtheCMBduetoresonantlinetransitionsofneutralatoms.Forsuchtransitions,theintegralof

cross-sectionoverfrequency,

2

σ(ν)dν=f12 πe

c3exp hν

c3exp hν

1

2 1dcosθσ(ν)uν(θ)×cosθvkT.(3)theabsorption

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

Sincetheabsorptioncross-sectionissharplypeakedaroundν0,wemayuseequation(1)toget,

F= 48π2h2f12ν0

mec2exp hν0

dt

orequivalently,dv+Hv=naF, (5)

ta,(6)

whereH=(˙a/a)istheHubbleexpansionrate,andtaisthecharacteristictimeoverwhichthepeculiarvelocityofthegasisdampedduetothedragforceontheresonantatoms,

ta(t)≡3mpλ40

e2kTkT .(7)

Here,λ0=c/ν0istheresonantwavelength,mpistheprotonmass,andXa≡na/(np+Aana),whereAa=ma/mpistheatomicweightoftheresonantatoms.Inthecosmologicalcontext,T=2.725K×(1+z)istheCMBtemperature(Matheretal.1999).BothTandXaarefunctions ofcosmictime,andsoequation(6)admitsthesolution,v=[v0/a(t)]exp{ dt/ta(t)},wherev0=constanda(t)isthecosmologicalscalefactor.Ingeneral,theright-hand-sideofequation(6)shouldincludeothertermswhichsourcethepeculiarvelocity eld,suchasgravitationalorpressureforcesduetodensityinhomogeneities.Thesigni canceofthedragforcecanbecalibratedintermsoftheHubbletime,H 1(z),throughtheproductHta.Fortheredshiftsofinterest,√H(z)≈

λ0na(z)

mec8πH(z),(8)

whereA21isthetransitionprobabilityperunittimeforspontaneousemissionbetweenthetwoenergylevels(ins 1),and(g2/g1)istheratiobetweenthestatisticalweightsoftheexcitedandgroundstates.TheopticaldepthisdominatedbythevelocitygradientoftheHubble ow,because

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

gravitationally–inducedpeculiarvelocitiesperturbthis owonlyslightlyattheearlycosmictimesofinteresthere.

Forτa 1,the uxofresonantphotonsinsidethemoving uidelementisreducedbyafactorof～τa(Rybicki&Hummer1978),andsothedragforceinequation(3)isloweredbythesamefactor.ThisreductionhasdramaticconsequencesfortheresonantLyαtransitionofneutralhydrogen,asweshownext.

3.ImplicationsForCosmologicalRecombination

3.1.Hydrogen

Forthe1S–2PLyαtransitionofhydrogen,λ0=1216 A,A21=6.262×108s 1,

f12=0.4162,and(g2/g1)=3,yieldinganexceedinglylargeSobolevoptical–depth,τH=7.5×108XH[(1+z)/103]3/2,whereXHdenotestheneutralfractionofhydrogen.Thethermally–broadenedLyαlinehasane ectivecross–sectionof σ ～3×10 17cm2(Peebles1993)andacorrespondingmean-free-pathof1/nH σ ～1014cm,atz～103.OnlyonsmallerscalescanLyαviscositydampvelocitygradientse ectively.OnthemuchlargerscaleswheretheCMBanisotropiesaremeasurable,thedragtimeinequation(7)islengthenedbyafactorof～τH,whichmakesitverymuchlongerthantheHubbletime.Thesituationissimilarfordeuterium.Balmerlinetransitionsofhydrogenhaveasmallopticaldepth,buttheoccupationprobabilityoftheirlowerlevelissuppressedbyanexceedinglylargeBoltzmannfactor,～exp{ 4.35×104/(1+z)}.

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