The W outhuysen-Field eect in a clum py intergalactic m edium

A B ST R A C T W eshow thatthehigh opticaldepth oftheintergalacticm edium to Lyphotonsbe- foretheEpoch ofReionization resultsin a negligiblem agnitudefortheW outhuysen- Field eect produced by a radiation source on its distant surroundings,unless (1) thescattering m edium hassucienttim efortheim pinging resonancelinephotonsto establish a steady-state frequency distribution or (2) the scattering gas is undergo- ing internalexpansion orhasa peculiarm otion oftensto hundredsof km s 1 away from the source.Because ofintergalacticattenuation,discrete structureswillreceive only radiation from a sourcedisplaced from theresonancelinefrequency by typically hundredsto thousandsofDopplerwidths.Theincidentradiation m ustdiuseacross the resonance line to produce a substantialscattering rate.W e presentsteady-state solutions in the radiative diusion approxim ation for the radiationeld trapped in a clum p ofgasand show thatthism ay resultin an enhancem ent ofthe strength of the W outhuysen-Field eect by as m uch as a factor of10 6 over the free-stream ing (single-scattering)lim it.Solutionsto thetim e-dependentdiusion equation,however, show thatthetim escalesrequired to establish a steady statewillgenerally exceed the lifetim eofthesources,resultingin asubstantiallyreduced scatteringrate.In thepres- enceofinternalexpansion,asteady statem aybeestablished asphotonsareredshifted acrossthe resonance line and into the red wing,and signicantenhancem entin the scattering rate over the free-stream ing lim it m ay again be produced.Alternatively, a substantialscattering rate m ay arise in system swith a peculiarm otion away from the source that redshifts the received radiation into the resonance line centre.As a consequence,atepochs z � 30,when collisionaldecoupling ofthehypernestructure ofhydrogen from theCosm icM icrowaveBackground issm allexceptin denseregions, and priorto the establishm entofany large-scale diuse radiationeld ofresonance line photons,the 21cm signature from the Intergalactic M edium produced by the W outhuysen-Field eectwillin generaltrace the peculiarvelocityeld ofthe gasin addition to itsdensity structure. K ey w ords: atom ic processess { cosm ology:theory { line:form ation { radiative transfer{ radio lines:general{ scattering