Colour corrections for high redshift objects due to intergal(2)

Corrections to the magnitudes of high redshift objects due to intergalactic attenuation are computed using current estimates of the properties of the intergalactic medium. The results of numerical simulations are used to estimate the contributions to reson

2A.Meiksin

blanketingduetotheresonant(Lymanseries)scatteringofphotonsassumingidealisedformsfortheHIcolumndensitydistributionoftheabsorbers.Thecontributionsofthedi er-entordersintheLymanseriesdependonthefullline-shapeoftheabsorber,precludingadirectscalingofline-centreopticaldepthsbasedonpureatomicphysicsconsiderations.Insteadthebroadeningoftheabsorbersmustbeincluded,thedistributionofwhichhassincebeenshowntobesensi-tivetocolumndensity(Kirkman&Tytler1997;Kim,Cris-tiani&D’Odorico2002b).Madau(1995)adoptedaconstantDopplerparameterforallabsorptionsystems,varyingthevaluetoprobethesensitivityofthetotalamountofattenua-tiontothisvariable.AblanketingformalismbasedonPois-sonplacementoftheabsorberswasusedtopredictthee ec-tiveopticaldepths,althoughinprinciplesmallscalecluster-ingoftheabsorptionsystemswilla ectthetotalamountofblanketing,andsuchcorrelationshavebeendetected(Kirk-man&Tytler1997;Kimetal.2002a).

SinceMadau’sseminalwork,numericalsimulationsoftheintergalacticmediumhaveyieldedresultsmatchingthemeasureddistributionsoftheLyα uxdistributionstoanaccuracyofafewpercent,aswellasthelinepa-rameters(allowingforextraheating)(Meiksin,Bryan&Machacek2001).Numericalsimulationshavealsorepro-ducedtheHIcolumndensitydependenceoftheDopplerparameterenvelope(Misawaetal.2004),aswellascor-relationsintheHI uxdistribution(Croftetal.2002;Meiksin&White2004).TheunderstandingofthemeanLyαintergalacticopticaldepthshasimprovedsubstantiallyoverthepastdecade(seeMeiksin&White2004forasum-maryandKirkmanetal.2005forsubsequentresults).Thesimulationscontaintheinformationnecessarytoextractthecontributionsfromallhigherordertransitionstotheblan-keting.Althoughsimulationsdonotrecoverthefullnum-bersofLymanLimitSystemsobserved(Gardneretal.1997;Meiksin&White2004),anassessmentoftheirnumbersover

theredshiftrange0.3<

zLarreaetal.(1995).～

These～<4hasbeenmadebyStengler-improvementsnowpermitamuchmoresecuredeterminationoftheamountofinter-galacticattenuationtobemade.

2

NUMERICALSIMULATIONPREDICTIONS

FORINTERGALACTICATTENUATION

Attenuationduetointerveningintergalactichydrogenarisesthroughtwoprinciplemechanisms,resonantscatteringbyLymantransitionsandphotoelectricabsorption.Additionalcontributionsaremadebyinterveningmetalsystemsandin-terveninghelium.ThecontributionsofmetalsandHeIaresmall(Madau1995),whileHeIIwillcontributeonlyatwavelengthsλ<228(1+z) Aforasourceatredshiftz.

Thehydrogenattenuationvaluesarebasedonthesim-ulationofaΛCDMmodelbyMeiksin&White(2004)with M=0.3, v=0.7,h=0.7,n=0.95,andnormalisedtoσ8=0.92,consistentwithWMAPconstraints.Thesimu-lationusedapureparticlemesh(PM)scheme(Meiksin&White2001),mimickingthetemperatureofthegasusingapolytropicequationofstateandassumingthegasanddarkmatterhavethesamespatialdistribution.Themeantrans-mittedLyα uxesarenormalisedusingthevalueslistedinTable3ofMeiksin&White(2004).Theattenuationvalues

Table1.Ratioofτ¯n/τ¯αforLymantransitionn→1forn=3to9.Eachtransitioncontributesatwavelengthλforanobjectatredshiftzonlyundertheconditionzn<z,wherezn≡(λ/λn) 1andλnisthe(rest)wavelengthofthetransition.

nτ¯n/τ¯α

resultingfromhigherorderLymantransitionsarecomputeddirectlyfromthesimulationresults.

ThemeanopticaldepthvaluefortheLymantransitionn→1isde nedbyτ¯n≡ ln exp( τn) ,

(1)

where exp( τn) isthecorrespondingmeantransmitted ux.(Here,theconventionτα=τ2,τβ=τ3,etc.willbeadopted.)For2<z<4,themeasuredvaluesofthemeanLyαtransmitted uxare ttowithin2%usingτ¯α=0.00211(1+z)3.7

(z<4).

(2)

Thesharpreductionin uxathigherredshiftsisadequately tby

τ¯α=0.00058(1+z)4.5

(z>4).

(3)

Forz>6,themeasuredvaluesbecomequiteuncertain,buttheobjectsbecomedimmedby4magnitudesormoresothataccuratevalueswillnormallynotberequired.

ThehigherordertermsintheLymanseriesarechar-acterisedbytheratioτ¯n/τ¯αtofactoroutmostofthered-shiftdependence.Aresidualdependence,however,remains.Theseareaccurately t(towithinafewpercent)byweakpowersof(1+z).Theratiosforthe rst7orders(LyβtoLyθ)afterLyαareprovidedinTable1.Higherorders(n>9)arefoundtoscaleverynearlyaccordingtotheatomicphysicspredictionforline-centreopticaldepthval-ues:τ¯n

n(n2 1).(4)

Termsupton=31areincluded:higherorderLymanseriestransitionscontributenegligibly.

Thecontributionduetophotoelectricabsorptionissplitintotwoparts,thecontributionfromsystemsopticallythinattheLymanedgeandthecontributionfromLymanLimitSystems.ThecontributionfromopticallythinsystemsisgiveninthelinearapproximationτL=r/r0(Zuo1992),whereristheproperdistancebetweentheemittingobjectatredshiftzandtheredshiftzL=λ/λL 1,whereλListhewavelengthattheLymanedge(λL=912 A),λistheobservedwavelength,ingtheresultfortheattenuationlengthfromMeiksin&White(2004),thisiswell-approximatedby

c2005RAS,MNRAS000,000–000