Colour corrections for high redshift objects due to intergal(3)

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

Colourcorrectionsforhighredshiftobjectsduetointergalacticattenuation

3

Figure1.Intergalactictransmissionasafunctionofobservedwavelength.(a)Meanintergalactictransmissionforasourceatredshiftz=3.5(solidlines).ThemeanintergalactictransmissionassumingnoLymanLimitSystemsliealongtheline-of-sightisshownbythedashedlines.(b)Meanintergalactictransmissionfor,fromlefttoright,sourcesatredshiftsz=2.5,3.5and4.5.Theheavylinesaretheestimatesfromthispaper.Inbothpanels,thelightlinesaretheestimatesfromMadau(1995).

IGMτL

=0.805(1+zL)

3

ThecontributionduetoPoisson-distributedLymanLimitSystemsisgivenby(Zuo1992)

LLSτL

1

1+z

.(5)

=

z

dz

zL

′

∞

dτL

2N

1+z′

1

3

,(6)

β

where 2N/ τL z=AτL(1+z)γisassumed,correspond-ingtoanumberdensitydN/dz=N0(1+z)γforsystemswithτL>1,whereN0=A/(β 1).TheintegralhasthepowerseriessolutionLLSτL=

N0

n+1 β

( 1)n

λL

3(β 1)

( 1)nλ

λ

(3n γ 1)(n+1 β)

λL

3n