Cosmological Obscuration by Galactic Dust: Effects of Dust Evolution

10 Pages·0.26 MB·English

by  Frank Masci

Mon.Not.R.Astron.Soc.000,000–000 (1998) Printed1February2008 (MNLATEXstylefilev1.4)
Cosmological Obscuration by Galactic Dust: Effects of
Dust Evolution
⋆
Frank J. Masci1 and Rachel L. Webster2†
1Infrared Processing and Analysis Center, M/S100-22, 770 South Wilson Avenue,
9 California Institute of Technology, Pasadena, CA 91125
9 2School of Physics, University of Melbourne, Parkville, Victoria3052, Australia
9
1
n ZerothDraft
a
J
ABSTRACT
8
We explore the effects of dust in cosmologically distributed intervening galaxies on

1 the high redshift universe using a generalised model where dust content evolves with
v cosmic time. The absorbing galaxies are modelled as exponential disks which form
7 coevally, maintain a constant space density and evolve in dust content at a rate that
7 is uniform throughout. We find that the inclusion of moderate to moderately weak
0 amounts of evolution consistent with other studies can reduce the mean observed B-
1 band optical depth to redshifts z>∼1 by at least 60% relative to non-evolving models.
0 Our predictions imply that intervening galactic dust is unlikely to bias the optical
9
counts of quasars at high redshifts and their evolution in space density derived there-
9
from.
/
h
Key words: dust, extinction — galaxies: ISM — galaxies: evolution — quasars:
p
general
-
o
r
t
s
a
: 1 INTRODUCTION theline-of-sight to a high redshift quasar hasa high proba-
v
bility of being intercepted by a galactic disk, particularly if
i The recent discovery of large numbers of quasars at ra-
X thedustdistribution islargerthantheoptical radiusof the
dio and X-ray frequencies with very red optical–to–near-
galaxy. Based on the dust properties of local galaxies, it is
r infraredcontinuasuggeststhatexistingopticalsurveysmay
a estimatedthatupto80%ofbrightquasarstoz ∼3maybe
be severely incomplete (eg. Webster et al. 1995 and refer-
obscured by dusty intervening systems. The principle issue
encestherein).Websteretal.(1995) andMasci (1998) have
in these calculations was that realistic dust distributions in
argued that theanomalous colours are duetoextinctionby
galaxies which are ‘soft’ around the edges, will cause many
dust,althoughthelocationofthedustremainsahighlycon-
quasars to appear reddened without removing them from a
troversialissue.Interveningdustygalaxies whichhappento
flux-limitedsample.
lie along the line-of-sight of otherwise normal blue quasars
areexpectedtoreddentheobservedopticalcontinuum,orif None of the above studies however considered the ef-
theopticaldepthishighenough,toremovequasarsfroman fects of evolution in dust content.Cosmic evolution in dust
optical flux-limitedsample (eg. Wright 1990). As suggested isindirectlysuggestedbynumerousclaimsofreducedchem-
by existing obervational and theoretical studies of cosmic ical enrichment at z>∼2. Evidence is provided by observa-
chemical evolution however (Pei & Fall 1995 and references tions of trace metals and their relative abundances in QSO
therein), one expects a reduction in the amount of dust to absorption-line systems to z ∼ 3 (Meyer & Roth 1990;
high redshift. Consequently, one then also expects that the Savaglio,D’Odorico&M¨oller1994;Pettinietal.1994;Wolfe
probabilityofabackgroundobjectbeingeitherreddenedor et al. 1994; Pettini et al. 1997; Songaila 1997), which are
obscured tobe reduced. thought to arise from intervening clouds or the haloes and
Theeffectsofforegrounddustonobservationsofobjects disks of galaxies. These studies indicate mean metallicities
at cosmological distances has been discussed by Ostriker & ≃ 10% and <∼1% solar at z ∼ 2 and z ∼ 3 respectively,
Heisler (1984); Heisler & Ostriker (1988); Fall & Pei (1989, and dust-to-gas ratios <∼8% of the galactic value at z ∼ 2.
1993);Wright(1986,1990)andMasci&Webster(1995).Us- These estimates are consistent with simple global evolution
ing models of dusty galactic disks, these studies show that models of star formation and gas consumption rates in the
universe (Pei & Fall 1995). If the observed metallicities in
QSOabsorptionsystemsarecommon,thentheirinterpreta-
⋆ Email:[email protected] tion as galactic disks implies that substantial evolution has
† Email:[email protected] taken place since z ∼ 3. If the quantity of dust on cosmic
2 F. J. Masci & R. L. Webster
scales also follows such a trend, then one may expect the 2.1 Evolution
effectsofobscurationtohighredshifttobereducedrelative
Equation (2) must be modified if the dust content in each
to non-evolvingpredictions.
galaxy is assumed to evolve with cosmic time. The opti-
Inthispaper,wecontinuetomodeltheeffectsofinter-
cal depth seen through the center of a single absorber at
vening galactic dust on the background universe at optical
some redshift, τ (z), will depend on the quantity of dust
wavelengthsusingamoregeneralised modelwherethedust 0
formedfrompaststellarprocesses.Forsimplicity,weassume
contentevolves.Weexploretheeffectsofourpredictionson
all galaxies form simultaneously, maintain a constant space
quasar number counts in the optical and their implication
density, and increase in dust content at a rate that is uni-
for quasar evolution.
form throughout. We also assume no evolution in the dust
This paper is organised as follows: The next section
law ξ(λ) with redshift. Even though a lower mean metal-
briefly describes the generalised model and assumptions.
licity at high redshift may suggest a different wavelength
Section 3 describes the model parameters and their values
dependence for the dust law, there is no evidence from lo-
assumedinourcalculations.Modelresultsarepresentedand
calobservationsofthediffuseISMtosupportthisview(eg.
analysed in Section 4. Implications on quasar statistics and
Whittet 1992).
evolution are discussed in Section 5. Otherimplications are
We parameterise evolution in dust content by follow-
discussedinSection6andallresultsaresummarisedinSec-
ingsimulationsoftheformation ofheavymetalsinthecold
tion 7. Unless otherwise stated, all calculations assume a
darkmatterscenarioofgalaxyformationbyBlain&Longair
Friedmanncosmology withq =0.5,andHubbleparameter
0 (1993a,1993b).Theseauthorsassumethatgalaxiesformby
h =1 where H =50h kms−1Mpc−1.
50 0 50 thecoalescence of gaseous protoclouds through hierarchical
clusteringasprescribedbyPress&Schechter(1974).Afixed
fraction of the mass involved in each merger event is con-
verted into stars, leading to the formation of heavy metals
2 THE EVOLUTIONARY DUST MODEL anddust.Itwasassumedthattheenergyliberated through
stellar radiation was absorbed by dust and re-radiated into
Wecalculate theprobability distribution intotal dust opti-
the far-infrared. They found that such radiation can con-
caldepthfrommodelgalaxiesalonganyrandomline-of-sight
tributesubstantiallytothefar-infraredbackgroundintensity
as a function of redshift by following the method presented
from which theyusetoconstrain amodelfortheformation
inMasci&Webster(1995).Thiswasbasedonamethodin-
of heavy metals as a function of cosmic time. Their models
troducedbyWright(1986)whichdidnotincludeanyeffects
show that thecomoving density of heavymetals created by
ofevolution with redshift. Herewe generalise thismodelby
some redshift z, given that star formation commenced at
considering the possibility of evolution in the dust proper-
some epoch z follows theform
tiesofgalaxies.Inthediscussionbelowandunlessotherwise SF
indicated bya subscript,we define τ tobe thetotal optical Ω (z) ∝ ln 1+zSF , wherez <z . (3)
depth encountered by emitted photons and measured in an m (cid:16) 1+z (cid:17) SF
observer’s B bandpass (effectively at λ=4400˚A). We assume that a fixed fraction of heavy metals con-
We assume the following properties for individual ab- denseintodustgrainssothatthecomovingdensityindust,
sorbing galaxies. Following previous studies (eg. Wright Ω (z), follows a similar dependence as equation (3). The
d
1986, Heisler & Ostriker 1988), we model galaxies as ran- density in dust relative to the present closure density in n
0
domly tilted exponential disks, where the optical depth exponentialdisks per unit comoving volume is given by
throughaface-ondiskdecreasesexponentiallywithdistance
n M
r from thecenter: Ω = 0 d, (4)
d ρ
c
τ(r,z) = τ (z)e−r/r0. (1)
0 where ρ = 3H2/8πG and M is the dust mass in a single
c 0 d
r isacharacteristicradiusandτ (z),thevalueofτ through exponentialdisk.ThismasscanbeestimatedusingEq.7-24
0 0
the center of the galaxy (r = 0). The redshift dependence from Spitzer (1978) where the total density in dust, ρd, is
ofτ0 isduetotheincreaseinabsorberrestframefrequency related to the extinction AV along a path length L in kpc
with redshift. by
Since we wish to model the observed B-band optical ǫ +2
depth to z<∼6, we require an extinction law ξ(λ) ≡ τλ/τB hρdi = 1.3×10−27ρg ǫo−1 (AV/L). (5)
thatextendstowavelengthsof∼630˚A .Weusetheanalyt- (cid:16) o (cid:17)
ρ andǫ arethedensityanddielectricconstantofatypical
ical fit for ξ(λ) as derived by Pei (1992) for diffuse galactic g o
dust in the range 500˚A<∼λ<∼25µm. The optical depth in an dsiuosntsgorfaginmrcemsp−e2ct-ivseeleySapnitdzethre(1n9u7m8)e.rUicsailnfgactthoerehxapsodniemnteina-l
observer’sframethroughanabsorberatredshift z (τ (z)in
0
profile (equation 1) where τ(r) ∝ A (r) and integrating
equation 1) can be written: V
along cylinders, the dust mass in a single exponential disk
τ (z) = τ ξ λB , (2) can be found in terms of the model parameters τB and r0.
0 B 1+z Wefind that thecomoving density in dust at some redshift
(cid:16) (cid:17)
scales as
where τ is the rest frame B-band optical depth through
B
thecenter of an individualgalactic absorber. Ω (z) ∝ τ (z)n r2, (6)
d B 0 0
where τ (z) is the central B-band optical depth and r
B 0
the dust scale radius of each disk. Thus, the central opti-
Cosmological Obscuration by Galactic Dust 3
havean evolvingeffective‘dust radius’ which follows chem-
ical enrichment from stellar processes.
8 Our parameterisation for evolution in galactic dust
(equations 7 and 9) is qualitatively similar to the ‘accre-
)
r
e tion models’ for chemical evolution of Wang (1991), where
b6
sor τ =4 theeffectsofgraindestructionbysupernovaeandgrainfor-
b B mationinmolecularcloudsistakenintoaccount.Theabove
a4 τ =0.5
e B model is also consistent with empirical age-metallicity rela-
gl tionships inferred from spectral observations in the Galaxy
n z =10
(sibs2 dust zdust=4 (eWvohlueteiloenr,oSnneadicnos&miTcrsucraalne 1im98p9li)e,danbdy mabosdoerlpstioofnc-lhinemeiocba-l
o
τ
0 servationsofquasars(Lanzettaetal.1995;Pei&Fall1995).
0 2 4 6
Redshift
3 MODEL PARAMETERS AND
ASSUMPTIONS
Figure1. Opticaldepthinanobserver’sB-bandpassasafunc-
3.1 Model Parameters
tionofredshiftthroughasinglemodelabsorberdefinedbyequa-
tion (8). τB is the rest frame central B-band optical depth and Our model depends on four independent parameters which
zdust thedustformationepoch. describe the characteristics and evolutionary properties of
intervening galaxies. The parameters defined ‘locally’ are:
thecomoving numberdensity of galaxies n , the character-
cal depth, τ (z), in any model absorber at some redshift is 0
B isticdustradiusr ,and dustopacityτ at thecenterofan
directly proportional to the mass density in dust or heavy 0 B
individualabsorber.Theevolutioninτ andr isdefinedby
metals as specified byequation (3): B 0
equations(7)and(9)respectively.Parametersdefiningtheir
τ (z) ∝ ln 1+zSF . (7) evolution are δ for r0, and the ‘dust formation epoch’ zdust
B 1+z for τ . Both n and r have been conveniently combined
(cid:16) (cid:17) B 0 0
intothe parameter τ where
The redshift dependence of optical depth observed in g
thefixed B-bandpassdueto a singleabsorber now involves τ = n πr2 c , (10)
two factors: first, the extinction properties of the dust as g 0 0 H0
defined by equation (2) and second, its evolution specified with c being the Hubble length. This parameter is pro-
by equation (7). The star formation epoch zSF can also be portioHn0altothenumberofgalaxiesandmeanopticaldepth
interpreted as the redshift at which dust forms. From here introducedalongtheline-of-sight(seeSection4).Italsorep-
on,wethereforerefertothisparameteraszdust -ahypoth- resents a ‘local’ covering factor in dustygalactic disks- the
esised “dustformation epoch”.Byconvolvingequations(2) fraction of sky at theobserver covered in absorbers.
and (7), and requiring that locally: τ0(z = 0) = τB, the Inallcalculations,weassumeafixedvalueforn0.From
observed optical depth through a single absorber at some equation(10),anyevolutioninthecomovingnumberdensity
redshift z<zdust now takes theform: n0 isincludedintheevolutionparameter δ forr0 (equation
9). Thus in general, δ represents an effective evolution pa-
λ ln(1+z)
τ0(z) = τBξ(cid:16)1+Bz(cid:17)(cid:20)1− ln(1+zdust)(cid:21). (8) braymfoetuerrpfoarrabmotehterrs0:aτnd, τn0,.Oδ uanrdmzodel.isthereforespecified
g B dust
Figure 1 illustrates the combined effects of evolution and
increase in observed frame B-band extinction with redshift
3.2 Assumed Parameter Values
defined by equation (8). The extinction initially increases
with z due to a decrease in corresponding rest frame wave- Ourcalculationsassumeacombinationofvaluesforthepa-
length. Depending on the value for zdust, it then decreases rameters(τg,τB)and(δ,zdust)that brackettherangecon-
duetoevolutionindustcontent.Thislattereffectdominates sistent with existing observations. The values (τ , τ ) are
g B
towards zdust. chosen from previous studies of dust distributions and ex-
The characteristic galactic dust radius r0 defined in tinction in nearby spirals. From the studies of Giovanelli
equation(1)isalsogivenaredshiftdependenceinthesense et al. (1994) and Disney & Phillipps (1995) (see also refer-
thatgalaxieshadsmaller dust-haloesatearlierepochs.The encestherein)weassumetherangeincentralopticaldepths:
following evolutionary form is adopted: 0.5<∼τB<∼4, while dust scale radii of 5<∼(r0/kpc)<∼30 are as-
r (z) = r (1+z)δ, δ<0, (9) sumedfromZaritsky(1994)andPeletieretal.(1995).Fora
0 0 nominal comoving galactic density of n = 0.002h3 Mpc−3
0 50
where δ gives the rate of evolution and r is now a ‘local’ (eg. Efstathiou et al. 1988), these scale radii correspond to
0
scaleradius.Evolution inradialdustextentissuggested by a range for τg (equation 10): 0.01<∼τg<∼0.18. These ranges
dynamical models of star formation in an initially formed areconsistentwiththoseassumedintheinterveninggalaxy
protogalaxy (Edmunds 1990 and references therein). These obscuration modelsof Heisler & Ostriker(1988) and Fall &
studies show that the star formation rate and hence metal- Pei (1993).
licityindiskgalaxieshasaradialdependencethatdecreases The values for (δ, z ) were chosen to cover a range
dust
outwardsatalltimes.Itisthusquiteplausiblethatgalaxies of evolution strengths for r and τ respectively. To cover
0 B
4 F. J. Masci & R. L. Webster
a plausible range of dust formation epochs, we consider
6≤z ≤20,consistentwitharangeofgalaxy‘formation’
dust
epochspredictedbyexistingtheoriesofstructureformation 0
(eg.Peebles1989).Theupperboundz =20corresponds
dust q=0
tothestarformation epochconsideredinthegalaxyforma- 0
q=0.5
0
tion models of Blain & Longair (1993b). )]
We assume values for δ similar to those implied by ob- (o −1
Z
servations of the space density of metal absorption systems )/
z
from QSO spectra as a function of redshift (Sargent, Bok- (
Z
senberg & Steidel 1988; Thomas & Webster 1990). These g[ −2
o
systemsarethoughttoarise in gas associated with galaxies L
and their haloes and it is quite plausible that such systems
also contain dust. Here we assume a direct proportionality
between theamount of dustand heavymetal abundancein −3
0 1 2 3 4 5
these systems.
Redshift
Ingeneral,evolutioninthenumberofmetalabsorption
line systems per unit z, that takes into account effects of
cosmological expansion, can beparameterised:
Figure 2.Relativemetallicityasafunctionofredshift.Regions
dN = c n πr (z)2(1+z)(1+2q z)−1/2. (11) withinthesolidanddashedcurvesrepresenttherangespredicted
dz H0 z 0 0 byourmodelforq0=0andq0=0.5respectively.Thefilledand
open data points with 1σ error bars are mean observed values
Evolution,suchasareductioninabsorbernumberswithred-
fromPettini etal.(1994) andSongaila(1997) respectively.
shift,canbeinterpretedaseitheradecreaseinthecomoving
number density n , or effective cross-section πr (z)2. With
z 0
our assumption of a constant comoving density n(z) = n ,
0
and an evolving dust scale radius r as defined byequation thatthemetallicityatanyredshiftZ(z),isgenerallydefined
0
(9), we have dN/dz ∝ (1+z)γ, where γ = 0.5+2δ for asthemassfractionofheavymetalsrelativetothetotalgas
q0 =0.5. Hence for no evolution, γ =0.5. mass: Z(z) = Ωm(z)/Ωg(z). At all redshifts, we assume a
Presentestimatesontheevolutionofabsorbernumbers constant dust-to-metals ratio, Ωd(z)/Ωm(z), where a fixed
with redshift are poorly constrained. Thomas & Webster fraction of heavy elements is assumed to be condensed into
(1990) have combined several datasets increasing absorp- dust grains. Therefore the metallicity Z(z), relative to the
tion redshift ranges to give strong constraints on evolution local solar value, Z⊙, can bewritten:
models.ForCIVabsorption (λλ1548, 1551˚A),whichcan be Z(z) Ω (z)Ω (0)
detected to redshifts z>∼3 in high resolution optical spec- Z⊙ = Ωdd(0)Ωgg(z). (12)
tra,evolutionhasbeenconfirmedforthehighestequivalent
width systems with W0>∼0.6˚A. It is more likely that these Fromtheformalism in section 2.1, themassdensityin dust
systemsarethoseassociatedwithdustratherthanthelower relativetothelocaldensity,Ωd(z)/Ωd(0),canbedetermined
equivalentwidth(presumablylesschemicallyenriched)sys- and is found to be independent of the galaxy properties r0
tems with W0<∼0.3˚Awhich have a trend consistent with no andτB,dependingonlyon ourevolution parameters, δ and
evolution.Theirvaluefortheevolutionparameterγ,forthe zdust. This is given by
highestequivalentwidthsystemsis−0.1±0.5atthe2σlevel.
Ω (z) ln(1+z)
Convertingthis2σrangetoourmodelparameterδusingthe d = 1− (1+z)2δ. (13)
discussion above, we assume therange: −0.5<δ<−0.05. Ωd(0) (cid:20) ln(1+zdust)(cid:21)
The gas ratio, Ω (0)/Ω (z), is adopted from studies of the
g g
evolution in gas content of damped Ly-α systems. These
3.3 Comparisons with QSO Absorption-Line
systems are believed to account for at least 80% of the gas
Studies
content in the form of neutral hydrogen at redshifts z>∼2
We can compare our assumed ranges in evolutionary pa- (Lanzettaetal.1991).WeadopttheempiricalfitofLanzetta
rameters: 6≤z ≤20 and −0.5<δ<−0.05 with recent et al.(1995), whofindthat theobserved evolution in Ω (z)
dust g
determinations of the heavy element abundance in damped is well represented by Ω (z) = Ω (0)exp(αz), where α =
g g
Ly-αabsorption systems and theLy-αforest to z ∼3. The 0.6±0.15and0.83±0.15forq =0andq =0.5respectively.
0 0
damped Ly-α systems are interpreted as the progenitors of Figure2showstherangeinrelativemetallicity implied
galacticdisks(Wolfeetal.1986),andrecentstudiesbyPet- by our evolutionary dust model (equations 12 and 13) as
tini et al. (1994; 1997) deduce metal abundances and dust- a function of redshift for two values of q . The solid and
0
to-gas ratios at z ∼ 1.8−2.2 that are ∼ 10% of the local dashed lines correspond to respectively q =0 and q =0.5
0 0
value. The Lyman forest systems however are more numer- andtheregionsbetweentheselinescorrespondtotheranges
ous, and usually correspond to gas columns > 107 times assumed forourassumed modelparameters: 6≤z ≤20
dust
lowerthanthoseofdampedLy-αabsorbers.Highresolution and −0.5 < δ < −0.05. For comparison, the mean metal-
metal-line observations bySongaila (1997) deducemetallic- licities Z ≈ 0.1Z⊙ and Z ≈ 0.01Z⊙ observed in damped
ities <∼1.5% solar at z∼2.5−3.8. Ly-αsystems at z≈2.2 and theLyman forest at z>∼2.5 re-
Torelatethesemetallicityestimatestocosmicevolution spectively are also shown. These agree well with our model
industcontentasspecifiedbyourmodel,wemustfirstnote predictions,suggestingthatourmodelassumptionswillpro-
Cosmological Obscuration by Galactic Dust 5
no evolution
δ=−0.1, z =10
dust
δ=−0.05, z =20
dust
δ=−0.5, z =6
dust (a) τ =0.2, τ =4
g B
1.5 0.8 0.8
z=1 z=3 z=5
) 1.0
z
τ| 0.4 0.4
(
p 0.5
0.0 0.0 0.0
0 2 4 6 0 2 4 6 0 2 4 6
(b) τ =0.01, τ =0.5
g B
200 200 200
z=1 z=3 z=5
)
z
τ| 100 100 100
(
p
0 0 0
0 0.01 0.02 0.03 0 0.01 0.02 0.03 0 0.01 0.02 0.03
B−band optical depth τ
Figure3.Opticaldepthprobabilitydistributionfunctionsp(τ|z)toredshiftsz=1,3and5,whereτ isthetotalopticaldepthobserved
intheB-band.Twodifferentsetsofgalaxyparameters(τg,τB)areconsidered:(a)(0.2,4)and(b)(0.01,0.5)(seesection3.1).Foreach
ofthese,weshowfourevolutionarymodelsspecifiedby(δ,zdust).‘Noevolution’correspondstoδ=0andzdust=∞andthe‘Strongest
evolution’toδ=−0.5andzdust=6.
vide a reliable measure of dust evolution which are at least andislargestfor‘noevolution’(solidlines).Thisbehaviour
compatible with other indirect estimates. is furtherinvestigated below.
In order to give a clearer comparison between the
amountofobscurationandstrengthofevolutionimpliedby
our model parameters (τ ,τ , δ,z ), we have calculated
g B dust
the mean and variance in total optical depth as a function
4 RESULTS AND ANALYSIS
of redshift. Formal derivations of these quantities are given
Usingtheformalism ofMasci&Webster(1995) andreplac- intheappendix.Herewebrieflydiscusstheirgeneraldepen-
ing theparameters τ and r bytheirassumed redshift de- denceon themodel parameters.
B 0
pendenceas defined in section 2.1, Fig. 3 shows probability A quantity first worth considering is the number of
density functions p(τ|z) for the total optical depth up to galaxies intercepted along the line-of-sight. In a q0 = 0.5
redshifts z =1, 3 and 5. Results are shown for two sets of (Λ=0)universe,theaveragenumberofintersectionswithin
galaxy parameters (τg, τB), with four sets of evolutionary a scale length r0 of a galaxy’s center bya light ray tosome
parameters (δ,z ) for each. redshift is given by
dust
TheareaunderanynormalisedcurveinFig.3givesthe
fraction of lines-of-sight to that redshift which have optical N¯(z) = 2 τ (1+z)1.5+2δ−1 . (14)
depths within some interval 0 → τ . Towards high red- 3+4δ g
max (cid:16) (cid:17) (cid:2) (cid:3)
shifts,wefindthatobscurationdependsmostsensitivelyon
the parameter τg, in other words, on the covering factor of Whereδandτg aredefinedinequations(9)and(10)respec-
absorbers(equation10).Figure3showsthatastheamount tively.
of dust at high redshift decreases, ie., as δ and z de- Inthecasewherewehaveno-evolution, ie.whereδ=0
dust
crease, thecurvesshowlittlehorizontal shift towardslarger andz =∞,andforadustlawthatscalesinverselywith
max
optical depths from z = 1 to z = 5. A significant shift be- wavelength (ie. ξ ∝1/λ which is a good approximation at
λ
comes noticeable however for the weaker evolution cases, λ>∼2500˚A), exact expressions follow for the mean and vari-
6 F. J. Masci & R. L. Webster
8 0.4
δ=−0.05, z =20 a. b.
dust
δ=−0.1, z =10
τ 6 δ=−0.5, zdduusstt=6 τg=0.01,τB=4
n
a4 0.2
e
m τ=0.2,τ=4
g B
2 τ=0.01,τ=0.5
τ=0.2,τ=0.5 g B
g B
0 0.0
0 2 4 6 0 2 4 6
z z
no evolution
10 10
c. d.
8 8
(τ,τ)=(0.2,4)
τn 6 g B 6 (δ,zdust)=(−0.05,20)
a (0.2,0.5) (−0.05,6)
e
m 4 4
(−0.5,20)
(0.01,4)
2 2
(−0.5,6)
(0.01,0.5)
0 0
0 2 4 6 0 2 4 6
z z
Figure 4. Behaviourinmeanreddening,hτi,asafunctionofredshiftforarangeofmodelparameters(τg,τB)and(δ,zdust).(a)For
(τg,τB)=(0.2,4) and(0.2,0.5), (b)Sameas(a)butfor τg =0.01, (c)Redshiftdependence ofmeanreddeninginno-evolutionmodelfor
arangeofparameters (τg,τB).(d)Scalingofthemeanreddeningwithrespecttotheevolutionary parameters (δ, zdust)with(τg,τB)
fixedat(0.2,4).
anceintotalopticaldepthalongtheline-of-sight.Themean z = 6 (dot-dashed curves), as compared to the ‘no’,
dust
optical depthcan be written: ‘weak’ and ‘moderate’ evolution cases indicated. The mean
opticaldepthflattensoutconsiderablytowardshighredshift
τ¯(z) = 0.8τ τ (1+z)2.5−1 , (15)
g B inthestrongevolutioncase,andgraduallysteepensasδand
and the variance:(cid:2) (cid:3) zdust areincreased.Notethatnosuchflatteningisexpected
in mean reddening for the no evolution case (Fig. 4c). The
στ2(z) = 0.57τgτB2 (1+z)3.5−1 . (16) meanopticaldepthtoredshiftsz>∼1inevolutionmodelscan
(cid:2) (cid:3) bereducedbyfactorsofatleastthree,evenforlowtomod-
Thevariance(equation16) or‘scatter’aboutthemean
erately low evolution strengths.
tosomeredshiftprovidesamoreconvenientmeasureofred-
dening. The mean optical depth has a simple linear depen- Figure4dshowsthescalingofmeanopticaldepthwith
dence on the parameters τg and τB and thus gives no in- respect to the evolutionary parameters. It is seen that red-
dication of the degree to which each of these parameters dening depends most sensitively on the parameter δ, which
contributestothescatter.Asseen from theprobability dis- controls the rate of evolution in galactic dust scale radius
tributions in Fig. 3, thereis a relatively large scatter about r . A similar trend is followed in Fig. 5, which shows the
0
themeanopticaldepthtoanyredshift.Fromequation(16), dependence of variance in optical depth on evolution as a
itisseenthatthestrongestdependenceofthevarianceison function of redshift, for fixed (τ , τ ). Considerable scat-
g B
thecentralabsorberopticaldepthτB.Thus,largervaluesof teris expectedifthedust radiusofatypicalgalaxy evolves
τB(whichimply‘harder-edged’disks),areexpectedtointro- slowlywithcosmictimeasshownforthe‘weakest’evolution
duce considerable scatter amongst random individual lines case δ=−0.05 in Fig. 5.
of sight, even to relatively low redshift.
In Fig. 4, we show how the mean optical depth varies Our main conclusion is that the inclusion of evolution
as a function of redshift for a range of evolutionary pa- in dust content, by amounts consistent with other indirect
rameters. ‘Strong evolution’ is characterised by δ = −0.5, studies can dramatically reduce the redshift dependence of
Cosmological Obscuration by Galactic Dust 7
inferred luminosities will be decreased by a factor of e−τ.
100
Sincethereisaprobabilityp(τ|z)ofencounteringanoptical
a. τ=0.2,τ=4,δ=−0.5 depthτ asspecifiedbyourmodel(seeFig.3),theobserved
g B
75 no evolution LFcan be written in terms of thetrueLF, φt as follows:
zdust=20 ∞
2στ 50 zzzdduusstt===11550 φo(L,z) = Z0 dτφt(eτL,z)eτp(τ|z) (18)
dust
25 The extra factor of eτ in equation (18) accounts for a de-
crease in luminosity interval dL in the presence of dust.
Equations(17)and(18)implythatthetrueLFcanbewrit-
1000
ten
75 b. τg=0.2,τΒ=4,zdust=10 φt(L,z) = φ∗t(z)L−β−1, (19)
no evolution
δ=−0.05 and theratio of observed to trueLF normalisation as
δ=−0.1
2στ 50 δ=−0.5 φ∗o(z) = ∞dτe−βτp(τ|z). (20)
φ∗t(z) Z0
25
Theobservedcomovingdensityofquasarsbrighterthan
someabsolutemagnitudelimitM asafunctionofredshift
lim
0
0 2 4 6 is computed by integrating the LF:
Redshift ∞
N (z|M <M ) = dLφ (L,z). (21)
o B lim o
Z
Llim=L(Mlim)
Figure 5. Variance (σ2) in optical depth as a function of red- Thus, the true comoving number density Nt, can be eas-
τ
shiftshowingscalingwithrespecttotheevolutionparameters(δ, ily calculated by replacing φo in equation (21) by φt ≡
zdust).(τg,τB)arefixedat(0.2,4).(a)δfixedat-0.05andzdust (φ∗t/φ∗o)φo leading to thesimple result:
isvaried.(b)zdust fixedat10andδ isvaried. N (z|M <M ) ≃ φ∗o(z) N (z|M <M ), (22)
t B lim (cid:18)φ∗t(z)(cid:19) o B lim
total reddening along the line-of-sight to z>∼1, contrary to where thenormalisation ratio is definedby equation (20).
non-evolvingmodels. Figure 6 shows both the observed and true comoving
density of bright quasars (with M < −26) as a function
B
of redshift. The observed trends are empirical fits deduced
5 IMPLICATIONS ON QSO NUMBER by Pei (1995). The true comoving density in all cases was
COUNTS determined by assuming relatively ‘weak’ evolution in the
dustproperties of interveninggalaxies. Two sets of galactic
There are numerous observations suggesting that the space dustparametersforeachq definedby(τ ,r )=(1,10kpc)
0 B 0
density of bright quasars declines beyond z ≈ 3 (Sandage (Figs a and c) and (τ ,r ) = (3,30kpc) (Figs b and d)
B 0
1972; Schmidt, Schneider & Gunn 1988). This has been are assumed. We shall refer to these as our “minimal” and
strongly confirmed from various luminosity function (LF) “maximal”dustmodelrespectivelywhichbrackettherange
estimates to z ∼ 4.5 (Hartwick & Schade 1990; Pei 1995 of parameters observed for local galaxies.
and references therein), where the space density is seen to Comparing the ‘true’ QSO redshift distribution with
decline by at least an order of magnitude from z = 3 to that observed, two features are apparent. First, the true
z =4. Heisler & Ostriker (1988) speculate that the decline numberdensityvs.z relationhasqualitativelythesamebe-
may be due to obscuration by intervening dust, which re- haviour as that observed. No flattening or increase in true
duces the number of quasars observed by ever-increasing quasar numbers with z is apparent. Second, there appears
amounts towards high z. The results of Fall & Pei (1993) tobeashiftintheredshift,z ,wherethequasardensity
peak
howevershowthattheobservedturnoveratz∼2.5andde- peaks. This shift is greatest for our maximal dust model
clinethereaftermaystillexistoncetheeffectsofintervening where z is increased by a factor of almost 1.5 relative
peak
dust(mainlyassociatedwithdampedLyαsystems)arecor- tothatobserved.Thisimpliesthatthebulkofquasarsmay
rected for. Since no evolution in dust content was assumed haveformed at earlier epochsthanpreviouslyinferred from
ineitherofthesestudies,weshallfurtherexploretheeffects direct observation.
of intervening dust on inferred quasar evolution using our Our predictions for QSO evolution, corrected for ob-
evolutionary galactic dust model. scuration by ‘evolving’ intervening dust differs enormously
Since we are mainly interested in “bright” quasars fromthatpredictedbyHeisler&Ostriker(1988).Themajor
(MB<∼−26) at high redshifts, a single power-law for the difference is that these authors neglected evolution in dust
observed LF should suffice: contentwithz.AsshowninFig.4,non-evolvingmodelslead
φo(L,z) = φ∗o(z)L−β−1, (17) to a rapid increase in dust optical depth with z and hence
this will explain their claim of a continuous increase in the
where β ≃2.5. This power law model immensely simplifies true QSO space density at z > 3. As shown in Fig. 6, the
therelationbetweenobservedand“true”LFs(correctedfor inclusion of even a low-to-moderately low amount of evolu-
obscuration by dust). In the presence of dust obscuration, tionindustcontentdramaticallyreducestheexcessnumber
8 F. J. Masci & R. L. Webster
orders of magnitude. These predictions can be reconciled
with the quasar number densities predicted from hierarchi-
calgalaxyformationsimulationsinvolvingcold-darkmatter
q=0.5 (eg.Katzetal.1994).Itisfoundthatthereare>103 times
0
8 potential quasar sites at z > 4 (associated with high den-
sity peaks) than required from current observations. Such
a b
numbers can be easily accommodated by our predictions if
4 a significant quantityof line-of-sight dust is present.
Tosummarise,wehaveshownthatwiththeinclusionof
evenweaktomoderatelyweakamountsofevolutionindust
−3] 0 "observed" content with z, the bias due to dust obscuration will not
c "true"
p be enough to flatten the trueredshift distribution of bright
G
quasars beyond z = 3. A significant excess however (over
/
6) that observed) in quasar numbersis still predicted.
2 q0=0.1
− 10
<
MB c d
( 6 DISCUSSION
N 5
[
g Our model predictions may critically depend on the dust
o
L properties of individual galaxies and their assumed evolu-
0
tion. For instance, is it reasonable to give galaxies an ex-
ponentialdustdistribution?Suchadistributionisexpected
−5 to give a dust covering factor to some redshift considerably
0 2 4 6 2 4 6 larger than if a clumpy distribution were assumed (Wright,
1986).Aclumpydustdistribution(forspiralsinparticular)
Redshift
is expected, as dust is known to primarily form in dense,
molecular star-forming clouds (Wang 1991 and references
therein).
AsnotedbyWright(1986),“cloudydisks”withdustin
Figure6. ComovingnumberdensityofquasarswithMB <−26 optically-thickclumpscan reducetheeffectivecross-section
asafunctionofredshift.Observedtrends(solidcurves)aretaken
fordustabsorptionbyatleastafactoroffiveandhence,are
fromtheempiricalfitsofPei(1995)whiledashedcurvescorrects
thesetrendsforobscurationbydust.Thesearepredictedassum- less efficient at both obscuring and reddening background
ingourevolvinginterveninggalacticdustmodelwithτB =1and sourcesathighredshift.Adependenceofthedegreeofdust
r0 = 10kpc (Figs a and c) and τB = 3 and r0 = 30kpc (Figs b ‘clumpiness’ on redshift, such as dust which is more dif-
andd).Inallcases,wehaveassumedrelatively“weak”evolution fuseatearly epochsandbecomes moreclumpywith cosmic
industcontentwithz,definedbytheparameters:zdust=20and time is unlikely to affect the results of this paper. This will
δ=−0.05. only reduce the effectivecross-section for absorption to low
redshifts, leaving the effects to high redshift essentially un-
changed.Thenumbersofreddenedand/orobscuredsources
of quasars at z > 3 than predicted by Heisler & Ostriker
at high redshift relative to those expected in non-evolving
(1988).
dust models however will always be reduced, regardless of
We find that there is no significant difference in the
thedependenceof aborption cross-section on redshift.
characteristic timescale, t for QSO formation at z >
QSO Observations of the optical reddening distribution of
z , where
peak quasars as a function of redshift may be used to test our
N predictions.Largeandcompleteradio-selectedsampleswith
t ≃ ∼ 1.5Gyr, (23)
QSO (cid:18)N. (cid:19) a high identification rate extending to high redshifts how-
z>zpeak ever are required. The reason for this is that first, radio
is found for both the observed and dust corrected results wavelegths are guaranteed to haveno bias against obscura-
in Fig. 6. We conclude that the decline in space density of tionbydust,andsecond,thestatisticsathighredshiftneed
bright QSOs at redshifts z > 3.5 is most likely to be real tobereasonablyhighinordertoprovidesufficientsampling
and an artifact of an intrinsic rapid turn-on of the QSO of an unbiased numberof random sight-lines.
population with time. This is consistent with estimates of The sample of Drinkwater et al. (1997) contains the
evolution inferred from radio-quasar surveys where no bias highestquasarfraction(>∼70%)thananyexistingradiosam-
from dust obscuration is expected (eg. Dunlop & Peacock ple with a redshift distribution extending to z ∼4. A large
1990). fraction of sources appear very red in B −K colour com-
Anincreasedspacedensityofquasarsatredshiftsz>3 paredtoquasarsselectedbyopticalmeans.Thedependence
predicted by correcting for dust obscuration has implica- of B−K colour on redshift is relatively flat which may at
tionsfortheoriesofstructureformationintheUniverse.Our first appear consistent with the predictions of figure 4, al-
minimal dust model (Figs. 6a and c) predicts that the true though the fraction of sources identified with z>∼2 is only
space density can be greater by almost two orders of mag- ∼5%. Also, this sample is known to contain large numbers
nitude than that observed, while our maximal dust model of sources which are reddened by mechanisms other than
(Figs. 6b and d) predicts this factor to be greater than 5 dustin theline-of-sight (eg. Serjent & Rawlings 1996). The
Cosmological Obscuration by Galactic Dust 9
role of dust, reddening the optical–to–near-IR continua of Drinkwater M. J., Webster R. L., Francis P. J., Condon J. J.,
radio-selectedquasars,andwhetheritisextrinsicornotstill EllisonS.L.,JaunceyD.L.,LovellJ.,PetersonB.A.Savage
remainsacontroversialissue.Oneneedstoisolatetheintrin- A.,1997, MNRAS,284,85
sicsourcepropertiesbeforeattributinganyexcessreddening DunlopJ.S.,PeacockJ.A.,1990, MNRAS,247,19
toline-of-sightdust.Opticalfollow-upofsensitiveradiosur- EdmundsM.G.,1990,MNRAS,246,678
Efstathiou G., Ellis R. S., Peterson B. A., 1988, MNRAS, 232,
veysthatdetectlargenumbersofhighredshiftsourceswith
431
knownintrinsicspectralpropertieswill benecessary toreli-
FallS.M.,PeiY.C.,1989,ApJ,337,7
ably constrain therate of evolution in cosmic dust.
FallS.M.,PeiY.C.,1993,ApJ,402,479
Giovanelli R., Haynes M. P., Salzer J. J., Wegner G., Da Costa
L.N.,FreudlingW.,1994,AJ,107,2036
HartwickF.D.A.,Schade D.,1990,ARA&A,28,437
7 SUMMARY AND CONCLUSIONS
HeislerJ.,OstrikerJ.P.,1988, ApJ,332,543
Katz N.,QuinnT.,Bertschinger E.,Gelb J. M.,1994, MNRAS,
Inthispaper,wehavemodelledtheopticaldepthingalactic
270,71
dust along the line-of-sight as a function of redshift assum-
Lanzetta K.M.,1991,ApJ,375,1
ing evolution in dust content. Our model depends on four
Lanzetta K. M., Wolfe A. M., Turnshek D. A., 1995, ApJ, 440,
parameterswhichspecify thedustpropertiesoflocal galax-
435
ies and their evolution: the exponential dust scale radius MasciF.J.,Webster R.L.,1995,PASA,12,146
r0,centralB-bandopticaldepthτB,“evolution strength”δ MasciF.J.,DrinkwaterM.J.,WebsterR.L.,1998,ApJ,Inpress,
where r0(z) = r0(1+z)δ, and zdust - a hypothesised dust astro-ph/9808286
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studies of the formation of heavy metals in the cold dark OstrikerJ.P.,HeislerJ.,1984, ApJ,278,1
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PeiY.C.,1992,ApJ,395,130
1. For evolutionary parameters consistent with exist-
PeiY.C.,FallS.M.,1995,ApJ,454,69
ing studies of the evolution of metallicity deduced from
PeiY.C.,1995,ApJ,438,623
QSO absorption-line systems, a significant “flattening” in
Peletier R. F., Valentijn E. A., Moorwood A. F. M., Freudling
the mean and variance of observed B-band optical depth
W.,KnapenJ.H.,BeckmanJ.E.,1995, A&A,300,L1
to redshifts z > 1 is expected. The mean optical depth to
PettiniM.,SmithL.J.,HunsteadR.W.,KingD.L.,1994,ApJ,
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8 ACKNOWLEDGMENTS
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edges support from an Australian Postgraduate Award.
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10 F. J. Masci & R. L. Webster
APPENDIX A: DERIVATION OF MEAN depthfollows the general form
OPTICAL DEPTH
z (1+z′)1+2δ λ
τ¯(z) = 2τ τ ξ B
Herewederiveexpressionsforthemeanandvarianceintotal g BZ0 (1+2q0z′)1/2 (cid:16)1+z(cid:17)
optical depth as a function of redshift in our evolutionary
ln(1+z′)
galactic dust model discussed in section 3.2. The galaxies × 1− dz′. (A7)
are modelled as exponential dusty disks, randomly inclined (cid:20) ln(1+zdust)(cid:21)
to theline-of-sight. Similarly, the variance in the optical depth distribution is
We first derive the average number of galaxies inter- definedas follows:
ceptedbyalightrayemittedfromsomeredshiftz (ie.equa- z ds
treiodnsh1i4ft).nGi(vze)n,aw‘ipthropeaecrh’nguamlabxeyrdheanvsiintgyoafngaelffaexciteisveatcsroomsse- στ2(z) = hτ2i−hτi2 = Z0 σng(z′)τ02(z′)(cid:16)dz′(cid:17) dz′. (A8)
g
sectional area µσ as viewed by an observer (µ is a random In terms of our model dependentparameters, this becomes
inclination factor, where µ = cos θ and θ is the angle be-
z (1+z′)1+2δ λ
tween the sky plane and the plane of a galactic disk), the σ2(z) = 2τ τ 2 ξ2 B
average number of intersections of a light ray along some τ g B Z0 (1+2q0z′)1/2 (cid:16)1+z(cid:17)
path length ds will be given by ln(1+z′) 2
× 1− dz′. (A9)
dN = n (z)µσds. (A1) (cid:20) ln(1+zdust)(cid:21)
g
In an expanding universe we have n = n (1+z)3, where
g 0
n isalocalcomovingnumberdensityandisassumedtobe
0
constant.Unitsof properlengthand redshift arerelated by
ds c 1
= (A2)
dz (cid:16)H0(cid:17) (1+z)2(1+2q0z)1/2
(Weinberg 1972). The effective cross-section projected to-
wards an observer for a randomly inclined disk is found by
averaging over the random inclination factor µ, where µ is
randomlydistributedbetween0and1,andintegratingover
theexponential profile assumed for each disk with scale ra-
diusr (z)(seeequations1and9).Theproductµσ inequa-
0
tion (A1) is thusreplaced by
1 ∞
µdµ e−r/r0(z)2πrdr = πr 2(1+z)2δ. (A3)
0
Z Z
0 0
Thus from equation (A1), the average number of intersec-
tions to some redshift z is given by
z ds
N¯(z) = µσn (z′) dz′
Z0 g (cid:16)dz′(cid:17)
c z (1+z′)1+2δ
= n πr2 dz′. (A4)
0 0(cid:16)H0(cid:17)Z0 (1+2q0z′)1/2
With τ definedbyn πr2 c ,thisdirectly leads toequa-
g 0 0 H0
tion (14) for q0 =0.5. (cid:0) (cid:1)
The mean optical depth τ¯ is derived bya similar argu-
ment. If τ (z) is the optical depth observed through a face
0
on galaxy at some redshift z (equation 8), then a galactic
disk inclined by some factor µ will have its optical depth
increased toτ (z)/µ. Multiplyingthis quantitybyequation
0
(A1), the extinction suffered by a light ray along a path
length ds is given by
dτ = n (z)στ (z)ds. (A5)
g 0
Thusthemean optical depthtosome redshift z can becal-
culated from
z ds
τ¯(z) = σn (z′)τ (z′) dz′. (A6)
Z0 g 0 (cid:16)dz′(cid:17)
Givenn (z), ds andσ(fromtheintegraloverrinequation
g dz
A3) above, a(cid:0)nd τ(cid:1)0(z′) from equation (8), the mean optical