Publ. Astron. Soc. Aust., 1998, 15, 299–308.
Obscuration by Di use Cosmic Dust
Frank J. Masci
School of Physics, University of Melbourne, Parkville, Vic. 3052, Australia [email protected] Received 1998 May 4, accepted 1998 August 27
Abstract: If the background universe is observed through a signi cant amount of di usely distributed foreground dust, then studies at optical wavelengths may be severely biased. Previous studies investigating the e ects of foreground dust on background sources assumed dust to be ‘compactly’ distributed, i.e. on scales comparable to the visible extent of normal galaxies. We show, however, that di use dust is more e ective at obscuring background sources. Galaxy clusters are a likely location for ‘large-scale’ di usely distributed dust, and its e ect on the counts of background sources is explored. We also explore the implications of a hypothesised di use intergalactic dust component uniformly distributed to high redshift with comoving mass density equal to that associated with local galaxies. In this case, we predict a de cit in background sources about three times greater than that found in previous studies.
Keywords: dust: extinction — ISM: general — intergalactic medium
1 Introduction extending to scales > 50 kpc have been con rmed There are a number of studies claiming that dust (Zaritsky 1994; Peletier et al. 1995). in foreground galaxies has a substantial e ect on Does uniformly distributed dust really exist in the colours and counts of optically-selected quasars the intergalactic medium (IGM)? Galactic winds (Ostriker & Heisler 1984; Heisler & Ostriker 1988; associated with prodigious star formation at early Fall & Pei 1993; Wright 1990). It is estimated that epochs may have provided a likely source of metal at least 50% of bright quasars at redshifts z > 3 enrichment and hence dust for the IGM (e.g. Nath may be obscured by foreground galactic dust and & Trentham 1997). Observations of metal lines hence missing from optical samples. These studies in Ly- absorption systems of low column density 15 2 assumed that dust was con ned only within the (NHI < 10 cm ) indeed suggest that the IGM visible extent of normal massive galaxies. However, was enriched to about Z 0 01Z by redshift distant populations such as faint eld galaxies and z 3 (Womble, Sargent & Lyons 1996; Songaila quasars may also be observed through foreground & Cowie 1996). A source of di use dust may also di use dust distributions. Such distributions may have been provided by an early generation of pre- be associated with galaxy clusters and extended galactic stars (i.e. population III stars) associated galactic haloes. with the formation of galactic haloes (McDowell A truly di use intergalactic dust component is 1986). Studies have shown that possible reddening ruled out on the basis of counts of quasars and from uniformly distributed IGM dust is limited reddening as a function of redshift (e.g. Rudnicki by observations of radio-selected quasars. Since 1986; Ostriker & Heisler 1984). Such observations radio-selected quasars should have no bias against indicate that if a signi cant amount of dust exists, reddening by dust, such a component must be of it must be patchy and di use, with relatively low su ciently low optical depth to avoid producing a optical depth so that quasars will appear reddened large fraction of ‘reddened’ sources at high redshift without being removed from ux-limited samples. (see Webster et al. 1995; Masci 1997). Galaxy clusters provide a likely location for ‘large- In this paper, we show that a given quantity of dust scale’ di usely distributed dust. Indirect evidence is has a much greater e ect on the background universe provided by several studies that report large de cits when di usely distributed. We shall investigate of distant quasars or clusters of galaxies behind the e ects of di use dust rst, from, possible nearby clusters (Boyle, Fong & Shanks 1988; Romani distributions on galaxy cluster scales and second, & Maoz 1992 and references therein). These studies from a hypothesised uniformly distributed component proposed that extinction by intracluster dust was the in the IGM. major cause. Additional evidence for di use dust This paper is organised as follows. In the next distributions is provided by observations of massive section, we explore the dependence of background local galaxies where, in a few cases, dust haloes source counts observed through a given mass of
᭧ Astronomical Society of Australia 1998 1323-3580/98/030299$05.00 300 F. J. Masci
dust on its spatial extent. In Section 3, we a slab of dust composed of grains with uniform investigate the spatial distribution of dust optical radius a is de ned as depth through galaxy clusters, and its e ect on the 2 counts and colours of background sources. Section 4 = Qext( , a) a ndld , (3) explores the consequences if all dust in the local universe were assumed to be uniformly distributed where Qext is the extinction e ciency, which depends in the IGM. Further implications are discussed in on the grain size and dielectric properties, nd is the Section 5, and all results are summarised in Section 6. number density of grains, and ld is the length of All calculations use a Friedmann cosmology with the dust column along the line of sight. Assuming q =0 5 and Hubble parameter h = 1, where that our cylindrical absorber (whose axis lies along 0 50 1 1 H0 =50h50 km s Mpc . the line of sight) has a uniform dust mass density 2 dust = Md/ R ld, where R is its cross-sectional 4 3 2 Compact versus Di use Dust Distributions radius, we can write nd = dust/ 3 a d, where d is the mass density of an individual grain. We In this section, we explore the dependence of use the extinction e ciency Q in the V -band as obscuration of background sources on the spatial ext parametrised by Goudfrooij et al. (1994) for a graphite distribution of a given mass of dust. For simplicity, and silicate mixture (of equal abundances) with mean we assume that the dust is associated with a grain size a 0 1 m, characteristic of the galactic cylindrical face-on disk with uniform dust mass ISM. The value used is Q (V,0 1 m)=1 4. We density. We quantify the amount of obscuration ext use a galactic extinction curve to convert to a B-band by investigating the number of background sources extinction measure, where typically 1 3 (e.g. behind our absorber that are missed from an optical B V Pei 1992). Combining these quantities, we nd that ux-limited sample. the B-band optical depth, , through our model The fraction of sources missing to some luminosity B absorber can be written in terms of its dust mass L relative to the case where there is no dust extinction and cross-sectional radius as is simply 1 N obs(>L)/N true(>L), where N obs(>L) represents the observed number of sources in the M R 2 a 1 ' 1 d presence of dust. For a uniform dust optical depth B 8 10 M 20 kpc 0 1 m , N obs(>L) N true(>e L). For simplicity, we assume that background sources are described by a 1 d , (4) cumulative luminosity function that follows a power 2gcm 3 law: ∝ L , where is the slope. This form for the luminosity function is often observed for ‘luminous’ where we have scaled to a dust mass and radius (L>L ) galaxies and quasars, which dominate typical of local massive spirals and ellipticals (e.g. high-redshift (z > 0 5) populations in ux-limited Zaritsky 1994). This measure is consistent with samples. With this assumption, the fraction of mean optical depths derived by other means (e.g. background sources missing over a given area when Giovanelli et al. 1994 and references therein). viewed through our dusty absorber with uniform From equation (4), we see that the dust optical optical depth is given by depth through our model absorber for a xed dust mass varies in terms of its cross-sectional radius R fmiss( )=1 e . (1) as ∝ 1/R2. For the nominal dust parameters in equation (4), the number of sources missed behind If the ‘true’ number of background sources per our model absorber (equation 2) can be written as unit solid angle is ntrue, then the total number of background sources lost from a ux-limited sample 2 2 R20 within the projected radius R of our absorber can Nlost( nominal parameters in equation (4). For values the optical radius of the galaxy. This prediction 2 of R in this range, we have Nlost ∝ R and the may be di cult to con rm observationally due to obscuration of background sources will depend possible contamination from light in the galactic most strongly on R. absorber. In the following sections, we explore 1 2. For 1/ or equivalently R20 2 , Nlost will two examples of possible ‘large-scale’ di use dust approach a constant limiting value, independent distributions that can be explored observationally. of the dust extent R. From equation (5), this limiting value can be shown to be Nlost( ) from the V eron-Cetty & V eron (1989) catalogue 2 R avoid rich foreground Abell clusters. They also found 0 (< de cits of 30% out to radii 5 from the clusters, (<20 kpc) lost and postulated a mean extinction of AV 0 4 mag. N 1 true The number of background sources behind clusters N is also expected to be modi ed by gravitational 0 lensing (GL) by the cluster potential. Depending on 012345the intrinsic luminosity function of the background R/20 kpc population, and the limiting magnitude to which the sources are detected, GL can cause either Figure 1—The number of sources missing from an optical an enhancement or a de cit in the number of ux-limited sample behind a face-on dusty disk with xed 8 background sources. The GL e ect has been mass Mdust =10M , as a function of its radial extent R. This number is normalised against the ‘true’ number of used to explain various reports of overdensities of background sources (in the absence of the absorber) that both optically and radio-selected quasars behind fall within the solid angle (20 kpc)2/D2 subtended by our foreground clusters (Bartelmann & Schneider 1993; nominal radius of 20 kpc at distance D—see equation (5). Bartelmann, Schneider &Hasinger 1994; Rodrigues- Williams & Hogan 1994; Seitz & Schneider 1995). We conclude that when dust becomes di use and The reported overdensities for optically selected extended on a scale such that the mean optical QSOs are contrary to the studies above where depth through the distribution satis es <1/ , anticorrelations with foreground clusters are found. where is the cumulative luminosity function slope These overdensities, however, are claimed to occur of background sources, obscuration starts to be 0 0 on angular scales 10 –30 from the cluster centres, important and is maximised for 1/ . The considerably larger than the scales on which most characteristic spatial scale at which this occurs will of the underdensities have been claimed, which are depend on the dust mass through equation (4). of order a few arcminutes. One interpretation is For the typical grain values in equation (4), this that dust obscuration bias may be greater towards characteristic radius is given by cluster centres due to the presence of greater 1 1 quantities of dust. On the other hand, the reported 2 M 2 R ' 31 d kpc . (7) anticorrelations on small angular scales can perhaps 8 2 5 10 M be explained by the optically crowded elds, where QSO identi cation may be di cult. At present, the The simple model in Figure 1 shows that the e ects of clusters on background source counts still obscuration of background sources due to a normal remains controversial. foreground galaxy will be most e ective if dust is More direct evidence for the existence of intra- distributed over a region whose radius is a few times cluster dust was provided by Hu, Cowie & Wang 302 F. J. Masci (1985) and Hu (1992), who compared the Ly- ux a/(0 1 m) the grain radius (Draine & Salpeter from emission line systems in ‘cooling ow’ clusters 1979). Dust injection timescales from galaxies are with Balmer line uxes at optical wavelengths. Ex- typically of order a Hubble time (e.g. Takeda et tinctions of AV 0 2–1 mag towards the cluster al. 1984) and hence grains are e ectively destroyed, centres were found, in good agreement with estimates with only the most recently injected still surviving from the quasar de cits above. Intracluster dust and possibly providing some measurable extinction. has been predicted to give rise to detectable di use The spatial distribution in dust mass density IR emission (e.g. Dwek, Rephaeli & Mather 1990). remains a major uncertainty. A number of authors The most extensive search was conducted by Wise have shown that under a steady state of continuous et al. (1993), who claimed to have detected excess injection from cluster galaxies, destruction by ther- di use 60–100 m emission at the 2 level from a mal sputtering at a constant rate, and assuming number of rich Abell clusters. They derived dust instantaneous mixing with the hot gas, the resulting temperatures in the range 24–34 K and dust masses mass density in dust will be of order 1010M within radii of 1 Mpc. Recently, Allen 31 a Zd 3 (1995) detected strong X-ray absorption and optical dust 10 h50 gcm (8) reddening in ellipticals situated at the centres of 0 1 m 0 01 rich cooling- ow clusters, providing strong evidence for dust. These studies indicate that intracluster (e.g. Dwek et al. 1990), where Zd is the injected dust is certainly present, however, the magnitude dust-to-gas mass ratio, assumed to be equal to the of its e ect in producing background source de cits mean value of the galactic ISM, Zd ' 0 01 (Pei remains a controversial issue. 1992). According to this simple model, the dust In this section, we give some predictions that may mass density is independent of gas density and be used to further constrain cluster dust properties, position in the cluster. If we relax the assumption or help determine the dominant mechanism (i.e. GL of instantaneous mixing of dust with the hot gas, or extinction) by which clusters a ect background however, so that the spatial distribution of gas observations. is di erent from that of the injected dust, the radial distribution of dust can signi cantly di er 3.1 Spatial Distribution of Cluster Dust from uniformity throughout a cluster. Such a non- X-ray spectral measurements show the presence uniform spatial dust distribution may be found in of hot, metal-enriched gas in rich galaxy clusters clusters exhibiting cooling ows. If, as was suggested with 0 5–1 solar metallicity. This gas is believed by Fabian, Nulsen & Canizares (1991), most of the to be of both galactic and primordial origin (i.e. cooled gas remains cold and becomes molecular in pre-existing IGM gas), with the bulk of metals cluster cores, then a relatively large amount of dust being ejected from cluster galaxies (see Sarazin may also form, resulting in a dust distribution which 1986 for a review). Ejection from galaxies may peaks within the central regions. occur abruptly through collisions between the cluster We explore the radial dependence of extinction galaxies, ‘sudden’ ram-pressure ablation, or through optical depth through a cluster, and the expected continuous ram-pressure stripping by intracluster de cit in background sources, by assuming that dust gas (e.g. Takeda, Nulsen & Fabian 1984). The is di usely distributed and follows a spatial density lack of signi cant amounts of dust (relative to what distribution: should have been produced by stellar evolution) 2 n and interstellar gas in cluster ellipticals provides R dust(R)= (0) 1 , (9) evidence for a mass loss process. On the other hand, Rc in ellipticals that avoid dense cluster environments, signi cant quantities of neutral hydrogen, molecular where Rc is a characteristic radius which we x and 3 gas and dust have been detected (e.g. Lees et al. n is our free parameter. Equation (9) with n = 2 1991). is the usual King pro le which, with Rc ' 0 25 If the dust-to-gas ratio of intracluster gas in Mpc, represents a good approximation to the galaxy rich clusters were similar to that of the Milky distribution in clusters. Thus for simplicity we keep Way, then a radial gas column density of typically Rc xed at Rc =0 25 Mpc and vary n. To bracket > 1022 cm 2 with metallicity Z =0 5Z would the range of possibilities in the distribution of > 3 produce an extinction of AV 4 mag. This, intracluster dust, we consider the range 0 destruction by a similar distribution of hot gas were of QSOs behind foreground clusters (e.g. Boyle et entirely absent. al. 1988), and that implied by the Balmer decrements of Hu et al. (1985). For a xed dust mass of 1010M , 3.2 Spatial Distribution of Dust Optical Depth and however, we can achieve larger values for the central Background Source De cits optical depth by steepening the radial dust-density To model the spatial distribution of optical depth, we distribution pro le, determined by the slope n in assume that intracluster dust is distributed within equation (9). a sphere of radius Rmax. The central dust mass Figure 2a shows the optical depth as a function density (0) in equation (9) is xed by assuming of projected cluster radius for the cases n =0, values for the total dust mass Mdust and Rmax such 0 5, 1 and 1 5. The case n =0 5 approximately that corresponds to the model of Dwek et al. (1990), Z which included e ects of mild sputtering by hot Rmax 2 Mdust = 4 R (R)dR . (10) gas in order to t the observed IR emission from 0 the Coma cluster. As shown, the case n =0 [ dust(R) = constant] predicts that the dust optical We assume a cluster dust radius of Rmax =1Mpc, depth should be almost independent of projected which represents a radius containing > 90% of the radius r. Within all projected radii, the optical virial mass of a typical dense cluster characterised depths predicted by our di use dust model lie in the by galactic velocity dispersion 800 km s 1 V range 0 < B <0 3. Turning back to the discussion (Sarazin 1986 and references therein). We assume of Section 2, where we show that background that the total dust mass within Rmax = 1 Mpc obscuration by di use dust reaches its maximum for is M =1010M . This value is consistent with dust B < 1/ , these optical depths satisfy this condition that derived from extinction measures by Hu et al. for < 2 5, typical of luminous background galaxies (1985), IR emission detections by Wise et al. (1993) and quasars. and theoretical estimates of the mean intracluster We now explore the e ects of these models on dust density as given by equation (8). background source counts as a function of projected Using equation (10), the B-band optical depth cluster radius. We rst give an estimate of the through our spherical intracluster dust distribution projected radius at which the number of background at some projected distance r from its centre can be sources lost from a ux-limited sample is expected to written as be a maximum. This is determined by investigating 3Q the dependence in the di erential number of sources (r)= ext B missing, dNlost, within an interval (r, r + dr)asa 4a d function of projected radius r. From equation (2), Z 1 2 2 2 2(Rmax r ) this di erential number will scale as 2 02 1 0 dust [r +R ] 2 dR , (11) (r) 0 dNlost(r) ∝ rdr 1 e , (14) where dust(R) is our assumed radial density distri- where (r) is given by equation (11). Figure 2b bution [equation (9)] and d the mass density of an plots dNlost/dr as a function of r for our various individual dust grain. For a uniform dust density models, where we have assumed =2 5. Thus [ dust(R)= dust(0) = constant], and our assumed from observations, an identi cation of the projected values of Rmax and Mdust given above, the radial radius at which the background source de cit peaks dependence dust optical depth can be written as can be used to constrain the spatial distribution of 2 1 intracluster dust. r 2 B(r)= B(0) 1 , (12) The cumulative fraction of background sources Rmax missing within a projected cluster radius is given by where B(0) is the optical depth through the centre of our cluster, which with grain properties characteristic Nlost( 0.3 0.08 (a)n = 0 (b) n = 1/2 0.06 0.2 n = 1 lost ) ) r r ( n = 3/2 0.04 B /d τ 0.1 N (d 0.02 0.0 0.00 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 r/Mpc r/Mpc 0.5 0.4 (c) (d) 0.4 0.2 n = 0 ) r 0.3 0.0 θ) ( (< 0.2 cq 0.2 w miss f 0.1 0.4 n = 3/2 0.0 0.6 0.0 0.2 0.4 0.6 0.8 1.0 110 θ/ r/Mpc h50 (arcmin) Figure 2—(a) Optical depth as a function of projected cluster radius for various dust density distributions as parametrised by equation (9). (b) Di erential number of background sources lost from a ux-limited sample (arbitrary scale). (c) Total fraction of background sources missing to some r. (d) Cluster–QSO two-point angular correlation function: lled circles, Boyle et al. (1988); squares, Romain & Maoz (1992); open circles, Rodrigues-Williams & Hogan (1994); triangles, Rodrigues-Williams & Hawkins (1995). These predictions can be compared with a number on di erent angular scales are found. The former of existing studies of the observed two-point angular have been interpreted in terms of extinction by correlation function between clusters and optically intracluster dust, the latter with reference to the selected QSOs. This function is usually de ned as GL phenomenon. In most cases the reported overdensities are too large to be consistent with hN (< )i w ( )= obs 1 , (16) GL models, given our current knowledge of cluster cq h i Nran(< ) masses and QSO distributions. It is interesting to note that the studies which where hN (< )i is the average number of observed 0 obs have reached the smallest angular scales ( < 5 ) cluster–QSO pairs within an angular radius and are also those in which anticorrelations between hNran(< )i is that expected in a random distribution. h i QSOs and foreground clusters have been reported. For our purposes, Nran(< ) can be replaced by This can be understood in terms of a larger dust the ‘true’ number of cluster–QSO pairs expected concentration and hence extinction towards cluster in the absence of dust, and hence, we can rewrite centres. These studies, however, may not be free of equation (16) as selection e ects, such as in the detection of QSOs h i from the visual inspection of objective prism plates. Nlost(< ) wcq( ) = fmiss(< ) . (17) From a cross-correlation analysis of galactic stars hN (< )i true with their cluster sample, however, Boyle et al. We compare our models with a number of studies (1988) found that such selection e ects are minimal. The maximum dust radial extent assumed in of wcq( ) for optically selected QSOs in Figure 2d. These studies di er considerably from each other our models, Rmax = 1 Mpc, corresponds to angular 0 in the selection of the QSO and cluster samples, scales 5 at the mean redshift of the clusters h i and as seen, both anticorrelations and correlations ( zc 0 15) used in these studies. Thus, as shown Obscuration by Di use Cosmic Dust 305 in Figure 2d, our model predictions only extend to In this section, we show that such a component 0 3 5 . As shown in this gure, the n = 2 model, which would have a low optical depth and an insigni cant corresponds to the case where the dust density is e ect on the colours of background sources, but assumed to follow the galaxy distribution, provides would be su cient to signi cantly bias their number the best t to the Boyle et al. (1988) data. We must counts in the optical. note that this is the only existing study performed 0 to angular scales 1 with which we can compare 4.1 Comoving Dust Mass Density our models. Further studies to such scales are necessary to con rm the Boyle et al. result, and/or To explore the e ects of a di use intergalactic dust provide a handle on any selection e ects. component, we need to assume a value for the mean mass density in dust in the local universe. This density 3.3 Summary must not exceed the total mass density in heavy metals To summarise, we have shown that for a plausible at the present epoch. An upper bound for the local value of the dust mass in a typical rich galaxy mass density in metals (hence dust) can be derived cluster, obscuration of background sources will be from the assumption that the mean metallicity of the most e ective if dust is di usely distributed on local universe is typically Z metals/ gas 0 01 scales 1 Mpc. This conclusion is based on our (i.e. the ratio of elements heavier than helium to total gas mass), as found from galactic chemical predicted optical depths ( B < 0 3) satisfying our evolution models (e.g. Tinsley 1976) and abundance condition for ‘maximum’ obscuration: B < 1/ (see Section 2), where typically < 2 5 for luminous observations (Grevesse & Anders 1991). Combining background galaxies and QSOs. this with the upper bound in the baryon density We have explored the spatial distribution in predicted from big-bang nucleosynthesis (Olive et < 2 dust optical depth, and the background source al. 1990), where gas baryon < 0 06h50 ,itis de cits expected through a typical rich cluster, apparent that by assuming di erent radial dust density pro les. (z =0)<6 10 4h 2 . (18) These predictions can be used to constrain cluster metals 50 dust properties. A dust density distribution with Let us now compute the total mass density in dust n = 3 [equation (9)] appears to best satisfy the 2 used in previous studies that modelled the e ects of ‘small-scale’ cluster–QSO angular correlation study dust in individual galaxies on background quasars. of Boyle et al. (1988). Both Heisler & Ostriker (1988) and Fall & Pei (1993) 4 Di use Intergalactic Dust? modelled these e ects by assuming that dust in each galaxy was distributed as an exponential disk with There have been a number of studies claiming that scale radius r ' 30 kpc and central face-on optical the bulk of metals in the local universe had already 0 depth =0 5. The comoving mean mass density formed by z 1 (e.g. Lilly & Cowie 1987; White & B in dust (relative to the critical density) in these Frenk 1991; Pei & Fall 1995). Similarly, models of studies, given a comoving galaxy number density dust evolution in the galaxy show that the bulk of 3 3 n0 =0 002h50 Mpc , can be shown to be its dust content was formed in the rst few billion years (Wang 1991). These studies suggest that the 6 n0 dust0 ' 7 3 10 h50 global star formation rate peaked at epochs z > 2 0 002 Mpc 3 when the bulk of galaxies were believed to have 2 formed. Supernova-driven winds at early epochs r 0 B (19) may thus have provided an e ective mechanism by 30 kpc 0 5 which chemically enriched material and dust were dispersed into the IGM. As modelled by Babul & (see Masci 1997). This is consistent with the Rees (1992), such a mechanism is postulated to be constraint in equation (18). Thus, as a working crucial in the evolution of the ‘faint blue’ galaxy measure, we assume the comoving mass density population observed to magnitudes B 28. Nath & de ned by equation (19) in the calculation that Trentham (1997) also showed that this mechanism follows. could explain the recent detection of metallicities Z 0 01Z in low-density Ly- absorption systems at z 3. Another source of di use IGM dust may 4.2 Obscuration by Di use Intergalactic Dust have been provided by an epoch of population III If the dust mass density given by equation (19) is star formation associated with the formation of assumed to be uniformly distributed and constant galactic haloes (e.g. McDowell 1986). on comoving scales to some redshift, the B-band What e ects on background sources would be optical depth through a dust sheet of width dl at expected if all dust formed to the present day was redshift z in an observer’s frame can be written [see completely uniform and di use throughout the IGM? equation (3)] 306 F. J. Masci 1 where f 1 e B(z) is the fraction of sources 6 dust0 a miss d B ' 7 2 10 h50 7 3 10 6 0 1 m missing per unit area. For a completely uniform dust distribution, Cd(U) = 1, and to redshift z =2, 1 dl f ' 10% for =2 5. d (1 + z) , (20) miss 2gcm 3 Mpc If dust is con ned to individual galaxies along the line of sight, however, the covering factor, assuming where for simplicity, we have assumed dust properties that they follow a Poisson distribution is typically characteristic of the galactic ISM. The factor (1+z) Cd ' Nz exp ( Nz), where Nz is the mean number is due to our assumption of a 1/ dependence for of absorber intersections to redshift z: the dust extinction law. This arises from the fact n r 2 that light received in the B-band corresponds to N ' 0 01h2 0 0 z 50 3 light of wavelength /(1 + z) at redshift z, which 0 002 Mpc 30 kpc B consequently su ers greater extinction. Although a (1 + z)1 5 1 (24) 1/ law is not fully representative of that observed in the galactic ISM, which includes the strong (see Heisler & Ostriker 1988). We have scaled to 2200 A feature, this is a good on-average relation the nominal parameters assumed in the intervening for the dust laws in many external galaxies (e.g. galaxy model of Heisler & Ostriker (1988) (hereafter Jansen et al. 1994). Such an assumption greatly HO). In this model, we nd a covering factor of simpli es the redshift dependence of extinction in an only C (HO) ' 0 04 to z = 2. We can estimate the observer’s frame. With dl/dz = 6000h 1(1 + z) 5/2 d 50 mean e ective optical depth observed in the B-band Mpc (for a q =0 5 and = 0 cosmology), the 0 through an individual absorber to z ' 2 in the HO total mean optical depth to some redshift in an model by using the formalism of Section 2. For a observer’s B-band will scale as xed mass of dust, equation (4) implies that the 1 dust0 a product of the area (or covering factor) and optical B(z) ' 0 1 7 3 10 6 0 1 m depth of a dust distribution, Cd, is a constant, depending on grain properties and dust mass alone. 1 d 1/2 Using this relation, the observed e ective absorber 3 1 (1 + z) . (21) ' 2gcm optical depth to z 2 in the HO model, B(HO), can be estimated by scaling from our values of This represents the total optical depth if all dust in B(U) and Cd(U) above for uniformly distributed the intervening galaxy model of Heisler & Ostriker dust: (1988) is assumed uniformly distributed throughout (HO) ' (U)C (U)/C (HO) the universe. B B d d Assuming that dust is uniformly distributed to 0 04 1 = =1. (25) z = 2, the observed B-band optical depth from 0 04 equation (21) will be of order Using this value, the fraction of background sources B(U)(z =2)'0 04 . (22) missed by obscuration from an individual absorber ' Using a galactic extinction law (Pei 1992), this is ‘e ectively’ fmiss =1 exp( 2 5 1) 91%. corresponds to an extinction in B R colour of Combining these results, we nd using equation (23) that the number of sources missing at z ' 2 EB R 0 02 mag. Thus, if background faint eld galaxies and QSOs are observed through a uniform due to a uniform foreground dust distribution is intergalactic dust distribution, their observed colours greater by a factor of (1 0 1/0 04 0 91) 3 are not expected to be signi cantly a ected. We now than that predicted by Heisler & Ostriker (1988). show, however, that the numbers of sources missing We must note that this estimate makes no at such redshifts could be signi cantly greater than allowance for possible evolution in dust content. those claimed by previous studies, which assume all E ects of foreground di use dust on source counts dust to be associated with massive galaxies alone. at z>2 may be signi cantly reduced if appreciable If dust to some distance D covers an area of evolution has occured. E ects of models where the 2 dust content evolves have been explored by Masci sky A and hence has covering factor Cd = A/4 D , the number of background sources lost from a ux- & Webster (1998) limited sample can be estimated from equation (2). 4.3 Summary In general, the number of background sources at some redshift lost from an area of sky with dust We conclude that the existence of a signi cant amount of di usely distributed dust (e.g. with mass density covering factor Cd will scale as on comoving scales of order that observed in local Nlost( ,z) ∝ Cdfmiss( ,z), (23) galaxies) can enhance the number of background Obscuration by Di use Cosmic Dust 307 sources missing in optical samples. Due to its of magnitude (e.g. White & Frenk 1991). If the relatively large covering factor, di use dust predicts only source of IGM dust was from these ‘low-mass’ a reduction in optical counts at z>2 about three galaxies, then the total optical depth to z > 2 would times greater than that claimed in previous studies. be insigni cant, and e ects on the background The colours of background sources are not expected universe would be minimal. to be signi cantly a ected. This implies that the use of background populations to measure a di use 6 Conclusions IGM dust component will be extremely di cult. In this paper we have shown that dust is more e ective at obscuring background sources when 5 Discussion di use or extended. We nd that obscuration of In this section we discuss some further uncertainties background sources by a given dust distribution and implications regarding the existence of di use with optical depth B will be most e ective when dust in the universe. B < 1/ , where is the cumulative luminosity First, the e ects of intracluster dust on background function slope of the sources. sources critically depend on the amount of dust We have explored the e ects of di use dust from, present, and its spatial distribution. Regardless of rst, galaxy clusters and, second, a hypothesised the mechanism by which grains are injected into the uniform IGM component. By assuming di erent intracluster medium from galaxies, it is possible that radial dust density pro les in a typical rich cluster, a signi cant fraction is destroyed in the injection we have predicted the optical depth and background process. Signi cant amounts of hot gas are also source de cit as a function of projected cluster believed to exist in the ISM of cluster ellipticals radius. These predictions can be compared with (e.g. Forman, Jones & Tucker 1985). This gas is future observations to constrain the properties of expected to destroy grains on timescales < 108 yr intracluster dust. Our predicted optical depth (Draine & Salpeter 1979), much shorter than injection measures ( B < 0 3) satisfy the above criterion timescales. Such destruction mechanisms can thus ( B < 1/ ) for background luminous QSOs and prevent the formation of signi cant quantities of galaxies. Existing studies claiming anticorrelations dust. in the distribution of QSOs with foreground clusters It is possible that the spatial distribution of down to scales 10 are consistent with a dust density intracluster dust is not ‘di use’ and uniformly pro le that follows the galaxy distribution. distributed, but inhomogeneous. For example, As a further illustration, we have explored the Fabian et al. (1991) proposed that if most of the e ects of a di use IGM dust component with cosmic cooled gas resulting from cluster cooling ows remains mass density equal to that observed in local galaxies. cold and becomes molecular, then this may provide Assuming this density to be constant on comoving suitable conditions for large amounts of dust to form. scales to z = 2, we nd a de cit in background A clumpy dust distribution that follows cooling- ow sources about three times greater than that predicted laments may result, reducing the e ective dust assuming dust in normal galaxies alone. covering factor and hence the background source The ‘di useness’ of the dust is the key parameter de cit. These issues need to be addressed before which we claim determines the e ectiveness of attributing such de cits to extinction by dust. obscuration of the background universe. Although The existence of a smooth IGM dust component such dust distributions may be di cult to detect, also remains a major uncertainty. Due to a deep we must not neglect their possible presence. Further gravitational potential, Margolis & Schramm (1977) studies of spatial dust distributions, preferably via showed that it is unlikely for supernovae-driven the counts and colours of background sources, will winds to expel signi cant quantities of dust from be essential in con rming our predictions. a massive galaxy to large scales. For low mass galaxies however (e.g. dwarfs), Babul & Rees (1992) Acknowledgments showed that this mechanism could be e ective. 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