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Astron. Astrophys. 356, 795-807 (2000)

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7. Disk opacity and obscuration effects

Part of the motivation for studying the dust content of external galaxies is to establish whether spiral disks are optically thick or essentially transparent to optical radiation. There exists a whole history of debate concerning the opacity of spiral galaxies. Indeed, various investigative techniques have produced quite disparate answers in the past (Davies & Burstein 1995; Valentijn 1990; Disney et al. 1989). More recent studies seem to be in favour of a V-band optical depth [FORMULA] through the centre of face-on disks (Xilouris et al. 1999; Kuchinski et al. 1998), although some authors still maintain spirals are optically thick right out to their [FORMULA] `edge' (Valentijn 1990). One reason why disk opacity is considered such an important topic is that we view the distant Universe through, what amounts to, a foreground `screen' of spiral galaxies. This has the effect of both attenuating and reddening light emitted by high redshift systems.

Alton et al. (1999b) have begun to assess the impact of nearby dusty disks on observations of high redshift (z) galaxies. For one of the disks which they had observed with ISO (NGC 6946), they adopted a bi-model grain distribution which followed the HI a nd H2 gas components according to a gas-to-dust ratio of 150. This gave an extended dust disk, following the atomic gas, with an exponential fall-off of 14 kpc. Combined with this was a compact grain component, tracing the H2, with a radial exponential scale-length of 4.3 kpc. A simulation was run with a Universe populated with disks of this parameterization and assuming a density for field spirals of [FORMULA] per Mpc3 (Loveday et al. 1992). Although this constituted a rather simple model (no account was taken of either galaxy clustering or a possible change in gas-to-dust ratio with look-back time) it produced some instructive results. Notably, for an Einstein-de Sitter cosmology and a value of 75 kms-1Mpc-1 for the Hubble constant, Alton et al. (1999b) predicted significant attenuation of light received in the B-band from high redshifts. Indeed, they concluded that 30-40% of the light originating from [FORMULA] would fail to reach the present-day observer due to intervening galactic disks. This attenuation arises principally from the extended dust component which is assumed to follow the atomic hydrogen. The scale-length and, indeed, total extent of this component is far more critical than the central optical depth associated with H2 because the peripheral regions of spirals occupy a relatively large filling factor in the plane of the sky. In the absence of information suggesting a radial cut-off for the dust disk, none was applied for this simulation.

NGC 6946 is a very gas-rich spiral galaxy (Tacconi & Young 1990) and, as such, might produce somewhat misleading results when determining high-z visibility (if we simply apply a constant gas-to-dust ratio). Therefore, we wish to repeat the calculations of Alton et al. (1999b) using the disk of NGC 891 as a model. We recognize that we will be basing our estimate on a single galaxy but it will be many years before the dust distribution has been accurately mapped out in a large number of nearby galaxies. Thus provisionally, we use the information contained in Fig. 4 regarding the gas-to-dust ratio along the major axis of NGC 891. One component of dust is given a radial exponential scale-length of 3.9 kpc, so that it follows the distribution of H2 with a gas-to-dust ratio of 260. We also prescribe a second grain component, with an exponential scale-length of 150 kpc. This traces the HI plateau with a gas-to-dust ratio of 350. The maximum radial extent of both components is set at 14 kpc, the point at which the HI column density appears to drop off sharply in the 21cm image of Rupen (1991). Our calculation only considers field spirals (using the density given by Loveday et al. 1992), but allows for the fact that light received in the B-band, by the observer, has been affected by the UV-FUV part of the extinction curve at higher redshifts. For each slice in redshift, the real density of spiral galaxies is calculated and, accordingly, their contribution to the optical depth at that redshift is determined. Finally, we compute a covering factor, f, which is defined as the fraction of light emitted at redshift z which fails to reach a B-band observer due to the sum of intervening disks. This quantity will naturally vary according to our chosen cosmology but we show in Fig. 7 our estimates for the important values of [FORMULA] and [FORMULA] (H0=75 kms-1Mpc-1). There is also a small dependance of the solution on the form chosen for the UV reddening law (e.g. Galactic or LMC-type). However, this is generally neglible for [FORMULA]. For more detail concerning our computation of f we refer to Trewhella (1997) and Heisler & Ostriker (1988) which adopt a similar approach to the current method.

[FIGURE] Fig. 7. The fraction of light, f, emitted at redshift z which fails to reach the B-band observer due to attenuation by foreground spiral disks. We show results for an open Universe and an Einstein-de Sitter cosmology. At all redshifts, a Galactic-type reddening law has been used to calculate the attenuation.

It is apparent from Fig. 7 that, in general, foreground attenuation is not a significant problem for galaxies less than a redshift of 4. Indeed, for galaxies detected in the Hubble Deep Field (assuming typically z=1-2 here), less than 5% of th e light appears to be lost. For quasars and related objects, at [FORMULA], small corrections are required in order to learn the true luminosity and colour from optical observations. These predictions rely heavily on the cut-off radius of the extended dust component (assumed to follow the HI in the present calculation). When using the NGC 891 SCUBA data, we have extrapolated to [FORMULA], slightly beyond the furthest radius at which we detect [FORMULA]m emission ([FORMULA]). Submm observations at the optical edge of spiral galaxies are required to ascertain the true gas-to-dust ratio and opacity within the outer HI envelope. In contrast, we do not expect the obscuration calculations to be affected severely by our neglect of dust clumping. GMCs have an optical depth of [FORMULA] whilst the diffuse ISM is characterized by an optical depth close to unity. Thus, for equal amounts of gas in the molecular and atomic phase, dust clumped into GMCs will occupy a filling factor of only 10%. As a point of reference, our opacity model for NGC 891, if it were not truncated at [FORMULA], would give a face-on optical depth of [FORMULA] at the [FORMULA] ([FORMULA]).

The calculations carried out above take no account of spirals belonging to clusters. At the same time, it is conceivable that a line-of-sight intercepting a foreground cluster may well be subject to significant attenuation. A proper examination of such effects would require inclusion of the correlation function of galaxies and a description of large-scale structure in our computation. To gauge the size of such effects we have calculated the opacity of various lines of sight through the nearby Virgo cluster. Sandage et al. (1985) classify 180 cluster spirals of type Sa [FORMULA] Sd within a radius of [FORMULA] (2 Mpc) of the Virgo centre. Clearly, there will be a whole range of optical depths through the cluster according to how the light path intercepts the cluster members. Nevertheless, we can evaluate filling factors for regions where [FORMULA], [FORMULA] etc. To do this, we use once again the optical depth inferred from our submm observations of NGC 891 i.e.

[EQUATION]

for radius [FORMULA]14 kpc and [FORMULA]=0 for [FORMULA]14 kpc. For [FORMULA], the effective cross-section of 180 spiral disks, randomly orientated in the cluster, is 180 [FORMULA] ([FORMULA] 3.5kpc2) or 7000 kpc2. The total surface area of the Virgo cluster is 4.4[FORMULA][FORMULA] kpc2, implying that the probability of a line-of-sight possessing an optical depth greater than 1, P([FORMULA]1.0), is 0.2%. At the lower end, P([FORMULA]0.2) is limited by the radial cut-off for the dust (14 kpc in Eq. 11). We derive a probability of only 2% for a line-of-sight with [FORMULA]0.2. This appears to be incompatible with observations of systematic reddening of background galaxies and QSOs by the intergalactic medium (IGM) in nearby clusters. Such studies imply [FORMULA] for most line of sights (Boyle et al. 1988; Romani & Maoz 1992). The discrepancy here between calculation and observation would be virtually removed if the radial grain cut-off were relaxed or if significant quantities of dust were believed to be expelled from spiral disks into the IGM during the lifetime of the cluster (Alton et al. 1999c; Davies et al. 1998). The first of these issues could be addressed by submm observations of cold dust near the optical edge of spiral disks where the HI column density is low ([FORMULA] cm-2).

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Online publication: April 17, 2000
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