3 Image processing

In order to classify features as "extraplanar'' (i.e. as existing outside the standard absorption lane) it is necessary to define the height and inclination of the stellar and dust layers within each of our objects. To this end, we used the radiation transfer model of Xilouris et al. (1997, 1998, 1999) to fit the observed B-band surface photometry with a model galaxy consisting of an exponential stellar disk, a $R^{\frac{1}{4}}$ bulge and an exponential dust distribution. This model carries out a pixel-to-pixel comparison between the real and simulated object in order to fit scale-heights (z-direction) and scale-lengths (radial direction) to both the stellar and dust disks and to determine the optical depth through the centre of the galaxy (as seen face-on). Consistent with an environment where stars and dust are mixed, the simulation takes account of photon scattering, through the Henyey-Greenstein phase function (Henyey & Greenstein 1941; Bohren & Huffman 1983), as well as radiation absorption. Our confidence in the Xilouris model is significantly boosted by the fact that, in the past, the output parameters from this technique have been highly consistent across several optical and NIR wavebands. Thus in NGC 891, for example, the radial scale-length for the grain distribution has been calculated to be 8.1 kpc in the V-band whilst an independent determination in other filters (K, J, I, B) strays by only 5-10% from this value (Xilouris 1998). The opacity derived from the Xilouris model, which is determined independently at each wavelength, is also remarkably consistent with a Galactic extinction law for all 7 edge-on disks previously analysed (Xilouris et al. 1999). Table 3 shows the properties we derive for each of the galaxies appearing in the sample. For NGC 5023 and UGC 4278 the irregular, clumpy appearance of the disk meant that we could not parameterize the dust layer satisfactorily with an exponential model. In these cases, we will assume that the grains are distributed with a scale-height $0.51\times$ that of the stars, and a scale-length $1.2\times$ that of the stars (in line with the mean properties of the other galaxies in Table 3). The surface photometry of NGC 4762 is completely smooth suggesting that this SO galaxy contains no absorption layer whatsoever. Therefore, no dust parameters are listed for this object.

 

  Table 3: Parametrization of the stellar and absorption disks using radiation transfer modelling. The parameters $z_{\rm d}$ and $z_{\rm s}$ represent the exponential scale-heights of the dust and B-band stars respectively. Similarly, $h_{\rm d}$ and $h_{\rm s}$ denote the exponential scale-lengths of dust and stars, respectively, whilst i corresponds to the inclination inferred for the stellar/dust disk

Galaxy	i	$z_{\rm d}$	$z_{\rm s}$	$h_{\rm d}$	$h_{\rm s}$
	(deg)	(kpc)	(kpc)	(kpc)	(kpc)
NGC 891	89.8	0.31	0.43	8.0	5.7
UGC 4278	87 - 90	-	0.31 - 0.47	-	3.3
NGC 4013	89.9	0.13	0.19	2.6	2.6
NGC 4217	85.5	0.19	0.34	4.5	3.2
NGC 4302	90.0	0.23	0.49	9.2	14
NGC 4762	90.0	-	0.43	-	4.5
NGC 5023	87.0	-	0.17	-	2.3
NGC 5746	86.2	0.20	0.55	7.3	5.5
NGC 5907	87.0	0.13	0.34	5.3	5.0
UGC 10288	87.0	0.09	0.21	5.4	3.4

A difficulty that we have encountered early on in the analysis is that, for objects within the sample that are not perfectly edge-on, there may exist line-of-sight confusion between structure within the plane and features that genuinely extend "vertically'' out of the plane. Consequently, we dismissed from the final sample objects with inclinations $i\leq 87^{\circ}$. This rather stringent condition arose from the fact that a disk inclined at $87^{\circ}$ to the line-of-sight will project vertically $h_{\rm D} \times$ Cos( $87^{\circ}$) onto the plane of the sky ($h_{\rm D}$ being the dust scale-length). This is then comparable to the grain scale-height, $z_{\rm D}$, indicating that confusion is likely to arise. The $i\leq 87^{\circ}$ criterion reduces our sample to only half its original size (now NGC 891, NGC 4013, NGC 4302, NGC 4762 and UGC 4278 remain). The reduction in sample size is unfortunate but it is important to be certain that the "vertical'' extinction features that we subsequently identify truly reside outside the notional dust lane.

Figure 1: B-band image (bottom) and an unsharp-mask B-band image (top) of the central part of NGC 891 shown to the same scale. Arrows indicate examples of dust features considered as extraplanar i.e. residing outside the main absorption layer. "A'' and "B'' refer to typical chimney-like structure extending away from the midplane, whereas "C'' and "D'' appear to be isolated dust clouds. It should be noted that all these annotated features are recognizable as regions of attenuation in the B-band image. A box has been overlayed in order to discriminate between extraplanar extinction and the conventional absorption layer (see text for details). The orientation adopted for both this figure and all subsequent unsharp-mask images (Figs. 2 to 6) is North at the top and East to the left

Figure 2: Unsharp-mask B-band image of the whole of the NGC 891 disk

Figure 3: Unsharp-mask image of UGC 4278 in a blue filter

In the past, authors have been less stringent in discriminating between features termed "extraplanar'' and the main absorption lane. The description of "vertical filaments and loops'' in NGC 253, for example, is based on a disk that is inclined by $30^{\circ}$ to the line-of-sight (Sofue et al. 1994). HS97 do not appear to state a criterion for separation of extraplanar dust from the central dark lane in NGC 891. For their larger sample (HS99) these authors use a generic height of 400 pc (projected) as the boundary between high-lattitude dust and the main extinction layer. This is close to twice the average scale-height determined for our own sample based on radiation transfer (Table 3). However, the projected height of the main dust layer will vary from galaxy to galaxy depending on inclination and, in contrast to previous authors, we feel obliged to take account of line-of-sight effects (see below). Notably, 2 galaxies which HS99 label as manifesting extraplanar dust are rejected from our final edge-on sample because they are believed to be too inclined for reliable separation of projected in-plane structure from bonafide vertical structures (NGC 5907 and NGC 4217). We use a projected z-height of $2 \times l$ to discriminate extraplanar extinction from the main absorption layer, where:

$$l = h_{\rm D} {\rm Cos}(i) + z_{\rm D}.$$ (1)

Here, i is the inclination of the disk, whilst $h_{\rm D}$ and $z_{\rm D}$ are the dust scale-length and scale-height, respectively, as listed in Table 3. A height of $2 \times l$ ensures that only structures extending to at least twice the scale-height of the main dust layer are recognized as extraplanar. The first term in Eq. (1) takes account of the fact that projection effects will contribute to the apparent height of the main dust lane if the disk is not seen perfectly edge-on.

   
3.1 Unsharp-masking

We adopt an unsharp-masking technique similar to that of previous authors (Sofue et al. 1994; HS99) in locating extraplanar dust features. The B-band image is smoothed with a Gaussian function and then the original B-band image subtracted from this smoothed version. This accentuates inhomogeneities in the surface photometry such as those caused by dust filaments. Additionally, we experimented with various rectangular median filters with dimensions longer along the in-plane direction (i.e. parallel to the major axis) than the vertical direction. In principle, the unsharp-mask image produced in this way is less susceptible to sharp gradients or cusps in the original surface photometry. However, we did not experience a significant increase in the number of extraplanar dust features that could be detected by this technique. After various trials, we settled on a Gaussian smoothing kernel of 0.5 kpc FWHM which was found to accentuate the chimney structures in an optimal fashion. This represents a compromise scale-length for absorption features which are generally long perpendicular to the disk (1-2 kpc) but short parallel to the disk (<0.1 kpc). Before subjected our images to unsharp-masking we masked out the brightest HII regions within the disk and nay foreground stars projected close to the disk. It is important to point out that the unsharp-mask only served to assist in locating features which could subsequently be recognized as areas of extinction in the original B-band image.

Figure 4: Unsharp-mask image of NGC 4013 in a blue filter

Figure 5: Unsharp-mask image of NGC 4302 in a blue filter

Figures 1 to 6 show unsharp-mask images for the 5 galaxies in final sample ( $i>87^{\circ}$). In Fig. 1 (NGC 891), we highlight various features in the unsharp-mask image corresponding to both chimney-like features and isolated high-latitude dust clouds. A rectangular box, of width $4\times l$, has been superimposed on this figure to show how we have discriminated between "extraplanar'' extinction and the main absorption layer (Eq. 1). Absorption features found to stretch from the midplane to regions outside the box were considered as extraplanar, so were isolated dust clouds found at least 2 l away from the midplane.

   
3.2 Derivation of opacity

The opacity of the extraplanar structures was derived in the following way. The relevant features were masked out of the original B-band image and then the surrounding pixels used to interpolate the surface brightness over the masked region. By dividing the original surface photometry by the interpolated values it was possible to infer the fraction of light lost due to attenuation by dust. In this way, we derived an opacity $\tau_{B}$ for each of the extraplanar structures. When computing $\tau_{B}$ we integrated the photometry along the whole feature, from one scale-height above the midplane to its maximum height over the disk. When deriving the corresponding dust mass we also used this range in z-height.

For a large number of reasons we expect to underestimate the amount of dust in the extraplanar layer. We are probably only sensitive to vertical features on the nearside of the disk and, in our selection of features, we are undoubtedly biased towards dust clouds seen against the luminous backdrop of the bulge. Our unsharp-masking technique is probably completely insensitive to any widely-distributed, diffuse dust that might exist in the lower halo (Davies et al. 1997), requiring as it does strongly-delineated absorption structures that contrast with the unextinguished stellar emissivity. Since we have used a simple, foreground screen approximation to infer $\tau_{B}$, the optical depth we derive for individual features will be severely underestimated. We have attempted to correct for this problem, to first order, by assuming that filaments viewed along lines of sight towards the galaxy centre are in fact situated at radii such that $\frac{1}{4}$ of the stellar light is emitted in front of the feature and passes to the observer without attenuation by the high-lattitude dust. Thus, in this case, we derive a corrected value of $\tau_{B}$ given by:

$$\frac{I}{I_{0}} = 0.25 + 0.75 {\rm e}^{(-{\tau}_{B})}$$ (2)

where I and I₀ are the observed attenuated and unextinguished light intensities respectively. This correction is roughly consistent with the inference made by HS97, that the reddening exhibited by chimneys viewed towards the centre of NGC 891 is consistent with 0.25 $\pm \ 0.21$ (s.d.) of the light emerging unattenuated. In contrast to Eq. (2), filaments identified at the maximum radius along the major axis are more likely to be situated half-way along the line-of-sight (due to reduced optical depth at the optical edge) and we modify Eq. (2) such that half the stellar light passes through the absorption feature. For intermediate locations along the major axis, $\tau_{B}$ is calculated assuming a linearly-interpolated value between 0.25 and 0.5 for the fraction of light emerging unattenuated. By taking some account of the true star-dust geometry, in this way, we increase the typical value derived for $\tau_{B}$ by $\sim$60% over the simple screen model. We emphasize that no account has been taken of scattering in this process, nor of dust-clumping in the high-z feature. Both of these would require first-order, upward corrections to $\tau_{B}$ (Witt et al. 1999; Bianchi et al. 1996).

For the 1-2'' seeing conditions characterizing the B-band images of our sample (Table 2), we expect the point spread function (PSF) to severely "smear out'' the chimney features. For example, HS97 estimate from HST images of NGC 891 that the width of many of these structures is only $\sim$ 30 pc parallel to the disk (equivalent to 0.7''). A consequence of this is that we shall severely underestimate the true value of $\tau_{B}$ (although we expect to recover the total dust mass present by integrating $\tau_{B}$ over the whole of the dust feature). Indeed, a comparison between chimneys classified by HS97 in their Table 3 (under seeing conditions of 0.6'') with the same structures identified in our own data, shows that we underestimate $\tau_{B}$ by a factor of at least 5. In contrast, the masses we derive for these selected features agree to within 15% with the HS97 values.