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6 Discussion

6.1 Relating high-z dust to the DIG

It is somewhat surprising not to find an association between extraplanar dust and increased H${\alpha }$ emission in either the disk or DIG layer. As mentioned previously, the observational methods we employ to map out the respective distributions of extraplanar dust and ionized gas have serious limitations. Nonetheless, we might expect to see some indication in our optical and emission-line images of NGC 55 that dust chimneys either form close to HII regions or are entrained by the gas they expel from the disk. In FIR-bright, starburst galaxies, where the dust chimneys and DIG appear well coupled, the H${\alpha }$ radiation originates as a shock cooling-line as the superbubble expands into the ambient halo gas (Heckman et al. 1990). The source of the DIG in quiescent spirals is more ambiguous. Energetically, it appears that only photons from massive stars in the disk below are capable of maintaining ionization of the DIG layer (Kulkarni & Heiles 1988). What is not clear is whether some sort of initial expulsion mechanism, akin to that operating in starburst galaxies (SNe explosions and fast stellar winds), is required for gas to reach its present location 1-2 kpc above the midplane. Such a process, if present, must evacuate a hole in the main gas layer with the possibility that dust is lifted out of the plane at the same time. Indeed, if high-energy photons from HII regions are expected to reach z-heights of a few kpc (where they can ionize the DIG), a significant proportion of the dust directly "above'' and surrounding the star-forming site must be swept clean from the optical path. The dimensions of the emission-line shells and bubbles in NGC 55 suggest than an area of $0.7
\times 0.7$ kpc2 must be cleared from the central disk of NGC 55 in order for $\lambda<900$ Å photons to reach the DIG unimpeded (Fig. 16). For a face-on optical depth of $\tau_{B}\sim1$ through the centre of the galaxy (Xilouris et al. 1999), $\sim 10^{5}$ $M_{\odot}$ of dust must then have been expelled from this region assuming Galactic type grains are present (Whittet 1992). Comparing with Table 4, this mass of material is sufficient to create numerous dust chimneys if the appropriate chimney formation mechanisms are present.

It is almost certain that the material visible as extraplanar dust in our B-band images represents a very different phase to the emission-line gas traceable at 6563 Å. If Galactic-type gas-to-dust ratios prevail, a vertical absorption feature of $\tau_{B}\sim1$ is likely to be associated with a gas column densities of $\sim 10^{21}$ cm-2 (Bohlin et al. 1978). For typical chimney dimensions of 30 pc $\times $ 1 kpc (Sect. 3.2) this yields a gas density of $\sim$10 cm-3 - a value well in excess of the density generally attributed to the DIG layer (<0.1 cm-3; R 96). This difference in density might explain the difficulty in comparing the respective distributions of the two media. The emission-line gas appears to be considerably more diffuse than that of the extraplanar dust and tends to occupy a far greater filling factor above the disk. We recognize, however, that our unsharp-mask technique is probably insensitive to any diffuse component of dust residing above the disk (material which may indeed relate to the DIG). In general the extraplanar H${\alpha }$ layer in our quiescent galaxies is far more widespread, and much less discernible as individual shell or bubble features, than say the emission-line nebulae characterizing starburst galaxies. The only exception to this might be NGC 891 but, even here, only a small fraction of the DIG appears to reside in well-defined filaments emanating from individual HII regions. The relatively diffuse nature of the emission-line gas in non-starburst systems tends to reinforce the idea that ionization, in this case, occurs via energetic photons escaping from the disk rather than a localized shock due to outflowing gas.


  Table 6: Properties of the "thick'' disk in NGC 891. We have collated, from the literature, references to an extended vertical distribution of material. The definition of scale-height depends on the source of the data. We use HWHM to denote the half-width half-maximum and "exp.'' to represent exponential scale-height (for dust chimneys we give the typical maximum height). The tabulated density refers to the number of atoms per cubic cm at approximately 1 scale-height above the midplane. The value given for HI is probably a lower limit because a filling factor of unity has been assumed when converting the column density to atoms/cm-3


Scale-height Density Temperature Mass Reference
  (kpc) (atoms/cm3) (K) $M_{\odot}$  
12CO 1.5 (HWHM) 100 $\sim 20$ $5\ 10^{8}$ Garcia-Burillo et al. (1992)
X-ray 2.4 (exp.) $\sim 10^{-3}$ $4\ 10^{6}$ $\sim 10^{8}$ Bregman & Pildis (1997)
radio cont. 1-2 (HWHM) ? non-thermal ? Allen et al. (1978); Rupen (1991)
H${\alpha }$ 0.5-1.0 (exp.) $\sim 0.1$ $\sim 10^{4}$ $\sim 10^{7}$ Rand et al. (1990); Dettmar (1990)
21 cm 1.9 (HWHM) 0.05 $\sim 80$ $2-6 \ 10^{8}$ Sancisi & Allen (1979); Swaters et al. (1997)
Dust Chimneys 1.5 $\sim 10$ ? $\sim 10^{7}$ this work; HS97


At this point we mention the "thick disk'' in NGC 891. A range of gas phases are known to extend to considerable distances above the conventional thin disk in this well-studied system. These different media include X-ray and synchrotron emitting gas as well as the more familiar atomic and molecular components. Table 6 presents the salient properties of each of these extraplanar layers, comparing the scale-heights and densities in each phase. Any robust theory addressing the exchange of material between disk and halo will need to account for the occurence of all these different media. Notably, the dust chimneys in NGC 891 do not appear to correspond closely to any of the other described phases (either in total mass or density). If the vertically-extended 21 cm emission were shown to be composed of individual, discrete structures, rather than a homogeneous layer, then the gas density of the HI thick disk may be comparable to that of the chimney structures. However, the mass contained in the extraplanar HI gas appears to be an order of magnitude greater than the total chimney mass. In Sect. 6.3, we compare observations of a thick disk in the Milky Way with the distribution of high latitude dust detected at FIR wavelengths (IRAS and COBE data).

6.2 Age-dependent effects

One possible explanation for the difficulty in establishing a close spatial correspondance between high-latitude dust and enhanced H${\alpha }$ emission is that the two phenomena might occur during different epochs of the star-formation process. H${\alpha }$ emission, emanating from HII regions, is diagnostic of O-stars and these massive stars are known to possess a lifetime of $\sim$106 yr (Leitherer & Heckman 1995). Thus, if some (small) quantities of gas are already present at high latitudes, ionization of the DIG may proceed relatively promptly after the onset of star formation. H${\alpha }$ images of blue compact dwarf galaxies (BCDs) indicate that the DIG may indeed form early on. Marlowe et al. (1995) detect kpc-scale, diffuse emission-line nebulae in several BCDs known to contain large numbers of Wolf-Rayet stars (the Wolf-Rayet signature indicates a burst age of only a few $\times
10^{6}$ yr; Vacca & Conti 1992). In contrast, as we show later (Sect. 6.4), the time required for dust chimneys to form is $\sim$107 yr. Indeed this appears to be true regardless of whether dust expulsion proceeds by gas convection or radiation pressure. Thus the creation of dust chimneys is synchronized with the emergence of B-stars in the star-forming region (few $\times 10^{7}$ yr) rather the O-star dominated phase (few $\times
10^{6}$ yr).

The scenario outlined above is not without problems. Although the density of atomic gas at heights of 1- 2 kpc above spiral disks may be sufficient to allow the DIG to form without prior expulsion of copious amounts of disk gas (Table 6), a path must be cleared if Lyman continuum disk photons are expected to keep the DIG ionized. This pre-condition has already been alluded to in connection with NGC 55 where it was noted that large amounts of dust would have to swept clear of the optical path (enough to produce $\sim 10$ chimneys). Thus, it is not immediately obvious that the DIG can form relatively early on in the star-formation process ( $\sim 10^{6}$ yr) with chimneys only appearing later ( $\sim 10^{7}$ yr). Another complication in distilling, temporally, dust chimneys from DIG formation, is that new stars in any particular part of the disk may not appear in a well-concerted burst but rather over a more protracted time period via sequential propogation (Kunth et al. 1988; Gerola et al. 1980). Thus, at any given time, young stellar clusters of $\sim$107 yr may reside in close proximity to concentrations of much younger stars ($\sim$106 yr). HS99 argue, on the basis of thermal crossing time, that chimneys could remain intact for 107-8 years even if they are not confined by magnetic fields.

If the formation of dust chimneys is disjunct from the appearance of the DIG in time rather than in location, it should still be possible to establish a global correlation between the two phenonemona. Thus those quiescent disks which exhibit an enhanced overall DIG brightness might conceivably possess the greatest number of dust chimneys across the whole disk. R96 has shown that the brightest DIG tends to occur above parts of the disk containing a larger number of HII regions. Similarly, Fig. 17 demonstrates that the total DIG luminosity correlates well with FIR luminosity of the disk (where the latter might be treated as a moderately sound indicator of massive star-formation). Equally, we see from the same figure that, those galaxies in our final sample which show the greatest evidence for dust chimneys (NGC 891, NGC 4013 and NGC 4302), do possess the highest FIR and H${\alpha }$ DIG luminosities. Thus there is some suggestion here that more prolific star-formation may lead to increased amounts of extraplanar dust. We emphasize, once again however, that the small number of galaxies composing our final sample prevents us from drawing any unequivocal conclusions here. A larger number of very edge-on galaxies will have to be observed (under very favourable seeing conditions) in order to confirm the trend of increased extraplanar dust with enhanced global star-forming activity.

\includegraphics[width=8cm]{}\end{figure} Figure 17: The luminosity of the diffuse ionized gas (DIG) in the H${\alpha }$ emission-line plotted against the FIR luminosity given in Table 1. We use $L_{\rm FIR}$ as an indicator of recent star-formation because it is optically thin (any optical tracers of star-formation in the disk will be severely distorted by extinction). We mark the position of the starburst galaxy M 82 on the plot refering to data given by McCarthy et al. (1987)

A deeper understanding of how dust expulsion relates to the star-formation process might be gleaned from suitable observations of the very closest galaxies. Both the LMC and SMC provide detail-rich testing grounds for theories of how young stars might interact with a dusty interstellar medium (ISM). Both galaxies are known to contain a "lacework'' of H${\alpha }$ shells and superbubbles resulting from recent star-formation across a large part of the ISM (Hunter et al. 1993; Meaburn 1980). A considerable limitation, however, is that neither object is characterized by either a well-defined stellar disk or a particularly dust-rich ISM. The Milky Way might also hold clues as to how recent star-formation and dust chimneys are related, if it can be shown that some fraction of Galactic dust is in fact extraplanar. In particular, the distribution and velocity information of neutral and ionized gas in the local ISM should, in principle, address an intractable problem from another perspective. Accordingly, we now turn our attention to allusions to a "thick disk'' in the Galaxy in order to establish whether significant dust resides outside the main gas layer.

6.3 High lattitude dust in the Milky Way

The Milky Way has often been cited as being similar to NGC 891, particularly in terms of its velocity field and the distribution of spiral arms (Guelin et al. 1993; Garcia-Burillo et al. 1992; Scoville et al. 1993). It is unclear, however, whether our own galaxy contains a thick disk or, indeed, such an active halo as NGC 891. Heiles (1984) famously described a network of "worms'' and "shells'' which partly comprise the HI disk in the Milky Way. These features can be interpreted as the walls of bubble-like cavities growing in the main gas layer. Although a certain fraction of these structures, the so-called "supershells'', possess dimensions comparable to the chimneys identified in our extragalactic sample (500-1500 pc), the majority appear to be only 30-100 pc in size (Heiles 1984; Hu 1981). A good example of these more diminutive features is the North Polar Spur, which due to its proximity appears conspicuous on HI and cirrus maps of the Galactic plane, but, in fact, has a z-height of only 120 pc (Crutcher 1982; Heiles et al. 1980). Curiously, most shells in the Galaxy do not manifest an obvious association with HII regions or SNe remnants. Generally, there has been no proven link between shells and any other phenomenon within the disk (although see the more recent radio recombination-line study of Heiles et al. 1996). Heiles also claims that most shell structures occur beyond the solar circle. Here the star-formation rate is reduced compared with the inner disk, weakening the argument that young, massive stars provide the appropriate driving mechanism (although a lower stellar density in these regions might allow gas to escape more easily from the disk).

In contrast to the Milky Way, HI observations of the face-on spiral NGC 6946 (Kamphuis & Sancisi 1993) have established a link between high-velocity atomic gas and OB associations in the disk. The material, travelling at z-velocities of up to 100 km s-1, occurs over holes in the HI disk where young stars have driven material upwards. The ejected mass in these "vertical'' structures is somewhat higher than the values we record for individual chimneys in the R96 sample (107 $M_{\odot}$ cf. 105-106 $M_{\odot}$ in Table 4). However, in total, the quantity of extraplanar material in question is remarkably similar in both cases ($\sim$ 2% of HI gas in NGC 6946 is believed to be displaced from the main disk).

Whilst detected at high latitudes, the Galactic cirrus is said to correlate well with local molecular gas clouds (Weiland et al. 1986). This material is typified by distances and z-heights of order 100 pc (rather than kpc). The opacity associated with molecular cirrus clouds is $\sim
1$ in $\tau_{B}$ i.e. close to the optical depth derived for dust chimneys. For cirrus coupled to atomic gas clouds the opacity is much lower ( $\tau_{B} \sim 0.1$; Low et al. 1984). Likewise, measurements of interstellar reddening towards A and F stars in the solar neighborhood suggest only small amounts of high-z dust at least locally (e.g. AB<0.1 mag above the sun; Burstein & Heiles 1982). In contrast, Davies et al. (1997) found that the 140 and $240~\mu$m emission detected by COBE indicated a much more vertically extended dust distribution. Indeed, they suggest a scaleheight of 500 pc for diffuse Galactic dust i.e. twice the scale-height of the stellar disk and 4 times greater than the conventional extinction layer. The method employed by Davies et al. consisted of fitting COBE FIR maps, in a latitude-longitude reference frame, with a dust disk of exponential fall-off in radius and z-height. Given the limited perspective, however, it is possible that the global fit might have been easily biased by local cirrus features (the nearby North Polar Spur, for example, appear prominently in the COBE images).

In conclusion, there is less compelling evidence for high-z dust in the Galaxy compared with spirals such as NGC 891. However, we recognize that our "in-plane perspective'' of the Milky Way disk may either distort or impair our perception of extraplanar material. The existence of HI shells with scale-heights of 1 kpc could indicate that dust chimneys, similar to those found in the R96 sample, are also present in the Galaxy.

6.4 Mass loss and intergalactic enrichment

The rate at which dust and heavy elements is expelled from the stellar disk may depend critically on the nature of the outflow mechanism. For example, if grains are driven primarily by gas pressure it may be appropriate to use the expansion velocity of the neutral gas out of the disk. The velocities recorded for Heiles' supershells are typically no more than 50 km s-1. The high velocity neutral gas detected in NGC 6946 is believed to be moving up 100 km s-1 away from the disk. Norman & Ikeuchi (1989) describe a scenario whereby the concentration of Type II SNe in Galactic OB associations should, in principle generate the kind of superbubble structures observed by Heiles. The chimney structures thereby constitute the dense, fragmented walls of the bubble as the expanding cavity bursts and hot gas from the OB association escapes into the halo. The expected timescale for this outflow, which assumes that the dust and neutral gas are entrained at the working surface of the superbubble, is $\sim 10^{7}$ yr. This value is consistent with an expulsion velocity of 100 km s-1 as observed for the neutral gas in NGC 6946.

As mentioned previously, there exists the strong possibility that extraplanar dust is propelled preferentially by radiation pressure rather than gas convective flow. Ferrara (1998) has carried out a number of simulations in which grains above a typical OB association form chimney-like structures around a cavity swept clean of dust by intense radiation pressure. The journey time is once again a few $\times 10^{7}$ yr with grains attaining upward velocities of $\sim$ 100 km s-1. In addition to gravitational and radiative forces, the Ferrara calculations attempt to take account of viscous and coulomb drag on the grains, the latter requiring some knowledge of the grain charge. In a similar vein, Davies et al. (1998) estimated the radiation pressure on various sizes of grains due to the general interstellar radiation field from the disk. Their model incorporated dark matter into the gravitational field and accounted for the fact that the grains themselves limit the distance over which photons can travel before being absorbed (self-shielding effect). The expulsion timescale, in this case, was $\sim 10^{8}$ yr for classical $0.1~\mu$m grains with a terminal velocity, $\sim$ 10 km s-1, controlled by the ambient gas density in the disk. The authors neglected the concentrated input of copious radiation from OB associations as well as the significant influence of magnetic fields on the grain movement.

The notion that radiation pressure might be responsible for the appearance of dust chimneys also raises some difficult issues. The absorption properties of extraplanar dust filaments are consistent with an optical depth of around unity along their shorter axis. Thus the middle of such structures might be significantly shielded from optical radiation propogating upwards from the disk. If the dust filament is, indeed, self-shielded in this sense, it is difficult to see how such structures can be pushed outwards via radiation pressure. Furthermore, the vertical dust features appear remarkable well-contained, in comparison with the DIG for example. Are such clearly-demarcated structures likely to arise naturally if grains are propelled by radiation pressure rather than gas pressure from the disk? A strong possibility is that dust grains are constrained to move along magnetic field lines due to their electric charge. Upwelling, ionized gas from star-forming regions in the disk appears capable of producing buckles in the toroidal magnetic field. This generates, over local regions of the disk (100 pc $\times $ 100 pc), a magnetic field orientated perpendicular to the disk. Such a phenomenon may prevent grains from dispersing during their upward passage, facilitating, in effect, the formation of vertical dust lanes (see Sofue et al. 1994 for a discussion).

In our estimate of dust seepage from the stellar disk we use an upward maximum velocity of 100 km s-1. This is in keeping with velocities observed for HI supershells in the Milky Way and NGC 6946 and, at the same time, remains consistent with the radiation pressure simulations carried out by Ferrara. The typical escape velocity from a large spiral disk is a few $\times 100$ km s-1 (Phillips 1993), somewhat greater than our estimated upward expansion. It seems unlikely then that dust can breach the halo into the intergalactic medium (IGM), unless it is caused to accelerate at greater z-height. An increase in acceleration does not seem plausible, however, because the respective forces due to gravity and radiation pressure are both governed by the same 1/r2 form. Thus, the balance of these two forces on the ascending grain is more or less fixed, for all z-heights, by the mass-to-light ratio of the disk (in fact, as the grain rises, it is the radiation pressure that diminishes preferentially due to increasing obscuration of disk starlight). Our unsharp-mask images of the R 96 sample, do not show any evidence for dust travelling to more than 2 kpc above the midplane. As already pointed out, however, techniques which employ extinction to locate extraplanar grains are rather insensitive to tenuous dust clouds situated so far above the stars that they are unable to produce well-defined absorption features. Some of the chimney features in our data are suggestive of a reconnection with the main absorption layer. This conceivably has more to do with the grains being tied to magnetic field lines rather than a genuine "fountain'' effect. As already mentioned, dust features may well follow "loops'' and "buckles'' in the main toroidal field allowing them to stretch upwards and then reconnect elsewhere with the disk.

Boyle et al. (1988) estimate that the IGM of the nearby Virgo Cluster systematically reddens background galaxies and QSOs by the equivalent of $\simeq 0.2$ in AB. This attenuating material presumably originates from the cluster members. Integrating over the surface area of Virgo ( $4.4 \ 10^{6}$ kpc2), the total dust mass residing outside the cluster members is expected to be large ( $\sim 10^{11}$ $M_{\odot}$). A straightforward calculation shows that the dust chimneys within quiescent disks are unlikely to constitute such prodigious sources of dust (even if ejected grains acquire the appropriate escape velocity). We assume that half the 180 spirals in the Virgo Cluster possess vertical dust structures and that these "ducts'' allow 1% of the disk's grain mass to enter the IGM over the course of 107 yr. These assumptions are based on the inferences of outflow rate reported above and the amount of extraplanar dust detected in our R 96 sample. Under such circumstances, it would require 1011 yr for outflows from conventional, quiescent disks to account for the dust accumulated in the Virgo IGM - a period well in excess of the cluster lifetime. Far more likely origins for intergalactic dust are "superwinds'', as certain cluster members undergo intense periods of starburst activity, or, indeed, tidal interactions between neighboring galaxies (Wiebe et al. 1999; Alton et al. 1999a; Yun et al. 1993). Doyon & Joseph (1989) also claim that ram-stripping may be an important dust removal mechanism amongst Virgo spirals. Here, the velocity of the cluster members with respect to the IGM is itself sufficient to strip loosely-bound gas and dust from the disk environment.

A corollary to the above calculation is that if chimneys deplete the ISM at a rate of 1% every 107 yr, then the total grain content of quiescent disks (5 107 $M_{\odot}$) must be replenished on timescales of 109 years. In fact, the current, best estimate of the rate at which stardust is added to the ISM is $\sim 0.04$ $M_{\odot}$ yr-1 (Whittet 1992). This indeed points to a replenishment timescale of 109 yr suggesting that dust chimneys could reasonably form part of the natural cycling and processing of interstellar material.

Although the chimneys we have been describing may not contribute significantly to the enrichment of the IGM with dust and metals, they are likely to play an important role in the circulation of heavy elements and gas around the disk. Any material that falls back to the disk will serve to homogenize the chemical make-up of the ISM allowing star-formation to proceed with greater efficiency than can be envisaged in a system with zero gas flow. Indeed, if models of chemical evolution are to successfully account for the efficiency of star formation in galactic disks a means of mixing the ISM must be supplied (Edmunds 1996; Edmunds & Phillipps 1997). Finally, as far as the distribution of dust in spirals is concerned, there is certainly increasing observational evidence that grains are more widely distributed than the stars that are expected to produce them. On the basis of systematic reddening of background galaxies, Zaritsky (1994) claims that galactic dust extends out to a radius of 60 kpc along the major axis of nearby spirals! Nelson et al. (1998) infer a more modest, but nonetheless very large, dust radial extent for nearby galaxies mapped in the $100~\mu$m IRAS Sky Survey (20-30 kpc). Likewise, ISOPHOT $200~\mu$m images of cold dust (15-20 K) are indicative of dust scale-lengths 70% larger than that of the stellar disk (Alton et al. 1998c). For grains to occur at larger galactocentric distances than the "edge'' of the stellar disk, either star-formation was more radial extensive in the past or galactic dust has been significantly displaced subsequent to its formation.

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