WHERE DOES A GALAXY END?

Since stars form from pre-existing gas, any study of the formation and evolution of disk galaxies should address the formation and evolution of the gaseous disk. For a theoretical look at the growth of disks with gas, see Evrard (1992). The most extended gaseous component (and most extended observable component altogether) appears to be the neutral hydrogen disk. Probably the best evidence that the neutral disk may evolve with time comes from observations of multiple absorption lines, most notably Ly, in the spectra of QSOs. Ly absorption lines are seen over many orders of magnitude in column density, from 10^12.5 cm^-2 (a detection threshold) to 10²² cm^-2 (Petitjean et al. 1993). At the high end of this range (i.e. N_H 10²⁰), the lines display damping wings and are associated with metal rich systems which, at redshifts between 2 and 3, contain most of the known baryonic matter in the universe. These systems have properties similar to nearby spirals and may be the progenitors of galactic disks (Wolfe 1989). Indeed, in some nearby cases, the absorbing galaxies have actually been identified (Bergeron & Boissè 1991). The apparent overabundance of the damped Ly lines at redshifts greater than 2 have led to suggestions that disks were larger in the past than they are at present (see Wolfe 1988; Sargent & Steidel 1989; Petitjean et al. 1992), although this interpretation is not unanimously accepted (see review by Steidel 1993). At the (much) lower end of the column density range, the lines have been thought to arise in ionized intergalactic clouds with very low neutral fractions (see review by Carswell 1988). However, recent Hubble Space Telescope (HST) observations which reveal an apparent overabundance of these low column density features in the nearby universe have led to questions as to how such fragile interstellar clouds could have survived in these numbers to the present time. Therefore, alternative models have been proposed in which these weaker lines also originate in the outer disks of nearby galaxies, i.e. from a small neutral hydrogen fraction in very extended ( Mpc-scale) ionized envelopes around ``normal'' spirals (Maloney 1992). Since the above conclusions depend upon what we know about galaxies in the nearby universe, it is important to understand the distribution and extent of HI disks in nearby spiral galaxies.

Unlike the optical disk whose surface brightness declines exponentially with radius, the HI distribution is usually much flatter, sometimes displaying a hole or depression towards the center and extending to much larger radii (see Bosma 1981 or van Gorkom 1993 for examples). Normal spirals, which contain the bulk of the HI in the nearby universe (Rao and Briggs 1993), have HI diameters about 1.8 x the optical diameter, if measured at the 1.26 x 10²⁰ cm^-2 column density (1 M pc^-2) and 25 magnitudes arcsec^-2 (D₂₅) blue isophote, respectively (Broeils 1992; Warmels 1986; see also van der Hulst et al. 1993) or of 2 -> 3 x D₂₅ if measured at the 5 x 10¹⁹ cm^-2 level (Rao and Briggs 1993). However, about 30% of normal spirals display HI disks which extend much farther than this (Bosma 1978; Briggs et al. 1980), though the number of spirals so far mapped in HI is still rather limited. M83, for example, has an HI envelope which extends to 6.5 Holmberg radii ( 15 x D₂₅) ² at the 10¹⁹ cm^-2 level (Huchtmeier 1984). NGC 628 (Fig. 3) also has a very extended HI disk which does not appear to be explainable by an interaction (Briggs et al. 1980; Shostak and van der Kruit 1984; Kamphuis and Briggs 1992).

Figure 3. The isolated spiral, NGC 628, showing contours of neutral hydrogen column density (adapted from Kamphuis and Briggs 1992, copyright European Southern Observatory, reproduced with permission) superimposed on an optical image (from the Digitized Sky Survey). The lowest HI emission is 1.3 x 1019 cm-2 and the highest is two orders of magnitude above this. The central 3 contours indicate declining emission.

Other examples of extended HI disks also abound. LSB galaxies, as a group, have more extended HI disks (2.4 as compared to 1.8 x D₂₅; van der Hulst et al. 1993). Interacting galaxies are also known to have extended HI envelopes or other irregular extended HI features associated with them. The interacting galaxies, Arp 144 (= NGC 7828/9), for example, have an HI envelope which, at the few x 10¹⁹ cm^-2 level, extends over 7.5 x the optical extent of the constituent galaxies (Higdon 1988). Giant HI envelopes also tend to be common around irregular and dwarf galaxies, for example, DDO 154 whose detectable HI distribution extends to almost 7 Holmberg radii (Carignan, private communication) or 16 x D₂₅, or NGC 4449 which has an HI extent some 14 x D₂₅ at the 1 x 10¹⁹ cm^-2 level (see Bajaja et al. 1994, and references therein).

As suggested by the values quoted above, most current neutral hydrogen column density limits tend to be in the range, 10¹⁹ -> 10²⁰ cm^-2, depending on the integration time and instrument used, and very few galaxies have been mapped to sensitivity levels below this. A few studies have achieved deeper observational limits, i.e. a few x 10¹⁸ cm^-2 (e.g. see Huchtmeier 1984 and references therein), especially using single dishes with large collecting areas, like the 305 m diameter Arecibo telescope. Briggs et al. 1980, for example, found relatively few extended HI disks at these lower levels. A notable exception is M33, which has been detected out to 2.2 x the Holmberg radius ( 5 x D₂₅) at the 4 x 10¹⁸ cm^-2 level. More recently, Corbelli et al. 1989 re-observed M33 with the Arecibo telescope to a limit of 2 x 10¹⁸ cm^-2 and found that the neutral hydrogen declines sharply with radius at a level of x 10¹⁹ cm^-2. Van Gorkom et al. 1994 found a similar result for NGC 3198, after a 100- hour integration with the Very Large Array (VLA) achieved a detection limit of 4 x 10¹⁸ cm^-2. For NGC 3198, the HI column density declines abruptly from 4 x 10¹⁹ cm^-2 to the detection limit within a single resolution element of 2.7 kpc (see also van Gorkom 1991, van Gorkom 1993, Dove and Shull 1994).

What are the possible causes of the apparent truncation of the HI distribution? Since it seems unlikely that the gas distribution itself suddenly truncates, there are several other possibilities. One is that lower column (and volume) density gas would be of such low optical depth that its spin temperature (T_S) would approach the 2.7 K background. Since the HI line is only detectable in excess of the background, this would effectively render the HI invisible. Watson and Deguchi 1984 and Deguchi and Watson 1985 have shown, however, that the Ly recombinations which follow ionization by intergalactic UV - X-ray radiation are sufficient to pump T_S to the kinetic temperature of the cloud (>> 2.7 K) (see also Giovanelli and Haynes 1988, Corbelli and Salpeter 1993a). A second (and more popular) model involves direct ionization of the gas by the extragalactic radiation field (Sunyaev 1969; Silk and Sunyaev 1976), i.e. the clouds become so ionized that too small a fraction of neutral gas is left to be detected. The cut-off would then be analogous to the boundary of a Strömgren Sphere, although not as sharp because of the harder UV background spectrum (see Kenney 1990 and references therein). Corbelli and Salpeter 1993b have modelled the cut-off in M33 in this way as well as Dove and Shull 1994 and Maloney 1993 for the HI edge of NGC 3198. In general, column densities larger than 10¹⁹ cm^-2 seem to be required to avoid ionization by extragalactic radiation (Brinks 1994).

At the present time, we have not yet fully explored HI parameter space for galaxies and the ubiquity of sharp HI edges must still be firmly established. For example, the detection of a sharp cut-off in M33 is based on a single radial slice. Complete, sensitive HI maps of this and other accessible galaxies are needed. Interferometric observations also are sensitive to only a specific range of spatial frequency, for example, the VLA cannot detect spatial scales of HI much larger than 15'. There are other ways of determining whether all spatial scales have been detected, for example, a comparison with the single-dish total flux or ensuring that the largest spatial scale actually detected on the maps is considerably smaller than this limit (e.g. NGC 3198, van Gorkom, private communication). However, HI envelopes of larger angular size, such as those around M33 and M83 which span at least 2.5° and 1.5°, respectively (see Huchtmeier 1984), would not have been detected by the VLA, regardless of integration time. A combination of data from both high and low resolution instruments (e.g. the VLA or the Westerbork Synthesis Radio Telescope with the Dominion Radio Astrophysical Observatory Synthesis Telescope) is ideal (e.g. Carignan et al. 1990). On the other end of HI parameter space, spatial resolution could also be a limiting factor. For example, if the distribution of HI at large radii were such that the gas accumulated in very small, more optically thick clouds, then the emission could be strongly beam diluted by current instruments.

The theory of extended HI/HII disks appears to be moving ahead at a somewhat faster pace than observation and better observational constraints are badly needed. For example, not all possible ionization models predict a sharp drop-off in HI. Good agreement depends upon the gas scale height and degree of clumpiness, the gas temperature and, especially, the intensity and spectral index of the extragalactic radiation field, most of which are not well constrained at the present time. The ionization models of Dove and Shull 1994, Maloney 1993, and Corbelli and Salpeter 1993b, for example, used the observed truncated HI distributions in order to put limits on the extragalactic flux. Also, it is important to address the redshift dependence of this effect, since one might expect HI disk sizes to decrease with increasing z in response to the increasing ionizing flux at higher redshifts (in contrast to the implication of the damped Ly absorbers). If correct, the ionization theory should predict that, for some range of conditions, all HI disks should be truncated and all such disks should be surrounded by ionized gas. Both predictions await observational confirmation.

3.2 Probing the Unseen Halos - Rotation Curves and Dark Matter

Aside from the information obtained about galaxy disks, themselves, neutral hydrogen observations also probe the large scale mass distribution (and therefore ``dark matter'') in spiral galaxies. The most convincing evidence of dark matter around galaxies is provided by HI rotation curves which tend to remain flat out to the largest measurable radii, suggesting that the mass of the galaxy continues to rise roughly linearly with radius (for isothermal dark matter halos) in these regions. The existence of dark matter, its nature, quantity, and extent is one of the most enduring problems in modern extragalactic astronomy. For recent reviews of the subject, see Ashman 1992 and Freeman 1992.

There have been various approaches to deriving the dark matter distribution in galaxies. Often, the HI rotation curve is used to constrain the total mass distribution and the optical (stellar) light then constrains the luminous mass distribution. A typical approach would be to assume that the inner rotation curve is dominated by the disk and the outer rotation curve is governed by the dark halo (see e.g. van Albada et al. 1985; Kent 1988; Sancisi and van Albada 1987; Casertano and van Albada 1990Salucci and Frenk 1989; Casertano and van Gorkom 1991), however, are now revealing these features in some bright spirals. Other methods involving neutral hydrogen have also been employed to delineate the dark matter distribution. For example, the shape of a galaxy's warp, most often seen in the outer HI, has been related to the concentration and oblateness of the halo (Sparke and Casertano 1988). Others (e.g Teuben 1991) have inferred, on the basis of warped disks, that dark halos exist in triaxial potentials. The observed flaring of the HI layer at the outer radii of some systems has also been used in attempts to constrain the dark matter distribution (Maloney, as quoted in Ashman 1992).

The success of these methods is a topic of current debate. While it appears that dark matter distributions as flat as the disk can be ruled out (but see Lequeux et al. 1993 for an alternate view), it is sometimes the case that a range of mass models can fit the observations. The main difficulty in determining the size of such a halo is simply that the rotation curve still does not extend to the ``edge'' of the mass distribution. Even galaxies displaying extremely large HI distributions in relation to their optical disks still show no evidence for declining rotation curves (e.g. NGC 628, Fig. 3, though the curve is difficult to measure in this particular case due to its nearly face-on aspect). Indeed, there are only a few cases in which declining curves have been observed, for example, the dwarf galaxy, DDO 154 (Carignan, as quoted in Ashman 1992), and several galaxies in the sample of Casertano and van Gorkom (1991). Broeils (private communication) also recently observed a declining rotation curve for NGC 4138, but this decline can also be explained in terms of a varying disk inclination in these regions. The fact that warps, flaring and other more chaotic motions (e.g. Kamphuis and Briggs 1992) tend to occur in the outermost HI disk, much of which may be due to external influences, complicates the process of extracting a unique rotation curve from neutral hydrogen data at large radii.

Other probes of dark matter halos include globular clusters (e.g. Huchra and Brodie 1987; Mould et al. 1990; Grillmair et al. 1994), planetary nebulae (Ford et al. 1989), hot X-ray emitting gas (e.g. Forman et al. 1985; Fabbiano 1989), and stellar velocity dispersions (e.g. Binney et al. 1990), all of which have been investigated in relation to elliptical galaxies where neutral hydrogen disks are not usually detected. Satellite galaxies are, of course, farther out, and could in principle constrain the large scale mass distribution, but there are usually not enough of them to obtain statistically significant results for any given galaxy.

The topic of dark matter in galaxies spans the fields of observational astronomy, cosmology, and particle physics, and a review of the possible constituents proposed, baryonic and non-baryonic, is beyond the scope of this paper. Some interesting recent work involving baryonic dark matter might be mentioned, however, ranging from the straightforward to the arcane. One is the possibility that halos do not consist only of ``dark matter'', but rather ``dim matter'', for example very faint stars, which simply require deeper scrutiny to be revealed. In support of this idea, Sackett et al. 1994 have detected a faint luminous halo of starlight around NGC 5907 whose slowly declining distribution is consistent with the dark matter distribution inferred from its rotation curve. Another is the on-going work to detect ``micro-lensing'' of background stars (in, for example, the Magellanic Clouds) due to massive compact halo objects (MACHOs) in the Galactic halo, if they exist. Several detections have so far been reported (e.g. Alcock et al. 1993; Aubourg et al. 1993). Another rather different idea is that dark matter exists as small cold (2.7 K) molecular cloudlets (``clumpuscules'') of primordial material which are present in a fractal distribution over a large disk (Pfenniger et al. 1994; Pfenniger and Combes 1994). For a recent review of baryonic dark matter, see Carr 1994.