The "size" of a galaxy as seen in HI is usually equated with the diameter of the furthest detectable HI isophote; this definition leads to a measurement which increases as observing hardware improves. Currently, routine observations of galaxies with synthesis instruments reach column densities of 1.0 × 1020 cm-2. With large, single dishes (mainly the Arecibo 305 m), mapping of large-angular-diameter galaxies to column densities of 2.0 × 1018 cm-2 has been obtained, albeit with limited angular resolution and for relatively few objects. A limiting factor in high-sensitivity measurements with single dishes is the contamination by radiation collected by sidelobes of the antenna beam; while well understood, this contamination can be difficult to remove at very low HI surface density levels if bright HI emission is found just outside the field of interest. In the absence of such sources, however, measurements to 5.0 × 1017 cm-2 can be reliably conducted. Systematic analysis shows that the size of HI disks, like the integral HI content, is dependent not only on the internal characteristics of the galaxy, but also on its environment, as discussed in Section 12.6. The outer regions of a disk are very fragile and can be severely affected, thermally or dynamically, by a violent environment. When statistical properties of HI distributions are mentioned, it should be assumed that they refer to relatively unperturbed systems. In addition, it should be kept in mind that relatively low column densities of HI may become undetectable. To see that, note first that typically, for a given line width, the HI column density is proportional to the line brightness temperature. However, as seen in Section 12.1.2, if the opacity of the gas becomes very low, the fractional deviation of the spin temperature from the 2.7 K of the microwave background, (Ts - 2.7) / Ts, is depressed. For a given column density, then, the line brightness temperature diminishes in the same measure, as described by Equation (12.2) and discussed in more detail by Watson and Deguchi (1984).
More readily obtained estimates of the size of the HI distribution are those which express it as an isophotal or as an effective radius, the latter identifying the radius within which a fraction of the total HI mass is contained. When expressed in terms of the isophote at NH = 1.82 × 1020 cm-2 the average ratio of the HI to the Holmberg radius is about 1.5; alternatively, 70% of the galaxy's HI mass is contained, on average; within 1.2 Holmberg radii. Dependences of HI radius on morphological type are very weak and difficult to discern; the distribution of sizes around the mean is strongly skewed, relative to the Gaussian. For reasons that are very poorly understand, some galaxies exhibit enormously extended HI disks. Notable are the cases of Mk 348, illustrated in Figure 12.3, and of NGC 628, in which HI is detected out to several Holmberg radii. In the nearby system M33, HI is detected out to three Holmberg diameters. The exceptional HI objects are not systematically unusual in any other respect. Still, the incidence of very large HI disks has important implications. Dynamically, it allows inspection of the gravitational potential of a galaxy at very large distances from its center; from a cosmological viewpoint, the "intervening galaxy" explanation of high-redshift absorption lines seen along the line of sight to QSOs demands large cross sections of the intervening galaxian disks in order to account for the number of such lines observed (see Section 12.7.4). Huchtmeier et al. (1981) have noted that a significant fraction of irregular galaxies contain extended HI components not correlated with their optical size; the role of the extended gas component in the evolution of a galaxy is however still unclear.