Martin A. Zwaan , Marc A. W. Verheijen , Frank H. Briggs, PASA, 16 (1), in press.
Next Section: The Ursa Major Cluster Title/Abstract Page: The Há I Column Density Previous Section: Introduction | Contents Page: Volume 16, Number 1 |
How to determine at z=0?
A simple but illustrative and instructive method is to take the analytical approach. This is illustrated in Figureá 1. Here we represent the radial distribution of the neutral hydrogen gas in galaxies by both an exponential and a Gaussian model. The differential cross sectional area of an inclined ring with a column density in the range N to N + dN is given by , where r(N) is the radius at which a column density N is seen, and i is the inclination of the ring. We assume that the luminosity function of the local galaxy population can be described by a Schechter function as indicated in the upper right panel of figureá 1. The local f(N) can be derived from and the area function by taking the integral
(1) |
(following Rao & Briggs 1993) and assume that the central gas surface density in disks is not dependent on morphological type or luminosity. The resulting f(N) for both models is shown in the lower left panel. The integral Há I gas density in
as a function of column density is shown in the lower right panel. This function can be calculated with
, where is the mass of the hydrogen atom.
The Gaussian models yield a CDDF of the form
, where for N smaller than the maximum column density seen in a face-on disk () and for the higher values of N. The exponential model gives a smoother function. The logarithmic slope is approximately -1.2 around
, slowly changing to -3 at higher column densities. In fact, it was shown already by Milgrom (1988) that
for for any radial surface density distribution. The lower right panel clearly illustrates that an overwhelming part of the total Há I mass in the local Universe is associated with column densities close to .
In addition to these simple models we also show the effect of disk truncation on the CDDF. The thin dashed line illustrates a Gaussian disk truncated at
, the level below which photo-ionization by the extragalactic UV-background is normally assumed to be important (e.g. Corbelli & Salpeter 1993, Maloney 1993). It appears that this truncation only seriously affects the CDDF below
. No significant changes occur at higher column densities.
A more reliable method than this analytical approach is to determine by using observed Há I distributions. 21cm maps of nearby galaxies routinely reach sensitivity limits comparable to column densities that typify DL absorbers. It therefore seems natural to calculate
, simply by adding cross sectional areas as a function of for a large sample of galaxies for which 21cm synthesis observations are available. However, this approach is complicated by the fact that there is an enormous variation in sensitivity and angular resolution of the 21cm maps, and the problem of choosing a fair and complete sample of galaxies. Most galaxies that have been studied extensively in the 21cm line were selected on having either a large Há I diameter, so that the rotation curve can be sampled out to large galactocentric radii, or on having peculiarities such as polar rings or warps. Thus, most samples for which 21cm synthesis data exist are not representative of the galaxy population of the local Universe and would likely be biased against dwarf and low surface brightness galaxies.
Next Section: The Ursa Major Cluster Title/Abstract Page: The Há I Column Density Previous Section: Introduction | Contents Page: Volume 16, Number 1 |
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