Statistics Martin A. Zwaan , Marc A. W. Verheijen , Frank H. Briggs, PASA, 16 (1), in press.
| Next Section: Contribution of Low Surface Title/Abstract Page: The Há I Column Density Previous Section: The Ursa Major Cluster | Contents Page: Volume 16, Number 1 |
The Column Density Distribution Function
Figureá 2 shows the CDDF determined from the 21cm observations of the Ursa Major sample. From left to right the function is shown for three different resolutions of the Há I maps: 15'', 30'', and 60''. The solid line is the determined CDDF; the dashed lines indicate the quality of the measured column densities. Each pixel in the Há I maps has an estimate of the signal to noise level assigned to it. In the determination of the CDDF we calculated an average S/N level for each bin in column density by averaging the S/N ratios for the individual pixels. The dashed lines show the average
errors on the column densities and should be interpreted as horizontal errorbars. Nonetheless, they clearly overestimate the real uncertainties on the CDDF as many pixels are used in each bin (2500 independent beams for full resolution). The lines merely serve as an indicator of the quality of the measurements at each resolution. The thin solid line represents the CDDF for a Gaussian model, where
for
and
for higher column densities.
 |
is also shown as a thin solid line. The points indicate the Há I CDDF for damped Ly
) taken from Storrie-Lombardi et al. (1997). Note the strong evolution, especially at the highest column densities. When comparing the CDDFs at different resolution, it appears that the highest resolution maps yield the smoothest CDDF. This occurs because there the measurements of column density have the lowest S/N ratios. The low resolution (but high S/N) CDDF is in excellent agreement with the Gaussian model for
1020<N<1021.5, but for higher column densities, the measured curve drops below the model since high column density peaks are smeared away. Going to higher resolutions leads to better agreement between the measured curve and the model for the highest 
, and at 15'' resolution the CDDF follows the
distribution up to
.
Besides beam smearing two other effects can cause a deviation from the
function. Firstly, the calculations assume that the gaseous disks are infinitely thin. Observations show that the bulk of the Há I indeed resides in a thin layer with axis ratio < 0.1 (Rupen 1991). The thin disk approximation is therefore valid for moderately inclined disks. However, the highest column densities in the models arise in highly inclined thin disks. A small degree of puffiness will prevent these high column densities from being observed. The second effect is Há I self absorption. The theoretical calculation of the CDDF is based on the assumption that the optical depth of the neutral gas layer is negligible. Column densities much higher than the maximal column density in a face-on galaxy can only be seen in a highly inclined disk when the gas is optically thin. It is remarkable that the full resolution CDDF follows the
line up to
, well above the value where Há I self absorption is normally assumed to set in. For example, Dickey & Lockman (1990) calculate that an Há I cloud with 
and an FWHM velocity dispersion of
becomes optically thick (
) at column densities
.
Also shown in Figureá 2 are the measurements of 
at high redshifts as determined by Storrie-Lombardi et al. (1997). We choose not to split up their high-z sample in different redshift bins in order to get reasonable signal to noise. The median redshift of the total DL
sample is z=2.5. A value of q0=0.5 has been used here. Lower values of q0 would not significantly change the slope of but would decrease the normalization by approximately a factor of 2. Strong redshift evolution of the CDDF from z=2.5 to the present is apparent. The intersection cross-section for Há I column density
has decreased by a factor of 6 (factor 3 for q0=0) from z=2.5 to z=0. Higher column densities show a larger decrease, the evolution accounting for a factor of 10 (5 for q0=0). Lanzetta et al (1995) report still stronger evolution of the higher column densities for higher redshift, although the highest column densities suffer from small number statistics and the effect is hardly seen by Storrie-Lombardi et al. (1997). The strong evolution of the higher column densities can be understood if gas consumption by star formation occurs most rapidly in regions of high neutral gas density (Kennicutt et al. 1994).
Rao & Briggs (1993) evaluated the CDDF at the present epoch by analyzing Arecibo observations of a sample of 27 galaxies with optical diameters in excess of 7'. Double-Gaussian fits to the observed radial Há I distribution were used to calculate . The disadvantage of this method is that the Gaussian fits automatically introduce the
for low and
for high . In the present study no modeling has been applied. The location of the change of the slope and the normalization are in excellent agreement between Rao & Briggs' work and the Ursa Major determination.
| Next Section: Contribution of Low Surface Title/Abstract Page: The Há I Column Density Previous Section: The Ursa Major Cluster | Contents Page: Volume 16, Number 1 |
á© Copyright Astronomical Society of Australia 1997