Statistics Martin A. Zwaan , Marc A. W. Verheijen , Frank H. Briggs, PASA, 16 (1), in press.
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The Ursa Major Cluster
The Ursa Major cluster of galaxies, studied extensively by Verheijen (1997), forms an ideal sample for an unbiased study of the column density distribution function. The Ursa Major cluster, at a distance of 15 Mpc, is different in many respects from famous, equally distant clusters like Virgo and Fornax. Ursa Major's member galaxies show no concentration towards a central condensation and their velocity dispersion is exceptionally low, approximately 150 km/s. The estimated crossing time is half a Hubble time and hence the galaxies do not seem to be seriously affected by tidal interactions. In addition to this, there is a predominance of late type galaxies and the morphological mix of galaxies is indistinguishable from that in the field. This combination of properties implies that the Ursa Major cluster is in fact an overdensity of galaxies and not comparable to classical clusters of galaxies. This justifies the use of the Ursa Major cluster for the study of the shape of the CDDF of neutral hydrogen in the local Universe.The Ursa Major cluster as defined by Tully et al. (1996) comprises a volume of 80 Mpc3, within which 80 galaxies are identified to date. For a complete sample of 62 galaxies intrinsically brighter than the Small Magellanic Cloud (
) 21cm synthesis observations have been performed with the WSRT1. H I has been detected by the WSRT in 49 galaxies. Details on observations and data reduction are described in Verheijen (1997).
An obvious advantage of using the UMa sample for this study is that all the member galaxies are at approximately the same distance. Therefore, the spatial resolution of the synthesis observations are constant for the whole sample. This simplifies the problem of assessing the influence of resolution on the determination of the CDDF and the comparison with the CDDF at high redshift.
The shape of the column density distribution function is determined by counting in each H I map the number of pixels per logarithmic bin of 0.1 dex in column density. The solid angle covered by pixels of a certain column density is then determined by multiplying the number of pixels with the angular pixel size which varies slightly from galaxy to galaxy.
The disadvantage of using a galaxy sample taken from a clear cosmic overdensity is that the CDDF is not automatically normalized. If we would naively assume that the Ursa Major cluster is a representative part of the nearby Universe, we would overestimate the normalization of the CDDF by roughly a factor of 12. This factor is obtained by comparing the H I mass function of the cluster with that of the field galaxy population (Zwaan et al. 1997). The shape of the Ursa Major mass function is indistinguishable from that of the field, but the normalization, 
, is larger by a factor of 
. Ideally, one would use a sample of galaxies with well understood selection criteria so that the normalization would occur automatically. Unfortunately, there are no such samples available for which H I synthesis observations with sufficient angular resolution have been performed. The HIPASS survey, a blind 21cm survey of the whole southern sky, will eventually yield a suitable galaxy sample for this purpose, if a representative subsample is followed up with the ATCA to obtain high spatial resolution maps.
There are several methods for normalizing the UMa CDDF. By assuming a local luminosity function (LF) or H I mass function (HIMF), each galaxy could be given a weight according to its absolute magnitude or H I mass. However, this method introduces extra uncertainty in the derived CDDF, due to uncertainties in the exact shape and normalization of the LF and the HIMF. Our preferred method of normalizing the CDDF is to scale the complete function, not the individual contributors to it. This can be achieved by scaling the integral H I mass density that is contained under the CDDF:
 | (2) |
, a result that is in excellent agreement with earlier estimates based on optically selected galaxies. Note that dependencies on H0 disappear in the final specification of the CDDF.
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