Astron. Astrophys. 322, 489-492 (1997)

Appendix A

For a line-of-sight passing through k clouds, the distribution of dispersion measures is given by a Gaussian (Eq.  5). The average value of the distribution of dispersion measures to a distance d is found by averaging the distributions for all k -values, weighted with the Poisson probability of getting k clouds:

where we use the fact that the integration over the dispersion measure is independent of the summation over k and we can extend the integration to because the mean is sufficiently displaced from 0. We now substitute and from Eq.  2to find

In a similar fashion we may estimate the variance of the dispersion measure distribution for distance d:

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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