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Given a population of objects with comoving number density n (z) (number per unit volume) and cross section sigma (z) (area), what is the incremental probability dP that a line of sight will intersect one of the objects in redshift interval dz at redshift z? Questions of this form are asked frequently in the study of QSO absorption lines or pencil-beam redshift surveys. The answer is

Equation 30 (30)

(Peebles 1993, pp. 323-325). The dimensionless differential intersection probability is plotted in Figure 7.


Figure 7. The dimensionless differential intersection probability dP / dz; dimensionless in the sense of n (z) sigma(z) DH = 1. The three curves are for the three world models, (OmegaM, OmegaLambda) = (1, 0), solid; (0.05, 0), dotted; and (0.2, 0.8), dashed.


Roger Blandford, Ed Farhi, Jim Peebles and Wal Sargent all contributed generously to my understanding of this material and Kurt Adelberger, Lee Armus, Deepto Chakrabarty, Alex Filippenko, Andrew Hamilton, Phillip Helbig, Wayne Hu, John Huchra, Daniel Mortlock, Tom Murphy, Gerry Neugebauer, Adam Riess, Paul Schechter and Douglas Scott caught errors, suggested additional material, or helped me with wording, conventions or terminology. I thank the NSF and NASA for financial support.

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