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We study the effect of a single columnar pin on a $(1+1)$ dimensional arrayof vortex lines in planar type II superconductors in the presence of pointdisorder. In large samples, the pinning is most effective right at thetemperature of the vortex glass transition. In particular, there is apronounced maximum in the number of vortices which are prevented from tiltingby the columnar defect in a weak transverse magnetic field. Usingrenormalization group techniques we show that the columnar pin is irrelevant atlong length scales both above and below the transition, but due to verydifferent mechanisms. This behavior differs from the disorder-free case, wherethe pin is relevant in the low temperature phase. Solutions of therenormalization equations in the different regimes allow a discussion of thecrossover between the pure and disordered cases. We also compute densityoscillations around the columnar pin and the response of these oscillations toa weak transverse magnetic field.Comment: 12 pages, 5 figures, minor typos corrected, a new reference adde

Vortex pinning by a columnar defect in planar superconductors with point disorder