The Zeldovich approximation is applied to study the accretion of hot and cold dark matter onto moving long strings. It is assumed that such defects carry a substantial amout of small-scale structure, thereby acting gravitationally as a Newtonian line source whose effects dominate the velocity perturbations. Analytical expressions for the turnaround surfaces are derived and the mass inside of these surfaces is calculated. Estimates are given for the redshift dependence of ${\Omega }_{\mathrm{nl}}$, the fraction of mass in nonlinear objects. Depending on parameters, it is possible to obtain ${\Omega }_{\mathrm{nl}}=1\mathrm{}$ at the present time. Even with hot dark matter, the first nonlinear filamentary structures form at a redshift close to 100, and there is sufficient nonlinear mass to explain the observed abundance of high redshift quasars and damped Lyman $\alpha$ systems. These results imply that moving strings with small-scale structure are the most efficient seeds to produce massive nonlinear objects in the cosmic string model.

• Received 11 July 1996

DOI:https://doi.org/10.1103/PhysRevD.54.7129