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We investigate cosmic string networks in the Abelian Higgs model using datafrom a campaign of large-scale numerical simulations on lattices of up to$4096^3$ grid points. We observe scaling or self-similarity of the networksover a wide range of scales, and estimate the asymptotic values of the meanstring separation in horizon length units $\dot{\xi}$ and of the mean squarestring velocity $\bar v^2$ in the continuum and large time limits. The scalingoccurs because the strings lose energy into classical radiation of the scalarand gauge fields of the Abelian Higgs model. We quantify the energy loss with adimensionless radiative efficiency parameter, and show that it does not varysignificantly with lattice spacing or string separation. This implies that theradiative energy loss underlying the scaling behaviour is not a latticeartefact, and justifies the extrapolation of measured network properties tolarge times for computations of cosmological perturbations. We also show thatthe core growth method, which increases the defect core width with time toextend the dynamic range of simulations, does not introduce significantsystematic error. We compare $\dot{\xi}$ and $\bar v^2$ to values measured insimulations using the Nambu-Goto approximation, finding that the latterunderestimate the mean string separation by about 25%, and overestimate $\barv^2$ by about 10%. The scaling of the string separation implies that stringloops decay by the emission of massive radiation within a Hubble time in fieldtheory simulations, in contrast to the Nambu-Goto scenario which neglects thisenergy loss mechanism. String loops surviving for only one Hubble time emitmuch less gravitational radiation than in the Nambu-Goto scenario, and areconsequently subject to much weaker gravitational wave constraints on theirtension.

Scaling from gauge and scalar radiation in Abelian Higgs string networks