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We present a new model for the synchrotron compact nebular emissions for Velaand PSR B1706-44, and derive fundamental pulsar/plerion parameters such as thepair production multiplicity, M, and wind magnetization parameter, sigma. Thepair cascade above the pulsar polar cap, combined with the energy from thepulsar wind, injects a pair plasma into the surrounding environment. This wind,consisting of particles and fields, is shocked by the environment, resulting insynchrotron emission from "thermalized" pairs in a compact nebula. The broadband nebular spectrum depends crucially on the spindown power, distance, pairmultiplicity, pulsar wind shock radius and sigma at this shock. We constructsuch a model for the particle spectra in the compact X-ray nebula of Vela andPSR B1706-44. Fits to the multiwavelength spectra of these sources indicatethat 300<M<1000, whereas 0.05<sigma<0.5 for Vela. The same sigma interval (asfor Vela) was independently derived from the radial gradients of the X-raycompact nebular emission from both Vela and PSR B1706-44, giving us confidencein our results. The M we derive for Vela is too small to be explained bycurvature losses in the open magnetoshere of Vela, but the presence of opticalpulsed photons could modify the predicted multiplicity.Comment: 29 pages, 4 figures, accepted for publication in Ap

Constraints on Pulsar Magnetospheric and Wind Parameters for the Compact Nebulae of Vela and PSR B1706−44