(shortened) PSR J1119-6127 is a high magnetic field (B=4.1E13 Gauss), young (<=1,700 year-old), and slow (P=408 ms) radio pulsar associated with the supernova remnant (SNR) G292.2-0.5. In 2003, Chandra allowed the detection of the X-ray counterpart of the radio pulsar, and provided the first evidence for a compact pulsar wind nebula (PWN). We here present new Chandra observations which allowed for the first time an imaging and spectroscopic study of the pulsar and PWN independently of each other. The PWN is only evident in the hard band and consists of jet-like structures extending to at least 7 from the pulsar, with the southern `jet being longer than the northern `jet. The spectrum of the PWN is described by a power law with a photon index~1.1 for the compact PWN and ~1.4 for the southern long jet (at a fixed column density of 1.8E22/cm2), and a total luminosity of 4E32 ergs/s (0.5-7 keV), at a distance of 8.4 kpc. The pulsars spectrum is clearly softer than the PWNs spectrum. We rule out a single blackbody model for the pulsar, and present the first evidence of non-thermal (presumably magnetospheric) emission that dominates above ~3keV. A two-component model consisting of a power law component (with photon index ~1.5--2.0) plus a thermal component provides the best fit. The thermal component can be fit by either a blackbody model with a temperature kT~0.21 keV, or a neutron star atmospheric model with a temperature kT~0.14 keV. The efficiency of the pulsar in converting its rotational power, Edot, into non-thermal X-ray emission from the pulsar and PWN is ~5E-4, comparable to other rotation-powered pulsars with a similar Edot. We discuss our results in the context of the X-ray manifestation of high-magnetic field radio pulsars in comparison with rotation-powered pulsars and magnetars.
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