We have discovered the pulsar associated with the supernova remnant G21.5-0.9. PSR J1833-1034, with spin period P = 61.8 ms and dispersion measure 169 cm-3 pc, is very faint, with pulse-averaged flux density of ≈70 μJy at a frequency of 1.4 GHz, and was first detected in a deep search with the Parkes telescope. Subsequent observations with Parkes and the Green Bank Telescope have confirmed this detection and yield a period derivative = 2.02 × 10-13. These spin parameters imply a characteristic age τc = 4.8 kyr and a spin-down luminosity ? = 3.3 × 1037 ergs s-1, the latter value exceeded only by the Crab pulsar among the rotation-powered pulsars known in our Galaxy. The pulsar has an unusually steep radio spectrum in the 0.8-2.0 GHz range, with power-law index ≈3.0, and a narrow single-peaked pulse profile with FWHM of 0.04P. We have analyzed 350 ks of archival Chandra X-Ray Observatory HRC data and find a pointlike source of luminosity ≈3 × 10-5?, offset from the center of an elliptical region of size ≈7'' × 5'' and luminosity ≈10-3? within which likely lies the pulsar wind termination shock. We have searched for X-ray pulsations in a 30 ks HRC observation without success, deriving a pulsed fraction upper limit for a sinusoidal pulse shape of about 70% of the pulsar flux. We revisit the distance to G21.5-0.9 based on H I and CO observations, arguing that it is 4.7 ± 0.4 kpc. We use existing X-ray and radio observations of the pulsar wind nebula, along with the measured properties of its engine and a recent detection of the supernova remnant shell, to argue that G21.5-0.9 and PSR J1833-1034 are much younger than τc and likely their true age is 1000 yr. In that case, the initial spin period of the pulsar was 55 ms.
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