We report the discovery of 31.18 ms pulsations from the INTEGRAL source IGR J14003-6326 using the Rossi X-ray Timing Explorer (RXTE). This pulsar is most likely associated with the bright Chandra X-ray point source lying at the center of G310.6-1.6, a previously unrecognised Galactic composite supernova remnant with a bright central non-thermal radio and X-ray nebula, taken to be the pulsar wind nebula (PWN). PSR J1400-6325 is amongst the most energetic rotation-powered pulsars in the Galaxy, with a spin-down luminosity of Edot = 5.1E+37 erg.s-1. In the rotating dipole model, the surface dipole magnetic field strength is B_s = 1.1E+12 G and the characteristic age tau_c = P/2Pdot = 12.7 kyr. The high spin-down power is consistent with the hard spectral indices of the pulsar and the nebula of 1.22 +/- 0.15 and 1.83 +/- 0.08, respectively, and a 2-10 keV flux ratio F_PWN/F_PSR ~ 8. Follow-up Parkes observations resulted in the detection of radio emission at 10 and 20 cm from PSR J1400-6325 at a dispersion measure of ~ 560 cm-3 pc, which implies a relatively large distance of 10 +/- 3 kpc. However, the resulting location off the Galactic Plane of ~ 280 pc would be much larger than the typical thickness of the molecular disk, and we argue that G310.6-1.6 lies at a distance of ~ 7 kpc. There is no gamma-ray counterpart to the nebula or pulsar in the Fermi data published so far. A multi-wavelength study of this new composite supernova remnant, from radio to very-high energy gamma-rays, suggests a young (< 1000 yr) system, formed by a sub-energetic (~ 1E+50 ergs), low ejecta mass (M_ej ~ 3 Msun) SN explosion that occurred in a low-density environment (n_0 ~ 0.01 cm-3).
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