We report on gamma-ray observations in the off-pulse window of the Vela pulsar PSR B0833 - 45 , using 11 months of survey data from the Fermi Large Area Telescope ( LAT ) .
This pulsar is located in the 8 ^ { \circ } diameter Vela supernova remnant , which contains several regions of non-thermal emission detected in the radio , X-ray and gamma-ray bands .
The gamma-ray emission detected by the LAT lies within one of these regions , the 2 ^ { \circ } \times 3 ^ { \circ } area south of the pulsar known as Vela-X .
The LAT flux is significantly spatially extended with a best-fit radius of 0.88 ^ { \circ } \pm 0.12 ^ { \circ } for an assumed radially symmetric uniform disk .
The 200 MeV to 20 GeV LAT spectrum of this source is well described by a power-law with a spectral index of 2.41 \pm 0.09 \pm 0.15 and integral flux above 100 MeV of ( 4.73 \pm 0.63 \pm 1.32 ) \times 10 ^ { -7 } cm ^ { -2 } s ^ { -1 } .
The first errors represent the statistical error on the fit parameters , while the second ones are the systematic uncertainties .
Detailed morphological and spectral analyses give strong constraints on the energetics and magnetic field of the pulsar wind nebula ( PWN ) system and favor a scenario with two distinct electron populations .