We report on the Fermi -LAT observations of the Geminga pulsar , the second brightest non-variable GeV source in the \gamma -ray sky and the first example of a radio-quiet \gamma -ray pulsar .
The observations cover one year , from the launch of the Fermi satellite through 2009 June 15 .
A data sample of over 60,000 photons enabled us to build a timing solution based solely on \gamma rays .
Timing analysis shows two prominent peaks , separated by \Delta \phi = 0.497 \pm 0.004 in phase , which narrow with increasing energy .
Pulsed \gamma rays are observed beyond 18 GeV , precluding emission below 2.7 stellar radii because of magnetic absorption .
The phase-averaged spectrum was fitted with a power law with exponential cut-off of spectral index \Gamma = ( 1.30 \pm 0.01 \pm 0.04 ) , cut-off energy E _ { 0 } = ( 2.46 \pm 0.04 \pm 0.17 ) GeV and an integral photon flux above 0.1 GeV of ( 4.14 \pm 0.02 \pm 0.32 ) \times 10 ^ { -6 } cm ^ { -2 } s ^ { -1 } .
The first uncertainties are statistical and the second are systematic .
The phase-resolved spectroscopy shows a clear evolution of the spectral parameters , with the spectral index reaching a minimum value just before the leading peak and the cut-off energy having maxima around the peaks .
Phase-resolved spectroscopy reveals that pulsar emission is present at all rotational phases .
The spectral shape , broad pulse profile , and maximum photon energy favor the outer magnetospheric emission scenarios .