The Fermi bubbles are two large structures in the gamma-ray sky extending to 55 ^ { \circ } above and below the Galactic center .
We analyze 50 months of Fermi Large Area Telescope data between 100 MeV and 500 GeV above 10 ^ { \circ } in Galactic latitude to derive the spectrum and morphology of the Fermi bubbles .
We thoroughly explore the systematic uncertainties that arise when modeling the Galactic diffuse emission through two separate approaches .
The gamma-ray spectrum is well described by either a log parabola or a power law with an exponential cutoff .
We exclude a simple power law with more than 7 \sigma significance .
The power law with an exponential cutoff has an index of 1.9 \pm 0.2 and a cutoff energy of 110 \pm 50 GeV .
We find that the gamma-ray luminosity of the bubbles is 4.4 ^ { +2.4 } _ { -0.9 } \times 10 ^ { 37 } erg s ^ { -1 } .
We confirm a significant enhancement of gamma-ray emission in the south-eastern part of the bubbles , but we do not find significant evidence for a jet .
No significant variation of the spectrum across the bubbles is detected .
The width of the boundary of the bubbles is estimated to be 3.4 ^ { +3.7 } _ { -2.6 } deg .
Both inverse Compton ( IC ) models and hadronic models including IC emission from secondary leptons fit the gamma-ray data well .
In the IC scenario , the synchrotron emission from the same population of electrons can also explain the WMAP and Planck microwave haze with a magnetic field between 5 and 20 \upmu G .