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The Spectrum and Morphology of the Fermi Bubbles

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$σ$ 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 $μ$G.